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+Electron Impact Ionization in the Icy Galilean Satellites’ Atmospheres
+Shane R. Carberry Mogan1,∗, Robert E. Johnson2,3, Audrey Vorburger4, Lorenz Roth5
+1Space Sciences Laboratory, University of California, Berkeley, Berkeley, USA; 2University
+of Virginia, Charlottesville, USA; 3New York University, New York, USA; 4University of
+Bern, Bern, Switzerland; 5KTH Royal Institute of Technology, Stockholm, Sweden;
+∗Corresponding author: Shane R. Carberry Mogan ([email protected])
+Abstract
+Electron impact ionization is critical in producing the ionospheres on many plan-
+etary bodies and, as discussed here, is critical for interpreting spacecraft and tele-
+scopic observations of the tenuous atmospheres of the icy Galilean satellites of Jupiter
+(Europa, Ganymede, and Callisto), which form an interesting planetary system. For-
+tunately, laboratory measurements, extrapolated by theoretical models, were devel-
+oped and published over a number of years by K. Becker and colleagues (see Deutsch
+et al. 2009) to provide accurate electron impact ionization cross sections for atoms
+and molecules, which are crucial to correctly interpret these measurements. Because
+of their relevance for the Jovian icy satellites we provide useful fits to the complex,
+semi-empirical Deutsch–M¨ark formula for energy-dependent electron impact ioniza-
+tion cross-sections of gas-phase water products (i.e., H2O, H2, O2, H, O). These are
+then used with measurements of the thermal plasma in the Jovian magnetosphere to
+produce ionization rates for comparison with solar photo-ionization rates at the icy
+Galilean satellites.
+1
+Introduction
+Since Galileo Galilei’s revolutionary discovery that Jupiter, the largest planet in the solar
+system, has four large planetary bodies revolving around it – the “Galilean” satellites: Io,
+Europa, Ganymede, and Callisto – our fascination with this planetary system has only
+grown with the advancement of observational technologies. Several spacecraft have been
+sent directly to or have at least passed by the Jovian system. In the 1970s, Pioneer 10 & 11
+and Voyager 1 & 2 utilized Jupiter’s gravity to enhance their trajectories and observed the
+giant planet and its moons up-close. From 1995–2003 Galileo orbited Jupiter, and made
+several close encounters with the namesake moons. At the time of this writing, the Juno
+spacecraft is currently orbiting Jupiter and has recently made close flybys of Ganymede and
+Europa with 2 flybys of Io forthcoming. In addition to these in-situ observations, the Hubble
+Space Telescope (HST), which has been situated in Earth’s orbit since 1990, has been used
+to observe and contribute new information to our understanding of this system. To better
+understand the Jovian system, the Galilean satellites, and their interconnected dynamics, as
+well as address certain prevailing mysteries, three forthcoming missions, ESA’s JUpiter ICy
+moons Explorer, NASA’s Europa Clipper, and CNSA’s Gan De, will send spacecraft back
+to the Jovian system.
+Our focus here is on the icy Galilean satellites (see Table 1) – Europa, Ganymede, and
+Callisto – and their tenuous atmospheres for which the dominant constituents are water
+1
+arXiv:2301.11380v1  [astro-ph.EP]  26 Jan 2023
+
+products: H2O, O2, H2, H, and O. Because these objects orbit Jupiter within its giant mag-
+netic field, they are exposed to an ambient plasma. Interactions between this plasma and the
+icy Galilean satellites’ atmospheres to a large extent determine the nature of the latter. One
+key aspect of this interaction is the role of the plasma electrons in dissociating, ionizing, and
+exciting the gas-phase water products via impacts, which can produce observable emission
+features (e.g., Hall et al. 1998, Feldman et al. 2000, Roth et al. 2017, Roth 2021, Roth et al.
+2021). In order to calculate the ionization rates to be used in future simulations of these at-
+mospheres, we use the extensive laboratory data of electron impact ionization cross-sections
+accumulated and summarized by K. Becker and his colleagues over a number of years as
+reviewed in Deutsch et al. (2009) and references herein. Since the various laboratory mea-
+surements can exhibit differences and typically cover only a limited range of energies, the
+group developed a fitting procedure also presented in those papers. In this method, the
+Deutsch–M¨ark (DM) formula, atomic orbital basis sets are used in expressions to fit and
+extrapolate the measurements, as well as to generate cross-sections when measurements are
+unavailable. In this way, they created a large number of energy-dependent electron impact
+ionization cross-section distributions. Although the DM formula provides a broad range of
+useful data, as well as allows the calculation of results for molecular targets to be determined
+from the constituent atomic orbitals, it is not easily implemented. For example, in detailed
+molecular kinetic simulations much simpler calculations are more often made, such as those
+recently implemented in Carberry Mogan et al. (2022) for describing electron impacts in Cal-
+listo’s atmosphere. More readily useful expressions are needed. Therefore, here we present
+much more simplified fits to the results obtained via the DM formula, which we then use with
+electron density and temperature data at the icy Galilean satellites to calculate ionization
+rates in their atmospheres. These rates are in turn needed to help interpret past, present,
+and future spacecraft and telescopic observations of these topical planetary bodies soon to
+be visited by several new spacecraft.
+Before we discuss the derivation of the electron impact ionization cross-section fits (Sec-
+tion 3) and present the corresponding ionization rates for each species considered (Section
+4), we first review the local space environment of the icy Galilean satellites, particularly the
+Jovian magnetospheric plasma in which they are embedded, as well as the observations of
+water products in their atmospheres.
+2
+Background
+The strong dynamo generated within the interior of Jupiter produces its magnetic field, which
+has a rotation period of ∼10 h. Jupiter’s magnetosphere, i.e., the environment controlled by
+the planet’s magnetic field, is filled with charged particles. While the volcanic moon Io is the
+main source, materials from the icy Galilean satellites’ surfaces are also a source of charged
+particles (either directly ionized or lost as neutrals and ionized later in the magnetosphere)
+(Johnson et al., 2004, Kivelson et al., 2004), which are picked-up, accelerated, and then
+become “trapped” by this rapidly rotating field.
+The combination of this fast rotating
+magnetic field and the large number of charged particles trapped within it gives rise to the
+plasma detected in Jupiter’s immense magnetosphere, which can extend as far as 45–100 RJ
+from the planet, where RJ = 71, 492 km is the radius of Jupiter. The Jovian magnetosphere
+2
+
+is typically divided up into three regions: the inner (<10 RJ), the middle (10–40 RJ), and the
+outer (>40 RJ) regions (Khurana et al., 2004); Europa resides within the inner region, while
+Ganymede and Callisto reside in the middle region. The Jovian magnetospheric plasma is
+typically described as being comprised of two populations: a “cold” thermal plasma with
+energies < 1 keV and a “hot” energetic plasma with energies ≥ 1 keV (Krupp et al., 2004,
+Bagenal and Delamere, 2011). Both populations are composed of electrons, as well as H+,
+On+, and Sn+ ions (Bagenal and Sullivan, 1981, Broadfoot et al., 1981, Nerney et al., 2017).
+The sulfur and oxygen ions, both of which are of various charge states, primarily originate
+from the volcanic moon Io (Bagenal and Dols, 2020). On the other hand, the hydrogen
+ions originate from two different sources depending on the magnetospheric region: in the
+inner region, they mainly originate in Jupiter’s atmosphere; and in the middle and outer
+magnetosphere, the solar wind can gain access to the magnetosphere, becoming the main
+provider of hydrogen ions thereafter.
+An additional plasma contribution (electrons, H+,
+On+) is associated with sputtering of the icy satellite’s surfaces (Cooper et al., 2001, Johnson
+et al., 2004, Szalay et al., 2022). Here we focus on the thermal electrons as these particles
+are the most relevant to ionization. Physical parameters for thermal electrons at the orbits
+of Europa, Ganymede, and Callisto based on Voyager and Galileo data are listed in Table
+1.
+Table 1: Physical Parameters of Europa, Ganymede, and Callisto, as well as of the Jovian
+magnetosphere at their orbits
+Parameters [units]
+Europa
+Ganymede
+Callisto
+Radius [km]
+1,561
+2,631
+2,410
+Mass [(×1023) kg]
+0.48
+1.5
+1.1
+Distance from Jupiter [RJ]
+9.38
+15.0
+26.3
+Orbital Velocity [km s−1]
+13.7
+10.9
+8.20
+Thermal Electron Density [cm−3]
+18–290 a,b
+1–10 a,c
+0.01–1.1 a,c
+Thermal Electron Temperature [eV]
+10–30 b
+100 c
+100 c
+Thermal Electron Flux d [cm−2 s−1]
+(0.4–1.1)×1011 e
+(0.7–6.7)×109
+(0.08–7.4)×108
+Plasma Azimuthal Velocity [km s−1]
+90 a
+150 a
+200 a
+Relative Plasma Velocity f [km s−1]
+76 a
+139 a
+192 a
+a Values taken from Kivelson et al. (2004) and references therein.
+b Values taken from Bagenal et al. (2015).
+c Values taken from Neubauer (1998) and references therein.
+d Thermal electron flux, φe = neve, where ne is the thermal electron density, ve =
+�
+8kBTe/π/me is the
+mean Maxwellian speed of the electrons, with kBTe the thermal electron temperature, kB the Boltzmann
+constant, and me the mass of an electron.
+e φe calculated according to the “low/hot” (kBTe = 30 eV, ne = 63 cm−3) and “high/cold”
+(kBTe = 10 eV, ne = 290 cm−3) plasma components from Table 5 in Bagenal et al. (2015).
+g Relative speed between plasma azimuthal velocity and the satellites’ orbital speeds.
+3
+
+As a result of the large relative velocities between the azimuthal velocity of the Jovian
+magnetosphere and the icy Galilean satellites’ orbital velocities (Table 1), the satellites
+are continuously overtaken and bombarded by the magnetospheric plasma.
+The spatial
+distribution of this bombardment is determined by the flow rate of the plasma particles
+past the satellite as well as their thermal velocities relative to the local magnetic field lines
+(Johnson et al., 2004). However, intrinsic or induced electric and magnetic fields as well
+as the interactions with the tenuous atmospheres and ionospheres at these satellites can
+radically modify the local fluxes of impinging particles at Ganymede (e.g., from Paranicas
+et al. 2022) and at Callisto (e.g., from Strobel et al. 2002). The cyclotron radii or gyro-
+radii of these charged particles depend on their mass, speed, and charge, as well as the
+local magnetic field strength. Due to their small mass, electrons primarily have gyro-radii
+much smaller than the satellite radius, and thus preferentially impact the satellites’ trailing
+hemispheres and poles as they move up and down the rotating field lines (Johnson et al.,
+2004).
+Following the Pioneer discovery of intense plasma trapped in the Jovian magnetic field
+(Smith et al., 1974, Wolfe et al., 1974, Trainor et al., 1974, Frank et al., 1976) a series of ex-
+periments were carried out to measure the effect this could have on the icy surfaces of Europa,
+Ganymede, and Callisto (Brown et al., 1978, Lanzerotti et al., 1978). These experiments
+showed that the ejection of water molecules from low-temperature ices by incident energetic
+particles, a process referred to as “sputtering”, is dominated by electronic excitations and
+ionizations produced in the ice (“electronic” sputtering), rather than by “knock-on” colli-
+sions of the ions with water molecules (“nuclear” sputtering), the hitherto typically studied
+sputtering process. Subsequent experiments led to the discovery that additional molecular
+species can form in and be released from the ice, namely H2 and O2, in a process referred to
+as “radiolysis” (Brown et al., 1982, Boring et al., 1983, Reimann et al., 1984, Brown et al.,
+1984), which occurs as bonds in H2O molecules are broken by the electronic energy deposited
+by the impinging charged particles and the fragmented molecules recombine. Moreover, the
+number of radiolytic products ejected from the icy surface per each incident charged particle
+(i.e., the “sputter yield”) was shown to display a strong temperature dependence.
+These discoveries had immense implications for the icy Galilean satellites: magneto-
+spheric plasma-induced sputtering could erode their surfaces, and the ejected atoms and
+molecules could migrate significant distances as well as escape the local gravitational en-
+vironment of its host satellite or form gravitationally bound atmospheres (Johnson, 1990).
+Indeed Europa was predicted to have a tenuous, predominantly O2 atmosphere due to the
+radiolytic decomposition of its icy surface by the incident Jovian plasma particles (Johnson
+et al., 1982, 1983, Johnson, 1990), which has been borne out by extensive HST observations
+(e.g., Roth et al. 2016, and references therein). Tenuous O2 atmospheres produced via similar
+processes have also been detected at Ganymede and Callisto: following the HST detection of
+O emissions indicative of an O2 atmosphere at Europa (Hall et al., 1995), airglow emissions
+were detected by HST in Ganymede’s O2 atmosphere (Hall et al., 1998) as well as in Europa’s
+atmosphere thereby confirming the earlier observation; O emissions were detected by HST
+in Callisto’s atmosphere (Cunningham et al., 2015), which were suggested to be induced by
+photoelectron impacts in a near-surface, O2-dominated atmosphere; and recently atomic O
+emissions have been detected at Ganymede (Roth et al., 2021) indicative of being produced
+via dissociative excitations of O2 (and H2O).
+4
+
+Although H2 can more readily escape from the atmospheres of these bodies than can the
+concomitant radiolytically produced O2, a steady-state H2 atmospheric component can also
+form (e.g., Carberry Mogan et al. 2022). Atomic H, the dissociated product of H2, has also
+been detected at Callisto (e.g., Roth et al. 2017, Carberry Mogan et al. 2022). Moreover,
+Carberry Mogan et al. (2022) and Roth et al. (2023) recently suggested that the H detected
+in the extended atmospheres of Europa (Roth et al., 2017, 2023) and Ganymede (Barth et al.,
+1997, Feldman et al., 2000, Alday et al., 2017, Roth et al., 2023) are also indicative of an H2-
+source. Although H2 is able to escape from these satellites’ atmospheres, it does not escape
+from the Jovian system; and since its lifetime is longer than the satellites’ orbital periods
+(e.g., Smyth and Marconi (2006), Leblanc et al. (2017), Carberry Mogan et al. (2022)), a
+detectable toroidal cloud of neutral H2 co-rotating with the bodies can form (e.g., Szalay
+et al. 2022).
+The sputtering and radiolytic sources of the icy Galilean satellites’ atmospheres compete
+with other sources, such as sublimation of water ice and the subsequent photochemistry of
+the newly formed water vapor (e.g., Yung and McElroy 1977, Kumar and Hunten 1982).
+However, with increasing distance from Jupiter, the plasma density and, as a result, the
+corresponding atmospheric source decreases (Johnson et al., 2004). For example, although
+gas-phase H2O has not been directly observed at Callisto, the outermost Galilean satellite,
+observed geomorphological features have been interpreted to be caused by sublimation of
+the surface ice rather than by sputtering (Spencer and Maloney, 1984, Spencer, 1987, Moore
+et al., 1999). Further, whereas sublimation has been suggested to be the primary source of
+Ganymede’s H2O atmosphere (Roth et al., 2021, Vorburger et al., 2022), sputtering has been
+suggested to be a primary source of Europa’s H2O atmosphere (Addison et al., 2021).
+Below we focus on deriving thermal electron impact ionization rates in these icy satellites’
+atmospheres, which are needed to help understand their evolution.
+3
+Method
+The Deutsch-M¨ark (DM) formula was developed to employ and extrapolate laboratory data
+to allow users to estimate reasonably accurate electron impact ionization cross-sections,
+σ(E), over a large range of energies, E. The “modified” DM formula (Appendix A) from
+Deutsch et al. (2004), hereafter referred to as “DM2004,” is a revised version of the original
+formula developed by Deutsch and M¨ark (1987) and used to calculate cross-sections up to
+energies ≲ keV. As discussed by Deutsch et al. (2000), hereafter referred to as “DM2000,”
+and references therein, σ(E) for atoms (e.g., H and O) can be converted to σ(E) for molecules
+composed of those atoms (e.g., H2O, O2, and H2).
+Here we present more easily usable fits to these complex models for species of interest to
+the planetary science community, and of particular interest at icy satellites. An exponentially
+modified Gaussian distribution is used to compute a non-linear least-squares fit to σ(E)
+derived for H, O, H2, O2, and H2O using DM2000 and DM2004. The resulting equation is
+as follows (in units of ×10−16 cm2):
+σ(E) = α
+2δ exp
+� γ2
+2δ2 + β − log10(E)
+δ
+� �
+erf
+�log10(E) − β
+√
+2γ
+−
+γ
+√
+2δ
+�
++ δ
+|δ|
+�
++ ϵ,
+(1)
+5
+
+where the coefficients α, β, γ, δ, and ϵ in Eq. 1 for H, O, H2, O2, and H2O are listed in
+Table 2.
+Table 2: Coefficients in Eq. 1 for H, O, H2, O2, H2O
+Species
+α
+β
+γ
+δ
+ϵ
+H
+0.951653
+1.40862
+0.271538
+0.804953
+-0.0397646
+O
+1.91899
+1.72847
+0.333420
+0.864596
+-0.121378
+H2
+2.27256
+1.39600
+0.277991
+1.08255
+-0.278929
+O2
+3.20403
+1.63262
+0.241759
+0.799914
+-0.0876336
+H2O
+4.41745
+1.48743
+0.291951
+1.01222
+-0.527864
+4
+Results
+Electron impact ionization cross-sections, σ(E), for H, O, H2, O2, and H2O as derived by
+DM2000 and DM2004, as well as the corresponding fits calculated via Eq.
+1 with the
+coefficients from Table 2, are illustrated in Figure 1. These fits, of course, account for the
+ionization threshold energies occurring around 10 and 20 eV for the species considered (e.g.,
+see Tables A.1–A.2 in Appendix A). By about ∼20 eV, the difference in σ(E) derived by
+DM2000/DM2004 and by the corresponding fits for all of the species considered fall below
+10%, except for that of O, which drops below 10% between 20 and 30 eV. From these lower
+bounds up to 1 keV, the difference remains below 10% for all species considered except for
+H2, for which it exceeds 10% by ∼800 eV but is only ∼14% by 1 keV. Thus, between ∼20 eV–
+1 keV (i.e., between the ionization energy of the species considered, (e.g., Tables A.1–A.2 in
+Appendix A), and the maximum energy of the thermal electrons in the Jovian magnetosphere
+at the icy Galilean satellites, Table 1), the fits provided here can determine electron impact
+ionization cross-sections within ∼10% accuracy of those determined via the more complex
+DM models, which have been extensively tested, modified, and improved over the years,
+demonstrating agreement with experimental data better than ∼20–35% (Deutsch et al. 2009
+and references therein).
+With the thermal electron fluxes and temperatures listed in Table 1, we use the fits for
+electron impact ionization cross-sections presented in Fig. 1 to determine the corresponding
+ionization rates in the water product atmospheres of Europa, Ganymede, and Callisto, which
+are presented in Table 3. The difference in σ(E) derived by DM2004 and by the corresponding
+fit for O electron impact ionization cross-section at 20 eV is ∼32%, making the latter (Eq. 1)
+in the region of Europa’s orbit not as accurate as those of the other species, for which
+the difference is always < 10% (Table 3). However, by 30 eV the difference for all species
+drops to < 5%. The differences for electron impact ionization rates at incident electron
+energies of 100 eV at Ganymede and Callisto are < 3% for all species. We compare these
+electron impact ionization rates to the analogous photoionization rates derived according
+6
+
+Figure 1: Top panel: Electron impact ionization cross-section, σ(E), for H (red lines), O
+(blue lines), H2 (green lines), O2 (cyan lines), and H2O (magenta lines) as a function of
+incident electron energy, E (x-axis). The dashed colored lines are from Deutsch et al. (2000)
+(“DM2000”) for H2, O2, and H2O and from Deutsch et al. (2004) (“DM2004”) for H and O;
+and the solid colored lines are the corresponding fits (“Fit”) calculated via Eq. 1 with the
+coefficients from Table 2. Note the values for σ(E) begin at the ionization energies of the
+species considered (e.g., Tables A.1–A.2 in Appendix A), hence the blank spaces below these
+energies. Bottom panel: The dash-dotted colored lines represent the difference between σ(E)
+calculated via DM2000/DM2004 and via Eq. 1, |fit−DM2000/2004|
+DM2000/2004
+×100 (“Error”).
+to solar activity (Huebner and Mukherjee, 2015) in Table B.1 in Appendix B. Since the
+electron temperature for the “high/cold” plasma component at Europa (Table 1) is less than
+the ionization energies of the atoms and molecules considered (e.g., Tables A.1 and A.2 in
+Appendix A), we show ionization rates over a temperature range of 20–30 eV (“medium” to
+“low/hot” plasma components from Bagenal et al. 2015). At Europa and Ganymede, electron
+impact ionization rates are greater than the photoionization rates for all species. On the
+other hand, at Callisto, where there is the most uncertainty in electron densities (see e.g.,
+Table 1), the upper bound electron impact ionization rates are greater than the upper bound
+photoionization rates for all species, but the lower bound electron impact ionization rates
+are less than the lower bound photoionization rates. We note, however, that the electron
+impact ionization rates relate to the upstream plasma properties, and the effective electron
+impact ionization strongly depends on the details of the interaction of the plasma flow with
+the moons’ atmospheres and ionospheres, which cool as well as divert the plasma around the
+moons (e.g., Saur et al. 1998, 2004, Rubin et al. 2015, Dols et al. 2016).
+7
+
+Energy, E[eV]
+101
+102
+103
+7
+10-15
+cm
+H
+10-17
+0
+H2
+02
+H20
+10-19
+100
+Fit
+90
+DM2000
+80
+0054320
+/DM2004
+Error
+Error[
+102
+103
+101
+Energy, E[eV]Table 3: Electron impact ionization cross-sections and rates in the water product atmo-
+spheres of Europa (E), Ganymede (G), and Callisto (C)
+Species
+Satellite
+Cross-Sectiona [cm−2]
+Rateb [s−1]
+Errorc [%]
+H
+E
+(3.07–5.11)×10−17
+(2.57–5.57)×10−6
+2.96–4.93
+G
+5.48×10−17
+(0.384–3.67)×10−7
+1.34
+C
+4.38×10−10 – 4.06×10−8
+O
+E
+(0.495–2.72)×10−17
+(0.414–2.97)×10−6
+4.92–32.6
+G
+1.03×10−16
+(0.719–6.88)×10−7
+1.36
+C
+8.22×10−10 – 7.60×10−8
+H2
+E
+(3.99–7.52)×10−17
+(3.34–8.20)×10−6
+4.64–6.86
+G
+9.48×10−17
+(0.664–6.35)×10−7
+2.04
+C
+7.58×10−10 – 7.01×10−8
+O2
+E
+(1.98–7.80)×10−17
+(1.66–8.50)×10−6
+1.22–6.91
+G
+2.22×10−16
+(0.155–1.49)×10−6
+2.12
+C
+1.77×10−9 – 1.64×10−7
+H2O
+E
+(0.401–1.24)×10−16
+(0.336–1.36)×10−5
+4.63–9.82
+G
+2.00×10−16
+(0.140–1.34)×10−6
+1.16
+C
+1.60×10−9 – 1.47×10−7
+a Electron impact ionization cross-sections are calculated via Eq. 1 at 20–30 eV for Europa and 100 eV
+for Ganymede and Callisto. Note we only consider temperatures kBTe ≥ 20 eV at Europa because the
+minimum temperature, kBTe = 10 eV (Table 1), is lower than the ionization energies of the species
+considered (e.g., Tables A.1–A.2 in Appendix A).
+b Electron impact ionization rates are calculated as the product of the electron impact ionization cross-
+sections and the range in thermal electron fluxes given in Table 1. Note, since the minimum temperature
+at Europa, kBTe = 10 eV, is lower than the ionization energies of the species considered, the lower
+bound thermal electron flux is calculated according to the “medium” plasma component (kBTe = 20 eV,
+ne = 158 cm−3) from Bagenal et al. (2015), Table 5 therein.
+c The differences in the cross-sections derived by DM2000/DM2004 and by the corresponding fits, the
+“errors,” are interpolated from that illustrated in Fig. 1 at 20–30 eV for Europa (with the lower value
+calculated at 30 eV) and 100 eV for Ganymede and Callisto.
+5
+Conclusion
+The importance to the space physics community of data on atomic and molecular processes
+driven by an ambient plasma cannot be overstated. There are so many difficult but important
+observations whose interpretation is limited by the uncertainties in the atomic and molecular
+database or by the limited range of energies and species studied in the laboratory. Therefore,
+8
+
+the combination of laboratory measurements with detailed, physically-based extrapolation
+procedures, as carried out by K. Becker and colleagues, will continue to be incredibly useful.
+Because the accurate DM formula used to develop useful electron impact cross sections
+over a large range of energies requires a considerable understanding of atomic physics, here
+we present more readily useful fits to their detailed analyses for use by the space physics
+community in order to prepare for the expected data from the forthcoming observations of
+plasma-atmosphere interactions at the icy Jovian satellites. These are used to show the
+relative importance of electron impact ionization in the icy Galilean satellites’ atmospheres
+as compared to photo-ionization.
+Finally, this study can be summarized as followed:
+• Fits to the Deutsch–M¨ark formula for energy-dependent electron impact ionization
+cross-sections have been derived for H2O, H2, O2, H, O from the species’ minimum
+ionization energies up to 1 keV.
+• These cross-sections are used in tandem with electron data at the orbits of Europa,
+Ganymede, and Callisto to determine the corresponding electron impact ionization
+rates in these bodies’ water-product atmospheres.
+• At Europa and Ganymede the electron impact ionization rates are shown to exceed
+the photoionization rates, whereas at Callisto, where the electron densities vary the
+most, likely a result of the moon being inside or outside of the Jovian plasma sheet,
+the electron impact ionization rates can be more or less than the photoionization rates.
+9
+
+Appendix
+A
+DM Formula
+The “modified” DM formula (Deutsch et al., 2004) derives the total energy-dependent
+electron-impact ionization cross section, σ(E), of an atom as:
+σ(E) =
+�
+n,l
+πgn,lr2
+n,lξn,lb(q)
+n,l(u) [ln(cn,lu)/u] .
+(2)
+Here rn,l is the radius of maximum radial density of and ξn,l is the number of electrons in
+the atomic subshell characterized by quantum numbers n and l; gn,l is a weighting factor
+originally determined from a fitting procedure; u = E/En,l, where E is the incident energy
+of the electrons and En,l is the ionization energy in the (n, l) subshell; and cn,l is a constant
+determined from measured cross-sections for various values of n and l. Tables A.1 and A.2 list
+values for the various terms in Eq. 2 for H and O atoms, respectively. The energy-dependent
+function b(q)
+n,l(u) [ln(cn,lu)/u] allows the DM formula to be applied up to keV-energy regimes,
+with b(q)
+n,l(u) written as the following:
+b(q)
+n,l(u) =
+A1 − A2
+1 + (u/A3)p + A2,
+(3)
+where A1−3 and p are constants determined from measured cross-sections for various values
+of n and l, and the superscript (q) refers to the number of electrons in the (n, l) sub-
+shell. Tables A.3 and A.4 list values for the various terms in the energy-dependent function
+b(q)
+n,l(u) [ln(cn,lu)/u] for H and O atoms, respectively. We refer the reader to the review by
+Deutsch et al. (2009) for how σ(E) of atoms are used to calculate σ(E) of molecules com-
+posed of those atoms; i.e., how to estimate σ(E) of H2, O2, and H2O from σ(E) of H and
+O.
+10
+
+Table A.1: Various terms in Eq. 2 for electron impact ionization cross-section of H atoms
+n
+l
+ξn,l
+En,l a [eV]
+rn,l a [(×10−11) m]
+gn,l b
+1
+0
+1
+13.6
+5.29
+2.81
+a En,l and rn,l are taken from Tables 2 and 4 in Desclaux (1973), respectively.
+b gn,l is determined by dividing En,l from the “reduced weighting factor” gn,lEn,l = 38.20 for 1s1 in
+Deutsch et al. (2000).
+Table A.2: Various terms in Eq. 2 for electron impact ionization cross-section of O atoms
+n
+l
+ξn,l
+En,l a [eV]
+rn,l a [(×10−11) m]
+gn,l b
+1
+0
+2
+563
+0.684
+0.124
+2
+0
+2
+34.1
+4.63
+0.587
+2
+1
+4
+16.7
+4.41
+1.79
+a En,l and rn,l are taken from Tables 2 and 4 in Desclaux (1973), respectively.
+b gn,l is determined by dividing En,l from the “reduced weighting factors” gn,lEn,l = 70.00, 20.00, and
+30.00 for 1s2, 2s2, and 2p4, respectively, in Deutsch et al. (2000).
+Table A.3: Various terms in the energy-dependent function b(q)
+n,l(u) [ln(cn,lu)/u] (Eqs. 2–3)
+for electron impact ionization cross-section of H atoms
+n
+l
+q
+cn,l
+A1
+A2
+A3
+p
+1
+0
+1
+1.00
+0.31
+0.87
+2.32
+1.95
+Table A.4: Various terms in the energy-dependent function b(q)
+n,l(u) [ln(cn,lu)/u] (Eqs. 2–3)
+for electron impact ionization cross-section of O atoms
+n
+l
+q
+cn,l
+A1
+A2
+A3
+p
+1
+0
+2
+1.01
+0.23
+0.86
+3.67
+2.08
+2
+0
+2
+1.01
+0.23
+0.86
+3.67
+2.08
+2
+1
+4
+1.02
+-0.15
+1.17
+4.05
+1.31
+11
+
+B
+Photoionization Rates
+Table B.1 lists the range of photoionization rates determined by Huebner and Mukherjee
+(2015) for a “quiet” Sun (i.e., solar minimum) – “active” Sun (i.e., solar maximum), which
+are then scaled to the average Jovian system’s distance from the Sun, 5.2 AU, ignoring any
+possible absorption with depth into the atmosphere.
+Table B.1: Photoionization rates at 5.2 AU
+Species
+Rate [s−1]
+H
+(2.68–6.36)×10−9
+O
+(0.880–2.44)×10−8
+H2
+(2.00–4.25)×10−9
+O2
+(1.73–4.36)×10−8
+H2O
+(1.22–3.06)×10−8
+Acknowledgments
+S.R.C.M. acknowledges the support provided by NASA through the Solar System Workings
+grant 80NSSC21K0152, A.V. acknowledges the support provided by the Swiss National Sci-
+ence Foundation, and L.R. was supported by the Swedish National Space Agency through
+grant 2021-00153 and by the Swedish Research Council through grant 2017-04897.
+Author Contribution Statement
+All authors contributed equally to this work.
+Data Availability Statement
+All data generated or analyzed during this study are included in this published article.
+12
+
+References
+Addison, P., Liuzzo, L., Arnold, H., and Simon, S. (2021). Influence of Europa’s time-varying
+electromagnetic environment on magnetospheric ion precipitation and surface weathering.
+Journal of Geophysical Research: Space Physics, 126(5):e2020JA029087.
+Alday, J., Roth, L., Ivchenko, N., Retherford, K. D., Becker, T. M., Molyneux, P., and
+Saur, J. (2017). New constraints on Ganymede’s hydrogen corona: Analysis of Lyman-α
+emissions observed by HST/STIS between 1998 and 2014. Planetary and Space Science,
+148:35–44.
+Bagenal, F. and Delamere, P. A. (2011). Flow of mass and energy in the magnetospheres of
+Jupiter and Saturn. J. Geophys. Res., 116:5209.
+Bagenal, F. and Dols, V. (2020). The space environment of Io and Europa. Journal of
+Geophysical Research: Space Physics, 125(5):e2019JA027485.
+Bagenal, F., Sidrow, E., Wilson, R. J., Cassidy, T. A., Dols, V., Crary, F. J., Steffl, A. J.,
+Delamere, P. A., Kurth, W. S., and Paterson, W. R. (2015). Plasma conditions at Europa’s
+orbit. Icarus, 261:1–13.
+Bagenal, F. and Sullivan, J. D. (1981). Direct plasma measurements in the Io torus and
+inner magnetosphere of Jupiter. Journal of Geophysical Research, 86(A10):8447–8466.
+Barth, C. A., Hord, C. W., Stewart, A. I. F., Pryor, W. R., Simmons, K. E., McClintock,
+W. E., Ajello, J. M., Naviaux, K. L., and Aiello, J. J. (1997). Galileo ultraviolet spec-
+trometer observations of atomic hydrogen in the atmosphere of Ganymede. Geophysical
+Research Letters, 24(17):2147–2150.
+Boring, J. W., Johnson, R. E., Reimann, C. T., Garret, J. W., Brown, W. L., and Marcan-
+tonio, K. J. (1983). Ion-induced chemistry in condensed gas solids. Nuclear Instruments
+and Methods in Physics Research, 218(1-3):707–711.
+Broadfoot, A. L., Sandel, B. R., Shemansky, D. E., McConnell, J. C., Smith, G. R., Holberg,
+J. B., Atreya, S. K., Donahue, T. M., Strobel, D. F., and Bertaux, J. L. (1981). Overview
+of the Voyager ultraviolet spectrometry results through Jupiter encounter.
+Journal of
+Geophysical Research, 86(A10):8259–8284.
+Brown, W. L., Augustyniak, W. M., Marcantonio, K. J., Simmons, E. H., Boring, J. W.,
+Johnson, R. E., and Reimann, C. T. (1984). Electronic sputtering of low temperature
+molecular solids. Nuclear Instruments and Methods in Physics Research Section B: Beam
+Interactions with Materials and Atoms, 1(2-3):307–314.
+Brown, W. L., Augustyniak, W. M., Simmons, E., Marcantonio, K. J., Lanzerotti, L. J.,
+Johnson, R. E., Boring, J. W., Reimann, C. T., Foti, G., and Pirronello, V. (1982).
+Erosion and molecule formation in condensed gas films by electronic energy loss of fast
+ions. Nuclear Instruments and Methods in Physics Research, 198(1):1–8.
+13
+
+Brown, W. L., Lanzerotti, L. J., Poate, J. M., and Augustyniak, W. M. (1978). “Sputtering”
+of ice by MeV light ions. Physical Review Letters, 40(15):1027.
+Carberry Mogan, S. R., Tucker, O. J., Johnson, R. E., Roth, L., Alday, J., Vorburger, V.,
+Wurz, P., Galli, A., Smith, H. T., Marchand, B., and Oza, A. V. (2022). Callisto’s atmo-
+sphere: First evidence for H2 and constrains on H2O. Journal of Geophysical Research:
+Planets.
+Cooper, J. F., Johnson, R. E., Mauk, B. H., Garrett, H. B., and Gehrels, N. (2001). Energetic
+Ion and Electron Irradiation of the Icy Galilean Satellites. Icarus, 149(1):133–159.
+Cunningham, N. J., Spencer, J. R., Feldman, P. D., Strobel, D. F., France, K., and Osterman,
+S. N. (2015). Detection of Callisto’s oxygen atmosphere with the Hubble Space Telescope.
+Icarus, 254:178–189.
+Desclaux, J. P. (1973). Relativistic Dirac-Fock expectation values for atoms with Z = 1 to
+Z = 120. Atomic data and nuclear data tables, 12(4):311–406.
+Deutsch, H., Becker, K., Matt, S., and M¨ark, T. D. (2000). Theoretical determination of
+absolute electron-impact ionization cross sections of molecules. International Journal of
+Mass Spectrometry, 197:37–69.
+Deutsch, H., Becker, K., Probst, M., and Maerk, T. D. (2009). The semiempirical Deutsch–
+M¨ark formalism: A versatile approach for the calculation of electron-impact ionization
+cross sections of atoms, molecules, ions, and clusters. Advances in Atomic, Molecular, and
+Optical Physics, 57:87–155.
+Deutsch, H. and M¨ark, T. (1987). Calculation of absolute electron impact ionization cross-
+section functions for single ionization of He, Ne, Ar, Kr, Xe, N and F. International journal
+of mass spectrometry and ion processes, 79(3):R1–R8.
+Deutsch, H., Scheier, P., Becker, K., and M¨ark, T. D. (2004). Revised high energy behavior
+of the Deutsch-M¨ark (DM) formula for the calculation of electron impact ionization cross
+sections of atoms. International Journal of Mass Spectrometry, 233(1-3):13–17.
+Dols, V. J., Bagenal, F., Cassidy, T. A., Crary, F. J., and Delamere, P. A. (2016). Europa’s
+atmospheric neutral escape: Importance of symmetrical O2 charge exchange.
+Icarus,
+264:387–397.
+Feldman, P. D., McGrath, M. A., Strobel, D. F., Moos, H. W., Retherford, K. D., and
+Wolven, B. C. (2000). HST/STIS ultraviolet imaging of polar aurora on Ganymede. The
+Astrophysical Journal, 535(2):1085.
+Frank, L. A., Ackerson, K. L., Wolfe, J. H., and Mihalov, J. D. (1976). Observations of
+plasmas in the Jovian magnetosphere. Journal of Geophysical Research, 81(4):457–468.
+Hall, D. T., Feldman, P. D., McGrath, M. A., and Strobel, D. F. (1998). The far-ultraviolet
+oxygen airglow of Europa and Ganymede. The Astrophysical Journal, 499(1):475.
+14
+
+Hall, D. T., Strobel, D. F., Feldman, P. D., McGrath, M. A., and Weaver, H. A. (1995).
+Detection of an oxygen atmosphere on Jupiter’s moon Europa. Nature, 373(6516):677.
+Huebner, W. F. and Mukherjee, J. (2015). Photoionization and photodissociation rates in
+solar and blackbody radiation fields. Planetary and Space Science, 106:11–45.
+Johnson, R. E. (1990). Energetic charged-particle interactions with atmospheres and surfaces.
+Springer Science & Business Media.
+Johnson, R. E., Boring, J. W., Reimann, C. T., Barton, L. A., Sieveka, E. M., Garrett,
+J. W., Farmer, K. R., Brown, W. L., and Lanzerotti, L. J. (1983). Plasma ion-induced
+molecular ejection on the Galilean satellites: Energies of ejected molecules. Geophysical
+research letters, 10(9):892–895.
+Johnson, R. E., Carlson, R. W., Cooper, J. F., Paranicas, C., Moore, M. H., and Wong,
+M. C. (2004). Radiation effects on the surfaces of the Galilean satellites. Jupiter: The
+planet, satellites and magnetosphere, pages 485–512.
+Johnson, R. E., Lanzerotti, L. J., and Brown, W. L. (1982). Planetary applications of ion
+induced erosion of condensed-gas frosts.
+Nuclear Instruments and Methods in Physics
+Research, 198(1):147–157.
+Khurana, K. K., Kivelson, M. G., Vasyliunas, V. M., Krupp, N., Woch, J., Lagg, A., Mauk,
+B. H., and Kurth, W. S. (2004). The configuration of Jupiter’s magnetosphere. Jupiter:
+The planet, satellites and magnetosphere, 1:593–616.
+Kivelson, M. G., Bagenal, F., Kurth, W. S., Neubauer, F. M., Paranicas, C., and Saur, J.
+(2004). Magnetospheric interactions with satellites. Jupiter: The planet, satellites and
+magnetosphere, pages 513–536.
+Krupp, N., Vasyliunas, V. M., Woch, J., Lagg, A., Khurana, K. K., Kivelson, M. G., Mauk,
+B. H., Roelof, E. C., Williams, D. J., Krimigis, S. M., Kurth, W. S., Frank, L. A., and
+Paterson, W. R. (2004). Dynamics of the Jovian magnetosphere. In Bagenal, F., Dowling,
+T. E., and McKinnon, W. B., editors, Jupiter. The Planet, Satellites and Magnetosphere,
+volume 1, pages 617–638. Cambridge University Press.
+Kumar, S. and Hunten, D. M. (1982). The atmospheres of Io and other satellites. Satellites
+of Jupiter, pages 782–806.
+Lanzerotti, L. J., Brown, W. L., Poate, J. M., and Augustyniak, W. M. (1978). On the
+contribution of water products from Galilean satellites to the Jovian magnetosphere. Geo-
+physical Research Letters, 5(2):155–158.
+Leblanc, F., Oza, A. V., Leclercq, L., Schmidt, C., Cassidy, T., Modolo, R., Chaufray, J.-Y.,
+and Johnson, R. E. (2017). On the orbital variability of Ganymede’s atmosphere. Icarus,
+293:185–198.
+Moore, J. M. et al. (1999). Mass movement and landform degradation on the icy Galilean
+satellites: Results of the Galileo nominal mission. Icarus, 140(2):294–312.
+15
+
+Nerney, E. G., Bagenal, F., and Steffl, A. J. (2017). Io plasma torus ion composition: Voy-
+ager, Galileo, and Cassini. Journal of Geophysical Research (Space Physics), 122(1):727–
+744.
+Neubauer, F. M. (1998). The sub-Alfv´enic interaction of the Galilean satellites with the
+Jovian magnetosphere. Journal of Geophysical Research: Planets, 103(E9):19843–19866.
+Paranicas, C., Mauk, B. H., Kollmann, P., Clark, G., Haggerty, D. K., Westlake, J., Liuzzo,
+L., Masters, A., Cassidy, T. A., Bagenal, F., and Bolton, S. (2022). Energetic charged
+particle fluxes relevant to Ganymede’s polar region. Geophysical Research Letters, page
+e2022GL098077.
+Reimann, C. T., Boring, J. W., Johnson, R. E., Garrett, J. W., Farmer, K. R., Brown, W. L.,
+Marcantonio, K. J., and Augustyniak, W. M. (1984). Ion-induced molecular ejection from
+D2O ice. Surface science, 147(1):227–240.
+Roth, L. (2021).
+A stable H2O atmosphere on Europa’s trailing hemisphere from HST
+images. Geophysical Research Letters.
+Roth, L., Ivchenko, N., Gladstone, G. R., Saur, J., Grodent, D., Bonfond, B., Molyneux,
+P. M., and Retherford, K. D. (2021).
+A sublimated water atmosphere on Ganymede
+detected from Hubble Space Telescope observations. Nature Astronomy, pages 1–9.
+Roth, L., Marchesini, G., Becker, T. M., Hoeijmakers, H. J., Molyneux, P. M., Rether-
+ford, K. D., Saur, J., Carberry Mogan, S. R., and Szalay, J. R. (2023).
+Probing
+Ganymede’s atmosphere with HST Ly-alpha images in transit of Jupiter. arXiv preprint
+arXiv:2301.05583.
+Roth, L., Retherford, K. D., Ivchenko, N., Schlatter, N., Strobel, D. F., Becker, T. M., and
+Grava, C. (2017). Detection of a hydrogen corona in HST Lyα images of Europa in transit
+of Jupiter. The Astronomical Journal, 153(2):67.
+Roth, L., Saur, J., Retherford, K. D., Strobel, D. F., Feldman, P. D., McGrath, M. A.,
+Spencer, J. R., Bl¨ocker, A., and Ivchenko, N. (2016). Europa’s far ultraviolet oxygen
+aurora from a comprehensive set of HST observations. Journal of Geophysical Research:
+Space Physics, 121(3):2143–2170.
+Rubin, M., Jia, X., Altwegg, K., Combi, M. R., Daldorff, L. K. S., Gombosi, T. I., Khu-
+rana, K., Kivelson, M. G., Tenishev, V. M., T´oth, G., van der Holst, B., and Wurz, P.
+(2015). Self-consistent multifluid MHD simulations of Europa’s exospheric interaction with
+Jupiter’s magnetosphere. Journal of Geophysical Research: Space Physics, 120(5):3503–
+3524.
+Saur, J., Neubauer, F. M., Connerney, J. E. P., Zarka, P., and Kivelson, M. G. (2004). Plasma
+interaction of Io with its plasma torus. Jupiter: The planet, satellites and magnetosphere,
+1:537–560.
+16
+
+Saur, J., Strobel, D. F., and Neubauer, F. M. (1998). Interaction of the Jovian magnetosphere
+with Europa: Constraints on the neutral atmosphere. Journal of Geophysical Research:
+Planets, 103(E9):19947–19962.
+Smith, E. J., Davis Jr, L., Jones, D. E., Coleman Jr, P. J., Colburn, D. S., Dyal, P., Sonett,
+C. P., and Frandsen, A. M. A. (1974). The planetary magnetic field and magnetosphere
+of Jupiter: Pioneer 10. Journal of Geophysical Research, 79(25):3501–3513.
+Smyth, W. H. and Marconi, M. L. (2006). Europa’s atmosphere, gas tori, and magnetospheric
+implications. Icarus, 181(2):510–526.
+Spencer, J. R. (1987). Thermal segregation of water ice on the Galilean satellites. Icarus,
+69(2):297–313.
+Spencer, J. R. and Maloney, P. R. (1984). Mobility of water ice on Callisto: Evidence and
+implications. Geophys. Res. Letters, 11(12):1223–1226.
+Strobel, D. F., Saur, J., Feldman, P. D., and McGrath, M. A. (2002). Hubble Space Telescope
+Space Telescope Imaging Spectrograph search for an atmosphere on Callisto: A Jovian
+unipolar inductor. The Astrophysical Journal Letters, 581(1):L51.
+Szalay, J. R., Smith, H. T., Zirnstein, E. J., McComas, D. J., Begley, L. J., Bagenal, F.,
+Delamere, P. A., Wilson, R. J., Valek, P. W., Poppe, A. R., N´enon, Q., Allegrini, F.,
+Ebert, R. W., and Bolton, S. J. (2022).
+Water-group pickup ions from europa-genic
+neutrals orbiting jupiter. Geophysical Research Letters, page e2022GL098111.
+Trainor, J. H., McDonald, F. B., Teegarden, B. J., Webber, W. R., and Roelof, E. C.
+(1974). Energetic particles in the Jovian magnetosphere. Journal of Geophysical Research,
+79(25):3600–3613.
+Vorburger, A., Fatemi, S., Galli, A., Liuzzo, L., Poppe, A. R., and Wurz, P. (2022). 3D
+Monte-Carlo simulation of Ganymede’s water exosphere. Icarus, 375:114810.
+Wolfe, J. H., Collard, H., Mihalov, J., and Intriligator, D. (1974). Preliminary Pioneer 10
+encounter results from the Ames Research Center plasma analyzer experiment. Science,
+183(4122):303–305.
+Yung, Y. L. and McElroy, M. B. (1977). Stability of an oxygen atmosphere on Ganymede.
+Icarus, 30(1):97–103.
+17
+

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@@ -0,0 +1,2939 @@
+The limits of human mobility traces to predict the spread of
+COVID-19
+Federico Delussu1,2, Michele Tizzoni1,3 †, and Laetitia Gauvin1,4†
+1ISI Foundation, via Chisola 5, 10126, Turin, Italy
+2Department of Applied Mathematics and Computer Science, DTU,
+Copenhagen, Denmark
+3Department of Sociology and Social Research, University of Trento, Trento, Italy
+4Institute for Research on Sustainable DevelopmentIRD, UMR 215 Prodig, 5
+cours des Humanit´es, F-93 322 Aubervilliers Cedex, France
+†these authors contributed equally to this work
+Abstract
+Mobile phone data have been widely used to model the spread of COVID-19, however,
+quantifying and comparing their predictive value across different settings is challenging.
+Their quality is affected by various factors and their relationship with epidemiological in-
+dicators varies over time. Here we adopt a model-free approach based on transfer entropy
+to quantify the relationship between mobile phone-derived mobility metrics and COVID-
+19 cases and deaths in more than 200 European subnational regions. We found that past
+knowledge of mobility does not provide statistically significant information on COVID-19
+cases or deaths in most of the regions. In the remaining ones, measures of contact rates
+were often more informative than movements in predicting the spread of the disease, while
+the most predictive metrics between mid-range and short-range movements depended on the
+region considered. We finally identify geographic and demographic factors, such as users’
+coverage and commuting patterns, that can help determine the best metric for predicting
+disease incidence in a particular location. Our approach provides epidemiologists and public
+health officials with a general framework to evaluate the usefulness of human mobility data
+in responding to epidemics.
+1
+Introduction
+The relationship between human movements and the spatial spread of infectious diseases has
+been recognized for a long time [1, 2, 3].
+Human movement has been shown to play a key
+1
+arXiv:2301.03960v1  [physics.soc-ph]  10 Jan 2023
+
+role in the dynamics of several pathogens, through two basic mechanisms: traveling infectious
+individuals may introduce a pathogen in a susceptible population, and, at the same time, human
+movement increase the contact rate between individuals, creating new opportunities for infection.
+In the past 15 years, the increasing availability of mobility data derived from mobile phones has
+fueled a large body of work aimed at identifying opportunities to use them for infectious disease
+modeling and surveillance [4, 5, 6, 7, 8, 9, 10].
+More recently, during the COVID-19 pandemic, mobile phone-derived data have been exten-
+sively harnessed to monitor the effect of non-pharmaceutical interventions (NPIs) across coun-
+tries, understand the early dynamics of COVID-19 diffusion, and forecast its spread at different
+spatial scales, from countries to cities [11, 12, 13, 14, 15, 16, 17]. By measuring human move-
+ments and combining them with phylogeography methods [18, 19], several studies shed light on
+the cryptic spread of new variants, their persistence over time and resurgence after the relaxation
+of NPIs [20, 21, 22].
+Human mobility has been shown to strongly correlate with the spread of COVID-19 during
+the early phase of the outbreak in China and in many other countries [23, 24, 25, 26, 27, 28].
+However, once COVID-19 established a foothold in a population, the relative importance of
+mobile phone-derived data to predict the epidemic dynamics on a local scale has been generally
+less understood and several studies have shown conflicting evidence about the use of mobility
+traces to model the spread of COVID-19 at later stages of the outbreak. For instance, it has been
+shown that the explanatory power of mobility metrics in relation to the case growth rate in the
+U.S., significantly declined in spring 2020, especially in rural areas [29, 30, 31]. Similar trends
+have been observed in Europe [32]. In parallel, mobile phone-derived data have been proven
+beneficial to model COVID-19 dynamics in largely populated urban areas of Western countries
+[33, 34], but less so in countries of the Global South [35].
+Several reasons have been proposed to explain the varying relationship between mobility
+metrics and epidemic indicators [29]. Mobility metrics are generally derived from raw mobile
+positioning data through complex and customized processing pipelines that can significantly
+vary across data providers [36].
+How raw data are processed, and the specific definitions of
+mobility metrics can significantly impact their interpretation with respect to epidemic variables
+[37]. Moreover, the relationship between mobility and epidemic patterns often relies on model-
+ing assumptions, typically considering linear dependencies, that may not capture the complex
+interplay of these quantities [32, 30]. Finally, mobile phone-derived metrics are generated from
+a sample of users who is generally not representative of the whole population. It is therefore of
+paramount importance to define standardized approaches that can quantify the added value of
+mobility metrics for epidemiological analysis, and make different metrics, across settings, directly
+comparable.
+Here, we extensively quantify the relationship between cell phone-derived mobility metrics and
+COVID-19 epidemiological indicators through a model-free approach, based on an information-
+theoretic measure, transfer entropy [38], adapted for small sample sizes. Leveraging granular
+2
+
+data provided by Meta that capture both users’ movements and colocation at a fine spatial scale
+[39], we measure the information flow between mobility metrics and time series of COVID-19
+incidence and deaths in four European countries, at a subnational scale, over a one year period.
+We find that the relative information added by the past knowledge of mobility metrics to the
+knowledge of the current state of COVID-19 time series is often not statistically significant.
+In statistically significant cases instead, we show that the relative information added by
+past knowledge of COVID-19 cases to the knowledge of current deaths is twice the information
+flow between past knowledge of mobility metrics and current deaths. We also show that the
+information flow of a given mobility metric to predict future COVID-19 incidence or deaths can
+be significant in one country but not in another, even if derived from the same original data
+source.
+Being a general framework, our approach provides a quantitative measure of the relative
+added explanation brought by mobile phone data to the prediction of epidemiological time series
+that does not depend on the choice of a specific forecasting model. It thus helps to better identify
+the most appropriate mobility metrics to use among those available. Our results can thus guide
+epidemiologists and public health practitioners in the evaluation of mobile phone-derived mobility
+metrics when they are interpreted as a precursor of epidemic activity.
+2
+Results
+Here, we first describe and then apply our framework to measure the information flow between
+human mobility traces and the time evolution of COVID-19 in four European countries.
+2.1
+A transfer entropy approach to link mobility behavior and COVID-
+19 epidemiology
+With the aim of quantifying the information flow from mobility-derived data to COVID-19 data,
+we first gathered a set of mobility and epidemiological indicators. Fig. 1 provides an overview
+of the datasets used in the study. In Materials and Methods, we provide a full description of all
+data sources and the data processing steps. We considered four European countries – Austria,
+France, Italy, and Spain – and their administrative subdivisions at NUTS3 level [40] which is
+the lowest, i.e. the most granular, level of the standard hierarchy of administrative regions in
+Europe (Fig. 1, leftmost column).
+In all administrative regions, we collected indicators of the COVID-19 epidemic dynamics,
+namely, the weekly and daily numbers of new COVID-19 cases and deaths over the period, from
+September 2020 until July 2021. During this period, the dynamics of COVID-19, exemplified by
+the incidence of new cases (Fig. 1, rightmost column), displayed subsequent waves, as a result of
+the complex interaction between the spread of new variants, the adoption of non-pharmaceutical
+interventions, the introduction of vaccines.
+3
+
+Figure 1:
+Summary of behavioral and epidemiological indicators.
+In each country
+under study (from top to bottom: Italy, France, Austria and Spain), we consider three different
+types of indicators: contact rates, movements (here for the sake of simplicity we only show the
+short-range movements), and COVID-19 cases. In each plot, the blue shaded area highlights
+the within-country variability, corresponding to time series in every administrative subdivision.
+The blue solid line represents the average value. All curves are normalized between 0 and 1,
+corresponding to their maximum value.
+In each country, we also collected weekly and daily time series describing movements and
+colocation patterns made available by Meta [41]. We computed contact rates from colocation
+maps (see Material and Methods and the SI for details), which measure the probability that
+two users from two locations are found in the same location at the same time [39]. Colocation
+maps were generated by Meta on a weekly basis, only. To study human movement patterns,
+we considered movement range maps provided by Meta, which report the number of users who
+moved between any two 16-level Bing tiles with an 8 hour frequency [42]. To make colocation
+and movement patterns comparable in terms of scale, we focused on short-range movements,
+i.e. movements that occurred within the same tile, and we separately considered the mid-range
+movements, i.e. movements that occur between two different tiles in the same province.
+4
+
+Country
+Contact Rate
+Movement
+Cases
+27
+2
+2
+20
+2
+DecFigure 2: Illustration of study design. We computed the transfer entropy TEX→Y to measure
+the information flow between source X (on the left) and target time series Y (right), for a given
+time lag l. In the figure example, as target time series we consider the number of COVID-19
+deaths, D(t). As source time series, we consider either mobility indicators, M s(t), M(t), CR(t),
+or COVID-19 cases C(t). Transfer entropy quantifies the amount of information that is added
+by past knowledge of mobility or cases (green and cyan bars, respectively) to current knowledge
+of deaths, with respect to the knowledge of past deaths only (blue bar). After correcting the
+TE for small sample sizes, and normalizing by the reference value represented by the blue bar,
+we finally compare the Normalized Effective Transfer Entropy of mobility and cases (rightmost
+box).
+We then processed the three datasets, starting from their raw form, to aggregate them at
+the NUTS3 resolution and create the time series: M s(t) for the short-range movements, M(t)
+for the mid-range movements and CR(t) for the contact rates. These time series were then used
+as source variables in the information-theoretic analysis. In the remainder of the paper, we will
+generally refer to CR(t), M s(t), and M(t) as mobility time series as they are all derived from
+human mobility data. We will also generally refer to the NUTS3 units as provinces, although
+their nomenclature varies across countries.
+Fig. 2 illustrates our study design based on the transfer entropy [38]. Transfer entropy is
+a metric that measures the directed statistical dependence between a source and a target time
+series and it has been applied to a wide range of research domains [43]. Here, our approach
+consists, first, in computing the transfer entropy between mobility time series, M s(t), M(t) and
+CR(t), and epidemiological time series such as the reported number of COVID-19 attributed
+deaths D(t) and cases C(t), in each administrative unit, and for different temporal lags l, using
+the definition of Shannon entropy, as described by the equations in Fig. 2.
+Intuitively, the
+transfer entropy between mobility and deaths, TEM s→D (resp. TEM→D), can be interpreted as
+5
+
+informationflow
+mobility
+p(Dt+1|Dt)
+small sample correction
+[+↓
+and normalization
+H(DD)
+cases
+p(Dt+1|D)
+-1± 1
+deaths
+H(Dt+1Dl) = Zp(Dt+1, D) 1og
+p(D+1Dthe degree of uncertainty of the reported deaths, D, at time t that is solved jointly by the time
+series of deaths and mobility trends M s (resp. M) and exceeds the current degree of uncertainty
+of D, which can be solved by D’s own past.
+It is known that transfer entropy estimates suffer in case of small sample sizes and non-
+stationarity of the source and target time series [44].
+Moreover, due to the non-parametric
+nature of the transfer entropy, values computed between different source-target time series are
+not directly comparable. To address these issues, we first adopted the definition of effective
+transfer entropy (ETE) [44]. ETE is obtained by subtracting from the original definition of TE
+a reference TE value using a shuffled version of the target time series (see Methods for details),
+thus removing spurious contributions to TE due to fluctuations observed in small sample sizes.
+Also, to address biases due to small sample sizes, we applied a Kernel Density Estimation, before
+the time series discretization that is necessary to compute the transfer entropy.
+Second, we
+normalized the effective transfer entropy by the Shannon entropy of the target variable, defining
+a normalized effective transfer entropy (NETE) [45]. We obtain a metric that is always positive
+when it is statistically significant and whose zero value indicates the absence of information
+transfer between time series. In the remainder of the article, we thus refer to the NETE between
+source X and target Y as our main quantity of interest, using the symbol NX→Y to denote it.
+To better understand the cause-effect relationship between mobility and COVID-19 deaths,
+which are encoded in the value of NM→D ,NM s→D and NCR→D, we compared them against
+the transfer entropy NC→D, where C is the time series of new COVID-19 cases. As the causal
+relationship between the number of cases and deaths is established by definition, we used the
+transfer entropy NC→D as a benchmark to evaluate the added value of mobility indicators to
+predict COVID-19 deaths. As an example, similar values of NM s→D and NC→D would suggest
+knowledge of past COVID-19 incidence encodes a similar amount of information as knowledge
+of past mobility when it comes to predicting future deaths.
+2.2
+The information flow between COVID-19 incidence and deaths
+As previously mentioned, to gauge our transfer entropy analysis framework, we first looked at
+the causal relationship between the incidence of COVID-19 cases and reported death counts. It is
+clearly expected that a major source of information that provides knowledge on future deaths is
+encoded in the time series of past case counts. We used the NETE to quantify such information
+flow.
+Fig. 3 shows the NETE between the weekly time series of COVID-19 cases and deaths in
+the four countries under study.
+In all countries, median values of NC→D increase from lags
+equal to 1 week up to a maximum of around 2-3 weeks, and then decline rapidly beyond the
+3 weeks time lag. This is in line with early estimates of the median time delay between case
+reporting and fatality, which was estimated to range between 7 and 20 days in different countries
+[46, 47]. At lag equal to 2 weeks, the mean relative explanation added by time series of cases
+with respect to deaths – that is how much of D(t) can be explained only by the past knowledge
+6
+
+Figure 3:
+Information flow between COVID-19 incidence and deaths.
+Normalized
+Effective Transfer Entropy (NETE) between COVID-19 weekly reported cases and deaths in
+the NUTS3 administrative subdivisions (provinces) of Austria, France, Italy and Spain. NETE
+is computed for lags ranging from 1 to 8 weeks, on the x-axis. Boxplots are computed on the
+distribution of NETE values of all the administrative subdivisions in each country. The horizontal
+red line marks the value NC→D = 0.
+C(t − l) – is 14% (SD=8) in Spain, 8% (SD=6) in Italy, 7% (SD=5) in Austria, and 6% (SD=5)
+in France. Boxplots computed on the distribution of administrative units in each country show
+a substantial heterogeneity of NETE across regions for lags shorter than 4 weeks. This may
+be partially explained by spatial heterogeneities in case and death reporting, and in testing
+strategies. Also, NC→D values appear to be higher in Spain, with respect to the other countries.
+A transfer entropy analysis of daily time series of COVID-19 cases and deaths displays consistent
+results (see Fig. S1), with NETE values that fall within the same range measured on a weekly
+time scale.
+These results suggest NETE estimates are robust with respect to the time scale at which
+source and target time series are compared. Moreover, it provides a reference value for NETE,
+in terms of orders of magnitude, when the existence of a causal relationship between time series
+is known.
+7
+
+0.4
+0.4
+Austria
+France
+0.3
+0.3
+ 0.2
+ 0.2
+0.1
+0.1
+0.0
+0.0
+1
+2
+3
+4
+5
+6
+1
+8
+1
+2
+3
+4
+5
+6
+7
+8
+Lag (weeks)
+Lag (weeks)
+0.41
+0.41
+Italy
+Spain
+0.3
+0.3
+ 0.2
+ 0.2
+Nc
+Nc
+0.1
+0.1
+0.0
+0.0
+1
+2
+3
+4
+5
+6
+7
+8
+1
+2
+3
+4
+5
+6
+8
+Lag (weeks)
+Lag (weeks)→ C(t)(%)
+→ D(t)(%)
+l (weeks)
+CR(t)
+M(t)
+M s(t)
+CR(t)
+M(t)
+M s(t)
+C(t)
+2
+9
+19
+3
+10
+7
+7
+79
+3
+20
+23
+5
+21
+8
+13
+69
+4
+27
+22
+9
+29
+9
+16
+46
+5
+33
+23
+10
+36
+8
+17
+18
+6
+35
+27
+10
+38
+14
+17
+7
+7
+29
+25
+11
+40
+12
+14
+4
+8
+27
+20
+11
+38
+15
+12
+8
+Table 1: Percentage of statistically significant NETE values across provinces in all
+the countries studied. This table shows the percentage of provinces, in all countries, in which
+the NETE is statistically significant (p < 0.01) for lags (l) from 2 to 8 weeks.
+2.3
+The information flow between mobility traces and COVID-19 dy-
+namics
+Having defined a benchmark of information transfer using NC→D, we measured the information
+flow between behavioral time series of mobility indicators and COVID-19 cases and deaths. Fig. 4
+summarizes the main results of our analysis. Values of NX→D, with X being either short range
+movements, mid-range movements or contact rates, were substantially smaller than NC→D in
+all countries, for any given time lag l. In particular, Fig. 4a allows to compare the distributions
+of NC→D, NCR→D, NM s→D, and NM→D, at the time lag l that maximized the median NETE
+for weekly time series, for all indicators. We found the largest median values of the normalized
+transfer entropy at l = 7 weeks for both contact rates and movements (short-range and mid-
+range). The upper quartile of the NETE distributions derived from the mobility traces generally
+fell below 5%, in all countries, while the lower quartile of NC→D was always above 5%. Also,
+the distributions of normalized transfer entropy computed from movements were much narrower
+and often including the value N = 0 within their interquartile range. Values of NM→C, shown
+in Fig. 4b, display a pattern similar to the normalized transfer entropy from the mobility time
+series to the death time series, with generally low values of NETE in all countries. Compared
+to movement time series, contact rates led generally to relatively higher values of NETE with
+both targets, cases and deaths, as shown in Fig. 4. Our result confirms the additional value
+of measuring contact rates from mobile phone data, with respect to other movement metrics
+[48]. Besides, it shows that short-range mobility within a province had often a limited predictive
+power to capture time trends of COVID-19 spread.
+To obtain a more detailed picture of the predictive power of different mobility metrics in terms
+of NETE, we computed the percentage of provinces for which mobility time series provided
+significant relative information added, with respect to the past knowledge of epidemiological
+8
+
+Figure 4:
+Information flow from mobility data to COVID-19 incidence and deaths.
+Comparison between the normalized effective transfer entropy computed from source time series
+X and target time series of reported COVID-19 deaths D (a) and cases C (b). Source time series
+are COVID-19 cases (only for deaths), contact rates, short range and mid-range movement.
+Boxplots are computed from the distribution of NETE values for a given time delay, l. In panel
+a: l= 2 weeks for cases, 7 weeks for contact rates and movement. In panel b: l= 6 weeks for
+short range and mid-range movement. The horizontal red line marks the value NX→D = 0.
+indicators only (see Tab. 1). On the one hand, our framework effectively captured the existing
+causal relationship between the time evolution of cases counts and the number of deaths, as
+the NETE between these indicators was statistically significant (p < 0.01) in about 80% of the
+provinces, at 2 weeks lag. On the other hand, we observed a statistically significant information
+transfer from mobility time series to epidemiological ones in a much smaller fraction of provinces.
+Short-range movements NETE was significant in less than 20% of provinces when considered as
+a predictor of both cases and deaths. Mid-range movement time series and contact rates were
+significant in at most 27% and 40% of provinces. This means that in most provinces, mobility
+traces did not provide any additional information to predict future COVID-19 cases or deaths,
+at any lag between 2 and 8 weeks.
+Measures of contact rate extracted from colocation maps were more suitable than movement
+9
+
+a
+C
+0.3
+CR
+Ms
+0.2
+M
+XN
+0.1
+0.0
+b
+Austria
+France
+Italy
+Spain
+CR
+0.3
+Ms
+M
+0.2
+C
+个
+XN
+0.1
+0.0
+France
+Italy
+Austria
+Spain
+Country→ C(t)(%)
+→ D(t)(%)
+l (weeks)
+CR(t)
+M(t)
+M s(t)
+CR(t)
+M(t)
+M s(t)
+C(t)
+2
+4 (1)
+4(1)
+4 (0)
+4 (1)
+5(2)
+4 (1)
+11 (6)
+3
+4 (2)
+4(2)
+4 (1)
+5 (2)
+4(1)
+4 (1)
+9 (4)
+4
+5 (2)
+4(1)
+4 (2)
+5 (2)
+4(1)
+5 (2)
+6 (3)
+5
+5 (2)
+4(1)
+5 (2)
+6 (3)
+4(1)
+5 (2)
+5 (2)
+6
+6 (2)
+4(1)
+5 (2)
+6 (3)
+4(2)
+5 (2)
+5 (2)
+7
+5 (2)
+5(1)
+5 (2)
+6 (3)
+5(2)
+6 (3)
+5 (2)
+8
+5 (3)
+5(1)
+5 (2)
+6 (3)
+5(2)
+6 (3)
+4 (1)
+Table 2: NETE results across provinces in all the countries studied. The table shows
+the average relative explanation added by source time series, with respect to past knowledge of
+the target only. Only provinces having a statistically significant NETE are considered. Numbers
+in parenthesis report the standard deviation computed over all provinces for which the NETE
+was statistically significant.
+data to capture behavioral patterns relevant to predict COVID-19 spread.
+By focusing only on those provinces where we could identify a significant information flow
+between mobility traces and COVID-19 indicators, we observe that the averaged relative expla-
+nation added by mobility data with respect to the epidemiological data ranges between 4 − 6%,
+which is about half of the averaged relative explanation added by past knowledge of cases to the
+prediction of future deaths (see Tab. 2 and Figs. S2-S9 in the SI).
+As a sensitivity analysis, we also computed the NETE on a shorter time window, between
+September 2020 and January 2021, to exclude the confounding effect of the introduction of na-
+tionwide vaccination programs. Since in those months all countries adopted mobility restrictions
+to mitigate the fall COVID-19 wave, we expect a stronger relationship between mobility and
+COVID-19 cases. Indeed, during this time frame, the information flow between movement time
+series and COVID-19 cases was consistently higher than in the full study period (see Fig. S10).
+This result indicates that, provided with time series of adequate size, the NETE can effectively
+capture the time-varying relationship between human mobility time trends and COVID-19 dy-
+namics.
+2.4
+Identifying the determinants of mobility data predictive power for
+COVID-19
+Maps of Fig. 5 highlight the spatial heterogeneity of NX→D values observed within the same
+country, Spain, for a given time lag and different source time series (see Figs. S11 - S13 for
+the maps of Austria, France, and Italy). As previously mentioned, NC→D displays higher and
+significant values in most of the country (Fig. 5a), with very few exceptions, while statistically
+10
+
+Figure 5:
+Spatial variations of normalized effective transfer entropy. Maps of NETE
+values computed for different source time series and weekly COVID-19 deaths, in the provinces
+of Spain: (a) source is COVID-19 cases at lag l=2 weeks, (b) source is contact rate at lag l=7
+weeks, (c) source is short-range movement at lag l=7 weeks. (d) source is mid-range movement
+at lag l=7 weeks. Dark grey indicates provinces with non-significant values of NETE (p > 0.01).
+Provinces in white are excluded from our sample.
+significant values of NM s→D are found only in 16 provinces out of 42 (Fig. 5c).
+To better understand the observed heterogeneity in NETE, and identify those features that
+can predict the likelihood to observe a statistically significant information transfer from mobility
+11
+
+b
+a
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+Nc-→D
+NcR→D
+d
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+Nms→D
+NM-Dp ≥ 0.01
+p <0.01
+precision
+0.64
+0.90
+recall
+0.95
+0.47
+f1-score
+0.77
+0.62
+(a) Movement
+p ≥ 0.01
+p<0.01
+precision
+0.71
+0.92
+recall
+0.95
+0.61
+f1-score
+0.81
+0.74
+(b) Contact rate
+Table 3: Classification performance metrics. Summary of model’s classification performance
+to predict the statistical significance of NETE at the p < 0.01 threshold when the input source
+is short-range movement (a) or contact rate (b) and target variable are COVID-19 deaths.
+to COVID-19 death counts, we resorted to a classification model. Namely, we used a random
+forest classifier to predict when the value NX→D is more likely to be statistically significant, using
+short-range movement and contact rate as source time series. We focused on these two metrics
+as they are quantities measured at the same spatial scale. Moreover, short-range movements
+represent on average 90% or more of all movements within a province (see Table S1). As input
+features to the model, we considered a set of attributes of the provinces in each country. In
+particular, we investigated the effects of population size, province area in square kilometers, the
+density of Facebook users, the number of total cumulative deaths, the ratio between the number
+of commuters traveling from or to the province, and those who live and work there, as reported
+by the census (commuting flow), and the coverage consistency, that is the correlation over time
+between the number of Facebook users sharing their location and the number of Facebook users
+taken into account to compute the colocation maps.
+The results summarized in Tab. 3 show that the model achieves a good overall performance in
+terms of precision and recall, as indicated by f1-scores generally higher than 0.6. In particular, of
+all provinces that are classified by the model as characterized by a statistically significant value of
+NETE, 90% or more display a significant transfer of information, as shown by precision values.
+On the other hand, the model’s recall is close to 0.95 when it comes to identifying provinces
+characterized by a not statistically significant NETE, therefore the model correctly identifies
+95% of those provinces where there is no actual transfer of information between mobility and
+deaths.
+To explore the importance of province features in our classification model, we examined the
+SHAP (SHapley Additive exPlanations) values associated with each, as shown in Fig. 6. SHAP
+is a method based on a game theoretic approach to explaining the output of classification mod-
+els [49]. As expected, the choice of the time lag to compute the NETE is crucial in determining
+the presence of a significant information transfer between mobility metrics and epidemiological
+indicators. Indeed, lag is ranked as the most and second most important feature explaining the
+classification, for contact rate and short-range movement, respectively. Commuting flow is the
+most important predictor of the statistical significance of NETE between short-range movements
+12
+
+(a) Movement
+(b) Contact rate
+Figure 6: SHAP plots of feature importance to predict the statistical significance of
+the NETE for all selected provinces. Color represents the feature value (blue is low and
+red is high). Panel a describes the results for NM s→D, panel b for NCR→D. The SHAP value,
+on the horizontal axis, indicates the feature importance on the model output, with larger values
+corresponding to higher relevance. Each dot represents a single observation. Features are ranked
+by importance.
+and deaths: when the number of commuters leaving or entering a province represents an impor-
+tant fraction with respect to those who remain within the province, the relationship between
+short-range mobility and COVID-19 dynamics gets weaker. However, the same feature has only
+a marginal impact on the NETE between contact rates and deaths, which suggests contact rate
+should be preferred over short-range movements to predict epidemic outcomes when a province is
+characterized by large population inflows/outflows. Province area and population size have also
+a significant impact on the information transfer between short-range movement and COVID-19
+deaths. Indeed, a larger area and population size correspond to a higher likelihood of NETE
+significance for short-range movements.
+This effect may partly explain why we observed NETE values that were statistically significant
+only in a few provinces of Austria, where spatial units were particularly small. When looking at
+the information flow between contact rates and time series of deaths, the total cumulative deaths
+represent an important explanatory variable for the classification model. Besides the analysis
+presented in Fig. 6 suggests that the coverage consistency needs to be sufficiently high in order
+to get a statistically significant transfer entropy from contact rate to deaths. In France, where in
+most provinces the coverage consistency is low and the commuting inflow and outflow are higher
+than in other countries (see Table S2), mid-range movements seem to provide a better alternative
+to contact rates and short-range movements to partially explain time trends of COVID-19 cases
+and deaths (see Fig. S14 of the SI).
+13
+
+High
+flow
+6
+Feature value
+area
+population
+cumulated deaths
+user density
+D.3D.2D.10.D
+0.1
+0.2
+0.3
+0.4
+SHAP value (impact on mpdel output)High
+lag
+cumulated deaths
+coverage consistency
+Feature value
+population
+flow
+area
+Wser density
+D.4D.3D.2D.10.D
+0.1
+0.2
+0.3
+SHAP value (impact on mpdel output)From our analysis, we thus conclude that NETE values computed using contact rates as
+source time series are less sensitive to the province’s geographic or demographic features, rather
+than to the noise of the target time series. Given good coverage, and consistency over time,
+contact rates thus represent a better epidemiological predictor of future COVID-19 deaths than
+short-range movements.
+3
+Discussion
+In this work, we have introduced a novel framework based on transfer entropy to quantify the
+amount of information that is transferred from mobile phone-derived mobility metrics to epi-
+demiological time series. Given the important role that mobility indicators have played in the
+COVID-19 pandemic, we tested our approach on mobility and epidemic time series collected
+in four European countries, between 2020 and 2021, at a subnational scale. We found that, in
+general, the relative explanation added by mobility time series to predict future epidemic trends,
+whether new cases or deaths, was relatively small, ranging between 4% and 6% on average, and
+not statistically significant in the large majority of the provinces we considered, for any mo-
+bility metric. As a comparison, these values were about half of the relative explanation added
+by past knowledge of COVID-19 incidence to predict future deaths. Our method allowed us
+to directly compare the relative explanation added by different mobile phone-derived metrics of
+mobility: short- and mid-range mobility, and contact rates. We generally found a higher informa-
+tion transfer from contact rates than movement, in line with previous studies [48], however, we
+also observed significant heterogeneities within the same country and between countries. With
+a classification model, we identified spatial features that may explain such heterogeneities. In
+provinces characterized by large populations, good coverage consistency over time, and small
+commuting in- and outflows, short-range movements can represent a useful metric to predict
+disease dynamics. Where commuting flows are large, such as in France, and Austria, mid-range
+movements, which represent less than 10% of the total movements, provided a better alternative
+to short-range ones. Our results suggest the choice of the best mobility metric to inform epi-
+demic predictions can depend on a number of different factors, even when using one single data
+provider. Moreover, our findings show that cell phone mobility metrics do not always capture
+epidemiologically-relevant behaviors and alternative data sources could be more effective for this
+aim, as, for instance, the collection of survey data [50].
+There is an emerging common understanding that mobility indicators measured from mobile
+phone data present significant gaps and do not provide a consistent picture of mobility across
+countries, and data providers [51, 52]. Previous studies have also highlighted the fact that cou-
+pling between mobility indicators and COVID-19 epidemiology is often weak, and it changes over
+time [29]. The approach we introduced here addresses the above challenges by providing a general
+framework to evaluate the quality of metrics derived from passively collected mobility traces as a
+predictor of epidemic outcomes. Our framework has the advantage of being model-free, meaning
+14
+
+that it does not depend on modeling assumptions regarding the expected relationship between
+mobility and epidemic dynamics, nor it requires any parametrization. The normalized effective
+transfer entropy we adopted is a general method. It allows us to rigorously compare different
+mobility indicators, across epidemiological settings, by measuring the relative information added
+by mobility time series to the prediction of future disease incidence. To this end, we release the
+code to reproduce our analysis between any two source and target time series (see Data and
+Code Availability). Researchers can use this tool in any epidemiological context to gauge the
+added value of a specific mobile phone-derived behavioral measure for epidemic intelligence.
+Our study comes with a number of limitations and opens new directions for future work. We
+considered mobility metrics derived from one data provider, Meta, whose user base is not rep-
+resentative of the population in the countries we considered. However, alternative data sources
+of mobility indicators in Europe with a similar breadth, such as Google or Apple, do not reach
+the same spatial granularity and provide their data only as relative changes with respect to a
+pre-pandemic baseline, thus limiting their use in a study like ours. On the other hand, movement
+and colocation maps by Meta have been extensively used in several studies, including European
+countries [53, 54, 55, 56, 57]. Here, we considered four countries with different public health
+systems, and that adopted different testing strategies. Observed differences in the predictive
+power of mobility metrics across countries may depend on the varying quality of their reporting
+systems, especially at the province level. However, all four countries belong to the European
+Union and we expect very similar standards of surveillance during the pandemic. Overall, it
+will be important to assess our findings on mobility data from other providers, and, most im-
+portantly, in countries of the non-Western world. Finally, it is important to note that transfer
+entropy measurements become more accurate as the length of the source and target time series
+increases [44]. We worked with a relatively short time series, addressing the bias due to the small
+sample by adopting the effective transfer entropy. However, we could not systematically investi-
+gate how the information transfer changed over time, performing our analysis over different time
+windows and comparing them. Future work could benefit from longer epidemic time series, over
+several years, to identify temporal changes in the information flow between human movements
+and COVID-19 dynamics.
+Measures of human mobility inferred from mobile phone data have been a critical ingredient
+to inform the public health response during the COVID-19 pandemic [58] and they will be an
+important asset in the fight against future pandemics. At the same time, their widespread use
+raises some relevant ethical concerns due to re-identification risks [59], therefore, it is fundamental
+to assess the added value of using cell phone mobility data in a given epidemic scenario and
+whether the benefits outweigh the risks. Our work provides a practical guide to identifying when
+and where mobile phone mobility metrics truly capture behavioral patterns that are relevant to
+predict disease dynamics.
+15
+
+4
+Materials and Methods
+4.1
+Epidemiological indicators
+We collected epidemiological time series in the 4 countries under study from 2 data sources.
+Daily reported cumulative COVID-19 cases were collected from the COVID-19 Data Hub [60],
+an open source aggregator of up-to-date COVID-19 statistics, at the NUTS3 level in Austria,
+France, Italy, and Spain.
+Daily reported cumulative deaths in Austria, France, and Spain were also collected from the
+COVID-19 Data Hub. For Italy, death statistics were only available on a weekly time scale from
+the public platform CovidStat (https://covid19.infn.it/iss/).
+For the analysis, we generated daily incidence time series from cumulative data by computing
+day-to-day differences. Then, we further aggregated the daily time series of deaths and cases
+into weekly ones, to perform the transfer entropy analysis on a weekly scale.
+4.2
+Mobility derived indicators
+In our study, we computed daily and weekly movement and contact rates from data provided
+by Meta through its Data for Good program [41]. Here, we first describe the raw data sources
+provided by Meta and then the data processing we applied to compute the time series for the
+transfer entropy analysis.
+4.2.1
+Raw data sources
+We collected the following datasets that were publicly released by Meta since the beginning of
+the COVID-19 pandemic, in Austria, France, Italy, and Spain:
+• Movement range maps. It reports the number of users who moved between any two
+16-level Bing tiles, with an 8-hour frequency.
+• Users’ population. It reports the number of active users in each tile with an 8-hour
+frequency. The tile resolution is 4800 x 4800 m2.
+• Colocation maps. It estimates the probability that, given any two administrative regions,
+p1 and p2, a randomly chosen user from p1 and a randomly chosen user from p2 are
+simultaneously located in the same place during a randomly chosen minute in a given week
+[39]. The dataset also reports the number of users in p1 and p2.
+• Stay put. It reports for a given administrative region the daily percentage of users staying
+put within a single location, defined at the 16-level Bing tile.
+We formalize the description of the above datasets with the notation described in Table 4:
+16
+
+Dataset name
+Xs,t
+spatial resolution
+temporal resolution
+population users
+N (pop)
+t,h
+t: tile (4800 x 4800 m2)
+h: 8 hour
+movement between tiles
+M(t1,t2),h
+(t1,t2): tile pair (600 x 600 m2)
+h: 8 hour
+colocation probability
+Pp,w
+p: province
+w : week
+colocation users
+N (coloc)
+p,w
+p: province
+w: week
+stay put
+Sr,d
+r: region
+d: day
+Table 4:
+Summary of raw data sources as time series records Xs,t, where s denotes the spatial
+resolution and t the temporal resolution.
+original data
+spatial aggregation
+temporal aggregation
+aggregated data
+name
+N (pop)
+t,h
+�(t ∈ p)
+h interpolation and mean (h ∈ w)
+N (pop)
+p,w
+province population users
+M(t1,t2),h
+� (t1, t2) ∈ p, t1 = t2
+mean (h ∈ w)
+M (within)
+p,w
+within tile province movement
+M(t1,t2),h
+� (t1, t2) ∈ p, t1 ̸= t2
+mean (h ∈ w)
+M (between)
+p,w
+between tiles province movement
+Sr,d
+∀p ∈ r
+r = p
+mean (d ∈ w)
+Sp,w
+province stay put
+Table 5: Aggregation of data sources described in Table 4, to generate our metrics of interest.
+4.2.2
+Aggregation of raw data
+We then processed the raw data sources of Table 4 to obtain a set of time series having the
+same spatiotemporal resolution, that is weekly, at the NUTS3 scale. Results of the aggregation
+process are described in Table 5. More in detail:
+• Province users population. (1) we performed a spatial aggregation by summing the
+population of tiles belonging to province p, thus obtaining a population at a (province,
+hour) level: N (pop)
+p,h
+. (2) we performed a linear interpolation of the temporal gaps that were
+present in N (pop)
+p,h
+(3) we performed a temporal aggregation by averaging in each province,
+the 8h population records within a week.
+• Within tile province movement (1) we first performed a temporal aggregation by
+averaging M(t1,t2),h for each pair (t1, t2) over a week and obtaining M(t1,t2),w (2) we then
+performed a spatial feature joining and assigned each pair (t1, t2) to the corresponding
+provinces (p1, p2) (3) from M(t1,t2),w we obtained a within tile province movement
+M (within)
+p,w
+, that is the sum of movements which occurred in the same province p and within
+the same tile.
+• Between tiles province movement in the pipeline above, from step (3) we obtain a
+between tile province movement M (between)
+p,w
+, that is the sum of movements which
+occurred in the same province p and between two different tiles, (t1, t2). By definition, the
+sum M (between)
+p,w
++ M (within)
+p,w
+represents the total volume of movements in a province, in a
+17
+
+week.
+• Province stay put (1) we performed a temporal aggregation on a weekly scale by perform-
+ing the average and obtaining Sr,w (2) we assign to each province p the regional stay-put
+time series Sr,w such that p ∈ r.
+4.2.3
+Computation of movement and contact rate
+We finally computed our metrics of interest, movement, and contact rates, as follows.
+The
+short-range movement rate is defined as:
+M s
+p,w = M (within)
+p,w
+N (pop)
+p,w
+(1)
+that is the proportion of users who moved within the same tile in a given province, in a given
+week. The mid-range movement rate is defined as:
+Mp,w = M (between)
+p,w
+N (pop)
+p,w
+(2)
+representing the proportion of users who moved between different tiles in a given province, in a
+given week. The contact rate is defined as:
+CR(t)p,w = ˆPp,w · N (pop)
+p,w
+(3)
+where ˆP denotes the colocation probability corrected by a factor that takes into account the
+overestimation of colocation probabilities due to the heterogeneous distribution of users across
+provinces and the presence of a significant fraction of static users in some periods of mobility
+restrictions [55] (see the SI for additional details).
+4.2.4
+Province sample selection
+The population of Facebook users who contribute to the generation of the movement and colo-
+cation time series varies across countries, and it changes over time. Moreover, the metrics of
+movement (short- and mid-range) and colocation, are computed from different users’ samples of
+different sizes: N (pop)
+p,w
+and N (coloc)
+p,w
+, respectively.
+In our analysis, to limit bias that may be caused by the little representativeness of the
+underlying sample of users, we selected NUTS3 regions in the 4 countries, according to the
+following criteria.
+First, we considered only regions where the sample N (pop)
+p,w
+represented at
+least 3% of the census population to guarantee we had at least 500 users in each province.
+Furthermore, we considered only those regions where the two sample sizes N (pop)
+p,w
+and N (coloc)
+p,w
+were always positively correlated over time, during the whole study period.
+We denote the
+Pearson’s correlation of weekly values of N (pop)
+p,w
+and N (coloc)
+p,w
+as coverage consistency.
+After the selection, our analysis includes 47 provinces in Austria, 51 provinces in France, 93
+provinces in Italy, and 42 provinces in Spain, for a total of 233 spatial units.
+18
+
+Given two discrete temporal signals represented as time series X and Y the Transfer Entropy
+(TE) [38] is a measure of the amount of information delivered from X to Y , defined as:
+TEXY = H(Y |Y (l)) − H(Y |Y (l), X(l)) ,
+(4)
+where X(l), Y (l) are respectively the l-lagged time series of X and Y and TEXY is formulated
+as a difference between two conditional entropy terms, where conditional entropy is expressed as
+H(a|b) = H(a, b) − H(b), and H(·) is the Shannon Entropy. Given a discrete time series S, its
+observations can be expressed as the sample {si; i = 1, .., n}, and we obtain the discrete proba-
+bility distribution p(sj). We compute the Shannon Entropy as: H(S) = �
+j p(sj) · log2(p(sj)).
+Thus TEXY can be expressed as:
+TEXY = H(Y, Y (l)) − H(Y (l)) − H(Y, Y (l), X(l)) + H(Y (l), X(l)).
+(5)
+The time series that we consider in our experiments are continuous, therefore they need to be dis-
+cretized before computing TEXY . We employ the Kernel Density Estimation (KDE) for Transfer
+Entropy estimation. KDE method evaluates the entropy terms of Eq.5 from the discretized den-
+sity estimated from each of the four features sets: {(Y, Y (l)), Y (l), (Y, Y (l), X(l)), (Y (l), X(l))}.
+KDE employs a Gaussian kernel for density estimation. Performing tests on synthetic datasets
+of different sizes, we checked this was the method the most adapted to small samples. For the
+selection of the kernel’s bandwidth, we use the Scott method [61]. The continuous density is
+then discretized with a grid obtained by an equal-width discretization of each feature’s density
+domain. We select 20 as the number of bins for each feature’s domain discretization. The dis-
+cretized density is computed with the integral of the continuous probability density functions
+over each grid cell. Concerning the implementation, for TE estimation we use the PyCausality
+Python package (https://github.com/ZacKeskin/PyCausality).
+Effective Transfer Entropy.
+We introduce the Effective Transfer Entropy (ETE) as a cor-
+rection to TE for small sample time series, as originally proposed by [44]:
+ETEXY = TEXY − 1
+Ns
+Ns
+�
+j=1
+TEX ˆ
+Yj ,
+(6)
+where the correction term is obtained by performing Ns iterations of Y shuffling, obtaining ˆYj
+and computing the average of {TEX ˆ
+Yj; j = 1, .., Ns}. In our experiments, we performed 500
+shuffling iterations.
+Normalized Transfer Entropy.
+We would like to employ TE in order to compare a set
+of input signals {Xj; j = 1, .., N} in terms of their Transfer Entropy TEXjY towards a specific
+output Y . From equation 4 we have that TEXjY is evaluated as a difference of conditional entropy
+where the first term H(Y |Y (l)) depends only on target Y . In order to ensure comparability over
+the set {TEXjY ; j = 1, .., N}, we reformulate the difference as a relative difference dividing by
+19
+
+H(Y |Y (l)). Thus the set of inputs are compared according to {TEXjY /H(Y |Y (l)); j = 1, .., N}
+and we refer to TEXY /H(Y |Y (l)) as Normalized Transfer Entropy (NTE).
+Normalized Effective Transfer Entropy.
+By combining the ETE and the NTE we can fi-
+nally introduce the Normalized Effective Transfer Entropy (NETE), which is obtained by dividing
+the ETE by the first conditional entropy term H(Y |Y (l)) as in [62]:
+NETEXY =
+TEXY −
+1
+Ns
+�Ns
+j=1 TEX ˆ
+Yj
+H(Y |Y (l))
+(7)
+In this way, the NETE accounts both for bias in small sample time series and it ensures compa-
+rability between different input sources {Xj} in terms of information transfer to different targets.
+Besides, it enables estimating the percentage of explanation value added with respect to only
+knowing the past of the time series used as a target.
+4.3
+Classification model
+The introduction of the ETE allows associating a p-value, a metric of statistical significance, to
+each NETE value computed between any pair of time series.
+In our study, we investigated a number of explanatory features to better understand why
+in some provinces the NETE could not identify a significant transfer of information between
+mobility time series and epidemiological indicators.
+More specifically, we trained a Random
+Forest classification model to predict the significance of NX→Y at the threshold of p < 0.01, in
+each province under study. The random forest was performed with 100 decision tree classifiers
+on various sub-samples of the dataset and used averaging to improve the predictive accuracy and
+control for over-fitting. The function to measure the quality of a split was the Gini impurity.
+Before applying the random forest, the data were split between training and test sets (30%). To
+compensate for the imbalance of the datasets, we applied a Synthetic Minority Oversampling
+Technique [63] on the test set.
+As input to the classification model we used a set of features that characterize each province:
+1. population size (as reported by the latest available census);
+2. area (in km2);
+3. density of Facebook users (measured as Np,w divided by area);
+4. total cumulative number of reported COVID-19 deaths during the study period;
+5. commuting flow;
+6. coverage consistency;
+20
+
+The commuting flow is defined as the ratio between the total number of daily commuters who
+travel from or to a province and the total number of commuters who work and live in that
+province.
+Commuting data were collected from the latest available census statistics in each
+country. The coverage consistency is the correlation over time between the users’ populations
+N (pop)
+p,w
+and N (coloc)
+p,w
+.
+To quantify the importance of different features in our classification model, we used their
+SHAP (SHapley Additive exPlanations) values [49]. SHAP is a method to explain model pre-
+dictions based on Shapley Values from game theory. In particular, we use TreeSHAP [64], an
+algorithm to compute SHAP values for tree ensemble models, such as the random forest classifier
+of our study.
+5
+Data and code availability
+The data and code to reproduce our analysis are available at: https://zenodo.org/record/
+7464949#.Y6L0CfxKhNg
+6
+Funding
+F.D. gratefully acknowledges support from the CRT Lagrange Fellowships in Data Science for
+Social Impact of the ISI Foundation, where this work was conducted. M.T. and L.G. acknowledge
+the Lagrange Project of the ISI Foundation funded by CRT Foundation. The funders had no
+role in the study design, decision to publish, or preparation of the manuscript.
+7
+Acknowledgements
+We gratefully acknowledge Alex Pompe for his help to understand the details of mobility data
+from Meta.
+8
+Author contributions
+FD collected data, conducted experiments, interpreted the results, made figures, and contributed
+to the writing of the paper.
+MT and LG conceived and designed the study, conducted the
+statistical analysis, interpreted the results, made figures, and wrote the paper. All authors read
+and approved the final version of the manuscript.
+9
+Competing interests
+The authors declare no competing interests.
+1
+
+Supplementary Information
+Correction to the colocation probability
+Colocation maps provided by Meta is defined as the number of colocation events over the number
+of possible events. This, by design, includes interactions between users staying within the same
+tile but not having actual contact with other users. For this reason, we estimate the contact
+rate in each province by removing the contribution due to the users staying put. We explain our
+approach to estimating such contribution in the following. Let us start by writing the original
+colocation probability P as:
+P = E
+N 2
+(8)
+where:
+• E is the number of colocation events within the province
+• N is the number of province colocation users.
+The exact formula should be P =
+E
+N(N−1) but as N is large we approximate it to 8. Let us
+denote R(c) the number of measured colocation events that are due to users who stay put only,
+then the corrected colocation probability should be written in the following way:
+ˆPp,w = E − R(c)
+N 2
+(9)
+We estimate R(c) by using the stay-put probability S, which is the probability of a user staying
+put. Let us call the tile population ratio probability distribution {ftl; t = 1, .., Tl} where T is
+the number of tiles in a province. This gives us an estimate of the contribution of the users who
+stay put to the colocation probability, as:
+R(c) =
+T
+�
+t=1
+N 2 · f 2
+t · S2.
+(10)
+So we rewrite:
+ˆPp,w = P − S2
+Tl
+�
+t=1
+f 2
+tl
+(11)
+We do not have access to the population of the tiles used for the colocation so we make an
+approximation using the population distribution given for each tile with dimensions 4800 m
+× 4800 m. As there are by definition 64 colocation tiles within a single population tile, the
+expression Eq.11 can be formulated as:
+ˆPp,w = Pp,w − S2
+p,w ·
+T
+�
+t=1
+64 ·
+�
+f (p)
+t,w
+64
+�2
+(12)
+where:
+2
+
+M s (%)
+M (%)
+Austria
+99.6 [97.9 – 100]
+0.5 [0.0 - 2.1]
+France
+91.3 [88.2 – 93.7]
+8.8 [6.3 – 11.9]
+Italy
+89.9 [86.4 – 92.8]
+10.2 [7.2 – 13.6]
+Spain
+91.5 [86.1 – 95.1]
+8.5 [4.9 – 13.9]
+Table S6: Relative proportion of mobility components in each country. Each row dis-
+plays the proportion of movements, as a percentage of the total movements within each province,
+that are represented by the short-range mobility (M s(t)) and the mid-range mobility (M(t)).
+Each table entry reports the median value and the IQR, computed over all provinces, and all
+weeks of the study period. Short-range mobility represents the large majority of movements
+within a province, in all countries.
+coverage consistency
+commuting flow
+Austria
+0.64 [0.45–0.79]
+1.05 [0.43–1.69]
+France
+0.32 [0.23–0.43]
+0.30 [0.22–0.51]
+Italy
+0.63 [0.42–0.77]
+0.21 [0.12–0.29]
+Spain
+0.86 [0.68–0.91]
+0.08 [0.05–0.10]
+Table S7: Coverage consistency and commuting flow distributions by country. Each
+table entry reports the median value and the IQR computed over all provinces, in each country,
+considered in the study.
+• f (p)
+t,w = Nt,w
+Np,w ; t ∈ p : tile t population frequency in province p.
+• Nt,w : population at (tile,week) resolution. It is obtained through mean temporal aggre-
+gation of Nt,h over the week interval denoted by w.
+• Np,w : population at (province, week) resolution.
+It is obtained through sum spatial
+aggregation of Nt,w over the tiles belonging to province p.
+• T is the number of tiles 4800 m × 4800 m
+We can introduce the quantity Qp,w as the sum of squared frequencies of the province tile
+distribution Qp,w = �
+t∈p(f (p)
+t,w)2, so that, finally:
+ˆPp,w = Pp,w − S2
+p,w · Qp,w
+64
+(13)
+References
+[1] Ira M Longini Jr.
+A mathematical model for predicting the geographic spread of new
+infectious agents. Mathematical Biosciences, 90(1-2):367–383, 1988.
+3
+
+Figure S1:
+Comparison of NETE values computed on weekly and daily time series.
+NC→D computed between time series data collected on a weekly time scale (bottom row) and a
+daily one (top row). Daily time series were available only for Austria, France and Spain.
+[2] Aidan Findlater and Isaac I Bogoch. Human mobility and the global spread of infectious
+diseases: a focus on air travel. Trends in parasitology, 34(9):772–783, 2018.
+[3] Duygu Balcan, Bruno Gon¸calves, Hao Hu, Jos´e J Ramasco, Vittoria Colizza, and Alessandro
+Vespignani. Modeling the spatial spread of infectious diseases: The GLobal Epidemic and
+Mobility computational model. Journal of Computational Science, 1(3):132–145, 2010.
+[4] Amy Wesolowski, Caroline O Buckee, Kenth Engø-Monsen, and Charlotte Jessica Eland
+Metcalf. Connecting mobility to infectious diseases: the promise and limits of mobile phone
+data. The Journal of infectious diseases, 214(suppl 4):S414–S420, 2016.
+[5] Amy Wesolowski, Nathan Eagle, Andrew J Tatem, David L Smith, Abdisalan M Noor,
+Robert W Snow, and Caroline O Buckee. Quantifying the impact of human mobility on
+malaria. Science, 338(6104):267–270, 2012.
+[6] Lorenzo Mari, Enrico Bertuzzo, Lorenzo Righetto, Renato Casagrandi, Marino Gatto, Igna-
+cio Rodriguez-Iturbe, and Andrea Rinaldo. Modelling cholera epidemics: the role of water-
+ways, human mobility and sanitation. Journal of the Royal Society Interface, 9(67):376–388,
+2012.
+4
+
+0.40
+0.40
+0.40
+Austria
+France
+Spain
+0.35
+0.35
+0.35
+0.30
+0.30
+0.30
+0.25
+0.25
+0.25
+0.20
+0.20
+→D
+0.20
+→D
+-ON
+0.15
+0.15
+0.15
+0.10
+0.10
+0.10
+0.05
+0.05
+0.05
+0.00
+0.00
+0.00
+-0.05
+-0.05
+-0.05
+14 21  28 35 42 49 56
+14 21 28 35 42 49 56
+14 21 28 35 42 49 56
+7
+Lag (days)
+Lag (days)
+Lag (days)
+0.40
+0.40
+0.40
+France
+Austria
+Spain
+0.35
+0.35
+0.35
+0.30
+0.30
+0.30
+0.25
+0.25
+0.25
+0.20
+0.20
+0.20
+D
+D
+D
+个
+个
+个
+0.15
+0.15
+0.15
+0.10
+0.10
+0.10
+0.05
+0.05
+0.05
+0.00
+0.00
+0.00
+-0.05
+-0.05
+-0.05
+2
+2
+3
+4
+6
+4
+5
+6
+7
+8
+2
+4
+7
+8
+3
+5
+6
+8
+1
+7
+Lag (weeks)
+Lag (weeks)
+Lag (weeks)[7] Caroline O Buckee, Amy Wesolowski, Nathan N Eagle, Elsa Hansen, and Robert W Snow.
+Mobile phones and malaria: modeling human and parasite travel.
+Travel medicine and
+infectious disease, 11(1):15–22, 2013.
+[8] Vivek Charu, Scott Zeger, Julia Gog, Ottar N Bjørnstad, Stephen Kissler, Lone Simonsen,
+Bryan T Grenfell, and C´ecile Viboud.
+Human mobility and the spatial transmission of
+influenza in the United States. PLoS Computational Biology, 13(2):e1005382, 2017.
+[9] Michele Tizzoni, Paolo Bajardi, Adeline Decuyper, Guillaume Kon Kam King, Christian M
+Schneider, Vincent Blondel, Zbigniew Smoreda, Marta C Gonz´alez, and Vittoria Colizza.
+On the use of human mobility proxies for modeling epidemics. PLoS Computational Biology,
+10(7):e1003716, 2014.
+[10] Corey M Peak, Amy Wesolowski, Elisabeth zu Erbach-Schoenberg, Andrew J Tatem, Erik
+Wetter, Xin Lu, Daniel Power, Elaine Weidman-Grunewald, Sergio Ramos, Simon Moritz,
+et al. Population mobility reductions associated with travel restrictions during the Ebola
+epidemic in Sierra Leone: use of mobile phone data. International journal of epidemiology,
+47(5):1562–1570, 2018.
+[11] Mengxi Zhang, Siqin Wang, Tao Hu, Xiaokang Fu, Xiaoyue Wang, Yaxin Hu, Briana Hal-
+loran, Zhenlong Li, Yunhe Cui, Haokun Liu, et al. Human mobility and COVID-19 trans-
+mission: a systematic review and future directions. Annals of GIS, pages 1–14, 2022.
+[12] Nuria Oliver, Bruno Lepri, Harald Sterly, Renaud Lambiotte, S´ebastien Deletaille, Marco
+De Nadai, Emmanuel Letouz´e, Albert Ali Salah, Richard Benjamins, Ciro Cattuto, et al.
+Mobile phone data for informing public health actions across the COVID-19 pandemic life
+cycle. Science Advances, 6(23):eabc0764, 2020.
+[13] Caroline O Buckee, Satchit Balsari, Jennifer Chan, Merc`e Crosas, Francesca Dominici, Urs
+Gasser, Yonatan H Grad, Bryan Grenfell, M Elizabeth Halloran, Moritz UG Kraemer, et al.
+Aggregated mobility data could help fight COVID-19. Science, 368(6487):145–146, 2020.
+[14] Marino Gatto, Enrico Bertuzzo, Lorenzo Mari, Stefano Miccoli, Luca Carraro, Renato
+Casagrandi, and Andrea Rinaldo.
+Spread and dynamics of the COVID-19 epidemic in
+Italy: Effects of emergency containment measures. Proceedings of the National Academy of
+Sciences, 117(19):10484–10491, 2020.
+[15] Estee Y Cramer, Evan L Ray, Velma K Lopez, Johannes Bracher, Andrea Brennen, Alvaro J
+Castro Rivadeneira, Aaron Gerding, Tilmann Gneiting, Katie H House, Yuxin Huang, et al.
+Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the
+United States. Proceedings of the National Academy of Sciences, 119(15):e2113561119, 2022.
+[16] Serina Chang, Emma Pierson, Pang Wei Koh, Jaline Gerardin, Beth Redbird, David Grusky,
+and Jure Leskovec. Mobility network models of COVID-19 explain inequities and inform
+reopening. Nature, 589(7840):82–87, 2021.
+5
+
+[17] Lorenzo Lucchini, Simone Centellegher, Luca Pappalardo, Riccardo Gallotti, Filippo Privit-
+era, Bruno Lepri, and Marco De Nadai. Living in a pandemic: changes in mobility routines,
+social activity and adherence to COVID-19 protective measures. Scientific reports, 11(1):1–
+12, 2021.
+[18] Philippe Lemey, Andrew Rambaut, Trevor Bedford, Nuno Faria, Filip Bielejec, Guy Baele,
+Colin A Russell, Derek J Smith, Oliver G Pybus, Dirk Brockmann, et al. Unifying viral
+genetics and human transportation data to predict the global transmission dynamics of
+human influenza h3n2. PLoS pathogens, 10(2):e1003932, 2014.
+[19] Philippe Lemey, Samuel L Hong, Verity Hill, Guy Baele, Chiara Poletto, Vittoria Colizza,
+´Aine O’toole, John T McCrone, Kristian G Andersen, Michael Worobey, et al. Accom-
+modating individual travel history and unsampled diversity in bayesian phylogeographic
+inference of sars-cov-2. Nature communications, 11(1):1–14, 2020.
+[20] Moritz UG Kraemer, Verity Hill, Christopher Ruis, Simon Dellicour, Sumali Bajaj, John T
+McCrone, Guy Baele, Kris V Parag, Anya Lindstr¨om Battle, Bernardo Gutierrez, et al.
+Spatiotemporal invasion dynamics of SARS-CoV-2 lineage B.1.1.7 emergence.
+Science,
+373(6557):889–895, 2021.
+[21] Jessica T Davis, Matteo Chinazzi, Nicola Perra, Kunpeng Mu, Ana Pastore y Piontti, Marco
+Ajelli, Natalie E Dean, Corrado Gioannini, Maria Litvinova, Stefano Merler, et al. Cryptic
+transmission of SARS-CoV-2 and the first COVID-19 wave. Nature, 600(7887):127–132,
+2021.
+[22] Philippe Lemey, Nick Ruktanonchai, Samuel L Hong, Vittoria Colizza, Chiara Poletto, Fred-
+erik Van den Broeck, Mandev S Gill, Xiang Ji, Anthony Levasseur, Bas B Oude Munnink,
+et al. Untangling introductions and persistence in covid-19 resurgence in europe. Nature,
+595(7869):713–717, 2021.
+[23] Matteo Chinazzi, Jessica T Davis, Marco Ajelli, Corrado Gioannini, Maria Litvinova, Ste-
+fano Merler, Ana Pastore y Piontti, Kunpeng Mu, Luca Rossi, Kaiyuan Sun, et al. The
+effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) out-
+break. Science, 368(6489):395–400, 2020.
+[24] Pedro S Peixoto, Diego Marcondes, Cl´audia Peixoto, and S´ergio M Oliva. Modeling future
+spread of infections via mobile geolocation data and population dynamics. an application
+to covid-19 in brazil. PloS one, 15(7):e0235732, 2020.
+[25] Moritz UG Kraemer, Adam Sadilek, Qian Zhang, Nahema A Marchal, Gaurav Tuli, Emily L
+Cohn, Yulin Hswen, T Alex Perkins, David L Smith, Robert C Reiner, et al. Mapping global
+variation in human mobility. Nature Human Behaviour, 4(8):800–810, 2020.
+6
+
+[26] Jayson S Jia, Xin Lu, Yun Yuan, Ge Xu, Jianmin Jia, and Nicholas A Christakis. Population
+flow drives spatio-temporal distribution of COVID-19 in China. Nature, 582(7812):389–394,
+2020.
+[27] Joel Persson, Jurriaan F Parie, and Stefan Feuerriegel. Monitoring the COVID-19 epidemic
+with nationwide telecommunication data. Proceedings of the National Academy of Sciences,
+118(26):e2100664118, 2021.
+[28] Stefano Maria Iacus, Carlos Santamaria, Francesco Sermi, Spyros Spyratos, Dario Tarchi,
+and Michele Vespe. Human mobility and COVID-19 initial dynamics. Nonlinear Dynamics,
+101(3):1901–1919, 2020.
+[29] Nishant Kishore, Aimee R Taylor, Pierre E Jacob, Navin Vembar, Ted Cohen, Caroline O
+Buckee, and Nicolas A Menzies. Evaluating the reliability of mobility metrics from aggre-
+gated mobile phone data as proxies for sars-cov-2 transmission in the usa: a population-based
+study. The Lancet Digital Health, 2021.
+[30] Sean Jewell, Joseph Futoma, Lauren Hannah, Andrew C Miller, Nicholas J Foti, and Emily B
+Fox.
+It’s complicated: Characterizing the time-varying relationship between cell phone
+mobility and COVID-19 spread in the US. NPJ digital medicine, 4(1):1–11, 2021.
+[31] Hamada S Badr and Lauren M Gardner. Limitations of using mobile phone data to model
+COVID-19 transmission in the USA. The Lancet Infectious Diseases, 21(5):e113, 2021.
+[32] Pierre Nouvellet, Sangeeta Bhatia, Anne Cori, Kylie EC Ainslie, Marc Baguelin, Samir
+Bhatt, Adhiratha Boonyasiri, Nicholas F Brazeau, Lorenzo Cattarino, Laura V Cooper,
+et al. Reduction in mobility and covid-19 transmission. Nature communications, 12(1):1–9,
+2021.
+[33] Alberto Aleta, David Martin-Corral, Ana Pastore y Piontti, Marco Ajelli, Maria Litvinova,
+Matteo Chinazzi, Natalie E Dean, M Elizabeth Halloran, Ira M Longini Jr, Stefano Merler,
+et al. Modelling the impact of testing, contact tracing and household quarantine on second
+waves of COVID-19. Nature Human Behaviour, 4(9):964–971, 2020.
+[34] Alberto Aleta, David Mart´ın-Corral, Michiel A Bakker, Ana Pastore y Piontti, Marco Ajelli,
+Maria Litvinova, Matteo Chinazzi, Natalie E Dean, M Elizabeth Halloran, Ira M Longini Jr,
+et al. Quantifying the importance and location of SARS-CoV-2 transmission events in large
+metropolitan areas. Proceedings of the National Academy of Sciences, 119(26):e2112182119,
+2022.
+[35] Tanjona Ramiadantsoa, C Jessica E Metcalf, Antso Hasina Raherinandrasana, Santatra
+Randrianarisoa, Benjamin L Rice, Amy Wesolowski, Fidiniaina Mamy Randriatsarafara,
+and Fidisoa Rasambainarivo. Existing human mobility data sources poorly predicted the
+spatial spread of SARS-CoV-2 in Madagascar. Epidemics, 38:100534, 2022.
+7
+
+[36] Nishant Kishore. Mobility data as a proxy for epidemic measures. Nature Computational
+Science, 1(9):567–568, 2021.
+[37] Roman Levin, Dennis L Chao, Edward A Wenger, and Joshua L Proctor. Insights into
+population behavior during the COVID-19 pandemic from cell phone mobility data and
+manifold learning. Nature Computational Science, 1(9):588–597, 2021.
+[38] Thomas Schreiber. Measuring information transfer. Physical review letters, 85(2):461, 2000.
+[39] Shankar Iyer, Brian Karrer, Daniel T Citron, Farshad Kooti, Paige Maas, Zeyu Wang,
+Eugenia Giraudy, P Alex Dow, and Alex Pompe. Large-Scale Measurement of Aggregate
+Human Colocation Patterns for Epidemiological Modeling. medRxiv, 2020.
+[40] Eurostat. Eurostat. Your key to European Statistics.
+[41] Ama¸c
+Herda˘gdelen,
+Alex
+Dow,
+Bogdan
+State,
+Payman
+Mohassel,
+and
+Alex
+Pompe.
+Protecting
+privacy
+in
+Facebook
+mobility
+data
+dur-
+ing
+the
+COVID-19
+response.
+https://research.fb.com/blog/2020/06/
+protecting-privacy-in-facebook-mobility-data-during-the-covid-19-response/,
+2020. Accessed: 2021-11-06.
+[42] Facebook Data for Good. Movement range maps. https://data.humdata.org/dataset/
+movement-range-maps, 2020. Accessed: 2021-11-06.
+[43] Terry Bossomaier, Lionel Barnett, Michael Harr´e, and Joseph T Lizier. Transfer entropy.
+In An introduction to transfer entropy, pages 65–95. Springer, 2016.
+[44] Robert Marschinski and Holger Kantz. Analysing the information flow between financial
+time series. The European Physical Journal B-Condensed Matter and Complex Systems,
+30(2):275–281, 2002.
+[45] Zefan Zeng, Guang Jin, Chi Xu, Siya Chen, and Lu Zhang. Spacecraft telemetry anomaly de-
+tection based on parametric causality and double-criteria drift streaming peaks over thresh-
+old. Applied Sciences, 12(4):1803, 2022.
+[46] Nick Wilson, Amanda Kvalsvig, Lucy Telfar Barnard, and Michael G Baker. Case-fatality
+risk estimates for COVID-19 calculated by using a lag time for fatality. Emerging infectious
+diseases, 26(6):1339, 2020.
+[47] Manuela Fritz. Wave after wave: determining the temporal lag in Covid-19 infections and
+deaths using spatial panel data from Germany. Journal of Spatial Econometrics, 3(1):1–30,
+2022.
+[48] Forrest W Crawford, Sydney A Jones, Matthew Cartter, Samantha G Dean, Joshua L
+Warren, Zehang Richard Li, Jacqueline Barbieri, Jared Campbell, Patrick Kenney, Thomas
+8
+
+Valleau, et al. Impact of close interpersonal contact on covid-19 incidence: Evidence from
+1 year of mobile device data. Science Advances, 8(1):eabi5499, 2022.
+[49] Scott M Lundberg and Su-In Lee. A unified approach to interpreting model predictions.
+Advances in neural information processing systems, 30, 2017.
+[50] Andreas Koher, Frederik Jørgensen, Michael Bang Petersen, and Sune Lehmann. Moni-
+toring Public Behavior During a Pandemic Using Surveys: Proof-of-Concept Via Epidemic
+Modelling. arXiv preprint arXiv:2210.01472, 2022.
+[51] Jack Wardle, Sangeeta Bhatia, Moritz UG Kraemer, Pierre Nouvellet, and Anne Cori. Gaps
+in mobility data and implications for modelling epidemic spread: a scoping review and
+simulation study. medRxiv, 2022.
+[52] Riccardo Gallotti, Davide Maniscalco, Marc Barthelemy, and Manlio De Domenico. The
+distorting lens of human mobility data. arXiv preprint arXiv:2211.10308, 2022.
+[53] Giovanni Bonaccorsi, Francesco Pierri, Matteo Cinelli, Andrea Flori, Alessandro Galeazzi,
+Francesco Porcelli, Ana Lucia Schmidt, Carlo Michele Valensise, Antonio Scala, Walter
+Quattrociocchi, et al.
+Economic and social consequences of human mobility restrictions
+under covid-19.
+Proceedings of the National Academy of Sciences, 117(27):15530–15535,
+2020.
+[54] Alessandro Galeazzi, Matteo Cinelli, Giovanni Bonaccorsi, Francesco Pierri, Ana Lucia
+Schmidt, Antonio Scala, Fabio Pammolli, and Walter Quattrociocchi.
+Human mobility
+in response to COVID-19 in France, Italy and UK. Scientific reports, 11(1):1–10, 2021.
+[55] Mattia Mazzoli, Eugenio Valdano, and Vittoria Colizza. Projecting the COVID-19 epidemic
+risk in France for the summer 2021. Journal of travel medicine, 28(7):taab129, 2021.
+[56] Alex Smolyak, Giovanni Bonaccorsi, Andrea Flori, Fabio Pammolli, and Shlomo Havlin.
+Effects of mobility restrictions during COVID19 in Italy.
+Scientific reports, 11(1):1–15,
+2021.
+[57] Harry ER Shepherd, Florence S Atherden, Ho Man Theophilus Chan, Alexandra Loveridge,
+and Andrew J Tatem. Domestic and international mobility trends in the united kingdom
+during the covid-19 pandemic: an analysis of facebook data. International journal of health
+geographics, 20(1):1–13, 2021.
+[58] Kyra H Grantz, Hannah R Meredith, Derek AT Cummings, C Jessica E Metcalf, Bryan T
+Grenfell, John R Giles, Shruti Mehta, Sunil Solomon, Alain Labrique, Nishant Kishore,
+et al. The use of mobile phone data to inform analysis of COVID-19 pandemic epidemiology.
+Nature communications, 11(1):1–8, 2020.
+9
+
+[59] Marcello Ienca and Effy Vayena. On the responsible use of digital data to tackle the COVID-
+19 pandemic. Nature medicine, 26(4):463–464, 2020.
+[60] Emanuele Guidotti and David Ardia. COVID-19 Data Hub. Journal of Open Source Soft-
+ware, 5(51):2376, 2020.
+[61] David W Scott. Multivariate density estimation: theory, practice, and visualization. John
+Wiley & Sons, 2015.
+[62] Juan R Perilla and Thomas B Woolf. Towards the prediction of order parameters from molec-
+ular dynamics simulations in proteins. The Journal of chemical physics, 136(16):04B619,
+2012.
+[63] Nitesh V Chawla, Kevin W Bowyer, Lawrence O Hall, and W Philip Kegelmeyer. SMOTE:
+synthetic minority over-sampling technique.
+Journal of artificial intelligence research,
+16:321–357, 2002.
+[64] Scott M Lundberg, Gabriel G Erion, and Su-In Lee.
+Consistent individualized feature
+attribution for tree ensembles. arXiv preprint arXiv:1802.03888, 2018.
+10
+
+Figure S2:
+NETE values from contact rates to deaths in Austria. Only statistically
+significant values are shown (p-value< 0.01).
+11
+
+Amsteten -
+0.025748
+0.026068
+0.035190
+Brauneu ami Inn -
+0.030781
+Bregenz -
+0.032432
+0.063635
+0.079792
+0.073301
+0.051136
+Bruck-Murzzschlag -
+0.048734
+0.047809
+Dornbim -
+0.042606
+0.048633
+0.028192
+0.037263
+0.055011
+0.036085
+0.038355
+0.036506
+E998E0'0
+0.037540
+0.030327
+0.028564
+0.040716
+Grez [Stadt] -
+0.037779
+0.076651
+0.097150
+0.055744
+Grez-Urngebung -
+0.029600
+0.064492
+0.077311
+Innshruck-Land -
+0.028612
+0.045289
+0.052419
+0.039591
+0.200
+Jerner'sdorf -
+0.035306
+0.069850
+0.113048
+0.068616
+Kirchdorf an der Krem8-
+0.065064
+0.080814
+Kitzbuhel -
+0.031631
+0.068131
+0.175
+Klagerfurt am Worthersee (Sadi) 
+0.045755
+0.073913
+0.069748
+Korreuburg -
+0.048235
+0.064034
+0.067645
+0.080225
+0.071908
+0.062741
+Kufstein ,
+0.084524
+0.078949
+0.050947
+0.036189
+0.028105
+0.040762
+0.043702
+Landeck -
+0.047941
+0.106637
+0.088543
+Leibnibz -
+0.026406
+0.125
+Leoben -
+0.029500
+Province
+Liezen -
+0.033578
+DOL'O -
+0.031302
+0.030106
+0.035957
+Midling -
+0.029218
+ETEEEO'O
+0.026258
+Neunkirchen -
+0.040286
+0.075
+Reutte -
+0.045268
+0.054860
+0.112349
+Ried in Innkreis -
+0.032220
+0.041101
+0.069890
+0.060479
+0.041664
+0.024491
+0.050
+Rahrbach -
+0.041602
+Sabzburg (Stadt) -
+0.043210
+0.072274
+0.075024
+0.073098
+0.042898
+Sazburg-Umgebung -
+0.041488
+0.032673
+0.025
+Sankt jahann im Pongau -
+0.034971
+0.068717
+SchwEz -
+0.038691
+0.091690
+0.184757
+ 0.000
+Spittal an der Drau -
+0.030718
+0.035796
+0.060162
+Steyr-Land -
+0.056514
+0.062967
+0.069762
+0.067400
+0.066843
+0.064067
+0.055595
+Urfahr-Umgebung -
+0.029842
+0.033754
+0.041654
+vbitsberg -
+0.042787
+0.043992
+0.046677
+vbcklabruck -
+0.045316
+EETEEOO
+0.087363
+0.054894
+Weiz -
+0.025742
+Webs (Stadt) -
+E660E0'0
+0.025064
+Wen -
+0.032377
+0.046296
+0.042533
+0.042002
+-1
+2
+m
+4
+6
+8Figure S3:
+NETE values from contact rates to deaths in France. Only statistically
+significant values are shown (p-value¿0.01).
+12
+
+Areyron -
+0.040657
+0.047058
+0.056892
+Bas- Rhin -
+0.033482
+0.041585
+0.028520
+BDpBA(E0
+0.031260
+Carital -
+0.024933
+0.058974
+0.043374
+Charente -
+0.025404
+TZZ8E00
+0.040474
+Creue -
+0.044353
+0.066560
+0.109015
+0.097901
+0.046231
+Cite-"or -
+0.050804
+0.083634
+0.101878
+0.112566
+0.057215
+Douhs -
+0.048890
+0.081594
+0.061416
+0.043711
+0.069546
+568E00
+Gard -
+0.035540
+0.041388
+0.028707
+0.200
+Haut-Rhin -
+0.029346
+0.032140
+0.031260
+0.059106
+TZTES00
+ZLTEEO0
+Haute-Garonne -
+0.029910
+0.039255
+0.037786
+0.036558
+Haute-Loire -
+0.034223
+EOLTEO'0
+0.175
+Haute-Marne 
+0.029728
+EZ9EE00
+Haute-Sevbie 
+0.040045
+0.077211
+0.057614
+9698E00
+0.023792
+0.151
+Haute-Seonie -
+Haute-Vienre -
+0.029789
+Hautes Pyrinees -
+0.046039
+0.052797
+0.073291
+0.087177
+0.118157
+0.097759
+0.079092
+0.125
+0.024660
+0.027809
+- 22]
+0.055111
+660600
+0.116728
+0.074720
+6580E0'0
+Province
+- Eunr
+0Z60E00
+EEL6Z00
+DOL'0
+Landes -
+0.056405
+0.091173
+0.090549
+Lair-et-Cher -
+0.027844
+5E68200
+Laire -
+0.054201
+0.085214
+0.105839
+0.095344
+0.069573
+0.075
+Laire- Atlantique -
+0.029233
+0.029794
+Lairet -
+0.025703
+0.031137
+Lat-et-Garcne -
+0.062904
+0.070896
+0.043991
+0.050
+Maine-et-Loire -
+0.034822
+0.046020
+0.048480
+Marne -
+0.025154
+Mayenne -
+0666E00
+TES9E00
+- 0.025
+0.025244
+0.049144
+0.053130
+0.042279
+Moselle -
+0.026739
+0.034717
+Nievre -
+0.022348
+0.00
+Nard -
+0.036407
+0.045561
+0.040334
+0.051478
+0.077228
+0.063907
+0.059029
+TZOEO0
+Pyrenees Alantiques -
+0.062096
+0.092766
+0.145174
+0.132909
+0.102827
+0.042085
+0.059519
+0.055424
+Savaie -
+0.034982
+0.060054
+0.057195
+Saane-et-Lnire -
+0.031605
+0.065657
+0.092507
+EOLO0
+0.038865
+0.039947
+arn-et-Garanne -
+0.045909
+8066L00
+0.109730
+0.065963
+vauckuse -
+0.026052
+L9TOE00
+Wheges -
+0.027052
+0.059475
+0.073040
+bnne -
+0.028840
+i
+2
+3
+4
+-5
+6
+1
+80Figure S4: NETE values from contact rates to deaths in Italy. Only statistically signifi-
+cant values are shown (p-value< 0.01).
+13
+
+Agigento -
+9880
+Alesaandria -
+EESZO0
+0.026729
+0.036095
+EESE00
+6006200
+SSSt00
+ZE6600
+E09ZE00
+Aeti -
+9218200
+0.037452
+Beri -
+0.024441
+E6S00
+80t9200
+81E8Z00
+ 66TZE00
+SLZOEO0
+0.047656
+886TS00
+E8L00
+0.047959
+0.051687
+0.043068
+0.032656
+E0
+0.026679
+Billa -
+ESE6E00
+00
+0.058615 
+EES00
+0.049609
+Bolpgne -
+0.031410
+0.034686
+0.025180
+Brindisi 
+0.022450
+8Tt000
+2666200
+0.040166
+0.060407
+0.081030
+Caserta -
+S6E00
+SEtOSO0
+0.054700
+EOESSO0
+LLE6500
+8L85E00
+ Catenia -
+60TE00
+0.077414
+0.112635
+0.117515
+0107535
+0.089910
+0.076614
+Caterzaro -
+0.034300
+E200
+Cornn -
+8TO00
+0.047368
+0.031005
+7 0.200
+QuneD -
+0.042780
+8800
+0.057480
+0.052452
+0.043510
+Ferno -
+0.028947
+0.074648
+Femra -
+8689200
+LTS6Z00
+Firerze -
+0.041079
+509t900
+0.086577
+0.08711
+0.044845
+0.175
+Fogpia-
+0.052670
+EEt00
+0.035560
+ESS9Z00
+Genava -
+0.046436
+00
+0.033568
+E6TTE00
+026000
+SST8500
+0.053584
+9L8500
+00LES00
+1t0800
+0.037490
+L6E620~0
+0.027724
+-0.151
+Isemia -
+0.032211
+0.048660
+0.042584
+0.031698
+L'Aqula -
+ST69E00
+EZ8500
+La Spezia -
+ZtE00
+Lece -
+0.125 
+Livarnp -
+0.033466
+0.055616
+0.071218
+0.048533
+0.029651
+0.048037
+Z9E00
+0.035697
+162600
+0.046853
+zz90500
+0.050894
+0.044390
+0.041952
+ 0.100
+0.050407
+z0800
+0106961
+0.19485
+98 T600
+0.035414
+- ruapon
+2618200
+0.41629
+0.043517
+TZOt00
+EtbE00
+0.042702
+- I iden
+T9Z6E00
+0.047751
+0.048102 
+ES6SE00
+Padova -
+0.040434
+0.044515
+0.064084
+0.074209
+0.075150
+0.056965
+0.075
+ Palerma -
+0.028142
+Parma -
+0.026819
+0.025800
+0.024981
+Perugia -
+0.042104
+ESE800
+T6ESt00
+0.044093 
+LL68E00
+EZOSZO0
+Pesaro e Uraind -
+LE00
+TZ9SE0 0
+89E00
+0.029094
+6ET00
+0.050
+Farcenza -
+0.034775
+L6SS00
+0.072717
+0.080463
+0.048326
+0.040556
+ -
+LL90S00
+0.066595
+8L8200
+0.091416
+LZ96600
+82L600
+ETT6500
+ Portienane
+0.029401
+0T0850 0
+#S690 0
+0.056462
+88T8E00
+0.037469
+Paternza -
+0.038844
+- 0.025
+- snled
+OE00
+0.039405
+0.026673
+Reggio di Calabria
+0.036117
+0.047436
+ 6E00
+0589E00
+SOtTE00
+T6TZE00
+0.046939
+Regi nleia -
+E00
+0.038054 
+0.042878
+0.037887
+0.023446
+- 0.00
+- n
+E08E600
+0.102254
+0.085088
+0.047687
+Rarma -
+0.043376
+0.052379
+0.044143
+6600
+Sracun -
+0.028196
+0.041731
+LS6E00
+0.037220
+Eranto -
+0.026919
+0.028592
+990TE00
+81 6200
+Erni -
+ETts00
+0
+0.058842
+0.054448
+9T95E00
+- auyg
+86E6E00
+EZ6t00
+9STES00
+65E00
+Tapani -
+186500
+0.069576
+0103436
+0.106727
+TEZ900
+Tentb -
+Z06SZ00
+S6S9E00
+0.047467
+0.040554
+Teva -
+T969Z00
+606E00
+0.047955
+0.052642 
+90ELt00
+- Bun
+8868200
+Varese.
+0.047314
+876 800
+0.093084
+TS95600
+0.081083
+EE9EE00
+vemezi 
+0.034065
+LE00
+OOEZEOO
+SBZTEO0
+EGEb00
+056t00
+0.031813
+8060500
+LEZ600
+0.078072
+0.104887
+0.111805
+Micenzi -
+8680200
+BELZ00
+L6TEE00
+0.033232
+Miterbo -
+TS6E00
+0.072240
+50L8600
+E9ETO
+0.087438
+ES6tE00
+1
+2
+3
+4
+5
+6
+8Figure S5:
+NETE values from contact rates to deaths in Spain.
+Only statistically
+significant values are shown (p-value< 0.01).
+14
+
+Amerfa -
+0.039917
+Aturias -
+0.031993
+Bertcekang
+0.064487
+0.049886
+0.035688
+Bizkain -
+0.024587
+0.022016
+0.042866
+0.042032
+Caritabrin -
+0.046025
+0.068889
+0.068396
+0.036596
+Castellon -
+0.048737
+0.063084
+0.051995
+0.036042
+0.200
+Ciudad Real -
+0.044180
+0.054436
+0.030186
+0.175
+Cirdaba -
+0.032927
+0.038618
+0.065027
+0.036654
+0.15
+GipuzkD8 -
+0.031801
+0.053539
+0.048215
+0.026072
+0.125
+Grenada -
+0.032374
+0.081161
+0.103030
+0.079209
+0.032532
+Province
+Huelva -
+0.033040
+0.100
+Huesch -
+0.046110
+0.031084
+0.075
+La Rinja -
+0.028844
+Lerida -
+0.033187
+0.041296
+DSIO -
+Madrid 
+0.043627
+0.037621
+ 0.025
+Murcia -
+0.045269
+0.044486
+Neverre -
+0.027031
+0.033968
+0.027792
+ 0.000
+Palencia -
+0.030504
+Pontevedra -
+6008E0'0
+Sevill -
+0.037439
+0.042436
+Earrapone -
+0.045793
+0.079908
+BzaBeJZ
+0.046435
+1
+-2
+-3
+-4
+-5
+15
+ 00Figure S6:
+NETE values from movements to deaths in Austria.
+Only statistically
+significant values are shown (p-value< 0.01).
+Figure S7: NETE values from movements to deaths in France. Only statistically signif-
+icant values are shown (p-value< 0.01).
+15
+
+Bregenz -
+0.036345
+0.066033
+Dornbim -
+0.043640
+0.067243
+ Eferding -
+0.035090
+Feldkirch -
+0.037236
+ Freistadt -
+0.038373
+0.047605
+0.048796
+0.055328
+Gmunden -
+0.031248
+Gmind -
+0.023410
+0.030299
+0.027167
+0.029017
+0.200
+ Hallein -
+0.027033
+0.034264
+0.027311
+Imst -
+0.029552
+0.175
+Innsruck-Stadt -
+0.055188
+0.080702
+0.094913
+0.085118
+0.151
+Kitzbthel -
+0.042733
+0.072762
+Krema an der Dcnau (Stadty) -
+0.036128
+0.048300
+0.055608
+0.125
+Kufstein -
+0.032149
+0.043879
+Province
+Landeck -
+0.029311
+0.040050
+0.072866
+0.061492
+DOLO-
+Liezen -
+0.025763
+0.048718
+0.034108
+0.D75
+Linz-Land -
+Rahrbach -
+0.036758
+0.044387
+0.050
+Sankt Polten (Stadt) -
+0.034767
+0.041224
+0.042029
+0.043476
+0.044951
+0.038877
+Schwaz -
+0.039763
+0.054913
+0.D25
+Scharding -
+0.032939
+0.034910
+0.042464
+0.041187
+ 0.000
+Steyr (Stadt) -
+Steyr-Land -
+0.035290
+0.035265
+0.039354
+TEamaweg -
+0.060463
+Urfahr-Umgebung -
+0.041795
+0.054897
+Waidhofen an der Ybba (Stadt] -
+0.030619
+0.037978
+0.037335
+Wien -
+0.021074
+0.022951
+Zell em See -
+0.034330
+-
+2
+1
+m
+-+
+-5
+-9
+-1
+1
+-8Haute-Garonne -
+0.039198
+Herault -
+0.035912
+0.20
+Landes -
+0.024899
+0.047341
+0.15
+g Pyrenees Aantiques -
+0.040966
+0.081955
+0.10
+Pyrenees-Orienbales -
+0.039209
+0.05
+- 2S1O.PH9n
+0.027723
+ 0.D0
+var -
+0.037235
+vendee -
+0.035500
+0.035709
+2
+1
+m
+4
+5
+1
+1
+LpFigure S8: NETE values from movements to deaths in Italy. Only statistically significant
+values are shown (p-value< 0.01).
+16
+
+Agnigento -
+0.035274
+0.060209
+0.067456
+0.063766
+0.045358
+Aosta -
+0.029482
+0.042370
+0.072343
+0.082323
+BolpgnB -
+0.030139
+0.028636
+Brescin -
+0.025976
+Brindisi -
+0.026128
+Crobne -
+0.030466
+0.040989
+0.058785
+0.075694
+0.055939
+Faggia -
+0.021785
+Grsseto -
+0.022906
+0.038876
+0.038155
+0.200
+Isernia -
+0.030238
+0.032921
+L Spezia -
+0.047417
+0.103764
+0.175
+Lecce -
+0.036225
+0.036709
+0.036007
+Livane -
+0.029951
+0.029072
+0.150
+Metera -
+0.038031
+0.043266
+0.029986
+Miland -
+0.038485
+0.060374
+0.090189
+0.111951
+0.119138
+0.076202
+0.043542
+0.125
+ Napoli -
+0.032169
+0.053370
+0.077585
+0.081536
+0.069873
+Province
+Palerrma -
+0.040487
+0.055997
+0.049803
+0.034437
+0.100
+Parmia -
+0.020899
+SEEEEOO
+0.045348
+Pescara -
+0.035626
+0.053516
+0.048144
+0.075
+Fisa -
+0.036115
+0.046651
+0.048108
+0.042774
+Ravenng -
+0.032001
+0.050158
+0.054213
+0.044289
+0.023382
+ 0.050
+Reggio nel'Emilia -
+0.036432
+Salermo -
+0.027822
+0.024835
+0.026877
+- 0.025
+Saana -
+0.021183
+Sandrio -
+0.025698
+ 0.000
+Earanto -
+0.041633
+0.042189
+0.028624
+0.027444
+0.033665
+0.035389
+Tevisn -
+0.026159
+0.020877
+vercelli -
+0.035478
+Vibo Valentia -
+0.028121
+0.044249
+0.055201
+0.037209
+0.028612
+Micerzr -
+0.022276
+0.022803
+viterbo -
+0.047049
+-T
+2-
+4
+5
+-9
+-L
+LpFigure S9: NETE values from movements to deaths in Spain. Only statistically significant
+values are shown (p-value< 0.01).
+Figure S10:
+Comparison of NETE values computed on full time series and reduced
+time series. NM→C computed between time series data collected including the vaccination
+campaign (full) and not (reduced). The reduced study period ranges from September 1, 2020 to
+January 31, 2021. The full study period extends up to July 31, 2021. We consider daily time
+series only to address biases due to small samples.
+17
+
+A Coruia -
+0.035725
+0.036865
+Balearea -
+0.068768
+0.044550
+Bercekana -
+0.039459
+0.035079
+0.030976
+Bizkain -
+0.027029
+0.028069
+Burgos -
+0.029288
+0.200
+Caritabrin -
+0.033294
+0.047135
+0.056197
+0.039901
+Castell6n -
+0.037745
+0.175
+0.030562
+0.037700
+- Bauar
+0.043924
+0.076964
+0.088080
+0.037164
+0.15
+Oceres -
+0.030211
+0.125
+Province
+0.055756
+DOL'O-
+Grenada -
+0.033007
+Guadalajara -
+0.034102
+0.036284
+0.075
+Lein -
+0.037108
+0.050
+Lugo -
+0.073411
+0.049612
+0.038789
+ 0.025
+Lerida -
+0.039123
+0.056995
+0.052213
+0.041481
+0010 -
+Palencia -
+0.049664
+0.033181
+0.034299
+0.037105
+Pontevedra 
+0.052307
+0.036459
+Segpvin -
+0.033276
+0.054284
+0.059599
+0.050507
+0.035978
+ pa
+0.047631
+0.040222
+0.037340
+valencia -
+0.057275
+0.040704
+-+
+-5
+2
+-9
+-8
+1
+LBp0.10
+0.08
+NMr-→c (reduced)
+0.06
+0.04
+0.02
+Austria
+France
+0.00
+Spain
+0.00
+0.02
+0.04
+0.06
+0.08
+0.10
+NMr→c (full)Figure S11: Spatial variations of normalized effective transfer entropy. Maps of NETE
+values computed for different source time series and weekly COVID-19 deaths, in the provinces
+of Austria: (a) source is COVID-19 cases at lag l=2 weeks, (b) source is contact rate at lag l=7
+weeks, (c) source is short-range movement at lag l=7 weeks. (d) source is mid-range movement
+at lag l=7 weeks. Dark grey indicates provinces with non-significant values of NETE (p > 0.01).
+Provinces in white are excluded from our sample.
+18
+
+b
+a
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+Nc→D
+NcR→D
+C
+0.25
+0.25
+0.00
+0.05
+0.10
+0.15
+0.20
+0.30
+0.35
+0.00
+0.05
+0.10
+0.15
+0.20
+0.30
+0.35
+Nms→D
+NM→DFigure S12: Spatial variations of normalized effective transfer entropy. Maps of NETE
+values computed for different source time series and weekly COVID-19 deaths, in the provinces
+of France: (a) source is COVID-19 cases at lag l=2 weeks, (b) source is contact rate at lag l=7
+weeks, (c) source is short-range movement at lag l=7 weeks. (d) source is mid-range movement
+at lag l=7 weeks. Dark grey indicates provinces with non-significant values of NETE (p > 0.01).
+Provinces in white are excluded from our sample.
+19
+
+b
+a
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+Nc→D
+NcR→D
+d
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.00
+0.30
+0.35
+Nms-D
+NM→DFigure S13: Spatial variations of normalized effective transfer entropy. Maps of NETE
+values computed for different source time series and weekly COVID-19 deaths, in the provinces
+of Italy: (a) source is COVID-19 cases at lag l=2 weeks, (b) source is contact rate at lag l=7
+weeks, (c) source is short-range movement at lag l=7 weeks. (d) source is mid-range movement
+at lag l=7 weeks. Dark grey indicates provinces with non-significant values of NETE (p > 0.01).
+Provinces in white are excluded from our sample.
+20
+
+b
+a
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+Nc→D
+NcR→D
+d
+C
+0.05
+0.10
+0.15
+0.20
+0.25
+0.30
+0.35
+0.00
+0.05
+0.10
+0.15
+0.20
+0.25
+0.00
+0.30
+0.35
+Nms-D
+NM-DFigure S14: Percentage of statistically significant NETE values, disaggregated by
+country and by mobility metric used as source variable. Target variables are: weekly
+COVID-19 cases (panel a) and weekly COVID-19 deaths (panel b).
+21
+
+b
+a
+60
+CR
+Ms
+30
+M
+40
+20
+E 20
+NETI
+10
+0
+0
+Austria
+Italy
+Austria
+Italy
+France
+Spain
+France
+Spain

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+arXiv:2301.00272v1  [hep-ph]  31 Dec 2022
+Quark spectral functions from spectra of mesons and vice versa
+V. ˇSauli1, ∗
+1Department of Theoretical Physics, Institute of Nuclear Physics Rez near Prague, CAS, Czech Republic
+Within the QCD functional formalism, having the approximations controlled by physical masses
+and decays of pseudoscalar mesons, we extract spectral function of quarks from which the meson
+are composed. We choose the pion for the case of light quarks and ηc(N) for the extraction of
+charm quark spectral function.
+For this purpose we solved improved ladder-rainbow truncation
+of the spectral Dyson-Schwinger equations for quarks coupled to Bethe-Salpeter equation for the
+pion and the pseudoscalar charmonia. We begin with indefinite gauge fixing method for class of
+covariant linear gauges and search for its optimal value in given fixed truncation of Dyson-Schwinger
+equations. All kernels are represented self-consistently by known or extrapolated solutions known
+form lattice or QCD DSEs solutions.
+We require the formalism gives us the spectral functions
+with arbitrarily high numerical accuracy, while providing known experimental properties of mesons
+simultaneously. , we found that the ladder rainbow approximation can serve for this purpose when
+the Yennie gauge is employed. Properties of such spectral functions are shown and its connection
+with confinement is discussed.
+PACS numbers: 11.10.St, 11.15.Tk
+I.
+INTRODUCTION
+QCD is a rigid part the Standard Model already for half century and passed many nontrivial tests when compared to
+the experiment. The knowledge of correlation functions at time-like momentum region is crucial for the first principle
+determination of hadronic resonances and understanding of production of hadrons [1, 2]. Lattice theory is formulated
+in the Euclidean space where it is also solved, however the analytical continuation to the timelike Minkowski subspace
+represents is quite often an ill defined numerical problem.
+A complementary and very attractive approach is the spectral functional formalism, where the analytical contin-
+uation is performed at very beginning and the set of Dyson-Schwinger equations is solved for spectral function in
+Minkowski space. Such method is appreciated quite recently [1, 3–7] and includes the topics of spectral renormal-
+ization - primary or secondary subtractions technique performed at the timelike momentum scale. A Yang-Mills
+sector of SU(3) gauge theory was considered in [8, 9] bringing a new insights in the conventional Landau gauge. In
+order to get agreement with lattice data, the importance of transverse vertices in pure gluodynamics was shown [4].
+A meaningful comparison to recent lattice data was missing when the first spectral DSEs study [10] has appeared.
+Nowadays, the transverse QCD vertices are known to be very important in the quark as well as in the gluon sector in
+the Landau gauge and they are responsible for a large enhancement (suppression) of the propagator (proper selfener-
+gies) in infrared domain. How to incorporate transverse vertices in spectral quark sector was only suggested in [1] for
+the case of quark-photon vertex but not yet implemented in practice. The purpose of presented paper is not a jump
+to bandwagon or chasing the train of DSEs scheduled in the Euclidean space [11, 12], but to push theory of spectral
+DSEs in its own direction.
+Since the relativity is less urgent for mutual interaction of heavy quarks Q = c, b inside heavy mesons, nonrelativistic
+quantum mechanic was widely used to describe quarkonia and their transitions ( for a review see [16]) instead. History
+tell us, that in addition to perturbative Coulomb “one gluon exchange” potential, the linear rising potential have been
+proposed to explain spectra of excited quarkonia [17]. If fine tuned and ignoring quark content mixing and ignoring
+resonant character of excited states, such models reasonably describe static spectra of strangeonia [18] as well. In
+lattice QCD, a confining potential for a static quark-antiquark pair are computed with Wilson loops. This technique
+lies aside of quark-antiquark scattering kernel used in the DSE/BSEs heavy quarkonia studies [13–15]). To match
+the two different approaches -the DSEs and Wilsonian static quark potential together, is longstanding desire but
+unfinished story (for attempts see [19]).
+Actually, to the author best knowledge, there is not known truncation of DSES, which naturally offer the interaction
+kernels, which is consistent with string picture of confinement. The string-like interaction is either introduced by hand
+∗Electronic address: [email protected]
+
+2
+[14, 15] or even completely avoided by the use of auxiliary entire function [13]. In all cases, the approximations made
+turns to be odd from perspective of spectral quark functions.
+Before presenting the details of truncation, which complies with the existence of quark spectral function, let us
+mention here the so called hindered transitions , which were measured at various channels [20–22]. The large discrep-
+ancy between of measured rate with nonrelativistic theory prediction were usually attributed to missing relativistic
+corrections. To explain the quarkonia and their transitions, a very recent treatments based either on BSE/DSEs
+formalism, nonrelativistic quantum mechanic or other techniques [23–32] still represent very different approaches with
+not completely clear connection to QCD. To this point, a systematically improvable truncation of DSEs with a clear
+bridge to analytic properties of S-matrix could be a reliable candidate. Notably the formalism of spectral DSEs we
+present here, leads to the dispersion relation for hadronic form factors (including the hindered transitions as well).
+The main aims of presented work is twofold: we solve the spectral quark DSE and extract thus information on the
+quark spectral function. Simultaneously, within the obtained quark propagators we solve the BSE for mesons and
+check the solution against the experimental data. We employ the calculation scheme, which gives us solution with
+desired analytical properties for physical meson from the very beginning. We expect the ladder-rainbow approximation
+gives the first estimate of spectra for both light and heavy mesons. For this purpose we leave popular Landau gauge
+and extrapolate known spectral solution obtained recently [4] into other linear gauges. Enchantingly, it turns out the
+pion and heavy quarkonium (pseudoscalar charmonia) can be described within the same kernel. A correctly obtained
+meson properties thus control reliability of obtained quark spectral functions. An on shell peak is washout specifically
+and anomalous branch point is generated, which naturally explains a large contribution of seemingly unphysical
+gauge term in considered approximation. We discuss the limitation methods as well as we suggest future prospects
+and directions where the method can provide useful results.
+II.
+TRUNCATION OF SDES SYSTEM FOR THE PION
+For purpose of completeness we write down all necessary equations here. The appropriate quark DSE for the quark
+propagator S can be written in the following way
+S−1(q, µ) = A(µ) ̸ q − Bq(µ) − [ΣR(q) − ΣR(µ)] ,
+ΣR(q) = i4
+3
+�
+dDk
+(2π)D γµS(k)ΓνGµν(k − q) ,
+(2.1)
+where for the product of the quark-gluon vertex Γ and the gluon propagator G we take
+ΓνGµν(p) = γνN(ξ)
+�
+−gµν + pµpν
+p2
+� �
+do
+ρT (o)
+p2 − o + iǫ − ξg2
+p2
+pµpν
+p2
+,
+(2.2)
+where ρT is the gluon spectral function obtained with Landau gauge in the paper [4].
+We adopt a conventional renormalization condition and we take ℜA(µ) = 1 ℜB(µ) = 300MeV at the timelike
+subtracting point µ2 = 0.5GeV 2, noting that the imaginary parts of functions A, B, which completely characterize
+the quark propagator
+S−1(p) ≠ pA(p) − B(p)
+(2.3)
+do note take arbitrary value at the timelike renormalization point, but they are matter of numerical search. The
+letter R stands for the fact that the quark selfenergy was (or can be) regularized before the secondary subtractive
+renormalization takes its place. Proper regularization is more crucial and unavoidable step in gluon sector of DSEs
+in order to prevent violation of gauge invariance by inappropriate numeric.
+The last term in the Eq. (2.2) is aforementioned gauge term appearing in the product with the gauge coupling
+g2. The prefactor N(ξ) nonlinearly depends on the coupling as well as on the gauge parameter ξ. The lattice data
+for the gluon propagator are known only for ξ gauge parameter ξ being smaller then 0.5 [33, 34] in QCD without
+quark. Solving a Nielsen identities the solution of truncated system of Yang-Mills DSEs has been obtained in [35].
+Both studies show the gluon propagator is suppressed gradually in the infrared domain when ξ is getting larger. We
+exploit this and perform a very simple extrapolation of our DSE kernel into other gauges.
+The overall prefactor N(ξ) the Eq. (2.2) is varied and represents the only change when we extrapolate to nontrivial
+value of the gauge parameter ξ. Gauge term is not getting dressed, due to the unbroken gauge invariance in QCD and
+ξ appears linearly in our LRA employed. The extrapolation to other gauges is implicit since the ratio of the transverse
+and gauge term is adjusted by the solution of Bethe-Salpeter equation for the pion. Hence we can estimate the gauge
+only at the end of (quite nontrivial) search of solution. Nevertheless, for the first time we provide the first naive guess
+
+3
+0
+0.5
+1
+1.5
+ [GeV]
+0
+2
+4
+6
+ σ v,s   [GeV
+-2,GeV
+-1] 
+u,d - s
+u,d - v
+charm v
+charm s
+u,d
+c
+FIG. 1: Quark spectral functions, solid line stand for the functions σv, , dashed line for σs plotted against the energy . The
+left two blobs are for light quarks, the one on the right for the charm quark.
+————————————————————————————-
+ξ ≃ 3, which is based on comparison with solutions of Yang-Mills system [35] performed for various gauge parameters.
+Notably, the agreement of both solutions [1] and [35] with lattice data [36] in Landau gauge in the infrared domain
+is enough for our rough estimate of the gauge parameter. Further approximation we describe in the next text could
+not be crucial since the meson physics is not sensitive to UV tails.
+The gluonic spectral function is a continuous function starting to be nonzero at p2 = 0, showing the violation of
+passivity bellow several GeV . Here however, in order to reduce number of numerical integration in our pioneering
+study we use a simplified (UV finite) fit for the gluonic spectral function
+ρT (o) = −δ(o − m2
+g) + δ(o − Λ2)
+(2.4)
+with mg = 0.6GeV and Λ = 2GeV .
+Thus we have estimated the gauge only at the end of (quite nontrivial) search of solution for the pion BSE which
+produces the correct pion mass mπ = 140MeV . The gauge choice for which the pion properties are obtained most
+effectively corresponds numerically with the following rate
+g2ξ
+N(ξ) = 3
+(2.5)
+while for the absolute value we get 4N(ξ)
+3(4π)2 = 16
+3 , ( 4g2ξ
+3(4π)2 = 16).
+It is tentative to identify our gauge with a Yennie gauge. Our guess is certainly naive, since based on comparison
+with different truncation of DSEs for the Yang-Mills system [35] performed for various gauge parameters, including
+the Landau gauge as well.
+The agreement of both solutions [1] and [35] with lattice data [36] in Landau gauge
+in the infrared domain is only approximate, also a further approximation represented by Eq. (2.4) calls for better
+identification of the gauge parameter if needed for any future purpose. As we have checked, the realistic picture can
+be obtained for the other rates (2.5), providing the range of our estimate ξ = 3 ± 1. Let us stress for clarity that
+extreme cases like Landau gauge ξ = 0 or complete neglections of the first term N(ξ) = 0 do not lead to satisfactory
+picture at all.
+As the name indicates, the spectral DSE is nothing else but rewritten original DSE in a way that it can be solved
+for the two quark spectral functions σv(o) and σs(o) , rather then for the propagator in momentum space. The quark
+propagator then can be calculated through its spectral representation:
+S(p) =
+� ∞
+0
+do̸ pσv(o) + σs(o)
+p2 − o + iǫ
+(2.6)
+in the entire complex plane of square momentum p2 ( real value p2 > 0 correspond with Minkowski space domain in
+our metric choice).
+The solution of spectral DSE is described in details in series of papers [1, 3, 4] and the only change is improved
+numeric for purpose of presented paper. We use two Gaussian integrator, the first is adjusted to fit the dominant peak
+
+4
+0
+0.5
+1
+1.5
+2
+2.5
+o
+1/2  [GeV]
+0
+0.5
+1
+1.5
+2
+DLSF
+charm v
+charm s
+u,d -v
+u,d -s
+FIG. 2: Dimensionless quark spectral functions oσv(o) (solid line) and
+�
+(o)σs(o) (dashed line) for the light and charm quark.
+At larger (smaller) energy scale the broad peak for the charm flavor (u,d) quark spectral function develops.
+————————————————————————————-
+in the quark spectral function, the second one has been suitably mapped to the rest of infinite interval of spectral
+variable o. The deviation from assumed analyticity σ2 as established in [3, 4], it can be arbitrarily minimized when
+approaching the correct values of imaginary parts of the functions A(µ) and B(µ) at renormalized point µ. The value
+σ2 = 10−6 can be achieved easily and seems to be limited by numeric rather then systematics.
+The BSE for the pion has been solved for the dominant BS vertex component by eigenvalue method in complex
+momentum space. Such single component approximation is working well not only for the ground state [44] but with
+a slight modification for the excited states as well [15]. The BSE involves product of the scalar functions Sv(k +
+P/2)Sv(k −P/2) and Ss(k +P/2)Ss(k −P/2) evaluated at complex momenta (kE is real Euclidean momentum, while
+the total momentum PE = (im, 0) in rest of the pion), which we evaluate within the use the spectral representation
+2.6). Since the shape of spectral functions is difficult to control (at least at this stage), we do not use some numerical
+fit and implement additional integration over the spectral representation to determine products SiSi i. As usually,
+numerical codes either for BSE and DSE are available for public [37]. An alternative way to solve BSE in Minkowski
+space are known, till now used simplified systems (e.g. for constituent quark models[38–40]). The method could be
+necessary if one evaluates the resonant hadronic form factor [1], however as the BSE is converted into more dimensional
+integro-differential equations, we prefer to solve BSE defined in the complex Euclidean space for purpose of presented
+paper.
+The resulting spectral functions for the the light quarks are shown in the figure 1. We work in the izospin limit
+and ignore electromagnetic interaction, thus the spectral function for the up quark is identical to the d quark one.
+According to broad shapes of both functions σv,s, they describe confined objects- the light quark excitations. The
+quarks continuously change colors inside hadrons by exchanging of gluons, hence a width of the main peak can be
+interpreted as the inverse of mean time τu,d ≃ 0.2GeV −1, which the quark of given flavor spent with a given color.
+Similarly to quark weak decays, they do not represent observable, we avoid the name “decay width” in this context.
+Attentive reader has surely noticed that the on-shell delta functions are absent in the spectrum. Consequently the
+thresholds vanishes at evaluated form factors, which is in expected accordance with Wilsonian area law. Such behavior
+is intuitively expected, and in fact it has been mimic in [41–43] by the introduction of certain infrared cutoff in the
+Feynman(Schwinger) parameter in various evaluations of hadronic form factors.
+III.
+ηc(N) QUARKONIA
+The same QCD kernel that govern interaction between quark-antiquark in the light meson is used to calculate the
+heavy quarkonia. However as the interaction is not flavor universal- it constitute by the quark-gluon vertex as well,
+a changes, e.g. softening of the interaction is expected.
+It can be done by a change of effective mass parameters which now takes rescaled values by the factor r = 0.721,
+more precisely they take the values
+mc
+g = 0.433 GeV ; mc
+Λ = 1.442 GeV ;
+(3.1)
+while the dimensionless couplings like g; ξ do not change their values. We renormalize such that ℜAc(µ) = 1 and
+
+5
+BSE EXP.
+2980 2980
+3442 3638
+4150 3810
+4720
+–
+TABLE I: Comparison with PDG data (second column) and calculated spectrum.
+ReBc(µ) = r1.3GeV . The search gives for the the imaginary parts ℑAc(µ) = 0.113 and ℑBc(µ) = 0.106rGeV at
+renormalization point µ2 = r20.5GeV 2.
+The kernel is not further tuned however as the excited states ranges over the relatively large scale, small further
+change we need is to incorporate the total momentum into the kernel. Elsewhere more important diamond diagrams
+(the diagrams with interupted quark horizontal lines by gluon lines) should contribute to the kernel with substantially
+small effect (note M(ηc) ≃ M(J/ψ) Instead of evaluating these complicated diagrams we mimic their small effect and
+insert the following prefactor
+fη =
+1
+√
+2
+�
+1 + M(ηc(2))2
+P 2
+.
+(3.2)
+This formally leaves the BSE for ηc(2) completely identical to the pion case, while the couplings are softened by few
+percentage for higher excited states.
+Thus as expected for charmonium, the two mutually opposite poles of the kernel are getting closer, which suppress
+the metric term when comparing to the pion. Nevertheless, the entire effect on the charm quark spectral function is
+very the same as for the light quark. The resulting charm quark spectral functions are added into the fig. 1. Since
+the spectral function are dimensinfull object, we introduce the dimensionless quantity
+�
+(o)σs(o) and oσv(o) for a
+better comparison of spectral function of different flavors. These object are compared in the figure 2. The on-shell
+singularity is washout to a broad peak and heavy free quark excitation does not exists at all. A picture of confinement
+that emerge in spectral framework of DSEs is very the same for the light as well for the heavy quarks. A scalar string
+interaction governed by a linear potential is not actually needed at any quark sector.
+The spectra of bottomonia can be obtained by a similar fashion, however our two mutually beating poles turns
+to be cruel approximation at bottomonium scale and slightly more honest approximation is required. We plan to
+perform more comprehensive study of BB system in the future.
+The obtained masses are tabled in the Tab I further predicted and not yet observed states we only list here:
+5436,6186,7030MeV,... Recal, those above the first excitation all they lie above open charm threshold and they
+become broad resonance and our predicted values ignores coupling to D mesons completely. Interestingly, not the
+sure of mass but the mass itself is linear in principal value N , not supporting the string/Regge trajectory at all.
+Furthermore, the vertex functions are not orthogonal in sense two states with different N can be produced in single
+photon annihilation of e+e− (this is a bit free extension of quantum mechanical orthogonality, it obviously relies on
+the formula for normalization of BSE). We also show our ultimate numerical search for eigenvalue λ and the deviation
+σ2 in the figure 3. A single point shown in this figure costed one day of work of recent single processor. Even working
+with multiprocessor machines the reader can imagine the time consumed before the truncation of DSE/BSE has been
+established.
+IV.
+CONCLUSION
+Using indefinite gauge fixing we have solved coupled set of spectral quark Dyson-Schwinger equations and Bethe-
+Salpeter equation for the pion and we have extended the method to the heavy quarks sector represented by pseudoscalar
+charmonia.
+Facing the resulting spectral functions we get simple picture of confinement of the light as well as the heavy quarks:
+quarks are never on-shell inside the hadrons, the inverse of quark propagator never gets zero for a real momenta. The
+sharp singularity is completely wash out due to the imaginary part which is gradually growing from the anomalous
+thresholds- the zero momenta.
+Notably, the interaction of heavy quarks in quarkonium is far from conventional
+historical wisdom: it does not lead color coulomb plus linear potential in the nonrelativistic limit.
+For the pion case the solution presented here has been already obtained for kindred model, albeit the renormalization
+and the kernels slightly differ numerically. That description of both - the light and heavy meson systems is possible
+
+6
+3000
+3500
+4000
+4500
+5000
+M [MeV]
+1e-06
+0.0001
+0.01
+1
+ σ
+2 :
+ λ :
+ η c (3)
+ η c (2)
+ η c (4)
+ η c (1)
+FIG. 3: The eigenvalue λ and the numerical error σ from the solution of BSE the solution for the ground state and the the
+first three excited state of pseudoscalar charmonium. The definitions can be find in [15], the bound states are for λ → 1 σ → 0
+when satisfied simultaneously for the meson mass M.
+————————————————————————————-
+within DSEs/BSEs formalism is not surprising fact [13]. However the use of almost identical kernel used for the
+charmonium and for the pion case is astonishing. Notably, the interaction of heavy quarks in quarkonium is far from
+conventional historical wisdom: it does not lead to static color coulomb plus linear potential in the nonrelativistic
+limit. The gauge term, which is not contribution for on-shell scattering fermions at all, turns to be important part.The
+form of kernels suggest that our gauge choice is very close to the Yennie gauge ξ = 3, known because of cancellation of
+infrared infinities in perturbation theory in this gauge. However here it comes out due to its perspective in truncation
+convergence of QCD gap equations.
+Obviously, using of spectral representation can be seen as heavy hammer tool for calculation of form factor for
+spacelike argument. There, the convenient calculation within the use of Euclidean metric works sufficiently irrespective
+of analytical property of the kernels. We also expect no big improvements when Isgur-Wise functions [45, 46] are
+calculated within the use of presented formalism as well. There are likely other quantities insensitive to the issue of
+confinement especially if vertices and quarks lines lie outside the timelike domain of momenta. On the other side, the
+methodology of calculation of form factor at resonant region is a challenge where spectral DSEs will take their correct
+place. Within the truncation presented here one can get the celebrated dispersion relation form [48] for Vacuum
+Hadron Polarization as well as one can enjoy the resulting dispersion relation for the electromagnetic meson form
+factor [1].
+At last but at not least we could stress again the reasoning and strategy of our indefinite gauge method. Obviously,
+If the quark SR exist in a given gauge, it is natural to expect that it exists in some other gauges as well. However to
+reach the resulting SR with the simultaneous reliable solution for meson spectra requires very different effort when
+one goes from one gauge choice to another one (here we the kernels are QCD vertices itself and they are not crippled
+presence by ad hoc auxiliar functions ). It is well known that LRA -Γµ = gT γµ- with the lattice gluon propagator
+obtained in Landau gauge, does not provide a good starting point for the calculation of mesons.
+That such LRA does not receive a proper strength one can see also from DSE solution alone. It has been checked
+that decreasing the fixing parameters, one gradually observe the growth of the peak in the quark spectral function
+and the dirac delta function is formed after passing through the critical coupling ξg2 with a lattice gluon propagator
+matched to the transverse (or metric tensor) part of interaction. At this critical point one gets non-confining (NC)
+propagator solution of familiar form
+SNC(p) =
+R
+̸ p − mp
++
+� ∞
+th
+doσv(o) ̸ p + σs(o)
+(p2 − o + iǫ)
+(4.1)
+with two continuous spectral functions σv,s being nonzero only from the threshold (being identical to the fermion pole
+mass mp, if one allows nontrivial gluon spectral function). Such solution typically arise at non-confining theory like
+QED, being preserved for not large coupling in toy quantum field models [47]. With the value R ≃ 0.75 the authors
+
+7
+of [6] obtained such solution for fermion propagator within LRA and lattice Landau gauge gluon data.
+[1] V. Sauli, Phys. Rev. D 106, 3, 034030 (2022).
+[2] V. Sauli, Phys. Rev. D 1021, 014049 (2020).
+[3] V. Sauli, Few Body Syst. 61 (2020).
+[4] V. Sauli, Phys. Rev.D 106, 9, 094022 (2022).
+[5] E.L. Solis, C.S.R. Costa, V.V. Luiz, G. Krein, Few Body Syst. 60 3, 49 (2019).
+[6] J. Horak, J. M. Pawlowski, N. Wink, arXiv:2210.07597.
+[7] C. Mezrag, G. Salm`e, Eur. Phys. J. C 81 1, 34 (2021).
+[8] J. Horak, J. M. Pawlowski, N. Wink, arXiv:2202.09333
+[9] J. Horak, J. Papavassiliou , J. M. Pawlowski, N. Wink, Phys. Rev. D 104,074017 (2021).
+[10] J.M. Cornwall, Phys. Rev. D 26,1453 (1982).
+[11] C. D. Roberts and A. G. Williams C. Roberts and A.G. Williams, Prog. Part. Nucl. Phys. 33, 477 (1994).
+[12] R. Alkofer, L. von Smekal, Phys. Rept. 353 281 (2001).
+[13] T. Hilger, C. Popovici, M. Gomez-Rocha, A. Krassnigg, Phys. Rev. D 91 3,034013 (2015).
+[14] V. Sauli, Phys. Rev. D 90, 016005 (2014).
+[15] V.Sauli,Phys. Rev. D 86, 096004 (2012).
+[16] E. Eichten, S. Godfrey, H. Mahlke, J. L. Rosner, Rev. Mod. Phys. 80 1161, (2008).
+[17] J. Kogut and L. Susskind, Phys. Rev. D10 3468 (1974).
+[18] Qi Li, Long-Cheng Gui, Ming-Sheng Liu, Qi-Fang L¨u, Xian-Hui Zhong, Chin. Phys. C 45 2, 023116 (2021).
+[19] P.Bicudo, G. Marques, M. Cardoso, N. Cardoso, O. Oliveira, PoS QCD-TNT09 003 (2009); ArXive: 0912.1274.
+[20] R. E. Mitchell et al. [CLEO Collaboration], Phys. Rev. Lett. 102, 011801 (2009).
+[21] M. Ablikim et al. BESIII Collaboration, Phys. Rev. D 106, 112002 (2022).
+[22] BESIII collaboration: M. AblikimBESIII Collaboration et al., Phys. Rev. D 96, 3, 032001 (2017).
+[23] V. Guleria, E. Gebrehana, S. Bhatnagar, Phys. Rev. D 104, 9, 094045 (2021).
+[24] Jun-Kang He, Hua-Zhong, Chao-Jie Fan, Phys. Rev. D 103, 11, 114006 (2021).
+[25] R. Bruschini, P. Gonz´alez, Phys. Rev. D 101,1 014027 (2020).
+[26] S. Bhatnagar, E. Gebrehana, Phys. Rev. D 102, 9, 094024 (2020).
+[27] I. Babiarz, V. P. Goncalves, R. Pasechnik, W. Sch¨afer, A. Szczurek, Phys. Rev. D 100 5, 054018 (2019).
+[28] N.R. Soni, B.R. Joshi, R.P. Shah, H.R. Chauhan, J.N. Pandya, Eur.Phys.J. C 78, 7, 592 (2018).
+[29] Meijian Li, Yang Li, P. Maris, J. P. Vary, Phys. Rev. D 98 3, 034024 (2018).
+[30] Wei-Jun Deng, Hui Liu, Long-Cheng Gui, Xian-Hui Zhong, Phys. Rev. D 95 3, 034026 (2017).
+[31] D. Becirevic, F. Sanfilippo, JHEP 01, 028 (2013).
+[32] Gang Li, Qiang Zhao, Phys. Rev. D 84 074005 (2011).
+[33] P. Bicudo, D. Binosi, N. Cardoso, O. Oliveira, P. J. Silva, Phys. Rev. D 92 11, 114514 (2015).
+[34] P. Bicudo, D. Binosi, N. Cardoso, O. Oliveira, P. J. Silva, talk at Lattice 2015, PoS LATTICE2015 (2016) 317; e-Print:
+1509.06737.
+[35] M Napetschnig, R. Alkofer, M. Q. Huber, J. M. Pawlowski Phys. Rev. D 104, 054003 (2021).
+[36] A. F. Falc˜ao, O. Oliveira, P. J. Silva, Phys. Rev. D 102, 114518 (2020).
+[37] author web pages at: gemma.ujf.cas.cz
+[38] V. Sauli, J. Phys. G 35, 035005 (2008).
+[39] T. Frederico, G. Salme, M. Viviani, Phys. Rev. D 89, 016010 (2014).
+[40] J. Carbonell, V. A. Karmanov, Eur. Phys. J. A 46,387 (2010).
+[41] T. Branz, A. Faessler, T. Gutsche, M. A. Ivanov, J. G. K¨orner, and V. E. Lyubovitskij, Phys. Rev. D 81, 034010 (2010).
+[42] G. Ganbold, T. Gutsche, M. A. Ivanov, and V. E. Lyubovitskij, Phys. Rev. D 104, 094048 (2021).
+[43] S. Dubnicka, A. Z. Dubnickova, M.A Ivanov , A. Liptaj, Phys. Rev. D 106 033006 (2022).
+[44] C.S. Fischer, D. Nickel, R. Williams, Eur. Phys. J. C60, 49 (2009).
+[45] N. Isgur and M. Wise , Phys. Lett. B232 (1989).
+[46] N. Isgur and M. Wise, Phys. Lett. B237, 527 (1990).
+[47] V. Sauli, JHEP 02,001 (2003).
+[48] N. Cabibbo and R. Gatto, Phys. Rev. 224 , 1577 (1961).
+

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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf,len=505
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='00272v1  [hep-ph]  31 Dec 2022  Quark spectral functions from spectra of mesons and vice versa  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' ˇSauli1, ∗  1Department of Theoretical Physics, Institute of Nuclear Physics Rez near Prague, CAS, Czech Republic  Within the QCD functional formalism, having the approximations controlled by physical masses  and decays of pseudoscalar mesons, we extract spectral function of quarks from which the meson  are composed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We choose the pion for the case of light quarks and ηc(N) for the extraction of  charm quark spectral function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  For this purpose we solved improved ladder-rainbow truncation  of the spectral Dyson-Schwinger equations for quarks coupled to Bethe-Salpeter equation for the  pion and the pseudoscalar charmonia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We begin with indefinite gauge fixing method for class of  covariant linear gauges and search for its optimal value in given fixed truncation of Dyson-Schwinger  equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' All kernels are represented self-consistently by known or extrapolated solutions known  form lattice or QCD DSEs solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  We require the formalism gives us the spectral functions  with arbitrarily high numerical accuracy, while providing known experimental properties of mesons  simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' , we found that the ladder rainbow approximation can serve for this purpose when  the Yennie gauge is employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Properties of such spectral functions are shown and its connection  with confinement is discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  PACS numbers: 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='St, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='Tk  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  INTRODUCTION  QCD is a rigid part the Standard Model already for half century and passed many nontrivial tests when compared to  the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The knowledge of correlation functions at time-like momentum region is crucial for the first principle  determination of hadronic resonances and understanding of production of hadrons [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Lattice theory is formulated  in the Euclidean space where it is also solved, however the analytical continuation to the timelike Minkowski subspace  represents is quite often an ill defined numerical problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  A complementary and very attractive approach is the spectral functional formalism, where the analytical contin-  uation is performed at very beginning and the set of Dyson-Schwinger equations is solved for spectral function in  Minkowski space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Such method is appreciated quite recently [1, 3–7] and includes the topics of spectral renormal-  ization - primary or secondary subtractions technique performed at the timelike momentum scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' A Yang-Mills  sector of SU(3) gauge theory was considered in [8, 9] bringing a new insights in the conventional Landau gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' In  order to get agreement with lattice data, the importance of transverse vertices in pure gluodynamics was shown [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  A meaningful comparison to recent lattice data was missing when the first spectral DSEs study [10] has appeared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Nowadays, the transverse QCD vertices are known to be very important in the quark as well as in the gluon sector in  the Landau gauge and they are responsible for a large enhancement (suppression) of the propagator (proper selfener-  gies) in infrared domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' How to incorporate transverse vertices in spectral quark sector was only suggested in [1] for  the case of quark-photon vertex but not yet implemented in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The purpose of presented paper is not a jump  to bandwagon or chasing the train of DSEs scheduled in the Euclidean space [11, 12], but to push theory of spectral  DSEs in its own direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Since the relativity is less urgent for mutual interaction of heavy quarks Q = c, b inside heavy mesons, nonrelativistic  quantum mechanic was widely used to describe quarkonia and their transitions ( for a review see [16]) instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' History  tell us, that in addition to perturbative Coulomb “one gluon exchange” potential, the linear rising potential have been  proposed to explain spectra of excited quarkonia [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' If fine tuned and ignoring quark content mixing and ignoring  resonant character of excited states, such models reasonably describe static spectra of strangeonia [18] as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' In  lattice QCD, a confining potential for a static quark-antiquark pair are computed with Wilson loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' This technique  lies aside of quark-antiquark scattering kernel used in the DSE/BSEs heavy quarkonia studies [13–15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' To match  the two different approaches -the DSEs and Wilsonian static quark potential together, is longstanding desire but  unfinished story (for attempts see [19]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Actually, to the author best knowledge, there is not known truncation of DSES, which naturally offer the interaction  kernels, which is consistent with string picture of confinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The string-like interaction is either introduced by hand  ∗Electronic address: sauli@ujf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='cas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='cz  2  [14, 15] or even completely avoided by the use of auxiliary entire function [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' In all cases, the approximations made  turns to be odd from perspective of spectral quark functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Before presenting the details of truncation, which complies with the existence of quark spectral function, let us  mention here the so called hindered transitions , which were measured at various channels [20–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The large discrep-  ancy between of measured rate with nonrelativistic theory prediction were usually attributed to missing relativistic  corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' To explain the quarkonia and their transitions, a very recent treatments based either on BSE/DSEs  formalism, nonrelativistic quantum mechanic or other techniques [23–32] still represent very different approaches with  not completely clear connection to QCD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' To this point, a systematically improvable truncation of DSEs with a clear  bridge to analytic properties of S-matrix could be a reliable candidate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Notably the formalism of spectral DSEs we  present here, leads to the dispersion relation for hadronic form factors (including the hindered transitions as well).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The main aims of presented work is twofold: we solve the spectral quark DSE and extract thus information on the  quark spectral function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Simultaneously, within the obtained quark propagators we solve the BSE for mesons and  check the solution against the experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We employ the calculation scheme, which gives us solution with  desired analytical properties for physical meson from the very beginning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We expect the ladder-rainbow approximation  gives the first estimate of spectra for both light and heavy mesons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' For this purpose we leave popular Landau gauge  and extrapolate known spectral solution obtained recently [4] into other linear gauges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Enchantingly, it turns out the  pion and heavy quarkonium (pseudoscalar charmonia) can be described within the same kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' A correctly obtained  meson properties thus control reliability of obtained quark spectral functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' An on shell peak is washout specifically  and anomalous branch point is generated, which naturally explains a large contribution of seemingly unphysical  gauge term in considered approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We discuss the limitation methods as well as we suggest future prospects  and directions where the method can provide useful results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  TRUNCATION OF SDES SYSTEM FOR THE PION  For purpose of completeness we write down all necessary equations here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The appropriate quark DSE for the quark  propagator S can be written in the following way  S−1(q, µ) = A(µ) ̸ q − Bq(µ) − [ΣR(q) − ΣR(µ)] ,  ΣR(q) = i4  3  �  dDk  (2π)D γµS(k)ΓνGµν(k − q) ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='1)  where for the product of the quark-gluon vertex Γ and the gluon propagator G we take  ΓνGµν(p) = γνN(ξ)  �  −gµν + pµpν  p2  � �  do  ρT (o)  p2 − o + iǫ − ξg2  p2  pµpν  p2  ,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='2)  where ρT is the gluon spectral function obtained with Landau gauge in the paper [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  We adopt a conventional renormalization condition and we take ℜA(µ) = 1 ℜB(µ) = 300MeV at the timelike  subtracting point µ2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5GeV 2, noting that the imaginary parts of functions A, B, which completely characterize  the quark propagator  S−1(p) ≠ pA(p) − B(p)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='3)  do note take arbitrary value at the timelike renormalization point, but they are matter of numerical search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The  letter R stands for the fact that the quark selfenergy was (or can be) regularized before the secondary subtractive  renormalization takes its place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Proper regularization is more crucial and unavoidable step in gluon sector of DSEs  in order to prevent violation of gauge invariance by inappropriate numeric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The last term in the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='2) is aforementioned gauge term appearing in the product with the gauge coupling  g2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The prefactor N(ξ) nonlinearly depends on the coupling as well as on the gauge parameter ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The lattice data  for the gluon propagator are known only for ξ gauge parameter ξ being smaller then 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5 [33, 34] in QCD without  quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Solving a Nielsen identities the solution of truncated system of Yang-Mills DSEs has been obtained in [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Both studies show the gluon propagator is suppressed gradually in the infrared domain when ξ is getting larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We  exploit this and perform a very simple extrapolation of our DSE kernel into other gauges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The overall prefactor N(ξ) the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='2) is varied and represents the only change when we extrapolate to nontrivial  value of the gauge parameter ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Gauge term is not getting dressed, due to the unbroken gauge invariance in QCD and  ξ appears linearly in our LRA employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The extrapolation to other gauges is implicit since the ratio of the transverse  and gauge term is adjusted by the solution of Bethe-Salpeter equation for the pion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Hence we can estimate the gauge  only at the end of (quite nontrivial) search of solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Nevertheless, for the first time we provide the first naive guess  3  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5  [GeV]  0  2  4  6  σ v,s   [GeV  2,GeV  1]  u,d - s  u,d - v  charm v  charm s  u,d  c  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 1: Quark spectral functions, solid line stand for the functions σv, , dashed line for σs plotted against the energy .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The  left two blobs are for light quarks, the one on the right for the charm quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  ————————————————————————————-  ξ ≃ 3, which is based on comparison with solutions of Yang-Mills system [35] performed for various gauge parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Notably, the agreement of both solutions [1] and [35] with lattice data [36] in Landau gauge in the infrared domain  is enough for our rough estimate of the gauge parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Further approximation we describe in the next text could  not be crucial since the meson physics is not sensitive to UV tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The gluonic spectral function is a continuous function starting to be nonzero at p2 = 0, showing the violation of  passivity bellow several GeV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Here however, in order to reduce number of numerical integration in our pioneering  study we use a simplified (UV finite) fit for the gluonic spectral function  ρT (o) = −δ(o − m2  g) + δ(o − Λ2)  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='4)  with mg = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='6GeV and Λ = 2GeV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Thus we have estimated the gauge only at the end of (quite nontrivial) search of solution for the pion BSE which  produces the correct pion mass mπ = 140MeV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The gauge choice for which the pion properties are obtained most  effectively corresponds numerically with the following rate  g2ξ  N(ξ) = 3  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5)  while for the absolute value we get 4N(ξ)  3(4π)2 = 16  3 , ( 4g2ξ  3(4π)2 = 16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  It is tentative to identify our gauge with a Yennie gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Our guess is certainly naive, since based on comparison  with different truncation of DSEs for the Yang-Mills system [35] performed for various gauge parameters, including  the Landau gauge as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The agreement of both solutions [1] and [35] with lattice data [36] in Landau gauge  in the infrared domain is only approximate, also a further approximation represented by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='4) calls for better  identification of the gauge parameter if needed for any future purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' As we have checked, the realistic picture can  be obtained for the other rates (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5), providing the range of our estimate ξ = 3 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Let us stress for clarity that  extreme cases like Landau gauge ξ = 0 or complete neglections of the first term N(ξ) = 0 do not lead to satisfactory  picture at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  As the name indicates, the spectral DSE is nothing else but rewritten original DSE in a way that it can be solved  for the two quark spectral functions σv(o) and σs(o) , rather then for the propagator in momentum space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The quark  propagator then can be calculated through its spectral representation:  S(p) =  � ∞  0  do̸ pσv(o) + σs(o)  p2 − o + iǫ  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='6)  in the entire complex plane of square momentum p2 ( real value p2 > 0 correspond with Minkowski space domain in  our metric choice).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The solution of spectral DSE is described in details in series of papers [1, 3, 4] and the only change is improved  numeric for purpose of presented paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We use two Gaussian integrator, the first is adjusted to fit the dominant peak  4  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5  o  1/2  [GeV]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5  2  DLSF  charm v  charm s  u,d -v  u,d -s  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 2: Dimensionless quark spectral functions oσv(o) (solid line) and  �  (o)σs(o) (dashed line) for the light and charm quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  At larger (smaller) energy scale the broad peak for the charm flavor (u,d) quark spectral function develops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  ————————————————————————————-  in the quark spectral function, the second one has been suitably mapped to the rest of infinite interval of spectral  variable o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The deviation from assumed analyticity σ2 as established in [3, 4], it can be arbitrarily minimized when  approaching the correct values of imaginary parts of the functions A(µ) and B(µ) at renormalized point µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The value  σ2 = 10−6 can be achieved easily and seems to be limited by numeric rather then systematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The BSE for the pion has been solved for the dominant BS vertex component by eigenvalue method in complex  momentum space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Such single component approximation is working well not only for the ground state [44] but with  a slight modification for the excited states as well [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The BSE involves product of the scalar functions Sv(k +  P/2)Sv(k −P/2) and Ss(k +P/2)Ss(k −P/2) evaluated at complex momenta (kE is real Euclidean momentum, while  the total momentum PE = (im, 0) in rest of the pion), which we evaluate within the use the spectral representation  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Since the shape of spectral functions is difficult to control (at least at this stage), we do not use some numerical  fit and implement additional integration over the spectral representation to determine products SiSi i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' As usually,  numerical codes either for BSE and DSE are available for public [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' An alternative way to solve BSE in Minkowski  space are known, till now used simplified systems (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' for constituent quark models[38–40]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The method could be  necessary if one evaluates the resonant hadronic form factor [1], however as the BSE is converted into more dimensional  integro-differential equations, we prefer to solve BSE defined in the complex Euclidean space for purpose of presented  paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The resulting spectral functions for the the light quarks are shown in the figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We work in the izospin limit  and ignore electromagnetic interaction, thus the spectral function for the up quark is identical to the d quark one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  According to broad shapes of both functions σv,s, they describe confined objects- the light quark excitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The  quarks continuously change colors inside hadrons by exchanging of gluons, hence a width of the main peak can be  interpreted as the inverse of mean time τu,d ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='2GeV −1, which the quark of given flavor spent with a given color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Similarly to quark weak decays, they do not represent observable, we avoid the name “decay width” in this context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Attentive reader has surely noticed that the on-shell delta functions are absent in the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Consequently the  thresholds vanishes at evaluated form factors, which is in expected accordance with Wilsonian area law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Such behavior  is intuitively expected, and in fact it has been mimic in [41–43] by the introduction of certain infrared cutoff in the  Feynman(Schwinger) parameter in various evaluations of hadronic form factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  ηc(N) QUARKONIA  The same QCD kernel that govern interaction between quark-antiquark in the light meson is used to calculate the  heavy quarkonia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' However as the interaction is not flavor universal- it constitute by the quark-gluon vertex as well,  a changes, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' softening of the interaction is expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  It can be done by a change of effective mass parameters which now takes rescaled values by the factor r = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='721,  more precisely they take the values  mc  g = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='433 GeV ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' mc  Λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='442 GeV ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='1)  while the dimensionless couplings like g;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' ξ do not change their values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We renormalize such that ℜAc(µ) = 1 and  5  BSE EXP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  2980 2980  3442 3638  4150 3810  4720  –  TABLE I: Comparison with PDG data (second column) and calculated spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  ReBc(µ) = r1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='3GeV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The search gives for the the imaginary parts ℑAc(µ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='113 and ℑBc(µ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='106rGeV at  renormalization point µ2 = r20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='5GeV 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The kernel is not further tuned however as the excited states ranges over the relatively large scale, small further  change we need is to incorporate the total momentum into the kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Elsewhere more important diamond diagrams  (the diagrams with interupted quark horizontal lines by gluon lines) should contribute to the kernel with substantially  small effect (note M(ηc) ≃ M(J/ψ) Instead of evaluating these complicated diagrams we mimic their small effect and  insert the following prefactor  fη =  1  √  2  �  1 + M(ηc(2))2  P 2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='2)  This formally leaves the BSE for ηc(2) completely identical to the pion case, while the couplings are softened by few  percentage for higher excited states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Thus as expected for charmonium, the two mutually opposite poles of the kernel are getting closer, which suppress  the metric term when comparing to the pion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Nevertheless, the entire effect on the charm quark spectral function is  very the same as for the light quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The resulting charm quark spectral functions are added into the fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Since  the spectral function are dimensinfull object, we introduce the dimensionless quantity  �  (o)σs(o) and oσv(o) for a  better comparison of spectral function of different flavors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' These object are compared in the figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The on-shell  singularity is washout to a broad peak and heavy free quark excitation does not exists at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' A picture of confinement  that emerge in spectral framework of DSEs is very the same for the light as well for the heavy quarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' A scalar string  interaction governed by a linear potential is not actually needed at any quark sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The spectra of bottomonia can be obtained by a similar fashion, however our two mutually beating poles turns  to be cruel approximation at bottomonium scale and slightly more honest approximation is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We plan to  perform more comprehensive study of BB system in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  The obtained masses are tabled in the Tab I further predicted and not yet observed states we only list here:  5436,6186,7030MeV,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Recal, those above the first excitation all they lie above open charm threshold and they  become broad resonance and our predicted values ignores coupling to D mesons completely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Interestingly, not the  sure of mass but the mass itself is linear in principal value N , not supporting the string/Regge trajectory at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Furthermore, the vertex functions are not orthogonal in sense two states with different N can be produced in single  photon annihilation of e+e− (this is a bit free extension of quantum mechanical orthogonality, it obviously relies on  the formula for normalization of BSE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We also show our ultimate numerical search for eigenvalue λ and the deviation  σ2 in the figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' A single point shown in this figure costed one day of work of recent single processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Even working  with multiprocessor machines the reader can imagine the time consumed before the truncation of DSE/BSE has been  established.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  CONCLUSION  Using indefinite gauge fixing we have solved coupled set of spectral quark Dyson-Schwinger equations and Bethe-  Salpeter equation for the pion and we have extended the method to the heavy quarks sector represented by pseudoscalar  charmonia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Facing the resulting spectral functions we get simple picture of confinement of the light as well as the heavy quarks:  quarks are never on-shell inside the hadrons, the inverse of quark propagator never gets zero for a real momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The  sharp singularity is completely wash out due to the imaginary part which is gradually growing from the anomalous  thresholds- the zero momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Notably, the interaction of heavy quarks in quarkonium is far from conventional  historical wisdom: it does not lead color coulomb plus linear potential in the nonrelativistic limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  For the pion case the solution presented here has been already obtained for kindred model, albeit the renormalization  and the kernels slightly differ numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' That description of both - the light and heavy meson systems is possible  6  3000  3500  4000  4500  5000  M [MeV]  1e-06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='0001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='01  1  σ  2 :  λ :  η c (3)  η c (2)  η c (4)  η c (1)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 3: The eigenvalue λ and the numerical error σ from the solution of BSE the solution for the ground state and the the  first three excited state of pseudoscalar charmonium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The definitions can be find in [15], the bound states are for λ → 1 σ → 0  when satisfied simultaneously for the meson mass M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  ————————————————————————————-  within DSEs/BSEs formalism is not surprising fact [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' However the use of almost identical kernel used for the  charmonium and for the pion case is astonishing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Notably, the interaction of heavy quarks in quarkonium is far from  conventional historical wisdom: it does not lead to static color coulomb plus linear potential in the nonrelativistic  limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' The gauge term, which is not contribution for on-shell scattering fermions at all, turns to be important part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='The  form of kernels suggest that our gauge choice is very close to the Yennie gauge ξ = 3, known because of cancellation of  infrared infinities in perturbation theory in this gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' However here it comes out due to its perspective in truncation  convergence of QCD gap equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  Obviously, using of spectral representation can be seen as heavy hammer tool for calculation of form factor for  spacelike argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' There, the convenient calculation within the use of Euclidean metric works sufficiently irrespective  of analytical property of the kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' We also expect no big improvements when Isgur-Wise functions [45, 46] are  calculated within the use of presented formalism as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' There are likely other quantities insensitive to the issue of  confinement especially if vertices and quarks lines lie outside the timelike domain of momenta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' On the other side, the  methodology of calculation of form factor at resonant region is a challenge where spectral DSEs will take their correct  place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Within the truncation presented here one can get the celebrated dispersion relation form [48] for Vacuum  Hadron Polarization as well as one can enjoy the resulting dispersion relation for the electromagnetic meson form  factor [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  At last but at not least we could stress again the reasoning and strategy of our indefinite gauge method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Obviously,  If the quark SR exist in a given gauge, it is natural to expect that it exists in some other gauges as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' However to  reach the resulting SR with the simultaneous reliable solution for meson spectra requires very different effort when  one goes from one gauge choice to another one (here we the kernels are QCD vertices itself and they are not crippled  presence by ad hoc auxiliar functions ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' It is well known that LRA -Γµ = gT γµ- with the lattice gluon propagator  obtained in Landau gauge, does not provide a good starting point for the calculation of mesons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  That such LRA does not receive a proper strength one can see also from DSE solution alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' It has been checked  that decreasing the fixing parameters, one gradually observe the growth of the peak in the quark spectral function  and the dirac delta function is formed after passing through the critical coupling ξg2 with a lattice gluon propagator  matched to the transverse (or metric tensor) part of interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' At this critical point one gets non-confining (NC)  propagator solution of familiar form  SNC(p) =  R  ̸ p − mp  +  � ∞  th  doσv(o) ̸ p + σs(o)  (p2 − o + iǫ)  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='1)  with two continuous spectral functions σv,s being nonzero only from the threshold (being identical to the fermion pole  mass mp, if one allows nontrivial gluon spectral function).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Such solution typically arise at non-confining theory like  QED, being preserved for not large coupling in toy quantum field models [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' With the value R ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='75 the authors  7  of [6] obtained such solution for fermion propagator within LRA and lattice Landau gauge gluon data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [1] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Sauli, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 106, 3, 034030 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [2] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Sauli, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 1021, 014049 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [3] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Sauli, Few Body Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 61 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [4] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Sauli, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='D 106, 9, 094022 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [5] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Solis, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Costa, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Luiz, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Krein, Few Body Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 60 3, 49 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Horak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Pawlowski, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Wink, arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='07597.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [7] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Mezrag, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Salm`e, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' C 81 1, 34 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Horak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Pawlowski, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Wink, arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='09333  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Horak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Papavassiliou , J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Pawlowski, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Wink, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 104,074017 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Cornwall, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 26,1453 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [11] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Roberts and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Williams C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Roberts and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Williams, Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 33, 477 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [12] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Alkofer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' von Smekal, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 353 281 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [13] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Hilger, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Popovici, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Gomez-Rocha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Krassnigg, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 91 3,034013 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [14] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Sauli, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 90, 016005 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [15] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='Sauli,Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 86, 096004 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [16] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Eichten, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Godfrey, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Mahlke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rosner, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 80 1161, (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Kogut and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Susskind, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D10 3468 (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [18] Qi Li, Long-Cheng Gui, Ming-Sheng Liu, Qi-Fang L¨u, Xian-Hui Zhong, Chin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' C 45 2, 023116 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [19] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='Bicudo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Marques, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Cardoso, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Cardoso, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Oliveira, PoS QCD-TNT09 003 (2009);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' ArXive: 0912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='1274.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [20] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Mitchell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' [CLEO Collaboration], Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 102, 011801 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Ablikim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' BESIII Collaboration, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 106, 112002 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [22] BESIII collaboration: M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' AblikimBESIII Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 96, 3, 032001 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [23] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Guleria, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Gebrehana, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Bhatnagar, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
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+page_content=' D 104, 9, 094045 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [24] Jun-Kang He, Hua-Zhong, Chao-Jie Fan, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
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+page_content=' D 103, 11, 114006 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [25] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Bruschini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Gonz´alez, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 101,1 014027 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [26] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Bhatnagar, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 102, 9, 094024 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [27] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Babiarz, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Goncalves, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Pasechnik, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Sch¨afer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
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+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 100 5, 054018 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [28] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Soni, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Joshi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Shah, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Chauhan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Pandya, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' C 78, 7, 592 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [29] Meijian Li, Yang Li, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Maris, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Vary, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 98 3, 034024 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [30] Wei-Jun Deng, Hui Liu, Long-Cheng Gui, Xian-Hui Zhong, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 95 3, 034026 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [31] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Becirevic, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Sanfilippo, JHEP 01, 028 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [32] Gang Li, Qiang Zhao, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 84 074005 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [33] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Bicudo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Binosi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Cardoso, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Oliveira, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Silva, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 92 11, 114514 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [34] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Bicudo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
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+page_content=' Cardoso, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Oliveira, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Silva, talk at Lattice 2015, PoS LATTICE2015 (2016) 317;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' e-Print:  1509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='06737.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [35] M Napetschnig, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Alkofer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Huber, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Pawlowski Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 104, 054003 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Falc˜ao, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Oliveira, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Silva, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 102, 114518 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [37] author web pages at: gemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='ujf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='cas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='cz  [38] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Sauli, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' G 35, 035005 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [39] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Frederico, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Salme, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Viviani, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 89, 016010 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [40] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Carbonell, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Karmanov, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' A 46,387 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [41] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Branz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Faessler, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Gutsche, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Ivanov, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' K¨orner, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Lyubovitskij, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 81, 034010 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [42] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Ganbold, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Gutsche, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Ivanov, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Lyubovitskij, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 104, 094048 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [43] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Dubnicka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Dubnickova, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='A Ivanov , A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Liptaj, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' D 106 033006 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [44] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Fischer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Nickel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Williams, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' C60, 49 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [45] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Isgur and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Wise , Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' B232 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [46] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Isgur and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Wise, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' B237, 527 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [47] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Sauli, JHEP 02,001 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content='  [48] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Cabibbo and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Gatto, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}
+page_content=' 224 , 1577 (1961).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2tAyT4oBgHgl3EQfb_cv/content/2301.00272v1.pdf'}

2tAzT4oBgHgl3EQfuP3I/content/tmp_files/2301.01689v1.pdf.txt

@@ -0,0 +1,1910 @@
+1
+Process Variation-Aware Compact Model of Strip
+Waveguides for Photonic Circuit Simulation
+Aneek James, Anthony Rizzo, Yuyang Wang, Asher Novick, Songli Wang, Robert Parsons, Kaylx Jang,
+Maarten Hattink, and Keren Bergman
+Abstract—We report a novel process variation-aware compact
+model of strip waveguides that is suitable for circuit-level sim-
+ulation of waveguide-based process design kit (PDK) elements.
+The model is shown to describe both loss and—using a novel
+expression for the thermo-optic effect in high index contrast
+materials—the thermo-optic behavior of strip waveguides. A
+novel group extraction method enables modeling the effective
+index’s (neff) sensitivity to local process variations without the
+presumption of variation source. Use of Euler-bend Mach-
+Zehnder interferometers (MZIs) fabricated in a 300 mm wafer
+run allow model parameter extraction at widths up to 2.5 µm
+(highly multi-mode) with strong suppression of higher-order
+mode excitation. Experimental results prove the reported model
+can self-consistently describe waveguide phase, loss, and thermo-
+optic behavior across all measured devices over an unprecedented
+range of optical bandwidth, waveguide widths, and temperatures.
+Index Terms—Silicon photonics, compact modeling, process
+variation.
+I. INTRODUCTION
+S
+ILICON photonics (SiPh) has seen explosive growth in
+demand as a technology platform, driven by its adoption
+in data centers (DC), high performance computing (HPC) [1]–
+[3], quantum computing [4]–[8], and radio-frequency com-
+munication systems [9]–[11]. SiPh’s rapid rise and matura-
+tion has been enabled by its ability to leverage decades of
+research in the complementary metal–oxide–semiconductor
+(CMOS) industry, drastically reducing the typical research and
+development (R&D) costs associated with new semiconductor
+technologies [12]–[14]. SiPh, however, has not yet been able
+to mimic CMOS yield prediction tools for evaluating photonic
+integrated circuits (PICs). Yield is a ubiquitous metric used
+across semiconductor manufacturing, with improvements in
+yield being strongly correlated with reductions in the time
+and costs associated with PIC design cycles [15]–[17]. The
+need for predictive yield models can be mitigated to some
+This work was supported in part by the U.S. Advanced Research Projects
+Agency–Energy under ENLITENED Grant DE-AR000843 and in part by
+the U.S. Defense Advanced Research Projects Agency under PIPES Grant
+HR00111920014.
+A. James, Y. Wang, A. Novick, S. Wang, R. Parsons, K. Jang, M. Hattink,
+and K. Bergman are with the Department of Electrical Engineering, Columbia
+University, New York, NY 10027, USA. (Corresponding author: Aneek James,
+e-mail: [email protected]).
+A. Rizzo is with the Air Force Research Laboratory Information Directorate,
+Rome, NY 13441, USA.
+© 2023 IEEE. Personal use of this material is permitted. Permission from
+IEEE must be obtained for all other uses, in any current or future media,
+including reprinting/republishing this material for advertising or promotional
+purposes, creating new collective works, for resale or redistribution to servers
+or lists, or reuse of any copyrighted component of this work in other works.
+TABLE I
+FEATURES FOR MODELING STRIP WAVEGUIDE PERFORMANCE. THE
+MODEL IN THIS WORK DESCRIBES PHASE, LOSS AND THERMAL BEHAVIOR
+EFFECTS OVER A BROAD RANGE OF WAVELENGTHS AND WAVEGUIDE
+GEOMETRIES.
+Model Features
+[25]
+[26]
+This Work
+Wavelength [nm]
+1550
+1520–1570
+1450–1650
+Nominal Width Range [nm]
+480
+480–500
+400–2500
+Considered Variation Sources
+w,t
+w,t
+Arbitrary
+Statistical Parameter Variations
+
+
+
+Waveguide Scattering Losses
+
+
+
+Thermo-optic Effect
+
+
+
+w - Waveguide Width Variations
+t - Waveguide Thickness Variations
+degree by designing variation-robust devices [18] or PICs
+such that performance variations can be tolerated or cor-
+rected for post fabrication [19], [20]. In each of these cases,
+however, quantitative yield data cannot be determined prior
+to fabrication—an obstacle that will be exacerbated as the
+number of components per PIC in silicon is projected to
+scale well into the millions within the next decade [21].
+Circuit designers also need tools to optimize system-level
+performance through device-level design choices [22]. To meet
+rising circuit design complexity, commercial foundries must
+develop process design kits (PDKs) that include compact
+models that are both parameterized over a wide range of
+relevant design and environmental variables and describe all
+important device figures of merit [23], [24]. It is essential
+that strip waveguides in particular—a critical component of
+most SiPh circuits—are accurately modeled according to their
+expected fabricated performance.
+Broadly speaking, there are three ways to construct compact
+models: (i) look up table-based models, obtained directly from
+measurements or device simulations, (ii) models based on
+empirical fit functions, and (iii) physics-based models [23].
+Most previously reported work falls under the look-up table-
+based category [25]–[29]. These models can be parameterized
+using look-up tables (LUTs), where interpolation is used to
+predict the performance of designs not explicitly defined in
+the table. Ensuring that LUT models are accurate over a wide
+range of input parameters, however, requires measuring all
+waveguide figures of merit for every combination of input
+parameters; a task that scales exponentially with the number of
+modeled independent variables. Prior demonstrations methods
+also require the explicit connection of the measured effective
+and group index variations to a predefined number of process
+variation sources, introducing the possibility of error if any
+arXiv:2301.01689v1  [physics.optics]  4 Jan 2023
+
+2
+Fig. 1.
+a, Example electric field profile taken from Lumerical MODE. b,
+Simulated (scatter) and modeled (dashed) effective index vs wavelength for
+several waveguide widths. Each waveguide was simulated with a thickness of
+220 nm.
+systemic deviations exist between the simulation configuration
+and the realities of the fabrication process.
+In this paper, we report to the best of our knowledge, the first
+geometry-parameterized compact model of strip waveguides
+that can capture device performance over a wide range of
+wavelengths and waveguide geometries (see Table I). Using a
+novel derivation of the thermo-optic effect that is accurate for
+high-index contrast waveguides, we demonstrate our model’s
+ability to describe both scattering loss and the thermo-optic
+effect as a function of both design and statistical parameters.
+A novel group-extraction-based method allows the characteri-
+zation of process variations without presumption of a source or
+its associated sensitivity. This extraction methodology is used
+to construct a model from dozens of geometric variations of
+Mach-Zehnder Interferometers (MZIs) fabricated in a 300 mm
+commercial foundry. These use of Euler bends in these MZIs
+permits the characterization of wide waveguide performance
+with minimal higher-order mode excitation. Experimental re-
+sults validate the model’s accuracy in describing the phase,
+loss, and thermo-optic performance across the entire wafer.
+The model is also implemented in Verilog-A to demonstrate
+compatibility with electronic-photonic co-simulation environ-
+ments [30]–[32]. This work represents a key step toward
+the modeling of waveguide-based PDK components, enabling
+true-to-measurement circuit simulation at massive integration
+densities.
+II. PHYSICS-AWARE MODEL DEVELOPMENT
+Because the mode condition of an optical waveguide
+is
+described
+via
+a
+transcendental
+equation,
+completely
+generalized analytical solutions for the effective index (neff)
+are impossible to derive [33]. We therefore propose, as
+discussed in [34], finding a behavioral model that accurately
+captures its dependence on all design parameters over the
+relevant ranges of interest. In this section, we develop
+dependency models for the design parameters available.
+Fig. 2. a-c, Plot of simulated (scatter) and modeled (dashed) neff parameters
+�
+∂2neff/∂λ2, ∂neff/∂λ, neff,0
+�
+vs waveguide width (respectively). These
+values were for a waveguide with a thickness of 220 nm at a wavelength
+of 1550 nm. d, Comparison of the model (dashed) and simulated (scatter)
+neff vs waveguide width for different thicknesses. Simulated at 1550 nm.
+The semi-physical nature of the model is then leveraged
+to describe both the scattering loss and the thermo-optic
+coefficient. Process variations, whether of a design parameter
+or not, will be covered in Section IV.
+A. Wavelength Dependence
+The wavelength dependence of the waveguide neff is first
+considered. The neff of several silicon-on-insulator (SOI)
+waveguide geometries were simulated in Lumerical MODE
+(Fig. 1a). From the results, it is shown that the wavelength
+dependence over the S-, C-, and L-bands for all geometries is
+well-approximated by a second-order Taylor expansion for a
+wide range of waveguide widths sufficiently above the cutoff
+condition (Fig. 1b):
+neff, model(λ) =
+2
+�
+i=0
+1
+i!
+∂ineff
+∂λi
+����
+λ=λ0
+(λ − λ0)i.
+(1)
+B. Geometric Dependence
+As the Taylor expansion only captures the wavelength-
+dependence, it is clear that the fitting parameters ∂2neff/∂λ2,
+∂neff/∂λ and ∂0neff/∂λ0 (hereafter referred to as neff,0) are
+responsible for capturing the dependence on waveguide geom-
+etry. With respect to width, all three fitting parameters were
+previously found in [35] to be well described by the following
+behavioral model:
+∂ineff
+∂λi (w) = pi0 · w2 + pi1w + pi2
+w2 + pi3w + pi4
+,
+(2)
+for a total of fifteen model parameters. To verify correctness
+of the model, all three parameters were fitted to the simu-
+lation data with (1)-(2) using ordinary least squares (OLS)
+
+a
+Thickness
+Width
+2.8
+2.6
+neff
+2.4
+2.2
+1450
+1500
+1550
+1600
+1650
+Wavelength [nm]
+400 nm
+580 nm
+ 760 nm
+940 nm215 nm
+235 nm
+255 nm
+275 nm
+295 nm3
+Fig. 3. Comparison between modeled (dashed) and simulated (scatter) neff
+for higher order modes and the fundamental TM mode. All waveguides were
+simulated with a thickness of 220 nm.
+regression. The model was able to match all three parameters
+over the entire range of the width sweep (Fig. 2a-c). The
+close matching of the modeled and extracted Taylor parameters
+means that our modification of (2) still preserves its ability to
+match the behavior of effective index as a function of wave-
+length. By extension, these three Taylor parameters allow for
+a robust description of neff as a function of waveguide width
+(Fig. 2d). The data also demonstrates this agreement is not
+unique to any particular waveguide thickness, with different
+thicknesses producing different sub-parameter fits. Finally, it
+should be noted that both the numerator and denominator in
+(2) are polynomials of equal order. Our model consequently
+predicts that, for a given wavelength, the effective index will
+asymptotically approach a constant value as w approaches
+infinity. The value that the model approaches as w tends
+towards infinity can be interpreted as the equivalent neff of
+an infinite slab of the same thickness:
+lim
+w→∞ neff(λ, w) = nslab(λ).
+(3)
+In this way, our behavioral model can elegantly capture all
+significant features of effective index for the design parameters
+of interest. The model’s accuracy holds true for higher order
+modes as well, provided that they are sufficiently far away
+from their respective waveguide cutoff condition (Fig. 3).
+C. Scattering Loss
+Scattering loss due to sidewall roughness (SWR) can be a
+significant source of loss in most reported waveguide designs,
+making it critical for designers to accurately model [36]. In this
+section, we demonstrate our model’s ability to capture SWR
+loss as a function of waveguide geometry. It was first noted
+in [37] that the traditional Payne and Lacey model of SWR-
+induced loss [38], [39] was found to be identical in behavior to
+the derivative of the effective index with respect to waveguide
+width:
+αSWR(λ, w) = R ∂
+∂w [neff(λ, w)] ,
+(4)
+where R is a proportionality constant. As our model can
+describe neff as a function of width, a closed-form repre-
+sentation of ∂neff/∂w can be exactly derived. This equation
+Fig. 4.
+a, Graphical representation of a waveguide simulated with some
+sidewall roughness. The inset is a magnified view of the waveguide to clarify
+the definition of σrms. b, Scattering losses estimated from FDTD compared
+to the fit using our model based on Lumerical MODE data.
+can then be fitted to measured waveguide loss data to extract
+the proportionality constant. We validate this by fitting (4)
+to the scattering loss of a 7 µm long SOI waveguide with
+some SWR wall roughness in Lumerical 3D-FDTD (Fig. 4a).
+The roughness Root Mean Square (RMS) and correlation
+length were arbitrarily chosen to be σrms
+= 5 nm and
+Lcorr = 1 µm respectively. These parameters were then used to
+generate a random, anisotropic SWR on the waveguide walls
+[40]. Propagation losses were simulated for waveguide widths
+ranging from 450 nm to 850 nm. The results of the fitting are
+shown in Fig. 4b, with our model closely matching trend of
+the scattering loss behavior extracted from FDTD simulations.
+D. Thermo-Optic Effect
+Our model can also completely describe the thermo-optic
+coefficient of an arbitrary waveguide geometry without the
+need for any thermal measurements. The thermo-optic co-
+efficient of a waveguide mode most importantly requires
+knowledge of the confinement factor, which is the fraction of
+a mode’s power confined within each constituent waveguide
+material. Kawakami showed in [41] that for a waveguide
+made up of N materials, each with with an index nk and a
+confinement factor Γk:
+N
+�
+k
+Γkn2
+k = ngneff
+(5a)
+�
+k
+Γk = 1,
+(5b)
+where (5b) is derived from noting that the sum of all con-
+finement factors must equal unity due to power conservation.
+
+2.5
+n
+2.0
+TEO
+TE1
+TE2
+TMO
+0.5
+1.0
+1.5
+2.0
+WG Width [um]20m
+Width
+SOl Waveguide4
+A closed-form of the confinement factor for a two-material
+waveguide (e.g. SOI wires) can then be derived:
+Γcore = ngneff − n2
+clad
+n2
+core − n2
+clad
+(6a)
+Γclad = n2
+core − ngneff
+n2
+core − n2
+clad
+,
+(6b)
+where Γcore is the power contained in the waveguide core and
+Γclad is the power contained in the cladding.
+Next, we must obtain an expression that describes the
+thermo-optic effect on neff in terms of the confinement factor.
+A common approximation of the thermo-optic coefficient of
+neff is
+∂neff
+∂T
+≈ Γ1
+∂n1
+∂T + Γ2
+∂n2
+∂T + . . . ,
+(7)
+where δ represents a small perturbation in the values, Γn is
+the confinement of the mode within material n and ∂nn/∂T
+is the thermo-optic coefficient of material n [42]. Though
+this equation is widely used [43]–[45] and may be accurate
+in certain scenarios, to the authors’ knowledge it has never
+been demonstrated to be a generally accurate approximation.
+We therefore start from first principles and consider a general
+perturbation of the wave equation [46]:
+δ
+�
+β2
+eff
+�
+= Γcore
+ω2
+c2 δ
+�
+n2
+core
+�
++ Γclad
+ω2
+c2 δ
+�
+n2
+clad
+�
+,
+(8)
+where βeff is the effective wavenumber, Γcore is the con-
+finement in the waveguide core, Γclad is the confinement in
+the waveguide cladding, and ncore and nclad are the core and
+cladding indices respectively. Carrying this operation through
+and combining with (1) (see Appendix A for details) yields:
+neff(λ, w, T) ≈ neff,T0(λ, w) + ∂neff
+∂T (T − T0)
+(9a)
+∂neff
+∂T
+= Γcore
+ncore
+neff, T0
+∂ncore
+∂T
++ Γclad
+nclad
+neff, T0
+∂nclad
+∂T
+,
+(9b)
+where neff,T0 is the neff at some reference temperature T0. The
+key addition to (9) compared to prior literature is the scaling
+of each thermo-optic term by ratio between the material and
+effective indices. As the index contrast between the core and
+cladding decreases, our model will approach the (7). Thus
+it is clear that our model will outperform (7) in accuracy
+when describing high index contrast materials, such as the
+SOI waveguide geometries prevalent in SiPh.
+With these expressions, our confinement factor and the
+thermo-optic coefficient models can be validated. The simu-
+lated confinement factor is compared to our model prediction
+at 1550 nm in Fig. 5a. The optical properties of silicon and
+silicon dioxide used in our model were taken directly from
+[47]. There was a near perfect agreement between the modeled
+and simulated confinement factor, showing that the general
+behavior of confinement factor is captured by our model
+(Fig. 5a). The modeled thermo-optic coefficient is validated
+by simulating how the neff of a SOI waveguide varies with
+temperature using Lumerical MODE (Fig. 5b). Silicon was
+assumed to have a thermo-optic coefficient of 1.9 × 10−4 K−1
+[48] and SiO2 was assumed to have a thermo-optic coefficient
+of 1 × 10−5 K−1 [49]. The model and simulations show
+Fig. 5.
+a Modeled (dashed) and simulated (scatter) confinement factor vs
+waveguide width for different thicknesses. b, Comparison between simulated
+(scatter), previously reported model (dotted, Eq. (7)) and our work (dashed
+line, Eq. (9)) describing neff vs Temperature of a 480 x 220 nm waveguide.
+exceptional agreement from 300 - 1200 K, despite the fact that
+our model does not require any data from thermal simulations
+or measurements. As predicted, the previously reported model
+of the thermo-optic effect (7) significantly under-predicts the
+expected change in neff. It should be noted that in real devices,
+waveguide geometry itself is a function of T due to thermal
+expansion. This can be accounted for by modeling w as a func-
+tion of T. Experimental results in Section V-C, however, show
+that assuming a constant width geometry provides sufficient
+accuracy.
+Having a model of the thermo-optic effect that is accurate
+over a wide range of conditions like this one holds a great
+deal of potential to enable more robust design exploration,
+such as evaluating photonic waveguide heater designs [50],
+[51], characterizing self-heating in micro-resonators [52], or
+studying the effect of ambient temperature fluctuations in a
+system.
+E. Parameter Extraction
+The practical utility of a compact model is greatly deter-
+mined by the associated parameter extraction procedure to
+connect the model to a given foundry process. This is particu-
+larly important when developing statistical models, as accurate
+parameter extraction is the only way to guarantee that process
+variations are accurately reflected in the model. A popular
+solution is to leverage the phase-sensitivity of interferometric
+optical filters—such as Mach-Zehnder interferometers (MZIs),
+microresonators, or arrayed waveguide gratings (AWGs)—to
+monitor process variations across a wafer. Regardless of the
+chosen device, a shared difficulty lies in accurately guessing
+what particular interference fringe position corresponds to a
+particular fringe order [25], [26], [53]. Our method is based on
+
+a
+0.80
+0.75
+210 nm
+220 nm
+230 nm
+215 nm
+225 nm
+0.4
+0.6
+0.8
+1.0
+WG Width [um]
+b
+2.7
+neff
+2.6
+400
+600
+800
+1000
+1200
+Temperature [K]
+This Work - Previous Model
+ Simulated5
+the curve-fitting method presented in [25] and [54], with some
+additional steps described to include waveguide dispersion as
+an extracted parameter.
+The first step in parameter extraction is to characterize
+the group index (ng) of a fabricated interferometer from
+a wavelength sweep of the device. To enable this, (1) is
+rearranged into a more suitable form:
+neff(λ) = 1
+2
+∂2neff
+∂λ2 λ2 + Bλ + C
+(10a)
+B = ∂neff
+∂λ − ∂2neff
+∂λ2 λ0
+(10b)
+C = 1
+2
+∂2neff
+∂λ2 λ2
+0 − ∂neff
+∂λ λ0 + neff,0,
+(10c)
+where B and C are fitting parameters that aggregate the 1st and
+0th order terms from (1) respectively. Following the procedure
+described in [54], it is first noted that the fringe condition of
+an inteferometric device is described by
+φ = 2π
+λ neff(λ)L = 2πm,
+(11)
+where φ is the phase difference between the interferometry
+arms, L is the path length of the interferometer, λ is a partic-
+ular fringe wavelength, and m is an integer corresponding to
+the particular fringe order. To extract our model parameters,
+a wavelength sweep of the interferometric device is required.
+Once this is performed, a peak finding algorithm can be used
+to detect the wavelength of all detected fringes. A function that
+relates the relative fringe locations to the ng of the waveguide
+is now required. This can be done by defining a continuous
+function that will yield an integer value at each of the detected
+fringe locations. Let m0 represent the particular fringe order
+corresponding to an arbitrarily chosen reference fringe located
+at λ0. The fringe order m of any other fringe can be defined
+relative to this reference as
+m = m0 +
+� λ
+λ0
+dm
+dλ dλ = m0 + ngL ·
+� 1
+λ − 1
+λ0
+�
+.
+(12)
+This continuous function now allows us to redefine the mea-
+sured fringes into a form suitable for parameter extraction.
+A reference fringe variable n is now defined by letting
+m = (m0 + n). Inserting this back into (12) produces:
+n = ngL ·
+� 1
+λn
+− 1
+λ0
+�
+,
+(13)
+where each relative fringe n is located at an associated
+wavelength λn. Using (13), the ng of the measured device
+is now directly related to the measured fringe locations. This
+fitting equation must now be extended to our specific model
+parameters. The ng of a waveguide is defined to be
+ng = neff − λ∂neff
+∂λ .
+(14)
+Combining with (10a) yields an expression for ng in terms of
+our compact model:
+ng = C − 1
+2
+∂2neff
+∂λ2 λ2.
+(15)
+Fig. 6. a, Captured spectrum of simulated MZI used for parameter extraction.
+The waveguide mode was simulated in Lumerical MODE, and then exported
+to a MZI waveguide simulation block in Lumerical INTERCONNECT. b,
+Linear Regression of fringe wavelengths to extract the ng performed on the
+detected fringes from a. c, Possible neff solutions (black, dashed), along with
+the actual solution (red), determined by the ng extracted in b.
+By inserting (15) back into (13), we can derive an OLS
+regression-compatible expression:
+n = CΛC − ∂2neff
+∂λ2 ΛS
+(16a)
+ΛC = L ·
+� 1
+λn
+− 1
+λ0
+�
+(16b)
+ΛS = L
+2 ·
+�
+λn − λ2
+n
+λ0
+�
+,
+(16c)
+where [ΛC, ΛS] are explanatory variables. Performing an OLS
+regression between n and [ΛC, ΛS] gives us two of our three
+fitting parameters in (10). Finally, B can be calculated by
+combining equations (11) and (10a):
+B = m
+L − 1
+2
+∂2neff
+∂λ2 λm − C
+λm
+,
+(17)
+where the only uncertainty is what fringe order m corresponds
+to each measured fringe λm. Once B is determined from (17),
+(10b) and (10c) can be used to determine the original fitting
+parameters in (1). It should be noted that each detected fringe
+(m, λm) location will yield very small variations in the B value
+due to resolution-based uncertainty in the exact value for λm.
+For a best guess, all values Bm taken from each measured
+fringe λm should be averaged together.
+To validate this method under ideal conditions, an MZI
+constructed using 480 nm x 220 nm waveguides is simulated in
+Lumerical INTERCONNECT. To ensure accuracy, the wave-
+guide’s neff was first simulated in MODE and then exported
+to a MODE Waveguide element in INTERCONNECT. As the
+full-width half-maximum (FWHM) of the MZI does not affect
+the extracted neff, the waveguides were arbitrarily assumed to
+have a 2.5 dB/cm loss and the coupling coefficient was chosen
+to ensure critical coupling. The spectrum of the simulated MZI
+
+a
+Power [dBm]
+20
+b
+10
+C
+2.5
+neff
+2.4
+2.3
+1500
+1550
+1600
+1650
+Wavelength [nm]6
+is shown in Fig. 6a. Fringe locations were extracted using
+a peak finding algorithm. The fringe located closest to the
+center of the sweep was arbitrarily chosen as n = 0. Using
+(16), OLS regression found ∂2neff/∂λ2 = −0.136 µm−2 and
+C = 3.9215 (Fig. 6b). From here, the family of solutions for
+neff is plotted in Fig. 6c. Each particular solution corresponds
+to a different guess on the fringe orders detected, e.g. m0 = 52
+vs. m0 = 53. The separation between each neff solution plotted
+in 6c is determined by the free-spectral range (FSR) of the
+interferometer, with a larger FSR corresponding more widely
+separated solutions.
+To determine the correct fringe order of the reference we
+use the fact that, from the simulations performed in Section
+II, we know the waveguide geometry has an neff of 2.411 at
+the reference fringe location. In Section III we explain how
+to increase the accuracy of this estimation to avoid errors
+introduced by this simulation. From this, the reference fringe
+order is found to be m0 ≈ 114.03. Since fringe orders must
+be integer numbers, the result is rounded to the nearest integer
+114. By combining (10a)-(10c), the original fitting coefficients
+are found to be ∂neff/∂λ = −1.078 µm−1 and neff,0 = 2.411.
+To evaluate accuracy of our extraction, we define the relative
+error between the extracted and simulated neff’s σerror by:
+σerror =
+��
+(neff, model − neff, sim)2 dλ
+�
+n2
+eff, simdλ
+,
+(18)
+where neff, sim is the effective index from the MODE simula-
+tion, used as a reference to quantify our method’s accuracy,
+and neff, model is the result from applying our extraction method
+to the simulated MZI. Upon evaluation, the total relative error
+was found to be 0.017%. Since the order of the reference
+fringe is correct, the remaining model error is attributed to
+inaccuracies in the initial regression fit using (16a)-(16c).
+III. MORE ROBUST neff EXTRACTION UNDER PROCESS
+VARIABILITY
+The reliability of the extraction is highly sensitive to the
+guessed value of the reference fringe order. For the example
+in Section II-E, we used a priori knowledge of the neff at the
+reference fringe to estimate its order. Therefore, any deviation
+between the assumed and actual waveguide dimensions risks
+introducing error. By noting that the initial order estimate
+rounded to the nearest integer, we can use (11) to define
+a boundary beyond which our fringe order guess will be
+incorrect [25]:
+|∆m| = |neff, actual − neff, guess| ≤ λm0
+2L .
+(19)
+We can see that, to raise confidence in the guessed fringe order,
+either the accuracy of our neff guess must be increased or the
+interferometric path length must be decreased. As explained in
+Section II-E, our extraction method begins by directly extract-
+ing the ng of a given interferometer via optical sweep. Process
+variations will therefore appear as variations in the extracted
+values for ∂2neff/∂λ2 and C. By measuring several devices
+of the same drawn width across the all measured dies, wafers,
+and lots, the influence of the random width and thickness
+variations can be eliminated by averaging their extracted fitting
+Fig. 7. a, Plot of the ng error function for one sample. The error function
+shows a minimum at roughly 491.5 nm, which closely agrees with the actual
+waveguide width of 490 nm. b, Convergence of the etch bias estimate for
+different numbers of samples averaged.
+parameters. As the sample size becomes sufficiently large—
+with the necessary sample size being a function of the severity
+of the process variations—any remaining deviation between
+the nominal and averaged parameters will be the result of a
+systemic etch biases on the waveguide width. We therefore
+propose estimating this etch bias by creating a preliminary neff
+model based on the results of a photonic mode solver, such as
+Lumerical MODE. Using this model, an equivalent waveguide
+width can be found by minimizing the error function
+min
+w
+��
+[ng, model(w, λ) − ng, meas(λ)]2 dλ
+�
+n2g, meas(λ)dλ
+,
+(20)
+where ng, meas is the extracted model of ng using the averaged
+extracted parameters and ng, model is the simulation-based,
+width-dependent a priori model of neff. The neff of our
+equivalent waveguide width can then be plugged into the a pri-
+ori model to provide a more accurate fringe order estimate.
+In this way, we can increase the accuracy of our guessed
+effective index, regardless of whether the modeled waveguide
+composition is accurate to the virtual device composition.
+We now discuss the robustness of this optimization routine
+in the presence of other systemic non-idealities and its ability
+to perform etch bias correction. To do this, we need a ’ground
+truth’ value for neff, which we obtain by simulating all the
+non-idealities in Lumerical MODE. Subsequently we perform
+the parameter extraction using Lumerical INTERCONNECT.
+By comparing the extracted neff to the known simulated
+value for neff, we can directly evaluate the robustness of our
+methodology.
+A. Statistical Geometric Variation
+To test the extraction procedure’s accuracy under process
+variations, a simulation of 100 random variations on the
+
+a
+2
+Actual
+Guess
+Error Function
+!
+460
+480
+500
+520
+540
+Guessed Widths [nm]
+b
+4 nm
+26 nm
+Etch Bias [nm]
+Estimated
+11 nm
+33 nm
+15
+18 nm
+40 nm
+10
+20
+40
+60
+80
+100
+Number of Samples7
+Fig. 8. Plot of mean error in neff over the simulation bandwidth per simulated
+device. Each FSR was simulated with 100 random deviations from the target
+waveguide geometries. Both width and thickness were assumed to have a
+3σ = 5 nm.
+waveguide geometry was run. The nominal waveguide di-
+mensions were assumed to be 480 x 220 nm. To simulate
+systemic variations, each waveguide was arbitrarily assumed
+to have an etch bias of +10 nm. Random fluctuations were
+simulated by subjecting each device to a normally distributed
+variation of 3σ = 5 nm on both the waveguide width and
+thickness, as this value is consistent with the worst-case
+reported values for geometric variations [25]–[27]. Each mode
+profile was then exported to INTERCONNECT and simulated
+with interferometer FSRs ranging from 4 - 40 nm to investigate
+the effect this had on the extraction error. The resulting error
+function for one of these samples, with a ground truth width of
+490nm, is shown in Fig. 7a. We see the convergence behavior
+of the etch bias estimate evolves as a function of device sample
+size increases for several FSR designs in Fig. 7b. It can be seen
+that all FSR designs can yield at least an estimated etch bias
+within 2 nm of the actual value, indicating the utility of our
+etch bias correction.
+Fig. 8 shows the relationship between the average, per sam-
+ple error and the interferometer FSR. The error is measured
+in three scenarios: i.) a ‘na¨ıve’ case, where the fringe order is
+estimated assuming no etch bias; ii.) where the fringe order is
+estimated through our etch bias prediction methodology, based
+on 30 measured samples; and iii.) where the exact neff from
+simulations is used to determine the actual fringe orders. The
+last scenario, that produced an average per sample error of
+roughly 0.017% represents an error floor for the first two.
+This error floor is completely determined by errors in the
+initial ng regression, as well as any fundamental limitations
+in our chosen behavioral model. As the FSR is increased,
+the average per sample error in both cases improves steadily
+until it reaches the aforementioned floor. This is consistent
+with (19), indicating that a larger FSR corresponds to a wider
+margin of error for the fringe order estimate. For both the na¨ıve
+and bias compensation methods, there is a critical FSR value
+beyond which the fringe order is correctly estimated for all
+samples. It is clear, however, that estimating the presence of
+any etch biases drastically improves the fringe order accuracy,
+reaching the error floor for a much smaller FSR than when
+using the na¨ıve method.
+Fig. 9.
+a, ng relative error vs simulated sidewall angle. b, Comparison
+between the simulated (scatter) and estimated (dashed) neff for different
+sidewall angles.
+B. Sidewall Angle
+We now consider how the parameter extraction behaves
+when used for waveguides with some sidewall angle. Up
+to this point, our simulations assumed the waveguides to
+have no sidewall angle. Real waveguides, however, typically
+deviate from this ideal [55]. To study how our bias correction
+behaves under these conditions, a SOI waveguide with the
+same nominal (480 x 220 nm) design as before was simulated
+with a series of sidewall angles from 85 to 90 degrees as
+this is a range typical of foundries [25], [56]. As only the
+aggregate behavior is being studied, width and thickness
+variations were not included. As seen in Fig. 9a, the minimum
+of the error function optimized in the etch bias estimation step
+remain roughly constant for all considered sidewall angles.
+This results in very accurate predictions of the effective index
+from our model, even though the fundamental geometry is
+different. We interpret this as our optimization routine is
+picking an ‘equivalent’ waveguide width that matches the
+extracted ng profile. This equivalent width always seems to
+result in a waveguide design with a similar confinement factor
+and effective index—and therefore behavior—as seen in Fig.
+9b.
+C. Material Variation
+This method for increasing the accuracy of the guessed neff
+relies on the assumption that the material properties of the
+fabricated waveguides generally match the assumed material
+properties used in the simulation data used to construct the
+model. In practice, however, there can be a great deal of
+deviation between the assumed and actual optical properties of
+the waveguide materials. As a workaround, the authors suggest
+extracting and building a model based around the dispersion
+of the waveguide ∂2neff/∂λ2, as this waveguide parameter
+
+Naive
+0.75
+Bias Correction
+neff Error [%]
+Exact
+0.50
+0.25
+0.00
+10
+20
+30
+40
+Target FSR [nm]Naive
+Bias Correction
+0 =90.0
+0 =87.5
+0 =85.08
+Fig. 10. a, Illustration of measured reticles on a custom 300 mm wafer, with a blown-up microscopic image of a die with 135 MZIs. b, Nominal neff and
+ng model extracted from device measurements. c, Width-based model extraction for each die tested. d, Total model parameter µm variance σ explained vs
+number of principal components included.e, Plot of the width-independent subparameters for neff,0, ∂neff/∂λ0,and ∂2neff/∂λ2
+0 vs V .
+can be extracted exactly from measurements. The nominal
+model of ∂2neff/∂λ2 can then replace ng in (20) to estimate
+the width of the measured device. This width can then be
+used in conjunction with simulation data to assign it an neff
+guess. Though the limits of such a technique are unclear to the
+authors, experimental results in Section V demonstrate to be
+effective enough for describing the neff, loss, and thermo-optic
+effect for all measured device performance.
+IV. EXTRACTING LOCAL PARAMETER VARIATIONS
+Process variations (e.g. thickness variation, cladding and
+core index variations) will appear in our model as varia-
+tions in the fifteen model parameters that comprise Eq. (1).
+Capturing these variations requires the ability to extract their
+value locally, which cannot be done just by looking at the
+performance of any individual device. It is commonly assumed
+in prior literature that most process parameters slowly vary
+across the entire wafer [25]. This assumption implies that
+the values of the parameters comprising our model also
+vary slowly across the wafer. The authors therefore propose
+analyzing the performance of several waveguide width designs
+in close proximity to each other to locally extract all of the
+fifteen model parameters. Each local extraction serves as the
+observations of each model parameter that are tracked across
+the entire wafer.
+The simplest way to create a statistical model is to treat each
+of fifteen sub-parameters as independent statistical variables.
+This is not ideal, however, as each additional variable drasti-
+cally increases the number of required iterations for accurate
+Monte Carlo simulations. To minimize model complexity, we
+would like to represent each sub-parameter as a linear function
+of an ensemble of variables:
+pni = pni,avg. + ⃗s · ⃗V .
+(21)
+⃗V is the vector of variables that represent the process varia-
+tions. Minimizing model complexity would be the equivalent
+of minimizing the size of ⃗V . ⃗s describes the corresponding
+sensitivities of a given parameter to each element in ⃗V . To
+minimize the size of ⃗V , we leverage the fact that each extracted
+model parameter will be strongly correlated to one another.
+This is because the variations in each model parameter share
+common origins such as wafer thickness, annealing time,
+etc. We therefore propose using principal component analysis
+(PCA), a technique for transforming a number of possibly
+correlated variables into a smaller number of uncorrelated
+variables (i.e principal components) [57], to minimize model
+complexity. The chosen principal components are then the
+variables that make up ⃗V . The chosen principal components
+are then the variables that make up ⃗V . The number of
+components in ⃗V is flexible (see Appendix B for details).
+Since our waveguide geometry is primarily a function of two
+process variables—waveguide width and thickness—we use
+only the first principal component to preserve its physical
+interpretation. The result is a model of effective index as a
+function of width and our process variations–∆w, representing
+width variations and an additional variable we will call V ,
+representing an aggregate of other process variations, including
+thickness variation:
+neff,model(w + ∆w, V ).
+(22)
+This full model of neff is then used in the local optimization
+and re-extraction of each measured device. The cost function
+
+b
+d
+2.75
+%1
+100
+2
+neff
+2.50
+Explained [
+15
+7
+17
+73
+24
+26
+75
+4.25
+4.00
+6
+3.75
+357
+9111315
+1000
+2000
+Number of Components
+Width [um]
+c
+e
+17
+24
+26
+2
+5
+13
+0.25
+re/Heue
+aneff/a2
+-0.75
+.00
+.25
+neff,0
+2.50
+2.25
+2 0.4
+2 0.4
+-0.5
+0.4
+2 0.4
+2
+-1.0
+0.0
+0.5
+2 0.4 2 0.4 2 0.4
+WG Width [um]
+V9
+Fig. 11. a, Measured vs modeled optical spectrum of a 480 nm waveguide MZI with ∆L = 100 µm. b, (i) Histogram of extracted V data along with its
+associated Gaussian distribution (red, dashed) overlaid on top. (ii) Spatial map of the average value for V per measured die across the wafer. c, Mean and
+standard deviation of ∆w, neff, and ng.
+is defined as the sum of the relative neff and ng errors to match
+both the measured fringe locations and FSR respectively.
+Thus, we can employ a two-stage direct statistical com-
+pact model extraction procedure [24]. In the first stage, we
+use group extraction to obtain the complete set of fifteen
+parameters for a uniform device. In a second step, a subset
+of model parameters are re-extracted for each member of a
+large ensemble of devices measurements. This approach will
+be the most accurate representation of how device performance
+varies across the wafer without any presumption of variation
+source, statistical distribution, correlation, and the resulting
+model sensitivity to the variation. An inherent strength of
+this approach over others is that it is potentially useful for
+modeling other waveguide geometries as well. This potential
+is due to the model designer having the option of picking
+the number of principal components based on a physical
+assumption on the key process variables or optimize the
+percentage of explained parameter variance (see Appendix B).
+While further investigation would be required to confirm this,
+the methodology’s flexibility holds a great deal of promise.
+V. EXPERIMENTAL DEMONSTRATION
+We measured 7 reticles, each with 135 MZIs consisting
+of 27 different waveguide widths (w) from 400 nm to 2500
+nm and 5 different arm length delays (∆L) from 100 nm to
+500 nm, fabricated on a custom 300 mm full wafer through
+AIM Photonics (Fig. 10a). All 135 MZI were measured on
+reticle 2 while a smaller subset of 30 MZIs were measured
+on each of the remaining reticles, totaling 315 measured
+devices. Devices with the same waveguide width are placed
+adjacently to minimize the impact of local process variations
+on device performance. All MZIs have a nominal waveguide
+height of 220 nm, and grating couplers designed for quasi-TE
+polarization are utilized for optical I/O. The two arms of each
+MZIs consist of symmetric waveguide bends to mitigate the
+impact of bending on the ng. For devices with waveguides
+beyond the single-mode cutoff width, Euler bends are used to
+maintain single mode operation and high mode isolation [18].
+A tunable laser was swept from 1450–1610 nm at a 10 pm
+resolution to characterize the transmission spectrum of each
+MZI.
+A. Nominal Extraction
+A nominal model neff is created by averaging the extracted
+parameters for all measured devices as shown in Fig. 10b. We
+apply the extraction method described in Section II-E to every
+collected transmission spectrum. A preliminary model is built
+using the simulation data described in Section II to estimate
+the expected device FSR for each waveguide width variation.
+This estimated FSR is then fed into a peak finding algorithm
+to extract the ng parameters, and then estimate fringe orders—
+and, therefore the neff—of each measured device. As the
+measured ng deviated a great deal from the simulated values,
+the technique described in Section III-C is employed where a
+preliminary model based on ∂2neff/∂λ2 is created and used
+to estimate waveguide geometry to estimate the fringe order.
+All three Taylor-expansion parameters are then derived using
+(10a)-(10c), and then averaged across for each width variation
+across the entire wafer to create a nominal experimental model.
+The extraction is then repeated locally for devices that are
+close in proximity to one another to extract local values for
+the model’s sub-parameters (Fig. 10c).
+Fig. 10d shows that using (31) this first principal component
+can explain 62.7% of all variance in the sub-parameter values
+across the wafer. The authors determined that due to the clear
+connection between the V and the three model parameters
+
+a
+0
+100
+(i)
+(ii)
+Power [dBm]
+100
+μAw
+MVo
+C
+50
+50
+-100
+Measurement
+Model
+0.1
+(!)
+(iv)
+1500
+1550
+1600
+yauo
+2.50
+Wavelength [nm]
+b
+2.25
+(i)
+(ii)
+0.0
+-0.38
+(v)
+(vi)
+4.25
+0.010
+-0.20
+0.07
+Ong
+4.00
+0.005
+-1
+0.47
+3.75
+0.30
+0.75
+2
+1
+1
+2
+-2
+0
+Width [um]
+Width [um]
+V10
+Fig. 12. a, Measured thermo-optic response of a measured MZI device. b,
+Extracted value of ∂Tchip/∂Theater vs waveguide width using (9).
+that determine device behavior as w → ∞, this principal
+component was likely capturing width-independent sources of
+variance such as thickness variations (Fig. 10e). The authors
+will now show that this provides a model robust enough for
+capturing statistical behavior while preserving the goal for
+clear physical interpretation.
+B. Statistical Extraction
+The sum of the relative neff and ng errors is optimized using
+the Nelder-Mead algorithm [58]. The drawn waveguide width
+and the extracted V from the local extraction performed in
+Fig. 10c are used as the initial guesses for w and V . Despite
+the limited sample size of collected data, we can already see
+several notable preliminary statistical trends in ∆w as a result
+of our model. The model of neff extracted from each local
+optimization was found to result in a close agreement between
+the measured and modeled MZI performance. The extracted
+values for V exhibits the intended physical behavior of process
+parameter that varies slowly across the wafer (Fig. 11b). Local
+optimization yielded a total, average intra-die, and average
+local device standard deviation σV of 0.603, 0.386, and 0.167
+respectively, showing a correlation between device proximity
+and their extracted V values. The mean values of V for die
+both (i) in close proximity to each other and (ii) equidistant
+from the center of the wafer tend to be similar in value, as
+shown in the inset of Fig. 11b.
+Decoupling the process variations of V from the width
+variations ∆w enables extraction of width-dependent systemic
+effects, as shown in Fig. 11c(i). Our method estimates that
+waveguide widths with smaller mean errors also tend to have
+smaller σ∆w (Fig. 11c(ii)). This carries over as an explanation
+Fig. 13. a, Microscopic image of a die with waveguide spiral test structures
+for measuring width-dependent loss. Inset: magnified image showing three of
+the test structures. b, Propagation loss measurement and fit data for a 440 nm
+waveguide.
+for why for w = 2µm, neff varies more than for w = 1.2µm,
+allowing insight on what waveguide geometry best minimizes
+both σneff and σng. This sort of process insight for circuit
+designers is only possible due to the group benchmarking of
+all device performance within a localized area.
+C. Thermo-optic Effect Model Validation
+To validate the thermo-optic effect model developed in
+Section II-D, we re-characterized the MZI transmission spectra
+from a single die of the chip shown in Fig. 10a. The thermal
+characterization was performed by adhering a Thorlabs TLK-
+H polyimide heater to the side of the chip stage. The heater
+was controlled by a Thorlabs TC200 Temperature Controller to
+set the heater temperature. Thermal paste was applied between
+the chip and the chip stage to minimize thermal resistance
+between the chip and the heater. The thermal response of one
+of the tested MZI is shown in Fig. 12. The fringe closest to
+1550 nm is tracked at each temperature step and plotted against
+temperature to extract ∂λ/∂T. This value is then compared to
+our predicted value for ∂λ/∂T gained by taking the derivative
+of λ in (11) with respect to temperature
+∂λ
+∂Tchip
+=
+∆L
+m
+∂neff
+∂Tchip
+∂Tchip
+Theater
+1 − ∆L
+m
+∂neff,model
+∂λ
+,
+(23)
+where m is the order of the tracked fringe, ∆L is the path
+length difference between the two arms, and ∂Tchip/∂Theater
+represents the heat transfer efficiency from the heater to the
+chip itself. This last term is included as the authors only know
+
+0
+a
+Power [dBm]
+10
+31.8 °C
+20
+36.8 °C
+41.7°C
+0.073 nm/K
+-30
+44.9 °C
+1527
+1528
+1529
+1530
+1531
+1532
+Wavelength [nm]
+b
+0.90
+0.85
+0.80
+500
+1000
+1500
+2000
+Width [nm]a
+ COLUMBIA UNIVERSITY
+DARPA
+IN THE CITY OF NEW YORI
+ch Lightwave Research Laborato
+1CM
+Power [dBm]
+-10
+-15
+α = 1.916 dB/cm
+2
+4
+Spiral Length [cm]
+400 um11
+Fig. 14.
+a, Plot of measured (scatter) and modeled (line) propagation loss
+vs ∂neff/∂w. Slope of fit represents R in (4), while the intercept represents
+non-SWR loss. b, Plot of measured (scatter) and modeled (line) propagation
+loss vs waveguide width.
+the temperature of the resistive heater rather than the chip
+temperature itself. We know ∂Tchip/∂Theater ≤ 1 as heater
+cannot raise the temperature of the chip to a value higher than
+its own. The extracted parameters for ∆w and V are used in
+calculating (23).
+On average, the measured thermo-optic effect was found to
+be 0.91× our model’s (9) prediction. This value was found to
+be independent of waveguide geometry with the exception of
+400 nm (Fig. 12b). This error for 400 nm is assumed to be be-
+cause this width is close enough to the cutoff condition for our
+model to lose accuracy. In contrast, the measured thermo-optic
+effect was 1.21× the previously reported model’s prediction.
+This implies that either the chip’s change in temperature is
+greater than the heater’s or the previously reported model is
+incorrect. The change in temperature of the PIC can only ever
+be smaller than the heater’s temperature delta, making the old
+model’s prediction clearly nonphysical.
+D. Scattering Loss Model Validation
+To validate the scattering loss model, we measured a die
+with 25 spiral loss structures consisting of 5 different wave-
+guide widths (w) from 400 nm to 500 nm and 5 different spiral
+lengths (∆L) from 1 cm to 5 cm, fabricated on a custom 300
+mm full wafer through AIM Photonics (Fig. 13). Again, all
+spiral structures have a nominal waveguide height of 220 nm,
+and grating couplers designed for quasi-TE polarization are
+utilized for optical I/O. The losses of each spiral length were
+recorded, and then fit to a linear equation. The slope of the
+this fit was taken to be the propagation loss associated with
+each waveguide width. The results of our model fit are shown
+in Fig. 14. The model built in Section V-B was used to build
+a model of ∂neff/∂w. Fitting our modeled ∂neff/∂w to the
+measured propagation loss yields proportionality constant of
+R = 6.206 × 10−8 cm and (Fig. 14a). The intercept of the loss
+Fig. 15. a, Cadence Virtuoso schematic of the MZI test circuit. All circuit
+models were written in Verilog-A. The optical stimulus is provided by
+a continuous-wave (CW) Laser and detected with a photodetector (PD).
+b, Comparison of measured and simulated performance for an MZI with
+w = 2 µm and ∆L = 100 µm.
+fit is interpreted as the aggregate non-SWR loss, with a value
+of 0.901 dB. Fig. 14b shows the excellent agreement between
+our model and the data, predicting the similar propagation
+losses of both the 440 nm and 460 nm waveguides. As
+mentioned in Section V-B, both 400 and 420 nm waveguide
+widths are likely near the cutoff condition. Since (4) is only
+valid sufficiently far away from this condition, those data
+points are not included in the plot.
+E. Verilog-A Implementation
+To demonstrate its compatibility with electronic-photonic
+co-simulation, the circuit model was implemented in Verilog-
+A within Cadence Virtuoso (Fig. 15a). As Verilog-A does not
+inherently support optical signals, some compatibility code as
+well as a small library of photonic device models were built
+based upon on previously reported demonstrations [32], [59],
+[60].
+VI. CONCLUSION
+In summary, we have demonstrated a novel compact model
+that can greatly expand the accuracy of circuit-level simulation
+capabilities of silicon PICs. In contrast to prior work that
+focused on providing metrology information that could be use
+to fabrication engineers [26], [61], [62], we present this PDK
+model as a tool suitable for true-to-measurement circuit simu-
+lation and optimization. By leveraging this underlying physical
+behavior and locally extracting process variations by perform-
+ing group extraction, we have demonstrated a framework for
+building a model of neff that is entirely driven by measurement
+data. This model was shown to accurately describing the phase,
+
+a
+Loss [dB/cm]
+R = 6.206e-08 cm
+1.9
+αnon-SwWR = 0.901 dB
+1.8
+1.7
+2.2
+2.3
+2.4
+2.5
+2.6
+2.7
+neff/Ow [um-1]
+b
+Loss [dB/cm]
+1.9
+1.8
+1.7
+440
+450
+460
+470
+480
+490
+500
+Width [nm]a
+ght<0:3
+50:50 Coupler
+50:50 Coupler
+Waveguides
+eftLig1<0:3>
+rightLig1<0:3>
+leftLig1<0:3>
+rightLig1<:3>
+leftLig2<0:3>
+coupler
+coupler
+rightLig2<0:3>
+eftLig2<0:3>
+rightLig2<0:3>
+inLight<0:3tatic_waveguide_R2_d1outLight<0:3>
+CW Laser
+lastightout<0:3
+PD
+b
+Transmission [dB]
+-20
+Measured
+VerilogA
+1520
+1530
+1540
+1550
+1560
+Wavelength [nm]12
+loss, and thermo-optic behavior of the measured integrated
+waveguides over 4× the optical bandwidth and over 80×
+the range of waveguides widths reported in prior work. We
+envision that the advancement over prior demonstrations this
+work represents can support the development of waveguide-
+based PDK components and enable the robust optimization of
+next generation PICs.
+VII. ACKNOWLEDGEMENTS
+This work was supported in part by the U.S. Advanced
+Research Projects Agency–Energy under ENLITENED Grant
+DE-AR000843 and in part by the U.S. Defense Advanced Re-
+search Projects Agency under PIPES Grant HR00111920014.
+The authors thank AIM Photonics for chip fabrication.
+APPENDIX
+A. Derivation of Thermo-Optic Model
+Starting from (8) from [46], the effect of a thermal pertur-
+bation on the effective index is investigated. Carrying out this
+perturbation and following the chain rule yields:
+2β ∂β
+∂T = 2Γcore
+ω2
+c2 ncore
+∂ncore
+∂T
++ 2Γclad
+ω2
+c2 nclad
+∂nclad
+∂T
+.
+(24)
+Noting that β = ωneff/c and inserting above, the relationship
+simplifies to (25). Combining with (1) yields:
+neff = neff, T0 + ∂neff
+∂T (T − T0)
+(25a)
+∂neff
+∂T
+= Γcore
+ncore
+neff
+∂ncore
+∂T
++ Γclad
+nclad
+neff
+∂nclad
+∂T
+.
+(25b)
+It is noted that neff appears on both sides of the equation.
+Multiplying both sides by effective index yields a quadratic
+equation whose solution is:
+neff = neff, T0
+2
++ 1
+2
+�
+n2
+eff, T0 + 4n
+′(T − T0)
+(26a)
+n
+′ = Γcorencore
+∂ncore
+∂T
++ Γcladnclad
+∂nclad
+∂T
+.
+(26b)
+The expression can be simplified by noting that n2
+eff, T0 ≫ 4n
+′
+for typical values for the thermo-optic coefficients. Under-
+standing this, it is clear that the behavior of the square root
+term is approximately linear. The 1st order Taylor expansion
+of the square root term is:
+neff, T0 + 1
+2
+4n
+′
+�
+n2
+eff, T0 + 4n
+′(T − T0)
+(T − T0).
+(27)
+Noting again that n2
+eff, T0 ≫ 4n
+′, (27) simplifies to:
+neff, T0 +
+2n
+′
+neff, T0
+(T − T0).
+(28)
+Replacing the square root term in (26) with this expression
+and simplifying will then yield (9).
+B. Principal Component Analysis
+To start, we form a matrix X our of our list of local sub-
+parameter extractions, where each column represents a model
+parameter and each row is an observation of said parameter:
+X =
+�
+������
+∂0neff
+∂λ0
+0,1
+∂0neff
+∂λ0
+1,1
+· · ·
+∂2neff
+∂λ2
+4,1
+∂0neff
+∂λ0
+0,2
+∂0neff
+∂λ0
+1,2
+· · ·
+∂2neff
+∂λ2
+4,2
+...
+...
+...
+...
+∂0neff
+∂λ0
+0,n
+∂0neff
+∂λ0
+1,n
+· · ·
+∂2neff
+∂λ2
+4,n
+�
+������
+.
+(29)
+A covariance matrix S is then created from X and find its
+eigenvectors:
+S =
+�
+����
+⃗v0
+⃗v1
+...
+⃗vn
+�
+����
+�
+����
+λ0
+0
+· · ·
+0
+0
+λ1
+· · ·
+0
+...
+...
+...
+...
+0
+0
+· · ·
+λn
+�
+����
+�
+����
+⃗v0
+⃗v1
+...
+⃗vn
+�
+����
+−1
+,
+(30)
+where
+[v0, v1, · · · , vn]
+lists
+the
+eigenvectors
+and
+[λ0, λ1, · · · , λn]
+are
+their
+associated
+eigenvalues.
+The
+eigenvectors of the correlation matrix represent the directions
+of the axes where there is the most variance (i.e. the most
+information). Each eigenvalue λi is proportional to how much
+variance is captured by its associated principal component
+vi. Picking the eigenvectors with the largest eigenvalues
+allows us to reduce data dimensionality at the expense of
+some accuracy. The percentage of variability explained by a
+principal component is calculated as
+�M
+i=0 λi
+�N
+i=0 λi
+,
+(31)
+where λi is the eigenvalue for each eigenvector, M is the
+number of principal components the designer has chosen
+to include, and N is the maximum number of principal
+components.
+REFERENCES
+[1] A. Rizzo, S. Daudlin, A. Novick, A. James, V. Gopal, V. Murthy,
+Q. Cheng, B. Y. Kim, X. Ji, Y. Okawachi, M. van Niekerk, V. Deena-
+dayalan, G. Leake, M. Fanto, S. Preble, M. Lipson, A. Gaeta, and
+K. Bergman, “Petabit-scale silicon photonic interconnects with inte-
+grated kerr frequency combs,” IEEE Journal of Selected Topics in
+Quantum Electronics, vol. 29, no. 1: Nonlinear Integrated Photonics,
+pp. 1–20, 2023.
+[2] Q. Cheng, M. Bahadori, M. Glick, S. Rumley, and K. Bergman, “Recent
+advances in optical technologies for data centers: a review,” Optica,
+vol. 5, no. 11, pp. 1354–1370, Nov 2018.
+[3] M. Wade, E. Anderson, S. Ardalan, P. Bhargava, S. Buchbinder, M. L.
+Davenport, J. Fini, H. Lu, C. Li, R. Meade et al., “Teraphy: a chiplet
+technology for low-power, high-bandwidth in-package optical i/o,” IEEE
+Micro, vol. 40, no. 2, pp. 63–71, 2020.
+[4] G. Moody, V. J. Sorger, D. J. Blumenthal, P. W. Juodawlkis, W. Loh,
+C. Sorace-Agaskar, A. E. Jones, K. C. Balram, J. C. Matthews, A. Laing
+et al., “2022 roadmap on integrated quantum photonics,” Journal of
+Physics: Photonics, vol. 4, no. 1, p. 012501, 2022.
+[5] G. R. Steinbrecher, J. P. Olson, D. Englund, and J. Carolan, “Quantum
+optical neural networks,” npj Quantum Information, vol. 5, no. 1, pp.
+1–9, 2019.
+[6] S. Takeda and A. Furusawa, “Toward large-scale fault-tolerant universal
+photonic quantum computing,” APL Photonics, vol. 4, no. 6, p. 060902,
+2019.
+
+13
+[7] N. C. Harris, D. Bunandar, M. Pant, G. R. Steinbrecher, J. Mower,
+M. Prabhu, T. Baehr-Jones, M. Hochberg, and D. Englund, “Large-scale
+quantum photonic circuits in silicon,” Nanophotonics, vol. 5, no. 3, pp.
+456–468, 2016.
+[8] J. E. Bourassa, R. N. Alexander, M. Vasmer, A. Patil, I. Tzitrin,
+T. Matsuura, D. Su, B. Q. Baragiola, S. Guha, G. Dauphinais et al.,
+“Blueprint for a scalable photonic fault-tolerant quantum computer,”
+Quantum, vol. 5, p. 392, 2021.
+[9] D. Marpaung, J. Yao, and J. Capmany, “Integrated microwave photon-
+ics,” Nature photonics, vol. 13, no. 2, pp. 80–90, 2019.
+[10] Y. Yang, Y. Yamagami, X. Yu, P. Pitchappa, J. Webber, B. Zhang,
+M. Fujita, T. Nagatsuma, and R. Singh, “Terahertz topological photonics
+for on-chip communication,” Nature Photonics, vol. 14, no. 7, pp. 446–
+451, 2020.
+[11] B. Zong, C. Fan, X. Wang, X. Duan, B. Wang, and J. Wang, “6g
+technologies: Key drivers, core requirements, system architectures, and
+enabling technologies,” IEEE Vehicular Technology Magazine, vol. 14,
+no. 3, pp. 18–27, 2019.
+[12] W. Shi, Y. Tian, and A. Gervais, “Scaling capacity of fiber-optic
+transmission systems via silicon photonics,” Nanophotonics, vol. 9,
+no. 16, pp. 4629–4663, 2020.
+[13] Z. Zhou, R. Chen, X. Li, and T. Li, “Development trends in silicon
+photonics for data centers,” Optical Fiber Technology, vol. 44, pp. 13–
+23, 2018.
+[14] R. Sabella, “Silicon photonics for 5g and future networks,” IEEE Journal
+of Selected Topics in Quantum Electronics, vol. 26, no. 2, pp. 1–11,
+2019.
+[15] R. Gardner, J. Bieker, and S. Elwell, “Solving tough semiconductor man-
+ufacturing problems using data mining,” in 2000 IEEE/SEMI Advanced
+Semiconductor Manufacturing Conference and Workshop. ASMC 2000
+(Cat. No. 00CH37072).
+IEEE, 2000, pp. 46–55.
+[16] N. Kumar, K. Kennedy, K. Gildersleeve, R. Abelson, C. Mastrangelo,
+and D. Montgomery, “A review of yield modelling techniques for
+semiconductor manufacturing,” International Journal of Production Re-
+search, vol. 44, no. 23, pp. 5019–5036, 2006.
+[17] W. Bogaerts and L. Chrostowski, “Silicon photonics circuit design:
+methods, tools and challenges,” Laser & Photonics Reviews, vol. 12,
+no. 4, p. 1700237, 2018.
+[18] A. Rizzo, U. Dave, A. Novick, A. Freitas, S. P. Roberts, A. James,
+M. Lipson, and K. Bergman, “Fabrication-robust silicon photonic
+devices in standard sub-micron silicon-on-insulator processes,” Opt.
+Lett., vol. 48, no. 2, pp. 215–218, Jan 2023. [Online]. Available:
+https://opg.optica.org/ol/abstract.cfm?URI=ol-48-2-215
+[19] Y. Wang, P. Sun, J. Hulme, M. A. Seyedi, M. Fiorentino, R. G.
+Beausoleil, and K.-T. Cheng, “Energy efficiency and yield optimization
+for optical interconnects via transceiver grouping,” J. Lightwave
+Technol., vol. 39, no. 6, pp. 1567–1578, Mar 2021. [Online]. Available:
+http://opg.optica.org/jlt/abstract.cfm?URI=jlt-39-6-1567
+[20] A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis,
+H. Thacker, I. Shubin, Y. Luo, K. Raj et al., “Exploiting cmos man-
+ufacturing to reduce tuning requirements for resonant optical devices,”
+IEEE Photonics Journal, vol. 3, no. 3, pp. 567–579, 2011.
+[21] N. Margalit, C. Xiang, S. M. Bowers, A. Bjorlin, R. Blum, and J. E.
+Bowers, “Perspective on the future of silicon photonics and electronics,”
+Applied Physics Letters, vol. 118, no. 22, p. 220501, 2021.
+[22] Y. Wang, S. Wang, A. Novick, A. James, R. Parsons, A. Rizzo, and
+K. Bergman, “Dispersion-engineered and fabrication-robust soi waveg-
+uides for ultra-broadband dwdm,” in 2023 Optical Fiber Communica-
+tions Conference and Exhibition (OFC) [To appear], 2023, pp. 1–3.
+[23] R. Woltjer, L. Tiemeijer, and D. Klaassen, “An industrial view on
+compact modeling,” in 2006 European Solid-State Device Research
+Conference.
+IEEE, 2006, pp. 41–48.
+[24] N. Moezi, “Statistical compact model strategies for nano cmos transis-
+tors subject of atomic scale variability,” Ph.D. dissertation, University
+of Glasgow, 2012.
+[25] Y. Xing, J. Dong, S. Dwivedi, U. Khan, and W. Bogaerts, “Accurate
+extraction of fabricated geometry using optical measurement,” Photonics
+Research, vol. 6, no. 11, pp. 1008–1020, 2018.
+[26] Z. Lu, J. Jhoja, J. Klein, X. Wang, A. Liu, J. Flueckiger, J. Pond, and
+L. Chrostowski, “Performance prediction for silicon photonics integrated
+circuits with layout-dependent correlated manufacturing variability,”
+Optics express, vol. 25, no. 9, pp. 9712–9733, 2017.
+[27] W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics
+manufacturing,” Optics express, vol. 18, no. 23, pp. 23 598–23 607, 2010.
+[28] Z. Zhang, S. I. El-Henawy, C. R´ıos, and D. S. Boning, “Inference of
+process variations in silicon photonics from characterization measure-
+ments,” in CLEO: Science and Innovations.
+Optica Publishing Group,
+2022, pp. SF3O–5.
+[29] T. H. Stievater, N. F. Tyndall, M. W. Pruessner, D. A. Kozak, and W. S.
+Rabinovich, “Optical and geometric parameter extraction for photonic
+integrated circuits,” Optics Express, vol. 30, no. 9, pp. 14 453–14 460,
+2022.
+[30] M. J. Shawon and V. Saxena, “Rapid simulation of photonic integrated
+circuits using verilog-a compact models,” IEEE Transactions on Circuits
+and Systems I: Regular Papers, vol. 67, no. 10, pp. 3331–3341, 2020.
+[31] Z. Zhang, R. Wu, Y. Wang, C. Zhang, E. J. Stanton, C. L. Schow, K.-
+T. Cheng, and J. E. Bowers, “Compact modeling for silicon photonic
+heterogeneously integrated circuits,” Journal of Lightwave Technology,
+vol. 35, no. 14, pp. 2973–2980, 2017.
+[32] C. Sorace-Agaskar, J. Leu, M. R. Watts, and V. Stojanovic, “Electro-
+optical co-simulation for integrated cmos photonic circuits with ver-
+iloga,” Optics express, vol. 23, no. 21, pp. 27 180–27 203, 2015.
+[33] B. E. Saleh and M. C. Teich, Fundamentals of photonics.
+John Wiley
+& Sons, 2019.
+[34] A. James, Y. Wang, A. Rizzo, and K. Bergman, “Flexible, process-aware
+compact model of effective index in silicon waveguides for commercial
+foundries,” in 2022 International Conference on Numerical Simulation
+of Optoelectronic Devices (NUSOD).
+IEEE, 2022, pp. 173–174.
+[35] A. E. James, A. Wang, S. Wang, and K. Bergman, “Evaluating
+regression-based techniques for modelling fabrication variations in sili-
+con photonic waveguides,” in Applications of Machine Learning 2021,
+vol. 11843.
+International Society for Optics and Photonics, 2021, p.
+1184305.
+[36] M. J. Heck, J. F. Bauters, M. L. Davenport, D. T. Spencer, and J. E.
+Bowers, “Ultra-low loss waveguide platform and its integration with
+silicon photonics,” Laser & Photonics Reviews, vol. 8, no. 5, pp. 667–
+686, 2014.
+[37] D. Melati, A. Melloni, and F. Morichetti, “Real photonic waveguides:
+guiding light through imperfections,” Advances in Optics and Photonics,
+vol. 6, no. 2, pp. 156–224, 2014.
+[38] J. Lacey and F. Payne, “Radiation loss from planar waveguides with
+random wall imperfections,” IEE Proceedings J-Optoelectronics, vol.
+137, no. 4, pp. 282–288, 1990.
+[39] F. Payne and J. Lacey, “A theoretical analysis of scattering loss from
+planar optical waveguides,” Optical and Quantum Electronics, vol. 26,
+no. 10, pp. 977–986, 1994.
+[40] E. Jaberansary, T. M. B. Masaud, M. Milosevic, M. Nedeljkovic, G. Z.
+Mashanovich, and H. M. Chong, “Scattering loss estimation using
+2-d fourier analysis and modeling of sidewall roughness on optical
+waveguides,” IEEE Photonics Journal, vol. 5, no. 3, pp. 6 601 010–
+6 601 010, 2013.
+[41] S. Kawakami, “Relation between dispersion and power-flow distribution
+in a dielectric waveguide,” JOSA, vol. 65, no. 1, pp. 41–45, 1975.
+[42] N. Y. Winnie, J. Michel, L. C. Kimerling, and L. Eldada, “Polymer-
+cladded athermal high-index-contrast waveguides,” in Optoelectronic
+Integrated Circuits X, vol. 6897.
+International Society for Optics and
+Photonics, 2008, p. 68970S.
+[43] P. Jean, A. Douaud, T. Thibault, S. LaRochelle, Y. Messaddeq, and
+W. Shi, “Sulfur-rich chalcogenide claddings for athermal and high-q
+silicon microring resonators,” Optical Materials Express, vol. 11, no. 3,
+pp. 913–925, 2021.
+[44] H. Zhang, J. Chen, J. Jin, J. Lin, L. Zhao, Z. Bi, A. Huang, and Z. Xiao,
+“On-chip modulation for rotating sensing of gyroscope based on ring
+resonator coupled with mach-zehnder interferometer,” Scientific reports,
+vol. 6, no. 1, pp. 1–9, 2016.
+[45] Z. Zhou, B. Yin, Q. Deng, X. Li, and J. Cui, “Lowering the energy con-
+sumption in silicon photonic devices and systems,” Photonics Research,
+vol. 3, no. 5, pp. B28–B46, 2015.
+[46] A. Yariv and P. Yeh, Photonics: optical electronics in modern commu-
+nications.
+Oxford university press, 2007.
+[47] E. D. Palik, Handbook of optical constants of solids.
+Academic press,
+1998, vol. 3.
+[48] B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent
+refractive index of silicon and germanium,” in SPIE Proceedings,
+E. Atad-Ettedgui, J. Antebi, and D. Lemke, Eds.
+SPIE, jun 2006.
+[Online]. Available: https://doi.org/10.1117%2F12.672850
+[49] A. W. Elshaari, I. E. Zadeh, K. D. J¨ons, and V. Zwiller, “Thermo-
+optic characterization of silicon nitride resonators for cryogenic photonic
+circuits,” IEEE Photonics Journal, vol. 8, no. 3, pp. 1–9, 2016.
+[50] D. Coenen, H. Oprins, Y. Ban, F. Ferraro, M. Pantouvaki, J. Van Camp-
+enhout, and I. De Wolf, “Thermal modelling of silicon photonic ring
+modulator with substrate undercut,” Journal of Lightwave Technology,
+2022.
+
+14
+[51] M. Jacques, A. Samani, E. El-Fiky, D. Patel, Z. Xing, and D. V. Plant,
+“Optimization of thermo-optic phase-shifter design and mitigation of
+thermal crosstalk on the soi platform,” Optics express, vol. 27, no. 8,
+pp. 10 456–10 471, 2019.
+[52] M. de Cea, A. H. Atabaki, and R. J. Ram, “Power handling of
+silicon microring modulators,” Opt. Express, vol. 27, no. 17, pp.
+24 274–24 285, Aug 2019. [Online]. Available: https://opg.optica.org/
+oe/abstract.cfm?URI=oe-27-17-24274
+[53] C. Oton, C. Manganelli, F. Bontempi, M. Fournier, D. Fowler, and
+C. Kopp, “Silicon photonic waveguide metrology using mach-zehnder
+interferometers,” Optics express, vol. 24, no. 6, pp. 6265–6270, 2016.
+[54] Q. Deng, L. Liu, X. Li, J. Michel, and Z. Zhou, “Linear-regression-
+based approach for loss extraction from ring resonators,” Opt. Lett.,
+vol. 41, no. 20, pp. 4747–4750, Oct 2016. [Online]. Available:
+http://opg.optica.org/ol/abstract.cfm?URI=ol-41-20-4747
+[55] W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Ku-
+mar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and
+R. Baets, “Silicon microring resonators,” Laser & Photonics Reviews,
+vol. 6, no. 1, pp. 47–73, 2012.
+[56] W. N. Ye, D.-X. Xu, S. Janz, P. Cheben, M.-J. Picard, B. Lamontagne,
+and N. G. Tarr, “Birefringence control using stress engineering in
+silicon-on-insulator (soi) waveguides,” Journal of Lightwave Technology,
+vol. 23, no. 3, pp. 1308–1318, 2005.
+[57] H. Abdi and L. J. Williams, “Principal component analysis,” Wiley
+interdisciplinary reviews: computational statistics, vol. 2, no. 4, pp. 433–
+459, 2010.
+[58] S. Singer and J. Nelder, “Nelder-mead algorithm,” Scholarpedia, vol. 4,
+no. 7, p. 2928, 2009.
+[59] E. Kononov, “Modeling photonic links in verilog-a,” Ph.D. dissertation,
+Massachusetts Institute of Technology, 2013.
+[60] J. C. Leu, “Integrated silicon photonic circuit simulation,” Ph.D. disser-
+tation, Massachusetts Institute of Technology, 2018.
+[61] Y. Xing, M. Wang, A. Ruocco, J. Geessels, U. Khan, and W. Bogaerts,
+“Compact silicon photonics circuit to extract multiple parameters
+for process control monitoring,” OSA Continuum, vol. 3, no. 2, pp.
+379–390, Feb 2020. [Online]. Available: https://opg.optica.org/osac/
+abstract.cfm?URI=osac-3-2-379
+[62] D. S. Boning, S. I. El-Henawy, and Z. Zhang, “Variation-aware methods
+and models for silicon photonic design-for-manufacturability,” Journal
+of Lightwave Technology, vol. 40, no. 6, pp. 1776–1783, 2022.
+Aneek James received his B.S. in Electrical and Electronics Engineering from
+the University of Georgia, Athens, GA in 2017 and his M.S., and M.Phil., in
+Electrical Engineering from Columbia University, New York, NY in 2019
+and 2021, respectively. He is working as a Ph.D. candidate in Electrical
+Engineering in the Lightwave Research Laboratory under Professor Keren
+Bergman. His research interests include modeling fabrication variations in
+silicon photonic devices, as well as the testing and automated control of silicon
+photonic systems for high-throughput optical interconnects.
+Anthony Rizzo received his B.S. in Physics from Haverford College,
+Haverford, PA in 2017 and his M.S., M.Phil., and Ph.D., all in Electrical
+Engineering, from Columbia University, New York, NY in 2019, 2021, and
+2022, respectively. He completed his doctoral research in the Lightwave
+Research Laboratory at Columbia University under Professor Keren Bergman,
+where he led the first demonstration of data transmission using an integrated
+Kerr frequency comb source and silicon photonic transmitter. He is currently a
+Research Scientist at the Air Force Research Laboratory (AFRL) Information
+Directorate in Rome, NY, with a focus in large-scale silicon photonic systems
+for quantum information processing and artificial intelligence.
+Yuyang Wang received the B.Eng. degree in electronic engineering from
+Tsinghua University, Beijing, China in 2015, and the M.S. and PhD degrees
+in computer engineering from the University of California, Santa Barbara
+(UCSB), CA, USA, in 2018 and 2021 respectively. He is currently a post-
+doctoral researcher in the Lightwave Research Laboratory under Professor
+Keren Bergman. He was a Design Engineering Intern at Cadence Design
+Systems in 2018 and a Visiting Intern at the Hong Kong University of
+Science and Technology in 2019. His research interests include variation-
+aware modeling, design, and optimization of silicon photonic interconnects
+and systems.
+Asher Novick received his M.Eng. and B.S. degrees in Electrical and
+Computer Engineering from Cornell University, Ithaca, NY, USA, in 2016 and
+2015,respectively. Between 2016 and 2019, he was at Panduit’s Fiber Research
+Lab, where he researched and developed new patentable technologies for
+optical fiber-based communication in data center and enterprise applications.
+He is currently working toward his Ph.D. degree in Electrical Engineering
+in the Lightwave Research Laboratory at Columbia University in the City
+of New York. His current research interest is in the modeling, design, and
+testing of silicon photonic systems and devices for scalable and efficient link
+architectures.
+Songli Wang received his B.Eng. in Optoelectronic Information Science and
+Engineering from Harbin Institute of Technology, Harbin, China, in 2019
+and his M.S. in Electrical Engineering from Columbia University, New York,
+NY in 2020. He is currently working towards the Ph.D. degree in Electrical
+Engineering in the Lightwave Research Laboratory at Columbia University.
+His current research interests include modeling, design and testing of silicon
+photonic devices and systems.
+Robert Parsons received the B.S. degree in biomedical engineering from
+George Washington University, Washington, D.C., USA, and the M.S. degree
+in electrical engineering from Columbia University, New York, NY, USA, in
+2020 and 2022, respectively. He is currently working toward the Ph.D. degree
+in electrical engineering with the Lightwave Research Laboratory, Columbia
+University under Professor Keren Bergman. His research interests include the
+modeling, testing, and co-optimization of link architectures and constituent
+silicon photonic devices for high-bandwidth, energy-efficient optical inter-
+connects.
+Kaylx Jang received his B.S. in Electrical Engineering from the University
+of California, Irvine, CA in 2020 and his M.S. in Electrical Engineering from
+Columbia University in 2022. In 2019 and 2020, he interned in the testing
+department at Ayar Labs and in 2021 did a co-op in the Silicon Photonics
+Design team at Nokia (former Elenion). He is working as a Ph.D. student
+in Electrical Engineering in the Lightwave Research Lab under Professor
+Keren Bergman. His research interests include modeling, design, and testing
+of high-performance silicon photonic devices for energy efficient and scalable
+link architectures.
+Maarten Hattink is a graduate student with Columbia University, New
+York, NY, USA. He received the B.S. and M.S. degrees from the Eindhoven
+University of Technology, The Netherlands, in 2015 and 2017, respectively.
+While pursuing these degrees, he worked at Prodrive Technologies B.V. as
+a Software and FPGA Engineer. He is currently working toward the Ph.D.
+degree and his research interest lies in photonic device integration and thermal
+control.
+
+15
+Keren Bergman (S’87–M’93–SM’07–F’09) received the B.S. degree from
+Bucknell University, Lewisburg, PA, in 1988, and the M.S. and Ph.D. degrees
+from the Massachusetts Institute of Technology, Cambridge, in 1991 and
+1994, respectively, all in electrical engineering. Dr. Bergman is currently a
+Charles Batchelor Professor at Columbia University, New York, NY, where she
+also directs the Lightwave Research Laboratory. She leads multiple research
+programs on optical interconnection networks for advanced computing sys-
+tems, data centers, optical packet switched routers, and chip multiprocessor
+nanophotonic networks-on-chip. Dr. Bergman is a Fellow of the IEEE and
+Optica.
+

5NAzT4oBgHgl3EQfu_1f/content/tmp_files/2301.01699v1.pdf.txt

@@ -0,0 +1,1534 @@
+Received:
+Added at production
+Revised:
+Added at production
+Accepted:
+Added at production
+DOI: xxx/xxxx
+RESEARCH ARTICLE
+Data-driven modelling of turbine wake interactions and flow
+resistance in large wind farms
+Andrew Kirby*1 | François-Xavier Briol2 | Thomas D. Dunstan3 | Takafumi Nishino1
+1Department of Engineering Science,
+University of Oxford, Oxford, UK
+2Department of Statistical Science,
+University College London, London, UK
+3Informatics Lab, UK MetOffice, Exeter,
+UK
+Correspondence
+*Andrew Kirby, Department of
+Engineering Science, University of
+Oxford, Oxford, OX1 3PJ, UK. Email:
+[email protected]
+Abstract
+Turbine wake and local blockage effects are known to alter wind farm power production in
+two different ways: (1) by changing the wind speed locally in front of each turbine; and (2)
+by changing the overall flow resistance in the farm and thus the so-called farm blockage
+effect. To better predict these effects with low computational costs, we develop data-driven
+emulators of the ‘local’ or ‘internal’ turbine thrust coefficient C∗
+T as a function of turbine
+layout. We train the model using a multi-fidelity Gaussian Process (GP) regression with a
+combination of low (engineering wake model) and high-fidelity (Large-Eddy Simulations)
+simulations of farms with different layouts and wind directions. A large set of low-fidelity
+data speeds up the learning process and the high-fidelity data ensures a high accuracy. The
+trained multi-fidelity GP model is shown to give more accurate predictions of C∗
+T compared
+to a standard (single-fidelity) GP regression applied only to a limited set of high-fidelity
+data. We also use the multi-fidelity GP model of C∗
+T with the two-scale momentum theory
+(Nishino & Dunstan 2020, J. Fluid Mech. 894, A2) to demonstrate that the model can be
+used to give fast and accurate predictions of large wind farm performance under various
+mesoscale atmospheric conditions. This new approach could be beneficial for improving
+annual energy production (AEP) calculations and farm optimisation in the future.
+KEYWORDS:
+Class file; LATEX 2ε; Wiley NJD
+1
+INTRODUCTION
+The installed capacity of wind energy is projected to increase rapidly in the next decades. A major challenge in the optimisation
+of wind farm design is the accurate prediction of wind farm performance 1. Existing wind farm models struggle to make accurate
+predictions of wind farm power production. This is partly because the ‘global blockage effect’ reduces the velocity upstream of large
+farms and hence the energy yield 2. It remains unclear how global blockage should be modelled and this is the subject of a large-scale
+field campaign 3.
+Wind farms are typically modelled using engineering ‘wake’ models. These models predict the velocity deficit in the wakes behind
+turbines 4 5. To account for interactions between multiple turbines, the wake velocity deficits are superposed 6,7. Simple wake models
+can give predictions of wind farm performance with very low computational cost ( 10−3 CPU hours per simulation 1). However, wake
+arXiv:2301.01699v1  [physics.flu-dyn]  4 Jan 2023
+
+2
+KIRBY et al
+models do not account for the response of the atmospheric boundary layer (ABL) to the wind farm which is likely to be important
+for large wind farms 8. It has been found that wake models compare poorly to Large-Eddy Simulations (LES) of large wind farms 9.
+Wind farms are also modelled in numerical weather prediction (NWP) models using farm parameterisation schemes. In these pa-
+rameterisations, farms are often modelled as a momentum sink and a source of turbulent kinetic energy 10. Turbine-wake interactions
+cannot be adequately predicted using these schemes. A new scheme was proposed 11 which uses a correction factor to model turbine
+interactions. More recently, data-driven approaches have been proposed 12 to model these effects in wind farm parameterisations.
+Data-driven modelling of wind farm flows is a promising new approach 13. Data from high-fidelity simulations with complex flow
+physics can be used to make predictions with low computational cost. Recent studies have applied machine learning techniques
+to data from a single turbine or from an existing wind farm. The data for these studies are from measurements 14,15,16,17, LES 18 or
+Reynolds-Averaged Navier-Stokes (RANS) simulations 19,20,21. A limitation of these approaches is that they are not generalisable to
+different turbine layouts unless they rely on wake superposition techniques to model farm flows. Another approach is modelling
+the effect of turbine layout using geometric parameters 17 or using the layout as a graph input to a neural network 22,23. However,
+these alternative approaches may struggle to fully capture the complex two-way interaction with the ABL as it seems impractical to
+prepare a data set that covers the entire range of scales involved in wind farm flows 1.
+The problem of modelling wind farm flows can be split into ‘internal’ turbine-scale and ‘external’ farm-scale problems 24. The
+‘internal’ problem is to determine a ‘local’ or ‘internal’ turbine thrust coefficient, C∗
+T , which represents the flow resistance inside a
+wind farm, i.e., how the turbine thrust changes with wind speed within the farm. Nishino 25 proposed an analytical model for an upper
+limit of C∗
+T by using an analogy to the classic Betz analysis. This analytical model is a function of turbine-scale induction factor but
+is independent of turbine layout and wind direction. Previous studies 24 25 8 showed that C∗
+T is usually lower than the limit predicted
+by Nishino’s model and can vary significantly with turbine layout due to wake and turbine blockage effects.
+The aim of this study is to develop statistical emulators of C∗
+T as a function of turbine layout and wind direction. The novelty of
+this approach is that we are modelling the effect of turbine-wake interactions on C∗
+T rather than turbine power. Both turbine-scale
+flows (e.g., wake effects) and farm-scale flows (e.g. farm blockage and mesoscale atmospheric response) affect turbine power within
+a farm. Therefore to create an emulator of turbine power, either (1) a very large set of expensive data such as finite-size wind farm
+LES is needed which covers a range of large-scale atmospheric conditions or (2) the model would not be generalisable to different
+mesoscale atmospheric responses. An emulator of C∗
+T is however applicable to different atmospheric responses modelled separately,
+following the concept of the two-scale momentum theory 24 8.
+In section 2 we give the definitions of key wind farm parameters in the two-scale momentum theory 24. Section 3 summarises
+the methodology of the LES and wake model simulations, followed by the machine learning approaches to develop the emulators
+in section 4. In section 5 we present the results from the trained emulators. These results are discussed in section 6 and concluding
+remarks are given in section 7.
+2
+TWO-SCALE MOMENTUM THEORY
+By considering the conservation of momentum for a control volume with and without a large wind farm over the land or sea surface,
+the following non-dimensional farm momentum (NDFM) equation can be derived 24,
+C∗
+T
+λ
+Cf0
+β2 + βγ = M
+(1)
+where β is the farm wind-speed reduction factor defined as β ≡ UF /UF 0 (with UF defined as the average wind speed in the nominal
+wind farm-layer of height HF , and UF 0 is the farm-layer-averaged speed without the wind farm present); λ is the array density
+defined as λ ≡ nA/SF (where n is the number of turbines in the farm, A is the rotor swept area and SF is the farm footprint area);
+
+KIRBY et al
+3
+C∗
+T is the internal turbine thrust coefficient defined as C∗
+T ≡ �n
+i=1 Ti/ 1
+2 ρU2
+F nA (where Ti is thrust of turbine i in the farm and ρ
+is the air density); Cf0 is the natural friction coefficient of the surface defined as Cf0 ≡ ⟨τw0⟩/ 1
+2 ρU2
+F 0 (where τw0 is the bottom
+shear stress without the farm present); γ is the bottom friction exponent defined as γ ≡ logβ(⟨τw⟩/τw0) (where ⟨τw⟩ is the bottom
+shear stress averaged across the farm); M is the momentum availability factor defined as,
+M =
+Momentum supplied by the atmosphere to the farm site with turbines
+Momentum supplied by the atmosphere to the farm site without turbines.
+(2)
+noting that this includes pressure gradient forcing, Coriolis force, net injection of streamwise momentum through top and side
+boundaries and time-dependent changes in streamwise velocity 24. The height of the farm-layer, HF , is used to define the reference
+velocities UF and UF 0. Equation 1 is valid so long as the same of HF is used for both the internal and external problem. HF is typically
+between 2Hhub and 3Hhub 8 (where Hhub is the turbine hub-height) and in this study we use a fixed definition of HF = 2.5Hhub.
+Patel 26 used an NWP model to demonstrate that, for most cases, M varied almost linearly with β (for a realistic range of β
+between 0.8 and 1). Therefore, M can be approximated by
+M = 1 + ζ(1 − β)
+(3)
+where ζ is the ‘momentum response’ factor or ‘wind extractability’ factor. Patel 26 found ζ to be time-dependent and vary between
+5 and 25 for a typical offshore site (note that ζ = 0 corresponds to the case where momentum available to the farm site is assumed
+to be fixed, i.e., M = 1).
+Nishino 25 proposed an analytical model for C∗
+T given by,
+C∗
+T = 4α(1 − α) =
+16C′
+T
+(4 + C′
+T )2
+(4)
+where α is the turbine-scale wind speed reduction factor defined as α ≡ UT /UF (UT is the streamwise velocity averaged over the
+rotor swept area) and C′
+T ≡ T/ 1
+2 ρU2
+T A is a turbine resistance coefficient describing the turbine operating conditions.
+For a given farm configuration at a farm site (i.e., for given set of C∗
+T , λ, Cf0, γ and ζ) the farm wind-speed reduction factor β
+can be calculated using equation 1. The (farm-averaged) power coefficient Cp is defined as Cp ≡ ���n
+i=1 Pi/ 1
+2 ρU3
+F 0nA (Pi is power
+of turbine i in the farm). Using the calculated value of β, Cp can be calculated by using the expression,
+Cp = β3C∗
+p
+(5)
+where C∗
+p is the (farm-averaged) ‘local’ or ‘internal’ turbine power coefficient defined as C∗
+p ≡ �n
+i=1 Pi/ 1
+2 ρU3
+F nA.
+3
+WIND FARM SIMULATIONS
+In this study we model wind farms as arrays of actuator discs (or aerodynamically ideal turbines operating below the rated wind
+speed). This is because, in real wind farms, the effects of turbine wake interactions on the farm performance are most significant
+when they operate below the rated wind speed. The ‘internal’ thrust coefficient C∗
+T is an important wind farm parameter which
+includes the effect of turbine interactions (including both wake and local blockage effects). In this study we will be modelling the
+effect of turbine layout on C∗
+T for aligned turbine layouts with various wind directions and a fixed turbine resistance of C′
+T = 1.33.
+We chose C′
+T = 1.33 because it leads to a turbine induction factor of 1/4 which is close to a typical value for modern large wind
+turbines. As such we will be considering
+C∗
+T = f(Sx, Sy, θ)
+(6)
+
+4
+KIRBY et al
+Figure 1 Design of numerical experiments: a) input parameters, b) maximin design of LES.
+where Sx is the turbine spacing in the x direction, Sy is the turbine spacing in the y direction and θ is the wind direction relative
+to the x direction (see figure 1a). However the true function C∗
+T cannot be easily evaluated so we will instead investigate C∗
+T using
+computer codes. One computer code we will use is LES (see section 3.1) to estimate C∗
+T
+C∗
+T,LES = fLES(Sx, Sy, θ).
+(7)
+We assume that the function fLES is close to the true function f because of the accuracy of LES to model wind farm flows. We will
+also use a wake model (see section 3.2) to provide cheap approximations of C∗
+T according to
+C∗
+T,wake = fwake(Sx, Sy, θ).
+(8)
+Engineering problems are often investigated using complex computer models. Evaluating the output of such computer models
+for a given input can be very computationally expensive. Therefore a common objective is to create a cheap statistical model of
+the expensive computer model; this is commonly known as emulation of computer models 27 28. In this study we aim to develop a
+statistical emulator which can cheaply emulate fLES.
+The emulators will only be valid for aligned layouts of wind turbines and for a given turbine resistance (here we use C′
+T = 1.33).
+We consider the input parameters for a realistic range of turbine spacings 1: Sx ∈ [5D, 10D], Sy ∈ [5D, 10D] and θ ∈ [0o, 45o]
+where D is the diameter of the turbine rotor swept area. In this study D is set as 100m and the turbine hub height is also 100m. We
+only need to consider wind directions of θ ∈ [0o, 45o] because of symmetry in the aligned turbine layouts. If θ is negative than the
+turbine layout given by (Sx, Sy, θ) is exactly the same as (Sx, Sy, −θ). When θ > 45o, then (Sx, Sy, θ) and (Sy, Sx, 90o − θ) give
+identical layouts.
+In this study we build several emulators to predict fLES. The models are trained using data from low-fidelity (wake model)
+and high fidelity (LES) wind farm simulations. One evaluation of C∗
+T,wake takes approximately 130 seconds on a single CPU and
+C∗
+T,LES requires around 400 CPU hours on a supercomputer. We use a space filling maximin design 29 30 to select training points
+in the parameter space. The maximin algorithm selects points which maximises the minimum distance to other points and to the
+boundaries. This provides a good coverage of the domain which ensures that the emulators can give good predictions across the
+whole of the domain 31. Figure 1b shows the LES training points in the parameter space.
+
+b)
+a)
+10
+40
+9
+Wind
+30
+200
+10
+5
+0
+6
+8
+10
+S/DKIRBY et al
+5
+Figure 2 LES a) instantaneous and b) time-averaged flow fields over a periodic turbine array (Sx/D = 7.59, Sy/D = 5.47 and
+θ = 37.6o).
+3.1
+Large-Eddy Simulations
+This study uses the data from 50 high-fidelity (LES) simulations of wind farms published in a previous study 8. Here we give a brief
+summary of the LES methodology. The LES models a neutrally stratified atmospheric boundary layer over a periodic array of actuator
+discs, which face the wind direction θ and exert uniform thrust. The resolution is 24.5m in the horizontal directions (4 points across
+the rotor diameter) and 7.87m in the vertical. This is a coarse horizontal resolution; however using a correction factor for the turbine
+thrust 32 makes the C∗
+T,LES values insensitive to horizontal resolution 8. For all simulations the vertical domain size was fixed at
+1km and the horizontal extent varied with turbine layout but was at least 3.14km. The horizontal boundary conditions were periodic
+(essentially an infinitely-large wind farm). The bottom boundary used a no-slip condition with the value of eddy viscosity specified
+following the Monin-Obukhov similarity theory for a surface roughness length of z0 = 1 × 10−4m. The top boundary had a slip
+condition with zero vertical velocity. The flow was driven by a pressure gradient forcing which was constant and in the direction θ
+throughout the domain. Figure 2 shows the instantaneous and time-averaged hub height velocities from one wind farm LES. See the
+original paper 8 for further details of the LES.
+3.2
+Wake model simulations
+Wake models are a cheap low-fidelity approach to modelling wind farm aerodynamics compared to expensive high-fidelity LES
+simulations 1. We use the wake model proposed by Niayafar and Porté-Agel 33 to evaluate C∗
+T,wake as a cheap approximation of C∗
+T .
+We use the Python package PyWake 34 to implement the wake model. The turbine thrust coefficient CT is needed as an input for
+the wake model. We use the value of C∗
+T predicted by equation 4 as the value of CT . For the turbine operating conditions used in
+this study (C′
+T = 1.33) the wake model has CT equal to 0.75 for all turbines. To model actuator discs, we consider a hypothetical
+turbine which has a constant CT for all wind speeds. We calculate C∗
+T,wake for a single turbine at the back of a large farm (marked X
+in figure 3). The farm simulated using the wake model is 10km long in the streamwise direction and 4km long in the cross-streamwise
+direction. The farm size was chosen so that C∗
+T no longer varied with increasing farm size. The wake growth parameter is calculated
+using k∗ = 0.38I +0.004 where I is the local streamwise turbulence velocity. The local streamwise turbulence intensity is estimated
+using the model proposed by Crespo and Hernández 35. The background turbulence intensity (TI) is set as a typical value of 10%.
+The velocity incident to the turbine is calculated by averaging the velocity across the disc area. We use a 4×3 cartesian grid with
+Gaussian quadrature coordinates and weights on the disc to average the velocity. The disc-averaged velocity, UT is then calculated
+by multiplying the averaged incident velocity by (1 − a) where a is the turbine induction factor set by the value of C′
+T (using the
+expression a = C′
+T /(4 + C′
+T )). To calculate the farm-average velocity, UF , we average the velocity across a volume around the
+
+b)
+a)
+0.4
+30
+30
+0.3
+20
+20
+D
+D
+n/n
+9
+9
+0.2
+10
+10
+0.1
+0
+0
+20
+0
+20
+c/ D
+c/ D6
+KIRBY et al
+Figure 3 Example of wind farm layout for wake model simulations.
+single turbine. The volume has dimensions of Sy in the y direction, Sx in the x direction and 250m in the z direction (the height of
+the nominal farm layer used in the previous LES study 8). To calculate the average velocity, we discretise the volume into 200 points
+in the horizontal directions and 20 points in the vertical. This was sufficient for the calculation of C∗
+T,wake to not vary with further
+discretisation. Figure 3 shows an example of the farm layout for the wake model simulations.
+4
+MACHINE LEARNING METHODOLOGY
+4.1
+Gaussian Process regression
+We will use Gaussian process (GP) regression 36 to build statistical emulators of fLES. A Gaussian process is a stochastic process
+g ∼ GP(m, k) described by a mean function m(v) = E[g(v)] and a covariance function k(v, v′) = E[(g(v) − m(v))(g(v′) − m(v′)].
+In our case v = (Sx, Sy, θ). We will use such a stochastic process as a model of fLES, the true mapping from v to C∗
+T,LES. Each
+realisation from this process will therefore be a function which could plausibly represent this mapping. The mean function represents
+the expected output value at an input v = (Sx, Sy, θ). The covariance function gives the covariance between output values at v and
+v′. Examples of covariance functions include squared exponential, rational quadratic and periodic functions 36. Different covariance
+functions will give differently shaped GPs. For example the squared exponential covariance function will give very smooth GPs
+whereas the periodic function will give GPs with a periodic structure. Other types of structure, for example symmetry, can also be
+encoded in the covariance function. Therefore the expected shape (for example smoothness) of the expected relationship and any
+properties (for example discontinuities or symmetries) need to be considered when choosing a covariance function for GP regression.
+Let V = (v1, ..., vn)T be a collection of design points then mV = (m(v1), ..., m(vn))T is the mean vector and kV V = (k(vi, vj))
+is the covariance matrix. We will start by positing a GP model with mean m and covariance k (called the ‘prior GP’), then condition
+this GP on LES observations; the outcome is a new GP (called the ‘posterior GP’). This gives the posterior distribution g|V, C∗
+T,LES ∼
+GP(mσ2, kσ2). mσ2 is the posterior mean function given by mσ2(v) = m(v) + kvV (kV V + σ2In×n)−1(C∗
+T,LES − mV ) where
+kvV = (k(v, v1), ..., k(v, vn)) and In×n is the identity matrix of size n. The posterior mean function mσ2 is used to make predictions
+at v = (Sx, Sy, θ). The posterior covariance function kσ2 quantifies the uncertainty in our prediction at v = (Sx, Sy, θ). The
+posterior covariance function is given by kσ2(v, v′) = k(v, v′) − kvV (kV V + σ2In×n)−1kV v′.
+Often in GP regression a zero prior mean is used. However, using an informative prior mean can improve the accuracy of the
+trained model. By using a prior mean, many of the trends in fLES can be incorporated into our model prior to making expensive
+
+Volume for
+UF calculation
+10 km
+X
+WindKIRBY et al
+7
+Figure 4 Demonstration of basic GP regression: a) shows the prior mean and covariance function prior to fitting with 3 GPs drawn
+from the distribution shown in colour; b) shows the effect of decreasing the lengthscale hyperparameter; c) the effect of variance
+hyperparameter; and d) the posterior mean and covariance functions.
+evaluations of C∗
+T,LES. Therefore, after training our model will likely better describe the true relationship between Sx, Sy, θ and
+fLES. In this study, we will use both C∗
+T,wake and the analytical model of C∗
+T as the prior mean for the standard GP regression. For
+the wake model prior mean we also vary the specified ambient TI input parameter.
+We expect fLES to be a smooth function of input variables Sx, Sy and θ, and to vary more rapidly with θ than Sx or Sy. Therefore
+we will use an anisotropic squared-exponential covariance function,
+k(v, v′) = σ2
+f exp
+�
+− (Sx − S′
+x)2
+2l2
+1
+�
+exp
+�
+−
+(Sy − S′
+y)2
+2l2
+2
+�
+exp
+�
+− (θ − θ′)2
+2l2
+3
+�
+(9)
+where σ2
+f > 0 is the signal variance hyperparameter and li > 0 is the lengthscale hyperparameter for each dimension. This is also
+called an ARD (automatic relevance detection) kernel. If we consider v = v′ then we can see that σ2
+f determines the variance of g(v).
+Therefore σ2
+f determines the prior uncertainty the model has about the value of g(v). As the lengthscale hyperparameter li gets
+smaller then k(v, v′) decreases (for v ̸= v′). Equally if li increases then k(v, v′) will also increase. A GP with a small li will therefore
+vary more rapidly across the parameter space in the ith dimension.
+Due to numerical issues associated with the matrix inversion/linear system solve operations in the formulae for the posterior GP,
+it is common to add a nugget σ2 > 0 to the kernel matrix. The hyperparameters σ2
+f and li are selected automatically during the
+fitting process by maximising the log marginal likelihood 36. This approach selects the model which maximises the fit to the data.
+Figure 4 shows the impact of the hyperparameters in an example GP regression setting (using the squared exponential covariance
+function). The mean function and 95% credible interval (+/-1.96 times the standard deviation) prior to fitting are shown in figure
+4a with 3 GPs drawn from the distribution (coloured lines). The effect of decreasing the lengthscale hyperparameter li is shown in
+figure 4b. The prior mean and 95% credible interval are unchanged however the example GPs drawn vary more rapidly because of
+the shorter lengthscale. Figure 4c shows the same setup as figure 4a but with a smaller value of σ2
+f. The example GPs still vary slowly
+but the magnitude of the variations is now smaller. Figure 4d shows the GPs conditioned on observations with hyperparameters
+selected by maximising the log marginal likelihood.
+
+a) α = 1.0, l = 1.0
+b) α² = 1.0, l = 0.5
+2
+2
+9
+0
+9
+0
+-2
+-2
+0
+2
+4
+6
+0
+2
+4
+6
+c) ² = 0.5, l = 1.0
+d)o
+= 1.41. = 1.57
+2
+2
+9
+0
+-2
+-2
+0
+6
+0
+2
+2
+4
+4
+6
+Observations
+Mean function
+95% credible interval8
+KIRBY et al
+Figure 5 Demonstration of a) basic GP regression and b) multi-fidelity GP regression. In this example f(x) = 1 + sin(6x) for the
+high-fidelity data and f(x) = −0.5 + 0.5sin(6x) for the low-fidelity data.
+4.2
+Non-linear multi-fidelity Gaussian Process regression
+In many applications there are several computational models available. These models can have varying accuracies and computational
+costs. The models which are more computationally expensive typically give more accurate predictions. The GP regression frame-
+work can be extended to combine information from low and high-fidelity models 37. This type of modelling uses the low-fidelity
+observations to speed up the learning process and the high-fidelity observations to ensure accuracy. In our scenario we will com-
+bine evaluations of from a low-fidelity (C∗
+T,wake) and a high-fidelity (C∗
+T,LES) model. Note that for the multi-fidelity models in this
+study we set the ambient TI to 10% for the wake model and use a zero prior mean. We will keep the number of high-fidelity training
+points fixed at 50 and we will vary the number of low-fidelity training points used.
+We combine information from our high and low-fidelity models using a nonlinear information fusion algorithm 38. The framework
+is based on the autoregressive multi-fidelity scheme given by:
+ghigh(v) = ρ(glow(v)) + δ(v)
+(10)
+where glow(v) is a model with a GP denoted fwake and ghigh(v) is a model with a GP denoted fLES. ρ is a model with a GP
+which maps the low-fidelity output to the high-fidelity output and δ(v) is a model with a GP which is a bias term. The non-linear
+multi-fidelity framework can learn non-linear space-dependent correlations between models of different accuracies. To reduce the
+computational cost and complexity of implementation the autoregressive scheme given by equation 10 is simplified. Firstly, the GP
+prior glow(v) is replaced by the GP posterior glow,∗(v) and secondly the GPs ρ and δ are assumed to be independent. Equation 10
+can then be summarised as
+ghigh(v) = hhigh(v, glow,∗(v))
+(11)
+where hhigh is a model with a GP which has both v and glow,∗(v) as inputs. More details of hhigh and the implementation of the
+multi-fidelity framework are given in Perdikaris et. al. 38.
+Figure 5 shows an example of how a multi-fidelity GP can outperform a standard GP regression. We implement the non-linear
+multi-fidelity framework using the ‘emukit’ package 39. We first maximise the log marginal likelihood whilst keeping the Gaussian
+noise variance fixed at a low value of 1 × 10−6. The fitting process is then repeated whilst allowing the Gaussian noise variance to
+be optimised too. This is to prevent a high noise local optima from being selected.
+
+a)
+b)
+3
+3
+High fidelity
+High fidelity
+2
+2
+1
+1
+9
+9
+0
+0
+-1
+-1
+Low fidelity
+2
+2
+-0.5
+0.0
+0.5
+-1.0
+1.0
+-1.0
+-0.5
+0.0
+0.5
+1.0
+True function
+Observations
+Posterior mean function
+95% credible intervalKIRBY et al
+9
+5
+RESULTS
+In this study, we build various statistical emulators of fLES using different techniques and compare the performance. A summary
+of the techniques is shown in the list below:
+1 Standard Gaussian Process regression (see section 4.1)
+a GP-analytical-prior: Gaussian Process using analytical model (equation 4) prior mean
+b GP-wake-TI10-prior: Gaussian Process using wake model (section 3.2) with ambient TI=10% prior mean
+c GP-wake-TI1-prior: Gaussian Process using wake model with ambient TI=1% prior mean
+d GP-wake-TI5-prior: Gaussian Process using wake model with ambient TI=5% prior mean
+e GP-wake-TI15-prior: Gaussian Process using wake model with ambient TI=15% prior mean
+2 Non-linear multi-fidelity Gaussian Process regression (see section 4.2)
+a MF-GP-nlow500: multi-fidelity Gaussian Process using 500 low-fidelity training points
+b MF-GP-nlow250: multi-fidelity Gaussian Process using 250 low-fidelity training points
+c MF-GP-nlow1000: multi-fidelity Gaussian Process using 1000 low-fidelity training points
+The code used to produce the results in this section is available open-access at the following GitHub repository: https://github.
+com/AndrewKirby2/ctstar_statistical_model.
+5.1
+Performance of standard GP regression
+We first assessed the accuracy of the standard GP models (section 4.1) by performing leave-one-out cross-validation (LOOCV). This
+is a method of estimating the accuracy of a statistical model when making predictions on data not used to train the model. We trained
+our model on 49 of the 50 training points and then calculated the prediction accuracy for the single high-fidelity data point which is
+excluded from the training set. This is then repeated for all data points in turn, and we took the average accuracy as an estimate of
+the model test accuracy. The standard GP models were implemented using the ‘GPy’ package 40.
+The standard GP gave accurate predictions of fLES with average errors of less than 2%. Table 1 shows the accuracy of the stan-
+dard GP models compared to the analytical and wake models. We calculated the errors by using the expression |mσ2 −C∗
+T,LES|/0.75
+where mσ2 is the posterior mean function of the emulator. The reference value for C∗
+T of 0.75 was chosen because this is the pre-
+diction from the analytical model. Both GP models give similar maximum errors of approximately 6%. Using the wake model as a prior
+mean gave a lower mean absolute error of 1.26%. The GP models reduced the average prediction error and significantly reduced
+the maximum error compared to the wake model and analytical model of C∗
+T .
+Table 1 Accuracy of models for C∗
+T prediction.
+Model
+MAE (%)
+Maximum error (%)
+GP-analytical-prior
+1.87
+6.09
+GP-wake-TI10-prior
+1.26
+6.11
+Analytical model
+5.26
+22.0
+Wake model (TI=10%)
+4.60
+9.28
+
+10
+KIRBY et al
+Figure 6 Posterior variance function of GP-wake-TI10-prior model.
+Figure 7 Sensitivity of fitted GP models to the ambient TI chosen for wake model prior means.
+The model GP-wake-TI10-prior has a high degree of confidence when making predictions in regions of the parameter space.
+Figure 6 shows the square root of the posterior covariance function kσ2, which quantities the uncertainty of the emulator. The
+uncertainty is uniform throughout the parameter space with regions of slightly higher uncertainty at θ = 0o and 45o.
+We also assessed the sensitivity of the model accuracy to the ambient TI used in the wake model prior mean. Figure 7 shows
+the impact of ambient TI on the wake model prior mean and the fitted GP model. Increasing the ambient TI increased the value of
+C∗
+T,wake. This is because of the enhanced wake recovery behind wind turbines. Increasing the ambient TI in the wake model results
+in C∗
+T,wake overpredicting C∗
+T,LES. The MAE from the LOOCV procedure for each fitted GP is shown in the bottom right corner.
+
+b)=5°
+c)=100
+d)  =15°
+a)=00
+e)=200
+10
+10
+10
+10
+10
+Dβ
+8
+8
+8
+8
+6
+6
+6
+6 
+6
+5
+10
+5
+10
+5
+10
+5
+10
+5
+10
+f) =250
+g)  =300
+h)=35°
+i)=40°
+j)=45°
+10
+10
+10
+10
+10
+D
+8
+8
+8
+8
+6
+6
+6
+6
+6
+5
+10
+5
+10
+5
+10
+5
+10
+5
+10
+Sα/D
+Sα/D
+Sα/D
+Sα/D
+Sαc/D
+0.000
+0.005
+0.010
+0.015
+0.020
+0.025
+0.030
+Vk.2a) Ambient TI=1%
+b) Ambient TI=5%
+0.8
+0.8
+0.7
+0.7
+*
+山秋
+0.6
+0.6
+GP-wake-TI1-prior
+.·
+GP-wake-TI5-prior
+0.5
+0.5
+MAE=3.02%
+MAE=2.16%
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+CT,LES
+C*,LES
+c) Ambient TI=10%
+d) Ambient TI=15%
+0.8
+0.8
+0.7
+0.7
+0.6
+0.6
+GP-wake-TI10-prior
+GP-wake-TI15-prior
+0.5
+0.5
+MAE=1.25%
+MAE=1.04%
+0.60
+0.65
+0.55
+0.70
+0.75
+0.80
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+Wake model prior mean
+Standard GP modelKIRBY et al
+11
+The fitted GPs became more accurate when the wake model ambient TI was increased. Increasing the ambient TI for the wake
+model causes the wakes to recover faster. The wakes become shorter in the streamwise direction and wider in the spanwise direction.
+As such, C∗
+T,wake becomes less sensitive to the turbine layout. When an ambient TI of 1% and 5% is used for the wake model,
+C∗
+T,wake is more sensitive to turbine layout than C∗
+T,LES (figures 7a and 7b). When the ambient TI is increased to 10% and above,
+the relationship between C∗
+T,wake and C∗
+T,LES becomes simpler (figures 7c and 7d). This seems to explain why the fitted GPs
+become more accurate.
+5.2
+Performance of non-linear multi-fidelity GP regression
+We then assessed the accuracy of the multi-fidelity GP models (section 4.2). All models used the 50 high-fidelity (C∗
+T,LES) training
+points and a varying number of low-fidelity (C∗
+T,wake) training points (using an ambient TI of 10% for C∗
+T,wake). The results from
+LOOCV are shown in table 2. For the LOOCV we train our model on 49 out of the 50 high-fidelity data points and all low-fidelity
+data points. Then we average the error in predicting the high-fidelity data point left of the training set and repeat this in turn for
+data points. Increasing the number of low-fidelity training points from 250 to 500 reduced the mean and maximum error. However,
+increasing this to 1000 low-fidelity training points did not increase accuracy and increased the fitting and prediction time. This is
+because the number of high-fidelity training points is fixed. There is a threshold where the model of the relationship between fLES
+and fwake, denoted ρ, limits the final accuracy of the emulator of fLES.
+The posterior mean mσ2 of glow(v) is an emulator of fwake and ghigh(v) is an emulator of fLES. Figure 8 gives the predictions
+from the posterior mean of ghigh(v) (for MF-GP-nlow500). The lowest mσ2 values were for a wind direction of θ = 0o. mσ2
+Table 2 Performance of the multi-fidelity Gaussian Process models.
+Model
+MAE (%)
+Maximum error (%)
+Training time (s)
+Prediction time (s)
+MF-GP-nlow250
+1.46
+7.12
+6.15
+0.00157
+MF-GP-nlow500
+0.828
+3.75
+9.73
+0.00167
+MF-GP-nlow1000
+0.866
+3.55
+26.8
+0.00236
+Figure 8 Posterior mean function for ghigh(v) of MF-GP-nlow500.
+
+b)=50
+d)  =15°
+a)=00
+c)=100
+e)=200
+10
+10
+10
+10
+10
+Dβ
+8
+8
+8
+8
+6
+6
+6
+6 
+6
+5
+10
+5
+10
+5
+10
+5
+10
+5
+10
+f) =250
+g)  =300
+h) =35°
+i)=40°
+j）)θ =45°
+10
+10
+10
+10
+10
+D
+8
+8
+8
+8
+6
+6
+6
+6
+6
+5
+10
+10
+5
+10
+5
+10
+5
+5
+10
+Sα/D
+Sα/D
+Sα/D
+Sα/D
+Sαc/D
+0.50
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+mg212
+KIRBY et al
+Figure 9 Posterior variance function for ghigh(v) of MF-GP-nlow500.
+increased rapidly with θ reaching a maximum of slightly over 0.75 at θ = 10o. For large values of θ (above θ = 25o) there were
+local minima in mσ2 which appear in figure 8 as diagonal strips of low mσ2 values. The main diagonal strip occurs along the line
+of Sy = Sx tan(θ). There are two smaller strips either side of with positions given by Sy = 2 tan(θ) and Sy = 0.5 tan(θ) (this is
+discussed further in section 6).
+The uncertainty the model MF-GP-nlow500 has in predicting fLES is shown in figure 9. The model uncertainty is uni-
+form throughout the parameter space with slightly higher values at θ = 0o and 45o. Compared to the posterior variance of
+GP-wake-TI10-prior (shown in figure 6) the uncertainty is lower. By incorporating information from C∗
+T,wake, the multi-fidelity GP
+model has more confidence about predicting fLES.
+The prediction errors from the LOOCV (for MF-GP-nlow500) are shown in figure 10. The box plot of prediction errors in figure
+10a shows that this model had no significant bias whereas both the wake and analytical models systemically overestimated C∗
+T,LES.
+Figures 10b-d show that for the statistical model there appears to be no part of the parameter space which had larger errors.
+The multi-fidelity approach used in this study builds a statistical model of both the low-fidelity (fwake) and high-fidelity (fLES)
+model. We can use the posterior means of glow(v) and ghigh(v) to see the differences between the wake model and LES. The
+posterior mean for both models are shown in figure 11. For the wake model the change in mσ2 with θ is greater than for the LES
+(especially between θ = 0o and 10o). For larger values of θ, there is a larger difference in mσ2 between waked and unwaked layouts
+for the low-fidelity model compared to the high-fidelity one. This suggests than the wake model is more sensitive to changes in wind
+directions than the LES.
+
+a) =00
+b) =5°
+c)=100
+d)θ=15°
+e)=20°
+10
+10
+10
+10
+10
+D∞
+8
+8
+8 
+8
+6
+6
+6
+6
+6
+5
+10
+5
+10
+5
+10
+5
+10
+5
+10
+f）θ =25°
+g) =300
+h) =350
+i)=40°
+j)θ=45°
+10
+10
+10
+10
+10
+Dβ
+8
+8
+8
+8
+6
+6
+6
+6 
+6
+5
+10
+5
+10
+5
+10
+5
+10
+5
+10
+Sα/D
+Sα/D
+Sα/D
+Sα/D
+S/D
+0.000
+0.005
+0.010
+0.015
+0.020
+0.025
+0.030
+Vkg?KIRBY et al
+13
+Figure 10 Comparison of LOOCV prediction errors (%) for different models a) and LOOCV prediction error (%) of MF-GP-nlow500
+against input parameters b) Sx/D, c) Sy/D and d) θ(o). Note that for the box plot in a) the orange line is the median LOOCV error
+and the box is the interquartile range of LOOCV error.
+Figure 11 Posterior mean function of MF-GP-nlow500 for different values of θ for a) to e) ghigh(v) and f) to j) glow(v).
+5.3
+Prediction of wind farm performance
+We use the predicted values of C∗
+T,LES from the emulators to predict the power output of wind farms under various mesoscale
+atmospheric conditions, following the concept of the two-scale momentum theory. We predict the (farm-averaged) turbine power
+coefficient Cp using C∗
+T,LES predictions from MF-GP-nlow500. We call this prediction of farm performance Cp,model. Firstly, we
+use the C∗
+T,LES prediction from the LOOCV procedure as C∗
+T in equation 1 to calculate β for a given value of wind extractability ζ.
+We substitute this value of β into the expression Cp = β3C∗
+T
+3
+2 C′
+T
+− 1
+2 (which is only valid for actuator discs) to calculate Cp,model.
+We compare the value of Cp,model with the turbine power coefficient recorded in the LES, Cp,LES. The effect of the coarse LES
+
+a)
+b)
+5.0
+20
+(%)
+Overprediction
+Overprediction
+Prediction errors (
+l errors
+2.5
+10
+0.0
+0
+2.5
+Underprediction
+Underprediction
+10
+5.0
+MF-GP-nlow500
+Wake
+Analytical
+5
+6
+7
+8
+9
+10
+model
+model
+Sα/D
+d)
+c)
+5.0
+5.0
+Prediction errors
+2.5
+errors
+2.5
+0.0
+0.0
+Prediction
+2.5
+2.5
+5.0
+1
+5.0
+5
+6
+7
+8
+9
+10
+10
+20
+30
+40
+0
+Sy/D
+ (°)b)=100
+d)  =300
+a)=00
+c)=200
+e)=400
+10
+10
+10
+10
+10
+Dβ
+8
+8
+8
+8
+6
+6
+6
+6 
+6
+5
+10
+5
+10
+5
+10
+5
+10
+5
+10
+f)=0°
+g)=100
+h)=20°
+i)=300
+j)=40°
+10
+10
+10
+10
+10
+D
+8
+8
+8
+8
+6
+6
+6
+6
+6
+5
+10
+5
+10
+5
+10
+5
+10
+5
+10
+Sα/D
+Sα/D
+Sα/D
+Sα/D
+Sαc/D
+0.50
+0.55
+0.60
+0.65
+0.70
+0.75
+0.80
+mg214
+KIRBY et al
+Figure 12 Comparison of Cp predictions with LES results for a realistic range of ζ values.
+resolution on turbine thrust (and hence also ABL response and Cp) has already been corrected 8. The LES was performed with
+periodic horizontal boundary conditions and a fixed momentum supply, i.e., ζ = 0. However, the Cp,LES has also been adjusted for
+a given ζ by scaling the velocity fields assuming Reynolds number independence 8.
+Similarly, the analytical model of C∗
+T can be used to give a theoretical prediction of wind farm performance called Cp,Nishino 8,
+which is given by
+Cp,Nishino =
+64C′
+T
+(4 + C′
+T )3
+�
+���
+−ζ +
+�
+ζ2 + 4
+�
+16C′
+T
+(4+C′
+T )2
+λ
+Cf0 + 1
+�
+(1 + ζ)
+2
+�
+16C′
+T
+(4+C′
+T )2
+λ
+Cf0 + 1
+�
+�
+���
+3
+.
+(12)
+We will compare the accuracy of both Cp,model and Cp,Nishino in predicting Cp,LES.
+Both Cp,model and Cp,LES are shown in figure 12 for a realistic range of wind extractability factors, along with the results from
+Cp,Nishino (equation 12). Cp,Nishino provides an approximate upper limit of farm-averaged Cp as it predicts very well the effects
+of array density and large-scale atmospheric response. The statistical model accurately predicts the effect of turbine layout on farm
+performance which becomes more important with larger ζ values. As ζ increases, there is a larger difference between Cp,LES and
+Cp,Nishino. Also, Cp,model becomes slightly less accurate when ζ increases.
+Table 3 shows the average prediction errors of Cp,model and Cp,Nishino. We quantified the mean absolute error using two
+different reference powers. Using Cp,LES as the reference power, Cp,Nishino had an error of around 5% and the error increases
+
+a)（=0
+b)（=5
+X
+0.04
+A
+0.15
+= 0.03
+P
+C
+C
+4
+0.02
+0.10
+0.01
+5
+10
+15
+20
+5
+10
+15
+20
+>/Cf0
+入/Cf0
+= 10
+d)（
+= 15
+）（
+0.25
+0.30
+△
+K
+△
+0.25
+0.20
+A
+C
+A
+0.20
+0.15
+0.15
+A
+A
+0.10
+1
+5
+10
+15
+20
+5
+10
+15
+20
+>/Cf0
+入/Cfo
+e)（= 20
+f)（
+= 25
+0.35
+必
+0.35
+X
+X
+0.30
+△
+AA
+△
+≥ 0.30
+公
+0.25
+X
+0.25
+又
+0.20
+0.20
+5
+10
+15
+20
+5
+10
+15
+20
+>/Cf0
+入/Cf0
+Cp,LES
+C
+X
+△
+p,NishinoKIRBY et al
+15
+Table 3 Comparison of models for Cp prediction.
+1
+50
+�50
+i=1 |Cp,i − Cp,LES|/Cp,LES
+1
+50
+�50
+i=1 |Cp,i − Cp,LES|/Cp,Betz
+ζ
+Cp,Nishino
+Cp,model
+ζ
+Cp,Nishino
+Cp,model
+0
+2.82%
+2.15%
+0
+0.142%
+0.108%
+5
+4.38%
+1.48%
+5
+0.954%
+0.338%
+10
+5.16%
+1.35%
+10
+1.67%
+0.459%
+15
+5.66%
+1.30%
+15
+2.24%
+0.542%
+20
+6.02%
+1.26%
+20
+2.72%
+0.601%
+25
+6.30%
+1.24%
+25
+3.11%
+0.648%
+with ζ. The mean absolute error of Cp,model was typically less than 1.5% and this decreased slightly as ζ increases (due to the
+reference power Cp,LES increasing). We also use the power of an isolated ideal turbine, Cp,Betz, as a reference power. Cp,Betz is
+calculated using the actuator disc theory with the expression Cp,Betz = 64C′
+T /(4 + C′
+T )3 (note that in this study C′
+T = 1.33 and
+hence Cp,Betz = 0.563). In this case the mean absolute error increased with ζ for both Cp,model and Cp,Nishino. However, the
+average prediction error of Cp,model remained below 0.65%.
+6
+DISCUSSION
+Data-driven modelling of the internal turbine thrust coefficient C∗
+T is a novel approach to modelling turbine-wake interactions. Data-
+driven models of wind farm performance typically focus on predicting the power output, which, however, depends on flow physics
+across a wide range of scales. Current data-driven approaches are either not generalisable to different atmospheric responses, or
+would require a very large set of expensive training data, such as finite-size wind farm LES data. Data-driven models of C∗
+T captures
+the effects of turbine-wake interactions, whilst also being applicable to different atmospheric responses (following the concept of
+the two-scale momentum theory).
+The statistical emulator of C∗
+T developed in this study was able to predict the farm power Cp of Kirby et. al. 8 with an average error
+of less than 0.65%. The high accuracy and very low computational cost of this approach shows the potential of this approach for
+modelling turbine-wake interactions. It has several advantages over traditional approaches using the superposition of wake models.
+Information from turbulence-resolving LES is included which ensures a high accuracy. It will also be more advantageous as wind
+farms become larger because wake models struggle to capture the complex multi-scale flows physics which are important for large
+farms. The statistical model of C∗
+T may therefore allow fast and accurate predictions of wind farm performance.
+All emulators developed in this study gave substantially better predictions of C∗
+T,LES compared to the analytical and wake
+models. Both the mean and maximum prediction errors were reduced by the emulators. The standard GP regression approach had
+a mean prediction error of 1.26% and maximum error of approximately 6%. The accuracy depends on the size of the LES data set
+and could be further decreased with a larger training set. The multi-fidelity GP approach gave more accurate predictions of C∗
+T,LES
+compared to the standard GP regression. This is because non-linear information fusion algorithm has incorporated information from
+many low-fidelity data points to improve the emulator of the high-fidelity (LES) model. This approach has the advantage that, unlike
+the standard GP regression approach, it is not necessary to evaluate the prior mean before making a prediction. Therefore, to predict
+C∗
+T it is only necessary to evaluate the posterior mean of the high-fidelity emulator for a specific turbine layout.
+The shape of the posterior mean in figure 8 gives insights into the physics of turbine-wake interactions. This is because C∗
+T,LES
+is low when a layout has a high degree of turbine-wake interactions. For the turbine operating conditions used, C∗
+T,LES is close to
+0.75 when a layout has a small degree of wake interactions. Figure 8a shows C∗
+T,LES when the wind direction is perfectly aligned
+
+16
+KIRBY et al
+Figure 13 Alignment of turbines for different combinations of Sx, Sy and θ.
+with the rows of turbines (θ = 0). This gives wind farms with a high degree of wake interactions which results in low C∗
+T,LES values.
+For θ = 0o, increasing Sx/D increases C∗
+T because there is a larger streamwise distance between turbines for the wakes to recover.
+When the cross-streamwise spacing (Sy/D) is increased the degree of wake interactions increases, i.e., C∗
+T,LES decreases. This is
+because there is a lower array density which results in a lower turbulence intensity within the farm and hence slower wake recovery.
+Yang 41 found that increasing the cross-streamwise spacing in infinitely-large wind farms increased the power of individual turbines
+and concluded that this was due to reduced wake interactions. However, the increase in turbine power found by Yang 41 may be also
+explained by to a faster farm-averaged wind speed caused by a reduced array density rather than reduced wake interactions.
+When the wind direction θ increases, C∗
+T,LES increases to a maximum of just over 0.75 at θ = 10o (figure 8c). This result agrees
+qualitatively with another study 42 in which it was found that the maximum farm power was produced by an intermediate wind
+direction. When θ increases above 20o regions of low C∗
+T,LES appear diagonally (see figures 8f-j). The regions of low C∗
+T,LES are
+centred on the surfaces given by Sy = 2Sx tan(θ), Sy = Sx tan(θ) and Sy = 0.5Sx tan(θ). These regions correspond to turbines
+being aligned along different axes throughout the farm (see figure 13). There are longer streamwise distance between turbines for
+these arrangements (compared to θ = 0o) and so the C∗
+T,LES values are higher than for θ = 0o.
+The accuracy of the statistical emulators could be further improved in future studies. Both the standard and multi-fidelity GP
+models can be improved by adding more evaluations of C∗
+T,LES. From table 2, the accuracy of the multi-fidelity GP models did not
+improve once we used more than 500 C∗
+T,wake evaluations. This shows that the error in predicting C∗
+T,LES for MF-GP-nlow500 is
+not due to the model of fwake. Instead the error arises from the learnt relationship between fwake and fLES.
+The statistical emulators developed are not applicable to all wind farms because of the limited nature of our data set. A limitation
+of the developed model is that it is only applicable to farms with perfectly aligned layouts. It should also be noted that our model
+was trained on data from simulations of a neutrally stratified boundary layer. Therefore a larger LES data set with an extended
+parameter space would be required to account for the effect of atmospheric stability on wake interactions and the resulting C∗
+T .
+Another limitation of our model is that it assumes all turbines have the same resistance coefficient C′
+T . It is likely that this condition
+can be strictly satisfied only in the fully developed region of a large farm where the wind speed does not change in the streamwise
+or cross-streamwise directions.
+Although we considered only actuator discs in this study for demonstration, the proposed approach using a data-driven model
+of CT ∗ can be applied to power prediction of real turbines as well in future studies. In this study, we calculate Cp,model using the
+expression Cp,model = β3C∗
+T
+3
+2 C′
+T
+− 1
+2 . This assumes that the relationship between C∗
+p and C′
+T is given by C∗
+p = C∗
+T
+3
+2 C′
+T
+− 1
+2 , which
+is only valid for actuator discs. For real turbines, the relationship between C∗
+p and C′
+T can be calculated using BEM theory 43 according
+to the turbine design and operating conditions (noting that the turbine induction factor can still be estimated as a = C′
+T /(4 + C′
+T )).
+Cp,model can then be calculated using equation 5 with β found using equation 1. However, for a data-driven model of C∗
+T to be
+applicable to real turbines, it will be necessary to model the impact of a variable C′
+T rather than assuming a fixed C′
+T value as in this
+study.
+
+b) Su = Sαtan(0)
+= 2Stan(0KIRBY et al
+17
+7
+CONCLUSIONS
+In this study we proposed a new data-driven approach to modelling turbine wake interactions and resulting flow resistance in large
+wind farms. We developed statistical emulators of the farm-internal turbine thrust coefficient C∗
+T,LES as a function of turbine layout
+and wind direction. C∗
+T represents the flow resistance within a wind farm and reflects the characteristics of the turbine-scale flows
+including wake and turbine blockage effects. We developed several emulators using both standard GP regression and multi-fidelity
+GP regression. The standard GP was trained using data from 50 infinitely-large wind farm LES (and using a low-fidelity wake model
+as a prior mean). The multi-fidelity GP was trained using data from both LES and wake model simulations. We estimated the test
+accuracy of the model by performing leave-one-out cross-validation and assessed the error in predicting C∗
+T,LES. All emulators had
+a mean test error of less than 2% for predicting C∗
+T,LES. The multi-fidelity GP gave the best performance with a mean prediction
+error of 0.849% and maximum prediction error of 3.78% with no bias for under or over-prediction. This is low compared to the mean
+error of the wake model (4.60%) and analytical C∗
+T model (5.26%) which both had a bias for overpredicting C∗
+T,LES.
+We used an emulator of C∗
+T,LES to make predictions of wind farm performance under various mesoscale atmospheric conditions
+(characterised by the wind extractability factor ζ) using the two-scale momentum theory 24. Our predictions of farm power produc-
+tion had an average error of less than 1.5% under realistic wind extractability scenarios compared to the LES. When the error in
+power prediction is expressed relative to the power of an isolated ideal turbine the average prediction error is less than 0.7%. We
+also used a previously proposed analytical model of C∗
+T
+25 to predict farm power output with an average error of less than 3.5% (with
+the power of an isolated turbine as the reference power). The analytical model correctly predicts the trends in farm performance
+with array density under different scenarios of large-scale atmospheric response, although it tends to overpredict the power where
+turbine-wake interactions are important. Using statistical emulators of C∗
+T is a new approach to modelling turbine-wake interactions
+and flow resistance within large wind farms. The approach can be extended in future studies by increasing the size of the training
+data set, for example, to account for the effects of C′
+T and atmospheric stability conditions on C∗
+T . The very low computational cost
+and high accuracy of the model could be beneficial for future wind farm optimisation.
+ACKNOWLEDGMENTS
+The first author (AK) acknowledges the NERC-Oxford Doctoral Training Partnership in Environmental Research (NE/S007474/1) for
+funding and training.
+Author contributions
+T.N. derived the theory. A.K. and T.D.D. performed the simulations. F-X.B. provided assistance and guidance for the machine learning
+methodology. A.K. wrote the paper with corrections from T.N., F-X.B and T.D.D.
+Financial disclosure
+None reported.
+Conflict of interest
+The authors report no conflict of interest.
+
+18
+KIRBY et al
+Data availability statement
+The data and code that support the findings of this study are openly available at https://github.com/AndrewKirby2/ctstar_statistical_
+model. This includes the results from the wind farm LES and wake model simulations. The repository also includes the code for the
+results presented in sections 5.1, 5.2 and 5.3.
+Author ORCID
+A. Kirby, https://orcid.org/0000-0001-8389-1619; F-X. Briol https://orcid.org/0000-0002-0181-2559; T. Nishino, https://orcid.
+org/0000-0001-6306-7702.
+References
+1. Porté-Agel F, Bastankhah M, Shamsoddin S. Wind-Turbine and Wind-Farm Flows: A Review. Boundary-Layer Meteorology 2020;
+174: 1-59. doi: 10.1007/s10546-019-00473-0
+2. Bleeg J, Purcell M, Ruisi R, Traiger E. Wind farm blockage and the consequences of neglecting its impact on energy production.
+Energies 2018; 11: 1609. doi: 10.3390/en11061609
+3. Carbon Trust . Global Blockage Effect in Offshore Wind (GloBE) [accessed 07/11/2022]. https://www.carbontrust.com/
+our-projects/large-scale-rd-projects-offshore-wind/global-blockage-effect-in-offshore-wind-globe; 2022.
+4. Jensen NO. A note on wind generator interaction. Risø-M-2411 Risø National Laboratory Roskilde 1983.
+5. Bastankhah M, Porté-Agel F. A new analytical model for wind-turbine wakes. Renewable Energy 2014; 70: 116-123.
+doi:
+10.1016/j.renene.2014.01.002
+6. Katic I, Hojstrup J, Jensen NO. A simple model for cluster efficiency. Proceedings of the European wind energy association
+conference and exhibition, Rome, Italy 1986: 407-409.
+7. Zong H, Porté-Agel F. A momentum-conserving wake superposition method for wind farm power prediction. Journal of Fluid
+Mechanics 2020; 889: A8. doi: 10.1017/jfm.2020.77
+8. Kirby A, Nishino T, Dunstan TD. Two-scale interaction of wake and blockage effects in large wind farms. Journal of Fluid Mechanics
+2022; 953: A39. doi: 10.1017/jfm.2022.979
+9. Stevens RJAM, Gayme DF, Meneveau C. Effects of turbine spacing on the power output of extended wind-farms. Wind Energy
+2016; 19: 359-370. doi: 10.1002/we.1835
+10. Fitch AC, Olson JB, Lundquist JK, et al. Local and mesoscale impacts of wind farms as parameterized in a mesoscale NWP model.
+Monthly Weather Review 2012; 140. doi: 10.1175/MWR-D-11-00352.1
+11. Abkar M, Porté-Agel F. A new wind-farm parameterization for large-scale atmospheric models. Journal of Renewable and
+Sustainable Energy 2015; 7. doi: 10.1063/1.4907600
+12. Pan Y, Archer CL. A Hybrid Wind-Farm Parametrization for Mesoscale and Climate Models. Boundary-Layer Meteorology 2018;
+168: 469-495. doi: 10.1007/s10546-018-0351-9
+
+KIRBY et al
+19
+13. Zehtabiyan-Rezaie N, Iosifidis A, Abkar M. Data-driven fluid mechanics of wind farms: A review. Journal of Renewable and
+Sustainable Energy 2022; 14: 32703. doi: 10.1063/5.0091980
+14. Renganathan SA, Maulik R, Letizia S, Iungo GV. Data-driven wind turbine wake modeling via probabilistic machine learning.
+Neural Computing and Applications 2022; 34: 6171-6186. doi: 10.1007/s00521-021-06799-6
+15. Optis M, Perr-Sauer J. The importance of atmospheric turbulence and stability in machine-learning models of wind farm power
+production. Renewable and Sustainable Energy Reviews 2019; 112: 27-41. doi: 10.1016/j.rser.2019.05.031
+16. Japar F, Mathew S, Narayanaswamy B, Lim CM, Hazra J. Estimating the wake losses in large wind farms: A machine learning
+approach. ISGT 2014 2014: 1-5. doi: 10.1109/ISGT.2014.6816427
+17. Yan C, Pan Y, Archer CL. A general method to estimate wind farm power using artificial neural networks. Wind Energy 2019; 22:
+1421-1432. doi: 10.1002/we.2379
+18. Zhang J, Zhao X. Wind farm wake modeling based on deep convolutional conditional generative adversarial network. Energy
+2022; 238: 121747. doi: https://doi.org/10.1016/j.energy.2021.121747
+19. Wilson B, Wakes S, Mayo M. Surrogate modeling a computational fluid dynamics-based wind turbine wake simulation using
+machine learning. 2017 IEEE Symposium Series on Computational Intelligence (SSCI) 2017: 1-8. doi: 10.1109/SSCI.2017.8280844
+20. Ti Z, Deng XW, Yang H. Wake modeling of wind turbines using machine learning. Applied Energy 2020; 257: 114025. doi:
+https://doi.org/10.1016/j.apenergy.2019.114025
+21. Ti Z, Deng XW, Zhang M. Artificial Neural Networks based wake model for power prediction of wind farm. Renewable energy
+2021; 172: 618-631. doi: https://doi.org/10.1016/j.renene.2021.03.030
+22. Park J, Park J. Physics-induced graph neural network: An application to wind-farm power estimation. Energy 2019; 187. doi:
+10.1016/j.energy.2019.115883
+23. Bleeg J. A Graph Neural Network Surrogate Model for the Prediction of Turbine Interaction Loss. Journal of Physics: Conference
+Series 2020; 1618. doi: 10.1088/1742-6596/1618/6/062054
+24. Nishino T, Dunstan TD. Two-scale momentum theory for time-dependent modelling of large wind farms. Journal of Fluid
+Mechanics 2020; 894: A2. doi: 10.1017/jfm.2020.252
+25. Nishino T. Two-scale momentum theory for very large wind farms. Journal of Physics: Conference Series 2016; 753: 032054. doi:
+10.1088/1742-6596/753/3/032054
+26. Patel K, Dunstan TD, Nishino T. Time-dependent upper limits to the performance of large wind farms due to mesoscale
+atmospheric response. Energies 2021; 14: 6437. doi: 10.3390/en14196437
+27. Sacks J, Welch WJ, Mitchell TJ, Wynn HP. Design and analysis of computer experiments. Statistical Science 1989; 4: 409-423.
+doi: 10.1214/ss/1177012413
+28. Currin C, Mitchell T, Morris M, Ylvisaker D. Bayesian prediction of deterministic functions, with applications to the de-
+sign and analysis of computer experiments. Journal of the American Statistical Association 1991; 86: 953-963.
+doi:
+10.1080/01621459.1991.10475138
+
+20
+KIRBY et al
+29. Johnson ME, Moore LM, Ylvisaker D. Minimax and maximin distance designs. Journal of Statistical Planning and Inference 1990;
+26: 131-148. doi: 10.1016/0378-3758(90)90122-B
+30. Santner TJ, Williams BJ, Notz W. The design and analysis of computer experiments. second ed. 2018.
+31. Wynne G, Briol FX, Girolami M. Convergence guarantees for gaussian process means with misspecified likelihoods and
+smoothness. Journal of Machine Learning Research 2021; 22.
+32. Shapiro CR, Gayme DF, Meneveau C. Filtered actuator disks: Theory and application to wind turbine models in large eddy
+simulation. Wind Energy 2019; 22: 1414-1420. doi: 10.1002/we.2376
+33. Niayifar A, Porté-Agel F. Analytical modeling of wind farms: A new approach for power prediction. Energies 2016; 9.
+doi:
+10.3390/en9090741
+34. Pedersen MM, Laan v. dP, Friis-Møller M, Rinker J, Réthoré PE. DTUWindEnergy/PyWake: PyWake. 2021. doi: 10.5281/zen-
+odo.2562662
+35. Crespo A, Hernández J. Turbulence characteristics in wind-turbine wakes. Journal of Wind Engineering and Industrial Aerodynamics
+1996; 61: 71-85. doi: 10.1016/0167-6105(95)00033-X
+36. Rasmussen CE, Williams CKI. Gaussian Processes for Machine Learning. the MIT Press . 2018
+37. Peherstorfer B, Willcox K, Gunzburger M. Survey of multifidelity methods in uncertainty propagation, inference, and optimiza-
+tion. SIAM Review 2018; 60. doi: 10.1137/16M1082469
+38. Perdikaris P, Raissi M, Damianou A, Lawrence ND, Karniadakis GE. Nonlinear information fusion algorithms for data-efficient
+multi-fidelity modelling. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 2017; 473.
+doi:
+10.1098/rspa.2016.0751
+39. Paleyes A, Pullin M, Mahsereci M, Lawrence N, González J. Emulation of physical processes with Emukit. 2019.
+40. GPy . GPy: A Gaussian process framework in python. http://github.com/SheffieldML/GPy; since 2012.
+41. Yang X, Kang S, Sotiropoulos F. Computational study and modeling of turbine spacing effects infinite aligned wind farms. Physics
+of Fluids 2012; 24: 11510. doi: 10.1063/1.4767727
+42. Stevens RJAM, Gayme DF, Meneveau C. Large eddy simulation studies of the effects of alignment and wind farm length. Journal
+of Renewable and Sustainable Energy 2014; 6: 023105. doi: 10.1063/1.4869568
+43. Nishino T, Hunter W. Tuning turbine rotor design for very large wind farms. Proceedings of the Royal Society A: Mathematical,
+Physical and Engineering Sciences 2018; 474(2220): 1–20. doi: 10.1098/rspa.2018.0237
+How to cite this article: Kirby A., Briol F-X., Dunstan T.D., and Nishino T. (2022), Data-driven modelling of wind turbine wake
+interactions in large wind farms, Wind Energy, xxxx.
+

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+Transport Model for the Propagation of Partially-Coherent,
+Polarization-Gradient Vector Beams
+J. M. Nichols and D. V. Nickel
+Naval Research Laboratory
+4555 Overlook Ave.
+SW.
+Washington D.C. 20375
+F. Bucholtz
+Jacobs Technology, Inc.
+2551 Dulles View Drive
+Herndon, VA 20171
+G. Rohde
+University of Virginia
+Dept.
+of Electrical and Computer Engineering
+Dept.
+of Biomedical Engineering
+415 Lane Rd.
+Charlottesville, VA
+In a recent work [20], we predicted and experimentally validated a new physical mechanism for
+altering the propagation path of a monochromatic beam. Specifically, we showed that by properly
+tailoring the spatial distribution of the linear state of polarization transverse to the direction of
+propagation, the beam followed a curved trajectory in free space. Here we extend the model to the
+partially coherent, polychromatic case by redefining the beam amplitude, phase, and polarization
+angle as appropriate statistical quantities.
+In particular, we propose an entirely new definition
+of linear polarization gradient as an average over the third generalized Stokes parameter in the
+spatial frequency domain. In the new model, the beam curvature matches that of our previous work
+in the fully coherent case, but is predicted to gradually vanish as the beam loses coherence and
+becomes depolarized. The model also clearly predicts, however, that there does not exist a natural
+mechanism in free space or due to atmospheric turbulence that will cause significant depolarization.
+Simulated beam trajectories are shown for varying levels of initial partial coherence and for different
+polarization profiles. A new class of non-diffracting beams is also suggested by way of example.
+Lastly, as a byproduct of the derivation we generalize a previously known result concerning the
+free-space propagation of generalized Stokes parameters [13] by showing the result also holds for
+propagation in inhomogeneous media.
+I.
+INTRODUCTION
+Recently we demonstrated that through proper choice of spatial distribution of linear polarization
+angle, a coherent, monochromatic beam follows a curved trajectory in free space [20]. The effect is similar
+in magnitude to that of Airy beam bending (both scale as k−2
+0
+where k0 is the free-space wavenumber).
+However, in our approach it is the centroid of the beam that experiences a transverse acceleration
+as opposed to the Airy beam case where the main intensity lobe transversely accelerates, but where
+the centroid of the beam does not.
+The physics of the vector beam bending were predicted via a
+transport model, whereby the parameters defining the optical field (intensity and phase) were shown to
+be governed by the transport of intensity equation (TIE) and an eikonal equation, expressing conservation
+of transverse linear momentum. The model was re-formulated in Lagrangian coordinates in order to solve
+for the transverse beam location which, under appropriate choice of polarization gradient, was shown to
+bend in the transverse plane. These predictions were subsequently verified in experiment [20].
+In this work we extend the model to the more general case of partially coherent light, showing that with
+appropriate definitions of optical phase, amplitude, and polarization gradient the model still predicts a
+bending effect. For perfectly coherent light, the governing equations reduce to the previously derived
+coherent case, while for incoherent light, the effect disappears. The resulting model also predicts that the
+state of linear polarization (including the degree of polarization) will remain unchanged on propagation.
+Collectively, these model predictions represent the main contribution of this work.
+A second, but related contribution is to provide a new definition of polarization angle gradient that
+is appropriate for modeling partially coherent vector beams. Our definition is based on the normalized
+integral of the third generalized Stokes parameter and incorporates the degree of polarization directly.
+While this definition falls naturally from the vector transport equations, it is also consistent with recent
+arXiv:2301.03994v1  [physics.optics]  10 Jan 2023
+
+work on scalar, partially coherent beams where a similar definition of generalized phase was proposed
+[35]. In what follows, we show that this scalar definition is also easily extended to the vector case and is
+also a natural consequence of the transport model.
+Finally, in the process of deriving this result, we generalize a previously known result from Korotkova
+[13]. In that work, the author showed that the transverse integral of the generalized Stokes parameters
+were conserved under free-space propagation. We confirm this result using an entirely different approach
+and extend it to the case of propagation in an inhomogeneous medium.
+Our approach is as follows.
+1. We begin with the wave equation in the general case of a weakly-inhomogenous medium.
+We
+make the paraxial assumption via the slowly-varying envelope approximation to obtain Helmholtz
+equations for each field component. In the instance where the medium warrants a probabilistic
+description, we additionally invoke the Markov Approximation [30].
+2. To accommodate the probabilistic nature of the partially coherent problem, the fields are
+represented in the coherency matrix formalism where each matrix element is an expectation of
+a product of finite-time Fourier transforms [24] of field components at two different transverse
+spatial locations. Importantly, we retain the dependence on spatially-separated points throughout
+the calculation in the form of Wigner Transforms with respect to the transverse spatial coordinate.
+This information is vital in our model as the state of polarization is not uniform in the transverse
+plane.
+3. We obtain a vector transport equation for the generalized Stokes parameters which is the partially
+coherent, vector counterpart to the transport of intensity equations obtained in our earlier paper
+[20]. It is entirely reasonable to expect that, in the case of partial polarization, individual com-
+ponents of the Stokes 4-vector must obey continuity equations while, in the fully-polarized case,
+continuity of the intensity is sufficient to characterize beam propagation.
+4. We extend the method of moments developed for the scalar problem [7, 18] to the vector case,
+leading to the coupled transport equations describing the evolution of expected amplitude, phase,
+and polarization angle. Importantly, the model reduces to our monochromatic, coherent model in
+those respective limits.
+The resulting model extends our prior coherent model variables (phase, polarization angle, and intensity)
+to the partially coherent case by taking appropriate averages over the Wigner spatial frequency and with
+these new definitions, predict the expected beam path.
+II.
+TRANSPORT MODELING OF PARTIALLY COHERENT, POLARIZED LIGHT
+A.
+Spectral Coherency Representation
+We start with the vector wave equation for electric-field vector E(x, t)
+∇2E(x, t) − ϵ(x)
+c2
+0
+∂2E(x, t)
+∂t2
+= 0
+(1)
+which presumes an inhomogeneous, isotropic medium characterized by dimensionless dielectric constant
+ϵ(x) > 1, where x denotes position in three-dimensional Cartesian space, where c0 = 1/√ϵ0µ0 is the
+speed of light in vacuum, and where ϵ0 and µ0 are the permittivity and permeability, respectively, of free
+space. We assume the inhomogeneity is weak and define
+ϵ1(x) = ϵ(x) − ⟨ϵ⟩
+⟨ϵ⟩
+<< 1
+(2)
+where ⟨ϵ⟩ is the average value of ϵ(x) taken over the entire region of interest.
+We assume the wave propagates in the +z-direction and we model the electric field vector as a sta-
+tionary random process, existing for times −T ≤ t ≤ T. Since (1) is linear in E(x, t), we may consider a
+superposition of monochromatic, transverse-wave solutions
+E(x, t) = 1
+2π
+� ∞
+−∞
+{EX(x, ω)T , EY (x, ω)T , 0} e−ik0zeiωtdω,
+−T ≤ t ≤ T
+(3)
+2
+
+represented here by the Fourier integral. Phase accumulation in the direction of propagation is captured
+by the e−ik0z term with wavenumber k0 = (ω/c0) ⟨ϵ⟩1/2 = (2π/λ) ⟨ϵ⟩1/2 at free-space wavelength λ. The
+quantities {EX(x, ω)T , EY (x, ω)T , 0}e−ik0z are therefore the associated Fourier amplitudes at frequency
+ω and possess units of electric field per Hz. Given the above construction, these are given by
+e−ik0zEX,Y (x, ω)T =
+� T
+−T
+EX,Y (x, t)e−iωtdt
+(4)
+as discussed in [24] (sec. 4.7). The explicit dependence of the Fourier amplitudes on T will be retained
+for the moment. The electric field and its Fourier amplitudes are distinguished by their arguments (t
+and ω resp.).
+Substitute (3) into (1) and make the slowly-varying envelope approximation in which it is assumed
+that changes in the amplitude of the field over z−distances of a wavelength are small compared to the
+amplitude itself.
+Then |∂zz(·)| ≪ |k0∂z(·)| and the net result is that spatial gradients in x become
+gradients only in the transverse plane leading to the parabolic equations
+�
+−i2k0∂z + ∇2
+X + k2
+0ϵ1(⃗x, z)
+�
+{EX(⃗x, z, ω)T , EY (⃗x, z, ω)T } = 0
+�
+i2k0∂z + ∇2
+X + k2
+0ϵ1(⃗x, z)
+�
+{E∗
+X(⃗x, z, ω)T , E∗
+Y (⃗x, z, ω)T } = 0
+(5)
+which must be satisfied by each vector component of Fourier amplitudes and their complex conjugates
+(denoted with ∗). Here we have denoted the position in the transverse plane as the vector ⃗x ≡ {x, y} to
+distinguish it from the propagation direction z (x ≡ {⃗x, z}), and have denoted the transverse gradient
+operator ∇X(·) ≡ {∂x(·), ∂y(·)}.
+Note that (5) comprises four separate equations in, respectively, EX, EY , E∗
+X, E∗
+Y which we will call (a-
+d). Now perform the following operations. Multiply (a) and (b) evaluated at ⃗x1 by E∗
+X(⃗x2, z, ω). Multiply
+(a) and (b) evaluated at ⃗x1 by E∗
+Y (⃗x2, z, ω).
+Multiply (c) and (d) evaluated at ⃗x2 by EX(⃗x1, z, ω).
+Multiply (c) and (d) evaluated at ⃗x2 by EY (⃗x1, z, ω). Note that in each of the above operations all four
+multiplications are performed from the right. The results, in order, are eight equations which we denote
+(i)-(viii).
+If we then subtract (v) from (i), (vii) from (ii), (vi) from (iii), and (viii) from (iv) we find (taking into
+account the chain rule for the derivatives in z):
+�
+i2k0∂z +
+�
+∇2
+X2 − ∇2
+X1
+�
++ k2
+0 (ϵ1(⃗x2, z) − ϵ1(⃗x1, z))
+�
+Ei(⃗x1, z, ω)T E∗
+j (⃗x2, z, ω)T =0, i, j ∈ {X, Y }
+(6)
+where the notation ∇2
+Xl indicates that the Laplacian operation is to be performed as a function of the
+transverse variable designated ⃗xl for l = 1, 2. Taking the expected value of (6) over realizations of the
+electric fields and performing the limiting operation
+�
+Ei(⃗x, z, ω)E∗
+j (⃗x, z, ω)
+�
+≡ lim
+T →∞
+�
+E
+�Ei(⃗x, z, ω)T E∗
+j (⃗x, z, ω)T
+2T
+��
+, i, j ∈ {X, Y }
+(7)
+then yields
+i2k∂zWij(⃗x1, ⃗x2, z, ω) +
+�
+∇2
+X2 − ∇2
+X1
+�
+Wij(⃗x1, ⃗x2, z, ω)
++ k2
+0 [ϵ1(⃗x2, z) − ϵ1(⃗x1, z)] Wij(⃗x1, ⃗x2, z, ω) = 0, i, j ∈ {X, Y }
+(8)
+where each Wij(⃗x1, ⃗x2, z, ω) is an element of the spectral density matrix
+Wij ∈ W(⃗x1, ⃗x2, z, ω) =
+� ⟨EX(⃗x1, z, ω)E∗
+X(⃗x2, z, ω)⟩ ⟨EX(⃗x1, z, ω)E∗
+Y (⃗x2, z, ω)⟩
+⟨EY (⃗x1, z, ω)E∗
+X(⃗x2, z, ω)⟩ ⟨EY (⃗x1, z, ω)E∗
+Y (⃗x2, z, ω)⟩
+�
+(9)
+and possesses units of electric field squared per Hz. Note that multiplying (9) by ϵ0/2 gives W(⃗x1, ⃗x2, z, ω)
+in units of power spectral density in Watts/Hz.
+Equation (8) treats the medium properties as deterministic, such as propagation through a medium
+of known refractive index profile, in which case it is common to set ⟨ϵ⟩ = 1 and ϵ1(⃗x, z) = n2(⃗x, z) − 1
+where n(⃗x, z) is the refractive index.
+Alternatively, we can assume the medium is described by its
+statistical properties. Treating ϵ1(⃗x, z) as a zero-mean, Gaussian random variable (e.g., as in a tur-
+bulent atmosphere) requires averaging over both the field amplitudes and the medium properties in
+taking the expectation of Eq.
+(6).
+Define these properties via the covariance ⟨ϵ1(⃗x2, z)ϵ1(⃗x1, z′)⟩ =
+�
+R3 SNN(⃗ξ, κ)ei⃗ξ·(⃗x2−⃗x1)+iκ(z−z′)d⃗ξdκ , that is, as the inverse Fourier Transform of the three-dimensional
+3
+
+spectral density associated with fluctuations in the dielectric constant.
+We then invoke the well-
+established Markov Approximation (MA) of Tatarskii [30], [9] (see extension to the vector electric field
+case in [5]) which assumes the medium is “delta” correlated in the direction of propagation so that
+⟨ϵ1(⃗x2, z)ϵ1(⃗x1, z′)⟩ ≈ δ(z − z′)A(⃗x2 − ⃗x1, z′). Under the MA, Tatarskii [30] showed that the required
+average in (6) can be written
+�
+[ϵ1(⃗x2, z) − ϵ1(⃗x1, z)] Ei(⃗x1, z, ω)T E∗
+j (⃗x2, z, ω)T
+�
+≈ ik0
+2 [A(0, z) − A(⃗x2 − ⃗x1, z)] Wij(⃗x1, ⃗x2, z, ω)
+(10)
+so that Eq. (8) becomes
+i2k∂zWij(⃗x1, ⃗x2, z, ω) +
+�
+∇2
+X2 − ∇2
+X1
+�
+Wij(⃗x1, ⃗x2, z, ω)
++ ik3
+0
+2 [A(0, z) − A(⃗x2 − ⃗x1, z)] Wij(⃗x1, ⃗x2, z, ω) = 0
+(11)
+As we will show, the choice of either a deterministic (8) or a stochastic (11) medium can be easily
+accommodated in the transport model. Also note that the last term in both (8) and (11) possess units
+of [m] so that kA(·) is dimensionless, as is ϵ(·). Note that in [5], the approximation ϵ1 ≈ 2η is invoked
+which would have led to the pre-factor in Eq. (10) being written as 2ik0.
+Equation (8) or (11) therefore contain four separate equations, each governing a different element of
+the spectral density matrix (see also Wolf et al. e.g. [25]). Note that at the spatial location ⃗x1 = ⃗x2 ≡ ⃗x
+the expressions ⟨Ei(⃗x1, z, ω)E∗
+j (⃗x2, z, ω)⟩ reduce to the more familiar power spectral density functions
+Sij(⃗x, z, ω) =
+�
+Ei(⃗x, z, ω)E∗
+j (⃗x, z, ω)
+�
+, i, j ∈ {X, Y }
+(12)
+that is, Sij(⃗x, z, ω) = Wij(⃗x, ⃗x, z, ω).
+B.
+Generalize Stokes Parameter Representation
+It will be convenient to describe propagation in terms of generalized Stokes parameters [15]. Define
+s0(⃗x1, ⃗x2, z, ω) = ⟨EX(⃗x1, z, ω)E∗
+X(⃗x2, z, ω)⟩ + ⟨EY (⃗x1, z, ω)E∗
+Y (⃗x2, z, ω)⟩
+= WXX(⃗x1, ⃗x2, z, ω) + WY Y (⃗x1, ⃗x2, z, ω)
+s1(⃗x1, ⃗x2, z, ω) = ⟨EX(⃗x1, z, ω)E∗
+X(⃗x2, z, ω)⟩ − ⟨EY (⃗x1, z, ω)E∗
+Y (⃗x2, z, ω)⟩
+= WXX(⃗x1, ⃗x2, z, ω) − WY Y (⃗x1, ⃗x2, z, ω)
+s2(⃗x1, ⃗x2, z, ω) = 2Re{⟨EX(⃗x1, z, ω)E∗
+Y (⃗x2, z, ω)⟩} = ⟨EX(⃗x1, z, ω)E∗
+Y (⃗x2, z, ω)⟩ + ⟨EY (⃗x1, z, ω)E∗
+X(⃗x2, z, ω)⟩
+= WXY (⃗x1, ⃗x2, z, ω) + WY X(⃗x1, ⃗x2, z, ω)
+s3(⃗x1, ⃗x2, z, ω) = −2Im{⟨EX(⃗x1, z, ω)E∗
+Y (⃗x2, z, ω)⟩} = i (⟨EX(⃗x1, z, ω)E∗
+Y (⃗x2, z, ω)⟩ − ⟨EY (⃗x1, z, ω)E∗
+X(⃗x2, z, ω)⟩)
+= i (WXY (⃗x1, ⃗x2, z, ω) − WY X(⃗x1, ⃗x2, z, ω)) .
+(13)
+Unlike conventional Stokes parameters which are evaluated at a single point in space, these generalized
+parameters depend on the field relationships at two points ⃗x1 and ⃗x2. As ⃗x2 → ⃗x1 ≡ ⃗x we recover the
+standard definitions. If the above holds, we can also write
+W(⃗x1, ⃗x2, z, ω) = 1
+2
+� s0(⃗x1, ⃗x2, z, ω) + s1(⃗x1, ⃗x2, z, ω) s2(⃗x1, ⃗x2, z, ω) − is3(⃗x1, ⃗x2, z, ω)
+s2(⃗x1, ⃗x2, z, ω) + is3(⃗x1, ⃗x2, z, ω) s0(⃗x1, ⃗x2, z, ω) − s1(⃗x1, ⃗x2, z, ω)
+�
+(14)
+which matches the result of [22] (Eq.
+3.54) and [26] (Eq.
+1.5), the only difference being the sign
+convention chosen for exp (iωt).
+C.
+Wigner Representation
+Because (8,11) are linear in Wij(⃗x1, ⃗x2, z, ω) we can consider still other forms. For example, (8) is also
+seen to govern the generalized Stokes parameters,
+�
+i2k0∂z +
+�
+∇2
+X2 − ∇2
+X1
+�
++ k2
+0 (ϵ1(⃗x2) − ϵ1(⃗x1))
+�
+sν = 0,
+ν = 0, · · · , 3
+(15)
+4
+
+where sν = sν (⃗x1, ⃗x2, z, ω) and where we have omitted the arguments for brevity. Applying the coordi-
+nate transformation ⃗x1,2 → ⃗x ∓ ⃗x ′/2 and noting that, in this new system the operator (∇2
+X2 − ∇2
+X1) →
+2∇X · ∇X′ [23], we have
+�
+i2k0∂z + 2(∇X · ∇X′) + 2k2
+0Φ(⃗x, ⃗x ′, z)
+�
+s′
+ν = 0,
+ν = 0, · · · , 3
+(16)
+where we again use the shorthand notation s′
+ν = s′
+ν(⃗x, ⃗x ′, z, ω) and where
+Φ(⃗x, ⃗x ′, z) = 1
+2
+�
+ϵ1(⃗x + ⃗x ′
+2 , z) − ϵ1(⃗x − ⃗x ′
+2 , z)
+�
+(17)
+will be referred to as the Wigner potential function. In free space Φ(⃗x, ⃗x′, z) = 0 while in the case of a
+stochastic medium, the Wigner potential of Eq. (16) becomes
+Φ(⃗x, ⃗x′, z) = ik0
+4 [A(0, z) − A(⃗x′, z)] .
+(18)
+In these differential coordinates the spectral coherency matrix then becomes
+Wij(⃗x, ⃗x ′, z, ω) ≡
+�
+Ei
+�
+⃗x − ⃗x ′
+2 , z, ω
+�
+E∗
+j
+�
+(⃗x + ⃗x ′
+2 , z, ω
+��
+, i, j = X, Y
+(19)
+Equation (16) matches that of Charnotskii [5] (Equation 22 in the cited work) and states that the
+generalized Stokes parameters obey a parabolic equation of the same basic structure as the complex
+electric field amplitude in the deterministic, coherent case (see also, [8]).
+Now consider the spatial Fourier Transform of (19) with respect to the variable ⃗x ′ and the resulting
+Fourier Transform pair
+�
+Wij(⃗x, ⃗ξ, z, ω) =
+�
+R2 Wij(⃗x, ⃗x ′, z, ω)e−i⃗ξ·⃗x′d⃗x ′
+Wij(⃗x, ⃗x ′, z, ω) =
+� 1
+2π
+�2 �
+R2
+�
+Wij(⃗x, ⃗ξ, z, ω)ei⃗ξ·⃗x ′d⃗ξ
+(20)
+where the hat �
+W denotes the spatial Fourier transform, the operator
+�
+Rn denotes the n−dimensional
+integral over the space of real numbers (e.g.,
+�
+R2 ≡
+� ∞
+−∞
+� ∞
+−∞), and where the differential element in
+transverse real space and reciprocal 2-space are denoted by, respectively, d⃗x ′ ≡ dx′dy′ and d⃗ξ ≡ dξxdξy.
+Note that, unlike in Eqn. (3), we do not need to restrict the limits of integration in defining the Fourier
+Transform as the beam spatial correlations are assumed to be naturally limited in transverse extent, that
+is |Wij(⃗x, ±∞, z, ω)| → 0. The quantity �
+Wij(⃗x, ⃗ξ, z, ω) is thus the Wigner transform [32] associated with
+complex arguments Ei(⃗x, z, ω), Ej(⃗x, z, ω), i, j ∈ X, Y .
+In the expressions (20), Wij(⃗x, ⃗x′, z, ω) is the spatial covariance between the two field components i, j
+as a function of separation ⃗x ′ in the transverse plane, at transverse position ⃗x and downrange position
+z, and within a small optical spectral range {ω, ω + dω}, while �
+Wij(⃗x, ⃗ξ, z, ω) is the covariance between
+Fourier amplitudes of electric field components i, j associated with transverse spatial frequency ⃗ξ, at
+downrange position z and within a small optical spectral range {ω, ω + dω}. Importantly, this latter
+quantity is proportional to the average phase difference between field components i, j with transverse
+separation ⃗x′ and corresponding spatial frequency ⃗ξ (see Priestly section 9.1 [24]). This point will be
+re-visited in section (III C).
+We replace the spectral density matrix in coordinates ⃗x, ⃗x ′ with its Wigner representation to obtain
+i2k0
+� 1
+2π
+�2
+∂z
+�
+R2 �sν
+′ei⃗ξ·⃗x′d⃗ξ + 2(∇X · ∇X′)
+� 1
+2π
+�2 �
+R2 �sν
+′ei⃗ξ·⃗x′d⃗ξ + 2k2
+0Φ(⃗x, ⃗x′, z)sν
+′ = 0
+� 1
+2π
+�2 �
+R2
+�
+∂z�sν
+′ + 1
+k0
+(⃗ξ · ∇X)�sν
+′ −
+�
+R2 ik0Φ(⃗x, ⃗x′, z)sν
+′e−i⃗ξ·⃗x′d⃗x′
+�
+ei⃗ξ·⃗x′d⃗ξ = 0, ν = 0, · · · , 3
+(21)
+where now the generalized Stokes parameters sν ′ have been replaced by their respective spatial Fourier
+transforms �sν ′ with respect to the differential coordinate ⃗x ′ and, hence, are written in terms of the
+5
+
+Wigner distribution functions
+�s0
+′(⃗x, ⃗ξ, z, ω) = �
+WXX(⃗x, ⃗ξ, z, ω) + ��
+WY Y (⃗x, ⃗ξ, z, ω)
+�s1
+′(⃗x, ⃗ξ, z, ω) = �
+WXX(⃗x, ⃗ξ, z, ω) − �
+WY Y (⃗x, ⃗ξ, z, ω)
+�s2
+′(⃗x, ⃗ξ, z, ω) = �
+WXY (⃗x, ⃗ξ, z, ω) + �
+WY X(⃗x, ⃗ξ, z, ω)
+�s3
+′(⃗x, ⃗ξ, z, ω) = i
+�
+�
+WXY (⃗x, ⃗ξ, z, ω) − �
+WY X(⃗x, ⃗ξ, z, ω)
+�
+(22)
+which comprise the same result as Luis’ [16] Eq. (19). Recognizing that the term in square brackets
+must be zero in order to satisfy (21), we obtain the vector transport equations,
+∂z �
+S(⃗x, ⃗ξ, z, ω) + 1
+k0
+(⃗ξ · ∇X) �
+S(⃗x, ⃗ξ, z, ω) =
+�
+R2 ik0Φ(⃗x, ⃗x′, z)S(⃗x, ⃗x′, z, ω)e−i⃗ξ·⃗x′d⃗x′
+= − ik0
+(2π)2
+�
+R4 Φ(⃗x, ⃗x′, z, ω) �
+S(⃗x, ⃗ξ′, z, ω)ei(⃗ξ′−⃗ξ)·⃗x′d⃗ξ′d⃗x′
+= − ik0
+(2π)2
+�
+R2 Φ(⃗x, ⃗ξ − ⃗ξ′, z, ω) �
+S(⃗x, ⃗ξ′, z, ω)d⃗ξ′
+(23)
+where the 4-vector �
+S ≡ {�s0 ′, �s1 ′, �s2 ′, �s3 ′}T and S is the associated inverse FT with respect to wavevector
+⃗ξ. Equation (23) thus denotes four separate transport equations, each governing one component �s ′
+ν, ν =
+0 · · · 3. The term involving the vector potential can be written in several useful forms; the second line
+and matches the results of [33] (Eqn. 2.4) and [12] (Eqn. 1.1), albeit with a different convention for the
+Fourier Transform, while the final convolution form is found in [4] (Eqn. 2).
+Expression (23) is the fundamental vector transport equation that governs the evolution of the gener-
+alized Stokes parameters in the direction of propagation, z. In the scalar case (e.g., analysis of the 1D
+Schr¨odinger equation [33] or scalar optical wave propagation [10], [23]), Eq. (23) is often taken as the
+starting point in predicting the evolution of �
+WXX(⃗x, ⃗ξ, z, ω). Here we have extended these prior works
+to the full vector electric field in order to account for spatially dependent polarization. Related works on
+the full vector transport equations for the Wigner distribution include [26] (Eq. 1.6), and [17]. However
+we believe this work to be the first extension of such analyses to partially polarized optical fields.
+III.
+PARTIALLY-COHERENT, VECTOR TRANSPORT OF INTENSITY
+In this section we extend the transport-of-intensity equations (TIEs) from the partially coherent scalar
+case, as described in [23, 35], to the partially-coherent vector case. To arrive at such a model, we follow
+an approach used in quantum mechanics for obtaining the so-called “hydrodynamic” model, so named
+for the resemblance of the model to the continuity and momentum equations commonly found in fluid
+mechanics. Specifically, we take “moments” of Eq. (23) with respect to the wavevector. The first two
+such moments are obtained by multiplying (23) by unity and ⃗ξ respectively, and then integrating over the
+wavevector. The resulting expressions govern the conservation of mass (intensity), momentum (phase),
+and energy of the system. This approach has been used in analysis of the 1-D Schr¨odinger equation (see
+[4, 7, 12]) and has only very recently been extended to the 2-D Pauli equation [17]. While the dominant
+application area has been quantum mechanics, Marcuvitz [18] has suggested the approach as a general
+technique for studying wave propagation in the scalar case.
+In this work, we extend this “method of moments” to the vector transport equation (23) for partially
+coherent propagation problems in optics. The first such conservation equation is obtained by directly
+integrating (23) (that is, taking the “zeroth” moment) which yields
+∂z
+�
+R2
+�
+S(⃗x, ⃗ξ, z, ω)d⃗ξ + ∇X · 1
+k0
+�
+R2
+⃗ξ �
+S(⃗x, ⃗ξ, z, ω)d⃗ξ = 0.
+(24)
+To see that the Wigner potential term integrates to zero, replace the generalized Stokes parameters by
+their inverse spatial Fourier transforms (in frequency variable ⃗ξ′), in which case integrating the right
+6
+
+hand side of (23) over wavevector ⃗ξ can be carried out as
+=
+�
+R6
+ik0
+(2π)2 �
+S(⃗x, ⃗ξ ′, z, ω)ei⃗ξ ′·⃗x′Φ(⃗x, ⃗x ′, z)e−i⃗ξ·⃗x ′d⃗x ′d⃗ξ ′d⃗ξ
+=
+ik0
+(2π)2
+�
+R4
+�
+S(⃗x, ⃗ξ ′, z, ω)ei⃗ξ ′·⃗x ′d⃗ξ ′
+�
+R2 e−i⃗ξ·⃗x ′d⃗ξΦ(⃗x, ⃗x ′)d⃗x ′
+=
+ik0
+(2π)2
+�
+R4
+�
+S(⃗x, ⃗ξ ′, z, ω)ei⃗ξ ′·⃗x ′d⃗ξ ′δ(⃗x ′)Φ(⃗x, ⃗x ′)d⃗x ′
+=
+ik0
+(2π)2 Φ(⃗x, 0)
+�
+R2
+�
+S(⃗x, ⃗ξ ′, z, ω)d⃗ξ ′ = 0.
+(25)
+In the last step we have leveraged the definition of Φ(⃗x, ⃗x ′, z) (17,18) which holds that when ⃗x′ = 0, the
+potential vanishes, that is, Φ(⃗x, 0) = 0. This statement is true whether we treat the dielectric constant
+fluctuations as a deterministic or a random process under the Markov approximation (18). Finally, to
+put (24) in the same form as the coherent Transport of Intensity Equation (TIE) [20], we require the
+definitions
+ρ(⃗x, z, ω) ≡
+�
+R2
+�
+S(⃗x, ⃗��, z, ω)d⃗ξ
+1
+k0
+�
+R2
+⃗ξ �
+S(⃗x, ⃗ξ, z, ω)d⃗ξ ≡ ρ(⃗x, z, ω) ◦ ⃗v(⃗x, z, ω)
+(26)
+where ◦ denotes the Hadamard product. Equation (26) therefore defines four generalized intensities
+ρν(⃗x, z, ω) ≡
+�
+R2 �sν ′(⃗x, ⃗ξ, z, ω)d⃗ξ, ν = 0, 1, 2, 3.
+In addition, (26) implicitly defines each element of
+⃗v(⃗x, z, ω) as
+⃗vν(⃗x, z, ω) ≡
+�
+R2 ⃗ξ �sν ′(⃗x, ⃗ξ, z, ω)d⃗ξ
+k0ρν(⃗x, z, ω)
+=
+�
+R2 ⃗ξ �sν ′(⃗x, ⃗ξ, z, ω)d⃗ξ
+k0
+�
+R2 �sν ′(⃗x, ⃗ξ, z, ω)d⃗ξ
+, ν = 0, 1, 2, 3
+(27)
+in which case (24) becomes
+∂zρ(⃗x, z, ω) + ∇X · [ρ(⃗x, z, ω) ◦ ⃗v(⃗x, z, ω)] = 0,
+(28)
+which is the vector TIE for partially coherent light. Note that whereas in our prior analysis [20], the above
+expression was a single scalar equation, in this case both ρ(⃗x, z, ω) and the product ρ(⃗x, z, ω) ◦⃗v(⃗x, z, ω)
+are column vectors each comprising four elements. Thus ρν and vν represent, respectively, the ν−th
+component of the Stokes 4-vector (ν = 0, 1, 2, 3) and, as we will show in section (III C), the rate of
+change with z of the transverse location of the ν−th component of the Stokes 4-vector. Hence, all eight
+components ρν and vν are real, the total beam intensity ρ0 must be non-negative, and the remaining
+seven components can be positive, negative, or zero. Just as for Stokes parameters for monochromatic
+light, the components of the Stokes 3-vector (ρ1, ρ2, ρ3) are proportional to intensity but are not limited
+to non-negative values.
+A.
+Mixture Model for Partially Coherent Stokes Parameters
+Equations (28) are transport equations governing each of the generalized Stokes parameters during
+propagation in a (possibly) inhomogeneous medium. By definition, the Stokes parameters were defined
+as an expectation over realizations of the X, Y components of the electric field Fourier amplitudes,
+EX(⃗x, z, ω), EY (⃗x, z, ω).
+Both the quantity being transported, ρ(⃗x, z, ω) and the “velocity” of that
+transport, ⃗v(⃗x, z, ω) carry simple physical interpretations when placed in the context of a particular
+model for the electric field as will be shown next.
+To aid in this interpretation, recall the electric field “transverse wave” model (3). Until now we have
+imposed no further model structure on the form of EX(⃗x, z, ω), EY (⃗x, z, ω). Leveraging prior work [20]
+for linearly-polarized, coherent beams, let the complex Fourier amplitudes take the form
+EX(⃗x, z, ω) = ρ1/2
+m (⃗x, z, ω)eiφm(⃗x,z,ω) cos(γm(⃗x, z, ω))
+EY (⃗x, z, ω) = ρ1/2
+m (⃗x, z, ω)eiφm(⃗x,z,ω) sin(γm(⃗x, z, ω))
+(29)
+7
+
+where the subscript m denotes “model”. The electric field is therefore described by a magnitude, phase,
+and spatially dependent linear polarization angle γm(⃗x, z, ω) which governs the ratio of Fourier amplitudes
+in the X and Y directions. It must be noted, however, that the model structure (29) presumes a polarized
+beam and should therefore be viewed as conditional on the beam being completely polarized. Such a
+model is clearly not appropriate for unpolarized light.
+While the first Stokes parameter �s0 is independent of the state of polarization, the same cannot be
+said of �sν, ν = 1 · · · 3. For partially polarized light it is therefore appropriate to use the mixture model
+[29]
+�
+�
+�
+�
+s′
+0(⃗x, ⃗x′, z, ω)
+s′
+1(⃗x, ⃗x′, z, ω)
+s′
+2(⃗x, ⃗x′, z, ω)
+s′
+3(⃗x, ⃗x′, z, ω)
+�
+�
+�
+� = [1 − P]
+�
+�
+�
+�
+s′
+0(⃗x, ⃗x′, z, ω)
+0
+0
+0
+�
+�
+�
+� + P
+�
+�
+�
+�
+s′
+0(⃗x, ⃗x′, z, ω)
+s′
+1(⃗x, ⃗x′, z, ω|P)
+s′
+2(⃗x, ⃗x′, z, ω|P)
+s′
+3(⃗x, ⃗x′, z, ω|P)
+�
+�
+�
+�
+(30)
+where the weighting is given by the Degree Of Polarization (DOP)
+P(⃗x, z, ω) =
+�
+(s1)2 + (s2)2 + (s3)2
+s0
+���
+⃗x1=⃗x2=⃗x =
+�
+1 − 4Det [W]
+Tr [W]2
+���
+⃗x1=⃗x2=⃗x.
+(31)
+Equation (31) thus defines a positive quantity 0 ≤ P(⃗x, z, ω) ≤ 1 which specifies the fraction of the beam
+intensity at location {⃗x, z} and within an infinitesimal range of optical frequencies {ω, ω + dω} that is
+fully polarized. The degree to which a beam is polarized is therefore directly related to coherence among
+the components of the optical field at a given transverse location. We note also that while P(⃗x, z, ω)
+varies spatially and with frequency, as defined it does not depend on the separation ⃗x ′ between two
+points on the beam face.
+Given the above definitions, we can better understand the quantities in the partially coherent TIE
+(28) as will be described next in sections (III B) and (III C). These definitions will also allow us to define
+a polarization gradient in the partially coherent case as will be shown in section (III D).
+B.
+Interpretation of the Partially Coherent Vector TIE
+To understand the meaning of ρ(⃗x, z, ω) we expand the first component of �
+S(⃗x, ⃗ξ, z, ω) which is just
+�s0 ′(⃗x, ⃗ξ, z, ω) and use the fact that the Wigner distributions can be expressed as Fourier transforms to
+obtain
+ρ0(⃗x, z, ω) =
+�
+R2 �s0
+′(⃗x, ⃗ξ, z, ω)d⃗ξ =
+�
+R4 (WXX(⃗x, ⃗x′, z, ω) + WY Y (⃗x, ⃗x′, z, ω)) e−i⃗ξ·⃗x′d⃗x ′d⃗ξ
+=
+�
+R2 (WXX(⃗x, ⃗x ′, z, ω) + WY Y (⃗x, ⃗x ′, z, ω)) δ(⃗x ′)d⃗x ′
+= SXX(⃗x, z, ω) + SY Y (⃗x, z, ω)
+(32)
+where we have invoked the definition of the delta function as the Fourier Transform of unity. Recall also
+that by definition, in transformed coordinates, at ⃗x ′ = 0,
+Wij(⃗x, 0, z, ω) = Sij(⃗x, z, ω), i, j = X, Y
+(33)
+so that the first component of ρ(⃗x, z, ω) is by definition the auto-spectral density of the field at transverse
+location ⃗x, z as demonstrated by (32). A similar analysis of the other components of ρ(⃗x, z, ω) shows
+that the full four-component Stokes vector is given by
+ρ(⃗x, z, ω) =
+�
+R2
+�
+�
+�
+�
+�
+�s′
+0
+P �s′
+1
+P �s′
+2
+P �s′
+3
+�
+�
+�
+�
+� d⃗ξ =
+�
+�
+�
+�
+SXX(⃗x, z, ω) + SY Y (⃗x, z, ω)
+P (SXX(⃗x, z, ω) − SY Y (⃗x, z, ω))
+P (SXY (⃗x, z, ω) + SY X(⃗x, z, ω))
+iP (SXY (⃗x, z, ω) − SY X(⃗x, z, ω))
+�
+�
+�
+� =
+�
+�
+�
+�
+s0
+Ps1
+Ps2
+Ps3
+�
+�
+�
+�
+⃗x1=⃗x2≡⃗x
+(34)
+Thus, the quantities being transported can be written simply as sums and differences of the transverse
+spectral densities that is, the generalized Stokes parameters for partially coherent light.
+8
+
+For example, substituting the model (29) for the first Stokes parameter
+s0 = ⟨EX(⃗x, z, ω)E∗
+X(⃗x, z, ω)⟩ + ⟨EY (⃗x, z, ω)E∗
+Y (⃗x, z, ω)⟩
+=
+�
+ρm(⃗x, z, ω) cos2(γm(⃗x, z, ω) + ρm(⃗x, z, ω) sin2(γm(⃗x, z, ω)
+�
+= ⟨ρm(⃗x, z, ω)⟩ ≡ ρ0(⃗x, z, ω).
+(35)
+Hence the first generalized Stokes parameter ρ0(⃗x, z, ω) is proportional to the expected beam spectral
+intensity at location {⃗x, z} in our model. Performing the same substitution for the remaining components
+in (34) we have
+ρ(⃗x, z, ω) =
+�
+�
+�
+�
+⟨ρm(⃗x, z, ω)⟩
+P(⃗x, z, ω) ⟨ρm(⃗x, z, ω) cos(2γm(⃗x, z, ω))⟩
+P(⃗x, z, ω) ⟨ρm(⃗x, z, ω) sin(2γm(⃗x, z, ω))⟩
+0
+�
+�
+�
+� .
+(36)
+The model structure (29) suggests a simple and well-known interpretation of the generalized Stokes
+parameters for linearly polarized light.
+However, for unpolarized light only the first component of
+ρ(⃗x, z, ω) is non-zero. The final intensity component is given by ρ3(⃗x, z, ω) = 0 due to the fact that we
+are considering only linear polarization.
+C.
+Interpretation of the Transport Velocity
+The components of ⃗v(⃗x, z, ω) in Eq. (28) are referred to as “velocities” as they were noted in the
+coherent case to govern the change in optical path in the transverse direction per unit change in the
+direction of propagation [11, 20]. We present a basic derivation supporting this interpretation in Appendix
+(A). This terminology is also in keeping with the wave mechanics interpretation of the transport equation,
+where the “transport” of intensity occurs in the transverse plane as the beam progresses in z. The first
+velocity term in this partially coherent case is obtained via (27),
+⃗v0(⃗x, z, ω) = 1
+k0
+�
+R2 ⃗ξ �s′
+0(⃗x, ⃗ξ, z, ω)d⃗ξ
+�
+R2 �s′
+0(⃗x, ⃗ξ, z, ω)d⃗ξ
+=
+�
+R2 ⃗ξ
+�
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ
+k0ρ0(⃗x, z, ω)
+(37)
+The non-negativity of �s′
+0 allows us to interpret (37) as an average spatial frequency in the transverse
+plane (see e.g., Boashash [2]) normalized by k0. In fact, in [2] it was noted that the generalized definition
+of frequency is an average change in phase per unit change in the independent variable, which in the
+present context corresponds to the transverse distance ⃗x. Thus, (37) implicitly defines a phase gradient
+∇Xφ(⃗x, z, ω) ≡
+�
+R2 ⃗ξ �s′
+0(⃗x, ⃗ξ, z, ω)d⃗ξ
+�
+R2 �s′
+0(⃗x, ⃗ξ, z, ω)d⃗ξ
+(38)
+so that ⃗v0(⃗x, z, ω) = k−1
+0 ∇Xφ(⃗x, z, ω), which is precisely the definition for velocity found in the monochro-
+matic case [20]. This definition of generalized phase was also used in [34] for scalar, partially coherent
+electric fields. Here, we have shown this definition to be appropriate for vector electric fields as well. In-
+deed, we will show momentarily that these definitions are not only appropriate for transport of intensity,
+ρ0(⃗x, z, ω), but for transport of two other generalized Stokes parameters.
+Now consider again the mixture model (30). Substituting these definitions into (37) yields for the
+denominator SXX(⃗x, z, ω)+SY Y (⃗x, z, ω) = ρ0(⃗x, z, ω). For the numerator, considering first the polarized
+9
+
+portion, we can expand using Eqn. (19) to give
+�
+R2
+��ξ
+�
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ
+=
+�
+R4
+⃗ξ
+��
+EX(⃗x − ⃗x′/2, z, ω)E∗
+X(⃗x + ⃗x′/2, z, ω)
+�
++
+�
+EY (⃗x − ⃗x′/2, z, ω)E∗
+Y (⃗x + ⃗x′/2, z, ω)
+��
+e−i⃗ξ·⃗x′d⃗ξd⃗x′
+=
+�
+R2
+��
+EX(⃗x − ⃗x′/2, z, ω)E∗
+X(⃗x + ⃗x′/2, z, ω)
+�
++
+�
+EY (⃗x − ⃗x′/2, z, ω)E∗
+Y (⃗x + ⃗x′/2, z, ω)
+�� �
+R2
+⃗ξe−i⃗ξ·⃗x′d⃗ξd⃗x′
+= i
+�
+R2
+��
+EX(⃗x − ⃗x′/2, z, ω)E∗
+X(⃗x + ⃗x′/2, z, ω)
+�
++
+�
+EY (⃗x − ⃗x′/2, z, ω)E∗
+Y (⃗x + ⃗x′/2, z, ω)
+��
+δ′(⃗x′)d⃗x′
+= i
+�
+R2 ∇X′
+��
+EX(⃗x − ⃗x′/2, z, ω)E∗
+X(⃗x + ⃗x′/2, z, ω)
+�
++
+�
+EY (⃗x − ⃗x′/2, z, ω)E∗
+Y (⃗x + ⃗x′/2, z, ω)
+��
+δ(⃗x′)d⃗x′
+= i∇X′
+��
+EX(⃗x − ⃗x′/2, z, ω)E∗
+X(⃗x + ⃗x′/2, z, ω)
+�
++
+�
+EY (⃗x − ⃗x′/2, z, ω)E∗
+Y (⃗x + ⃗x′/2, z, ω)
+�� �����
+⃗x′→0
+= ⟨ρm(⃗x, z)∇Xφm(⃗x, z)⟩ .
+(39)
+where the final line substitutes Eq. (29) for EX, EY and takes the required gradient ∇X′. In the second
+to last line we leveraged the identity in Eq. (7) of [3] concerning integrals over derivatives of the delta
+function. The end result is that under the mixture model, and assuming amplitude and transverse phase
+gradient are statistically independent,
+⟨∇Xφm(⃗x, z, ω)⟩ = ∇Xφ(⃗x, z, ω)
+1
+k0
+⟨∇Xφm(⃗x, z, ω)⟩ = ⃗v0(⃗x, z, ω)
+(40)
+The definition (38) therefore can be interpreted as the expected model phase and the corresponding
+“velocity” as the expected change in optical path in the transverse direction per unit change in the
+direction of propagation. Notably, this result is independent of the DOP. We may perform a similar
+analysis on the remaining components of ⃗v(⃗x, z, ω), finding that
+⃗v1(⃗x, z, ω) =
+�
+R2 ⃗ξ �s′
+1(⃗x, ⃗ξ, z, ω)d⃗ξ
+k0ρ1(⃗x, z, ω)
+= P(⃗x, z, ω) ⟨ρm∇Xφm(⃗x, z, ω) cos(2γm(⃗x, z, ω))⟩
+k0P(⃗x, z, ω) ⟨ρm cos(2γm(⃗x, z, ω))⟩
+= ⃗v0(⃗x, z, ω)
+⃗v2(⃗x, z, ω) =
+�
+R2 ⃗ξ �s′
+2(⃗x, ⃗ξ, z, ω)d⃗ξ
+k0ρ2(⃗x, z, ω)
+= P(⃗x, z, ω) ⟨ρm∇Xφm(⃗x, z, ω) sin(2γm(⃗x, z, ω))⟩
+k0P(⃗x, z, ω) ⟨ρm sin(2γm(⃗x, z, ω))⟩
+= ⃗v0(⃗x, z, ω). (41)
+Thus, in the case of linear polarization, all three non-zero generalized Stokes parameters are transported
+with the same transverse velocity.
+∂zρν(⃗x, z, ω) + ∇X · [ρν(⃗x, z, ω)v0(⃗x, z, ω)] = 0, ν = 0, 1, 2.
+(42)
+This is sensible as it suggests that, in expectation, both the beam intensity and properties related to the
+state of linear polarization are moving together in the transverse plane during propagation. Importantly,
+this also suggests that while the transport model requires an equation governing ⃗v0 (see section IV), it
+does not require separate equations for ⃗v1, ⃗v2.
+It it worth mentioning the relationship between the velocity vector and the well-known Poynting vector.
+Begin by noting that the numerator in (27) is of the form of the average Poynting vector for partially
+coherent light,
+P(⃗x, z) ≡ 1
+k0
+�
+R2
+⃗ξ �s′
+0(⃗x, ⃗ξ, z, ω)d⃗ξ,
+(43)
+so that ˜P(⃗x, z) ≡ ⃗v(⃗x, z, ω) is, in fact, the normalized Poynting vector as defined in [21] (Eq. 8 of the
+cited work). Also in [21] is was suggested that the normalized Poynting vector be decomposed via the
+Helmholtz decomposition theorem as
+⃗v(⃗x, z, ω) ≡ ⃗vS(⃗x, z, ω) + ⃗vV (⃗x, z, ω)
+= k−1
+0 ∇XφS(⃗x, z, ω) + k−1
+0 ∇X × ⃗φV (⃗x, z, ω)
+(44)
+10
+
+where S and V refer to scalar and vector contributions, respectively.
+If we let the scalar phase be
+φS(⃗x, z, ω) = φm(⃗x, z, ω) and define
+φV (⃗x, z, ω) =
+�dγ(⃗x, ω)
+dy
+z, −dγ(⃗x, ω)
+dx
+z, 0
+�
+(45)
+then we have that ⃗Ω(⃗x, z, ω) = [∇ × φV (⃗x, z, ω)]X. The partially coherent vector TIE would then be
+written
+∂zρ(⃗x, z, ω) + ∇X · [ρ(⃗x, z, ω)⃗vS(⃗x, z, ω)] + ∇X · [ρ(⃗x, z, ω)⃗vV (⃗x, z, ω)] = 0
+(46)
+which would clearly suggest that ∇X ·
+�
+ρ(⃗x, z, ω)⃗Ω(⃗x, z, ω)
+�
+= 0 given Eq. (28). In fact, we will show in
+the next section that this relationship indeed holds for linearly polarized light.
+D.
+Definition and Interpretation of the Polarization Angle Gradient
+Since we are considering a linearly polarized vector beam ρ3(⃗x, z, ω) = 0. However, although the first
+term in (24) is zero, the second term inside the transverse divergence operator is (following the same
+model interpretation and simplification as in (39))
+1
+k0
+�
+R2
+⃗ξ �s′
+3(⃗x, ⃗ξ, z, ω)d⃗ξ = −
+�
+ρm(⃗x, z, ω)P(⃗x, z, ω)
+k0
+∇Xγm(⃗x, z, ω)
+�
+= −ρ0(⃗x, z, ω)⃗Ω(⃗x, z, ω)
+(47)
+so that by (24) we have the condition
+∇X ·
+�
+ρ0(⃗x, z, ω)⃗Ω(⃗x, z, ω)
+�
+= 0
+(48)
+as we implied at the end of the previous section. This relationship was also found to hold in the coherent
+case [20] and will be leveraged later in the derivation. However, also note that in arriving at (48) we have
+produced a definition for the spatial gradient of the polarization angle that is appropriate for partially
+coherent light, given by
+⃗Ω(⃗x, z, ω) =
+−iP(⃗x, z, ω)
+�
+R2 ⃗ξ
+�
+�
+WXY (⃗x, ⃗ξ, z, ω) − �
+WY X(⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ
+k0ρ0(⃗x, z, ω)
+= P(⃗x, z, ω)
+k0
+⟨∇Xγm(⃗x, z, ω)⟩ .
+(49)
+The DOP is appropriately part of the definition (49) as one cannot define ⃗Ω for an unpolarized beam.
+Note also that in accordance with the works of Salem et al. [28] and Korotkova et al. [14] we allow that
+the DOP can vary in frequency ω, as well as the transverse location ⃗x, and the direction of propagation
+z.
+Just as with the normalized phase gradient, Eqn. (49) is expressed as a suitable average wavevector over
+the distribution �s′
+3. Similarly, it can be interpreted as a transverse, spatial gradient in the angle (phase)
+between the X and Y components. In the limit of a fully coherent beam we recover our deterministic
+definition. Importantly, as the beam de-polarizes we will see the terms involving ⃗Ω(⃗x, z, ω) vanish, a
+point we elaborate on in the next section.
+We note that a definition of polarization angle for partially coherent beams was proposed previously
+by Korotkova et al. [25], [13]
+θ(⃗x, z, ω) ≡ 1
+2 arctan
+�
+2Re {SXY (⃗x, z, ω)}
+SXX(⃗x, z, ω) − SY Y (⃗x, z, ω)
+�
+.
+(50)
+This definition is somewhat consistent with our model structure (29) in the sense that substituting the
+polarized electric field (29) into (50) gives
+θ(⃗x, z, ω) ≡ 1
+2 arctan
+�s2(⃗x, z, ω)
+s1(⃗x, z, ω)
+�
+= 1
+2 arctan
+� ⟨sin(2γm(⃗x, z, ω))⟩
+⟨cos(2γm(⃗x, z, ω))⟩
+�
+.
+(51)
+However, this definition only yields our model polarization angle in the deterministic case as the ratio of
+expectations of the sin, cos terms does not equal the mean of the ratio in general. Moreover, the DOP
+11
+
+does not appear explicitly in the expression as it does in (49) and instead must be viewed as a part of
+the quantity SXY (⃗x, z, ω).
+More importantly, as we will see in section (IV), the quantity that governs the transverse movement
+of intensity is the polarization angle gradient as opposed to the angle itself. As we have just shown,
+the gradient is obtained via the first moment, Eq. (47). The resulting expression (49) accounts for the
+spatial frequencies ⃗ξ and yields directly the expected value of polarization angle gradient. On the other
+hand, differentiating (50) with respect to the transverse coordinates yields
+∇Xθ(⃗x, z, ω)
+= [SXX(⃗x, z, ω) − SY Y (⃗x, z, ω)]∇XSXY (⃗x, z, ω) − SXY (⃗x, z, ω)∇X[SXX(⃗x, z, ω) − SY Y (⃗x, z, ω)]
+4SXY (⃗x, z, ω)2 + [SXX(⃗x, z, ω) − SY Y (⃗x, z, ω)]2
+.
+(52)
+As with Eq. (51), this definition of phase gradient results in products and sums of expectations of sin, cos
+functions so that the result equals ⟨∇Xγm(⃗x, z, ω)⟩ only in the deterministic case where no averaging
+operations are performed.
+Finally, we note that our definition (49) arose quite naturally as a consequence of 1) the paraxial
+transport equation for the generalized Stokes parameters, Eq. (24) and 2) the model Eq. (29) governing
+the expected amplitude, phase, and polarization angle of the electric field at location (⃗x, z) and frequency
+ω. The definition is also consistent with the definition of partially coherent phase used in the literature
+(Eqn. 38), and will therefore be used in what follows for the expected polarization angle gradient of our
+vector beam.
+E.
+Conservation of the generalized Stokes parameters
+To conclude this section, we point out an interesting result concerning the conservation of the gener-
+alized Stokes parameters during propagation through a (possibly) inhomogeneous medium. Since each
+of the parameters sν obey the same transport equation (28), the integrals of these quantities in the
+transverse plane are constant and are therefore conserved during propagation. To see that this is true,
+expand Eq. (28), recall the definition of the material derivative D(·)/Dz ≡ ∂z(·) + (⃗v · ∇X)(·), and
+then convert to Lagrangian coordinates whereby the spatial coordinates ⃗x are written as functions of z
+and the initial value, that is, ⃗x → ⃗xz(⃗x0) (which we will abbreviate as simply ⃗xz and the corresponding
+gradient ∇Xz). These steps can be written
+∂zρν(⃗x, z, ω) + ∇Xρν(⃗x, z, ω) · ⃗vν(⃗x, z, ω) + ρν(⃗x, z, ω) [∇X · ⃗vν(⃗x, z, ω)] = 0
+Dρν(⃗x, z, ω)
+Dz
++ ρν(⃗x, z, ω) [∇X · ⃗vν(⃗x, z, ω)] = 0
+dρν(⃗xz, ω)
+dz
++ ρν(⃗xz, ω) [∇Xz · ⃗vν(⃗xz, ω)] = 0,
+ν = 0, 1, 2, 3.
+(53)
+The resulting ordinary differential equation possesses the solution
+ρ(⃗xz, ω) = ρ(⃗x0, ω) exp
+�
+−
+� z
+s=0
+∇Xs · ⃗v(⃗xs, ω)d⃗xs
+�
+.
+(54)
+Therefore, the integral of the generalized Stokes parameters at any point along the propagation path is
+related to their initial values via the divergence of the velocity field. It can also be shown (see Appendix
+B, ref. [6]) that the expression (54) can be written alternatively as
+ρ(⃗xz, ω) = det |J⃗x0(⃗xz)|−1ρ(⃗x0, ω).
+(55)
+where the Jacobian J⃗x0(⃗xz) is the derivative of the coordinate functions ⃗xz(⃗x0, z) with respect to the
+fixed (initial) coordinates ⃗x0. If the Lagrangian coordinate mappings ⃗xz(⃗x0, z) are one-to-one, smooth
+functions of ⃗x0, this expression can be shown via the change of variables theorem to be equivalent to the
+integral formulation [1]
+�
+X
+ρ(⃗xz, ω)d⃗xz =
+�
+X
+ρ(⃗x0, ω)d⃗x0
+(56)
+12
+
+(see also Villani Chapter 11 [31]). Thus, it can be stated that the integral of each of the generalized
+Stokes parameters over the transverse plane is conserved on propagation. Interestingly, this conclusion
+was reached by an entirely different approach in [13]. However, in that work the claim was made with
+respect to propagation in free-space whereas here we see the integrals of the Stokes parameters are
+conserved even in an inhomogeneous medium.
+IV.
+MOMENTUM EQUATION FOR PARTIALLY-COHERENT, LINEARLY-POLARIZED
+LIGHT
+The above discussion defined both intensity and velocity in the general case of a propagating, linearly
+polarized, partially coherent optical field. Each of the generalized Stokes parameters were shown to be
+transported with a single velocity. In this section, we will derive the equation that governs this velocity.
+As we described in section (II), the process for obtaining the continuity equation can be viewed as
+taking the zeroth “moment” of the fundamental transport equation with respect to wavenumber, that is,
+integrating 23; (see again [18], [7], and [12]). Thus, to derive the partially coherent momentum equation
+we multiply (23) by ⃗ξ and integrate over wavenumber. The result is written
+∂z
+�
+R2
+⃗ξ �
+S(⃗x, ⃗ξ, z, ω)d⃗ξ + ∇X · 1
+k0
+�
+R2(⃗ξ ⊗ ⃗ξ) �
+S(⃗x, ⃗ξ, z, ω)d⃗ξ =
+�
+R2
+�
+R2 ik0⃗ξ �
+S(⃗x, ⃗ξ′, z, ω)Φ(⃗x, ⃗ξ − ⃗ξ′, z)d⃗ξ′d⃗ξ.
+(57)
+The first challenge associated with (57) is the term on the right-hand-side, integration of Wigner poten-
+tial. This term can be greatly simplified if we are willing to restrict the model to a weakly inhomogeneous
+medium where the transverse gradient in dielectric constant is small at a given transverse location ⃗x. In
+this case, we explore a series solution for the terms inside the potential function, for example,
+ϵ1(⃗x + ⃗x′
+2 , z) − ϵ1(⃗x − ⃗x′
+2 , z) ≈ ϵ1(⃗x, z) ± ∇Xϵ1(x, z) · ⃗x′ + · · ·
+(58)
+so that the potential functions (17,18) become
+Φ(⃗x, ⃗x′, z) ≈ ⃗x′ · ∇X
+�1
+2ϵ1(⃗x, z)
+�
++ O(⃗x′3)
+Φ(⃗x, ⃗x′, z) ≈ ⃗x′ · ∇X
+�
+−ik0
+4 A(0, z)
+�
++ O(⃗x′2)
+(59)
+Using these expressions, and representing the terms inside the transverse gradient generically as g(⃗x)
+(to accommodate a deterministic or stochastic medium), we we see that the inner double integral on the
+right hand side of Eq. (57) can be expanded using the Fourier representation of the potential as
+� 1
+2π
+�2 �
+R2
+�
+R2 ik0 �
+S(⃗x, ⃗ξ′, z, ω)
+�
+ei(⃗ξ−⃗ξ′)·⃗x′⃗x′ · ∇Xg(⃗x, z)d⃗x′
+�
+d⃗ξ′
+= −
+� 1
+2π
+�2 �
+R2
+�
+R2 k0 �
+S(⃗x, ⃗ξ′, z, ω)
+�
+∇ξ′ei(⃗ξ−⃗ξ′)·⃗x′ · ∇Xg(⃗x, z)d⃗x′
+�
+d⃗ξ′
+= −
+� 1
+2π
+�2 �
+R2 k0 �
+S(⃗x, ⃗ξ′, z, ω)∇ξ′
+��
+R2 ei(⃗ξ−⃗ξ′)·⃗x′d⃗x′
+�
+· ∇Xg(⃗x, z)d⃗ξ′
+= −
+�
+R2 k0∇⃗ξ′ δ(⃗ξ − ⃗ξ′) �
+S(⃗x, ⃗ξ′, z, ω) · ∇Xg(⃗x, z)d⃗ξ′
+= −
+�
+R2 k0δ(⃗ξ − ⃗ξ′)∇⃗ξ′ �
+S(⃗x, ⃗ξ′, z, ω) · ∇Xg(⃗x, z)d⃗ξ′
+= −k0∇⃗ξ �
+S(⃗x, ⃗ξ, z, ω) · ∇Xg(⃗x, z)
+(60)
+where we have used the trick found in [19]( Eq.
+5.29), which is to note that ∇ξ′
+�
+ei(⃗ξ−⃗ξ′)·⃗x′�
+=
+−i⃗x′ei(⃗ξ−⃗ξ′)·⃗x′. The expression (60) is the “linearized” Wigner potential (see, for example, [33]) and
+transforms Eqn. (57) into
+∂z
+�
+R2
+⃗ξ �
+S(⃗x, ⃗ξ, z, ω)d⃗ξ + ∇X · 1
+k0
+�
+R2(⃗ξ ⊗ ⃗ξ) �
+S(⃗x, ⃗ξ, z, ω)d⃗ξ = −k0∇Xg(⃗x, z)
+�
+R2
+�
+⃗ξ · ∇⃗ξ �
+S(⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ.
+(61)
+13
+
+We have already shown via Eq. (26) that the first term in (61) can be written
+∂z
+�
+R2
+⃗ξ �s′ν(⃗x, ⃗ξ, z, ω)d⃗ξ = k0∂z [ρν(⃗x, z, ω)⃗v0(⃗x, z, ω)] , ν = 0, · · · , 2
+(62)
+while for the third Stokes parameter we showed previously in Eqn. (47) that
+∂z
+�
+R2
+⃗ξ �s′
+3(⃗x, ⃗ξ, z, ω)d⃗ξ = −k0∂z
+�
+ρ0(⃗x, z, ω)⃗Ω(⃗x, z, ω)
+�
+.
+(63)
+The integral in the last term can also be simplified via integration by parts. Presuming that the Stokes
+parameters vanish at the boundaries of integration (as |⃗ξ| → ∞), the result is simply
+�
+R2
+�
+⃗ξ · ∇⃗ξ �
+S(⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ = −ρ(⃗x, z, ω)
+(64)
+for the first three Stokes parameters (ν = 0, 1, 2), while the integral disappears for the third since, in the
+absence of ellipticity, ρ3(⃗x, z, ω) = 0. With these simplifications, Eqn. (61) becomes
+∂z [ρν(⃗x, z, ω)⃗v0(⃗x, z, ω)] + ∇X · 1
+k2
+0
+�
+R2(⃗ξ ⊗ ⃗ξ) �s′ν(⃗x, ⃗ξ, z, ω)d⃗ξ = ρν(⃗x, z, ω)∇Xg(⃗x, z), ν = 0, 1, 2
+−∂z
+�
+ρ0(⃗x, z, ω)⃗Ω(⃗x, z, ω)
+�
++ ∇X · 1
+k2
+0
+�
+R2(⃗ξ ⊗ ⃗ξ) �s′
+3(⃗x, ⃗ξ, z, ω)d⃗ξ = 0
+(65)
+Equation (65) is a vector equation describing the evolution of the “momentum” ρ ◦ ⃗v for each of the
+generalized Stokes parameters and it allows us to develop expressions for the unknowns ⃗v0 and ⃗Ω. As
+we noted in section (III C), because there is only a single velocity associated with the first 3 equations,
+we need only focus on the expression (65) for ν = 0 and the last expression where ν = 3. We also note
+that the right hand side of the second expression is zero for the linearized potential since ρ3(⃗x, z, ω) = 0.
+As we will show, this leads to the conclusion that the polarization angle gradient will not change on
+propagation. Depolarization during propagation would therefore be a consequence of higher-order terms
+in the expansion of the Wigner potential or retention of the electric field divergence in the starting wave
+equation (see e.g., [5]).
+Recall the continuity equation (28) was obtained as the zeroth moment of the wave-vector with respect
+to the Stokes parameters (Eqn. 23) and contained the “velocity”, which is the first moment of the wave-
+vector with respect to the Stokes parameters. In turn, (65) contains the second moment of the wave-vector
+with respect to the Stokes parameters. As might be expected, if we were to construct the expression for
+the second moment it would contain the integral of third order wave-vector terms and so on. This is the
+so-called “closure problem” (see [12] Eqs. 3.3-3.5 and surrounding discussion of [17]).
+Obtaining closure requires an expression for this second moment (the term involving the outer product)
+in terms of already defined quantities. In our context, this means writing the integral involving the outer
+product in terms of ρ and ⃗v. This can be accomplished by again leveraging our electric field model (29).
+Note that using this particular field model as an expression to fix the closure problem was employed in
+both [17, 18]. To see how this can be done, expand the second term in (65) as was done in [18]. Doing
+so requires us to expand the Wigner-averaged outer product into its four constituent terms which are of
+the two basic forms.
+Using the first of equations (65) as an example, the outer product is seen to produce the following four
+integrals,
+�
+R2 ξ2
+ii
+�
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ,
+i ∈ X, Y
+�
+R2 ξiξj
+�
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ,
+i, j ∈ X, Y.
+(66)
+Both the unpolarized and polarized portions of the mixture model can be simplified in the same manner
+as was done for the velocity terms, Eq.
+(39).
+Substituting in the definition of either the unpolar-
+ized/polarized Wigner Transforms �
+WXX(⃗x, ⃗ξ, z, ω) and �
+WY Y (⃗x, ⃗ξ, z, ω), the first of the needed moments
+14
+
+in (66) can be simplified as
+�
+R2 ξ2
+XX
+�
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ
+= − ∂2
+∂x′2
+�
+EX
+�
+⃗x − ⃗x′
+2 , z, ω
+�
+E∗
+X
+�
+⃗x + ⃗x′
+2 , z, ω
+�
++ EY
+�
+⃗x − ⃗x′
+2 , z, ω
+�
+E∗
+Y
+�
+⃗x + ⃗x′
+2 , z, ω
+�� ����� x′ → 0
+y′ → 0
+.
+(67)
+Using our model for the electric field, Eq. (29), substituting into the above and taking the derivative
+and subsequent limits (and noting the procedure in the “y” direction is the same) yields
+�
+R2 ξ2
+XX
+�
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ = k2
+0ρ0(v2
+x + Ω2
+x) + (∂xρ0)2
+4ρ0
+− ∂2
+xρ0
+4
+�
+R2 ξ2
+Y Y
+�
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ = k2
+0ρ0(v2
+y + Ω2
+y) + (∂yρ0)2
+4ρ0
+− ∂2
+yρ0
+4
+(68)
+where vx,y and Ωx,y are, respectively, the “x” and “y” components of those vectors. In this and several
+subsequent expressions we omit the arguments (⃗x, z, ω) from the model quanitities for brevity.
+The
+“mixed” averages follow a similar procedure and are found to be
+�
+R2ξXξY
+�
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ = k2
+0ρ0(vxvy + ΩxΩy) + ∂xρ0∂yρ0
+4ρ0
+− ∂xyρ0
+4
+(69)
+so that we may finally write
+1
+k2
+0
+�
+R2
+�
+⃗ξ ⊗ ⃗ξ
+� �
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ =
+ρ0⃗v ⊗ ⃗v + ρ0⃗Ω ⊗ ⃗Ω +
+1
+4k2
+0
+�
+�
+(∂xρ0)2
+ρ2
+0
+− ∂2
+xρ0
+ρ0
+∂xρ0∂yρ0
+ρ2
+0
+− ∂xyρ0
+ρ0
+∂xρ0∂yρ0
+ρ2
+0
+− ∂xyρ0
+ρ0
+(∂yρ0)2
+ρ2
+0
+−
+∂2
+yρ0
+ρ0
+�
+� ρ0
+(70)
+Repeating this same process for the third Stokes parameter (second equation in (65)) yields the equations
+∂z
+� ρ0⃗v
+−ρ0⃗Ω
+�
++
+�
+� ∇X ·
+�
+ρ0⃗v ⊗ ⃗v + ρ0R + ρ0⃗Ω ⊗ ⃗Ω
+�
+−∇X ·
+�
+ρ0⃗v ⊗ ⃗Ω + ρ0⃗Ω ⊗ ⃗v
+�
+�
+� =
+� ρ0∇Xg(⃗x, z)
+0
+�
+(71)
+where we have defined the matrix
+R =
+1
+4k2
+0
+�
+�
+(∂xρ0)2
+ρ2
+0
+− ∂2
+xρ0
+ρ0
+∂xρ0∂yρ0
+ρ2
+0
+− ∂xyρ0
+ρ0
+∂xρ0∂yρ0
+ρ2
+0
+− ∂xyρ0
+ρ0
+(∂yρ0)2
+ρ2
+0
+−
+∂2
+yρ0
+ρ0
+�
+�
+(72)
+A convenient simplification occurs upon expansion of the outer product via ∇·( ⃗B ⊗ ⃗A) = ⃗A(∇· ⃗B)+( ⃗B ·
+∇) ⃗A. This identity, along with Eqs. (42) and (48), specifically ∂zρ0+∇X ·(ρ0⃗v) = 0 and ∇X ·(ρ0P⃗Ω) = 0,
+transforms (71) into
+� ρ0D⃗v/Dz
+ρ0D⃗Ω/Dz
+�
++
+�
+� ∇X ·
+�
+ρ0R + ρ0⃗Ω ⊗ ⃗Ω
+�
+�
+ρ0⃗Ω · ∇X
+�
+⃗v
+�
+� =
+� ρ0∇Xg(⃗x, z)
+0
+�
+.
+(73)
+where we have again leveraged the material derivative defined earlier in section (III E). The only com-
+ponents of (73) that are influenced by the DOP are those involving the polarization angle gradient. To
+simplify further, note that the divergence of ρ0(⃗x, z, ω)R(⃗x, z, ω) is
+∇X · [ρ0(⃗x, z, ω)R(⃗x, z, ω)] = − 1
+2k2
+0
+ρ0(⃗x, z, ω)∇X
+�
+∇2
+Xρ1/2
+0
+(⃗x, z, ω)
+ρ1/2
+0
+(⃗x, z, ω)
+�
+.
+(74)
+15
+
+Expanding the outer product and invoking (48), the first of Eqns (73) can be written
+D⃗v0(⃗x, z, ω)
+Dz
+= −
+�
+⃗Ω(⃗x, z, ω) · ∇X
+�
+⃗Ω(⃗x, z, ω) + ∇Xg(⃗x, z) +
+1
+2k2
+0
+∇X
+�
+∇2
+Xρ1/2
+0
+(⃗x, z, ω)
+ρ1/2
+0
+(⃗x, z, ω)
+�
+.
+(75)
+which is of precisely the same form as the coherent momentum equation [20]. In the case of a deterministic
+medium, the gradient potential forcing term is ∇Xϵ1/2. In [20] the commonly used medium assumptions
+were used whereby, ⟨ϵ⟩ = 1 and ϵ1 = n2(⃗x, z)−1. In this case Eq. (75) matches exactly that found in [20]
+for P = 1 (fully polarized light). For a stochastic, homogeneous medium where g(⃗x, z) = −ik0A(⃗x, z)/4
+we have
+∇Xg(⃗x, z) = −ik0
+4 ∇XA(0, z)
+= −ik0
+4
+�
+R2 i⃗ξSNN(⃗ξ, 0)ei⃗ξ·⃗0d⃗ξ
+= k0
+4
+�
+R2
+⃗ξSNN(⃗ξ, 0)d⃗ξ
+(76)
+Taking as a simple model for the refractive index fluctuations as Eqn.
+(38) of [5], we have that
+∇Xg(⃗x, z) = 0, i.e., the gradient of the refractive index covariance is zero. Thus, the time-averaged
+transverse location is unchanged due to the turbulence. Note, the model (75) can also be used to derive
+known results for “beam wander” in the coherent case following the approach in [11]. In that case,
+an expression for the transverse coordinate variance is developed and is seen to be proportional to the
+variance of the refractive index gradient (as opposed to the gradient of the variance) and one recovers
+the established result (see [11] for details).
+As in our prior work, it is advantageous to switch to Lagrangian coordinates ⃗x → ⃗xz(⃗x0) which are
+functions of propagation distance z and initial value ⃗x0. With this transformation, and noting that the
+“velocities” are the coordinate derivatives with respect to z, (75) becomes
+d⃗v0(⃗xz, ω)
+dz
+= d2⃗xz(ω)
+dz2
+= −
+�
+⃗Ω(⃗xz, ω) · ∇Xz
+�
+⃗Ω(⃗xz, ω) + ∇Xzg(⃗xz) +
+1
+2k2
+0
+∇Xz
+�
+∇2
+Xzρ1/2
+0
+(⃗xz, ω)
+ρ1/2
+0
+(⃗xz, ω)
+�
+.
+(77)
+This is a sensible model as it suggests that a fully depolarized beam will follow a path that is influenced
+only by diffraction (last term in 77) and refractive index fluctuations. However, if the beam is polarized
+and if the polarization angle distribution possesses non-zero first and second spatial derivatives, there
+is an additional effect that must be considered, given by the first term on the right hand side of (75).
+In the case of diffraction only, the model (77) recovers the known result for the beam path in both the
+Gaussian beam [11]) and Airy beam [20]) situations.
+The second equation in (73) governs the evolution of the polarization angle. Following the derivation
+in Appendix (C), this expression reduces to
+D⃗Ω
+Dz +
+�
+⃗Ω · ∇X
+�
+⃗v = 0
+(78)
+or in Lagrangian coordinates
+d⃗Ω(⃗xz, ω)
+dz
+= 0.
+(79)
+Thus, for partially coherent light, the time-average polarization gradient as defined in (49) will remain
+unchanged during propagation when observed in Lagrangian coordinates. This result is consistent with
+our prior work which held that in the fully coherent case, the polarization angle remained unchanged on
+propagation [20]. By definition, depolarization will decrease ⃗Ω, ultimately resulting in ⃗Ω = 0 for P = 0.
+However, no mechanism exists in (79) to cause this to occur. While it is known that the atmosphere can
+serve as a depolarizing element, under the MA model such an effect can only be observed by retaining
+higher-order spatial variations in the refractive index (stemming ultimately from retaining the electric
+field divergence term in the wave equation) [5, 11]. In both of the cited works retention of such terms
+has almost no influence on beam propagation but for very long distances.
+This distance scales as
+O(k2
+0ℓ3
+0/σ2
+ϵ ) ∼ 1010m, even when considering strong turbulence (refractive index variance σ2
+η ∼ 10−10),
+16
+
+small inhomogeneities (length scale ℓ0 ∼ 10−3m), and 1.55µm wavelength light [5]. Other works have
+predicted depolarization will arise due to asymmetries in the initial spatial correlations across the beam
+face [25]. We have not included this effect in our model given that lasers do not naturally possess such
+asymmetry and creating such a beam would be challenging.
+In summary, we conclude that whether we are considering coherent, monochromatic, or partially
+coherent, polychromatic wave propagation, the basic governing equations are the same.
+ρ0(⃗xz, ω) = | det J⃗x0(⃗xz)|−1ρ0(⃗x0, ω).
+d2⃗xz
+dz2 = −
+�
+⃗Ω(⃗xz, ω) · ∇Xz
+�
+⃗Ω(⃗xz, ω) + ∇Xzg(⃗xz) +
+1
+2k2
+0
+∇Xz
+�
+∇2
+Xzρ1/2
+0
+(⃗xz, ω)
+ρ1/2
+0
+(⃗xz, ω)
+�
+d⃗Ω(⃗xz, ω)
+dz
+= 0
+(80)
+It is the definition of quantities in the expression that is different in the two cases. These can be
+summarized as follows:
+Coherent, monochromatic
+ρ(⃗x, z) = EX(⃗x, z)E∗
+X(⃗x, z) + EY (⃗x, z)E∗
+Y (⃗x, z)
+⃗v(⃗x, z) = 1
+k0
+∇Xφ(⃗x, z)
+⃗Ω(⃗x, z) = 1
+k0
+∇Xγ(⃗x, z)
+(81)
+Partially coherent, polychromatic
+ρ0(⃗x, z, ω) =
+�
+R2
+�
+�
+WXX(⃗x, ξ, z, ω) + �
+WY Y (⃗x, ξ, z, ω)
+�
+d⃗ξ = SXX(⃗x, z, ω) + SY Y (⃗x, z, ω)
+⃗v0(⃗x, z, ω) = 1
+k0
+⟨∇Xφ(⃗x, z, ω)⟩ =
+�
+R2 ⃗ξ
+�
+�
+WXX(⃗x, ⃗ξ, z, ω) + �
+WY Y (⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ
+k0ρ0(⃗x, z)
+⃗Ω(⃗x, z, ω) = P(⃗x, z, ω)
+k0
+⟨∇Xγ(⃗x, z, ω)⟩ =
+−iP
+�
+R2 ⃗ξ
+�
+�
+WXY (⃗x, ⃗ξ, z, ω) − �
+WY X(⃗x, ⃗ξ, z, ω)
+�
+d⃗ξ
+k0ρ0(⃗x, z)
+(82)
+where we can see that the latter reduce to the former in the coherent limit.
+V.
+EXAMPLES
+In our previous work we showed that for a particular functional form of polarization angle gradient
+the beam would “accelerate” in the transverse direction following a curved path and we have shown in
+(80) that this is also true in the partially coherent case. Using a new definition of polarization angle
+gradient (49), we see the the beam will follow the same coherent path as in [20] for P = 1 but will follow
+a different path as the DOP decreases P < 1.
+Consider first the simple case of a beam with Gaussian intensity distribution of equal amplitude in
+the x and y components. As in [14] (see Eqn. 3.6 in the cited work) we take P(⃗x, z) = P as a constant
+representing the correlation coefficient between the x and y components of the electric field and obeying
+0 ≤ P ≤ 1. In our prior work we set P = 1 and used the polarization profile
+γ(y0) = π
+2
+(y0 − a)2
+a2
++ π
+8
+(83)
+which varies in y0 only and not in x0. Thus, the polarization gradient terms becomes simply
+⃗Ω(y0) =
+�
+0, P π(y0 − a)
+a2
+�
+(84)
+17
+
+and the second of Eqs. (80) becomes the ordinary differential equations
+d2xz
+dz2 = x0
+d2yz
+dz2 = −P2
+k2
+0
+dγ(y0)
+dy0
+d2γ(y0)
+dy2
+0
+(85)
+subject to the initial velocity dx0/dz = dy0/dz = 0 and initial displacements x0 and y0. This expression
+can be solved to give the the partially coherent beam path
+xz = x0
+yz = P2π2z2
+2k2
+0a4 (a − y0) + y0.
+(86)
+The prediction is that for fully polarized light, P = 1, the beam will follow the same path obtained in
+[20] while, for unpolarized light, P = 0, and the beam will simply follow a straight path. Figure (1) shows
+a family of such curves associated with the beam center, y0 = 0, for different degrees of polarization.
+Also shown is the polarization angle profile across the beam face, plotted as a function of the transverse
+coordinates ⃗x0. The result is the expected behavior. As the DOP is reduced, so too is the degree to which
+FIG. 1: (a) Transverse displacement of the beam center as the DOP is reduced from unity to 0 in
+increments of 0.2. The model parameters were the same as those used in our prior work [20] and (b)
+The associated polarization angle profile, Eq. (83)
+the path of the beam center is altered. We also note that in this example the effects of diffraction could
+have been included just as they were in our coherent model [20]. The result is the standard Gaussian
+beam spreading about the path predicted in Eqn. (86).
+As a second example, we consider the case where both bending and diffraction are retained in the model.
+Specifically, we tailor the polarization profile so that the polarization-induced bending acts in opposition
+to the diffractive effect, thereby mitigating the degree to which the beam spreads on propagation. Using
+the polarization profile
+γ(y0) = κπ
+2
+y2
+0
+a2 − π
+8
+(87)
+we solve the coupled system of Equations (80) using an initial Gaussian intensity profile
+ρ0(⃗x0, ω) = I(ω)e−(x2
+0+y2
+0)/(2σ2)
+(88)
+with width σ. The solution is obtained analytically in this case using the approach outlined in [20] which
+18
+
+(a)
+X10-3
+5
+Transverse displacement y(z) meters
+= 0.8
+3
+2
+P = 0.6
+P = 0.4
+P = 0.2
+0
+P = 0.0
+.1
+0
+5
+10
+15
+20
+25
+30
+Propagation distance z meters(b)
+2
+(mm)
+0
+1
+-2
+-2
+-1
+0
+1
+2
+(uw) °xleads to the transverse path
+xz = x0
+�
+z2 + σ4k2
+0
+σ2k0
+yz = −(Pκ)2π2z2
+2k2
+0a4
+y0 + y0
+�
+z2 + σ4k2
+0
+σ2k0
+=
+��
+1 +
+z2
+k2
+0σ4
+�1/2
+− π2
+2
+(Pκ)2
+k2
+0a4 z2
+�
+y0.
+(89)
+The corresponding determinant of the Jacobian is therefore
+det J⃗x0(⃗xz) = 1 +
+z2
+σ4k2
+0
+− (Pκ)2π2z2�
+z2 + σ4k2
+0
+2a4σ2k3
+0
+.
+(90)
+and the desired intensity profile on propagation is given by the first of Eqs. (80). The polarization profile
+(87) has the effect of bending the outer edges of the beam, y0 = ±a/2, toward the center thus mitigating
+the outward spreading caused by the diffractive term. These results can be seen visually in Fig. (2) for
+a fully polarized beam of wavelength 1.55 µm, width σ = 1.2 mm and extending over transverse spatial
+dimension a = 4.17 mm. In this fully polarized case we set κ = 1.
+FIG. 2: (a) Normal beam diffraction profile over the range z = [0, 250] m, (b) diffraction profile
+associated with the polarization angle distribution given by Eq. (87) and for P = 1. Here the spreading
+due to diffraction is compensated by the bending due to the polarization angle gradient. These effects
+cancel each other out at range zc ≈ (2a4k0)/ (Pπσ)2 (obtained by setting yz = 0). Beyond this range
+the beam super diffracts and the spreading is proportional to (z − zc)2. Plots (c) and (d) use the same
+polarization profile but with P = 0.75 and P = 0.5 respectively.
+The normalized beam intensity is plotted for z = [0, 250] m in order to clearly show the effects of the
+polarization gradient. By altering the polarization of the light across the beam face we can control, to
+some extent, the degree to which the beam diffracts. Of course, in this example the diffractive effect
+causes transverse spreading that is linear in z while the bending we show here is quadratic. Thus, at a
+19
+
+(a)
+50
+4
+P=0
+6'0
+ Transverse Displacement (mm)
+0.8
+¥2
+0.7
+0
+0.6
+0
+0.5
+-10
+0.4
+0.3
+-30
+0.2
+-40
+0.1
+-50
+0
+0
+20
+40
+60
+80
+100
+120
+140
+160
+180
+200
+220
+240
+Propagation Distance (m)(q)
+50
+P=1
+40
+0.9
+Transverse Displacement (mm)
+0.8
+2
+0.7
+0
+0.6
+0
+0.5
+-10
+0.4
+-20 
+0.3
+-30
+0.2
+-40
+0.1
+-50
+0
+0
+20
+40
+60
+80
+100
+120
+140
+160
+180
+200
+220
+240
+Propagation Distance (m)(c)
+50
+40
+P=0.75
+0.9
+ Transverse Displacement (mm)
+0.8
+2
+0.7
+0
+0.6
+0
+0.5
+-10
+0.4
+-20 
+0.3
+30
+0.2
+-40
+0.1
+-50
+0
+0
+20
+40
+60
+80
+100
+120
+140
+160
+180
+200
+220
+240
+Propagation Distance (m)(d)
+50
+40
+P=0.5
+0.9
+ Transverse Displacement (mm)
+0.8
+2
+0.7
+0
+0.6
+0
+0.5
+-10
+0.4
+-20 
+0.3
+30
+0.2
+-40
+0.1
+-50
+0
+0
+20
+40
+60
+80
+100
+120
+140
+160
+180
+200
+220
+240
+Propagation Distance (m)distance zc, obtained by setting yz = 0 in Eqn. (89), the rays are predicted to come to a focus. Then
+zc =
+√
+2
+π2
+k0
+(Pκ)2
+� a4
+σ2
+� �
+1 +
+�
+1 + π4(Pκ)4
+�σ
+a
+�8
+�1/2
+(91)
+and in the limit zc ≫ k0σ2 we find the particularly simple form
+zc = 2a4k0
+(Pπσ)2 .
+(92)
+(Note also this limit is also obtained when π4(Pκ)4(σ/a)8 << 1, a condition that will always be met
+when the beam width 2σ is less than the output aperture dimension 2a). Beyond z > zc, however,
+the beam diverges strongly and the intensity rapidly diminishes. Thus, using this polarization profile
+diffraction can be mitigated, but only over a prescribed range. As the beam depolarizes the degree
+to which diffraction is mitigated will change, however, by increasing the constant κ in the polarization
+gradient such that Pκ = 1, we expect to see the same results as in Fig. (2b). In practice, of course,
+there will be a limit to how large a polarization gradient can be produced. As the DOP decreases (with
+κ = 1) we see the expected results in Figs. (2c-d), namely that the beam gradually moves toward the
+standard diffraction profile associated with an incoherent beam, Fig. (2a).
+Fig. (3) shows a plot of zc from (91) for fixed polarization gradient (κ = 1) as a function of degree
+of polarization P in the range 0.01 ≤ P ≤ 1. The zc ∝ P−1 behavior continues indefinitely as P → 0,
+that is, regardless of the degree of polarization, there exists a z−value for which the effects of diffraction
+could be completely compensated. Of course in practice, there is a limit to κ as one can not generate
+a beam with an infinitely sharp polarization gradient. The practical limit will for such a beam will be
+determined by the resolution of the device used in its creation, e.g., the spatial light modulators used in
+reference [20].
+The results in Fig. 3 are consistent with the following interpretation of the mixture model in (30). The
+term ”mixture” cannot be taken literally to mean that the beam comprises a collection of photons in
+which a fraction P are fully polarized and fraction (1 − P) are completely unpolarized. If that were true
+then the polarization gradient could only compensate diffraction for the polarized photons and the beam
+spread at z = zc would necessarily increase as P decreased. Instead, we found that the beam width at
+the focus, in the y− direction for this example, is independent of P. Hence, we interpret (30) to mean
+that every photon in the beam is described by Stokes vector
+�
+S =
+�
+�
+�
+�
+s′
+0(⃗x, ⃗x′, z, ω)
+Ps′
+1(⃗x, ⃗x′, z, ω|P)
+Ps′
+2(⃗x, ⃗x′, z, ω|P)
+Ps′
+3(⃗x, ⃗x′, z, ω|P)
+�
+�
+�
+� .
+(93)
+Every photon thus exhibits properties of partial polarization with degree of polarization P.
+VI.
+SUMMARY
+We have generalized our prior, coherent vector beam model to the partially coherent case by introducing
+a mixture model for the generalized Stokes vector and by subsequently choosing appropriate definitions
+of amplitude, phase, and polarization angle gradient in describing propagation of the generalized Stokes
+parameters. The resulting “transport” model predicts the time-averaged optical path of a vector beam
+propagating through an inhomogeneous medium (e.g., an atmosphere). Importantly, the model reduces
+to that of our previous work on vector beams in the coherent limit [20] and matches the predictions
+found in [30] and [5] in the absence of a polarization gradient. Consequently, it predicts the same optical
+path as in our coherent model in the fully polarized case, while reducing to the standard “unaltered”
+path in the unpolarized situation.
+Notably, the model requires a new definition of polarization angle gradient that is consistent with
+more recent definitions of phase for partially coherent beams. These definitions become important in the
+governing equations as the movement of intensity during propagation is governed by phase and angle
+gradients as opposed to the phase and angle variables. As a by-product of the model development we
+were also able to demonstrate conservation of the generalized Stokes parameters on propagation, even in
+20
+
+FIG. 3: zc as a function of degree of polarization P for λ = 1.55 µm, a = 4.17 mm, and σ = 1.15 mm.
+For these parameters, zc ∝ P−1 and the trend continues indefinitely as P → 0.
+the case where the intervening medium possesses refractive index fluctuations. This is a generalization
+of the result established in [13].
+An obvious prediction of the model Eqn. (79) is that the state of linear polarization (as captured
+by ⃗Ω) remains unchanged on propagation from a Lagrangian viewpoint. Because the definition of ⃗Ω
+includes the DOP, this is also tantamount to the statement that the DOP is unchanged on propagation.
+The result is consistent with the result of Charnotskii [5] which found that no significant depolarization
+occurs due to the presence of a turbulent atmosphere. Had we included the higher order refractive index
+variations (by retaining the electric field divergence in the wave equation) and/or retained the full Wigner
+potential in forming Eqn. (61) (as opposed to using the linearized potential) this effect may have been
+observable in our model as well.
+We considered two such examples, one in which the curved path taken by the beam studied in [20] was
+slowly altered by changing the degree of polarization. In the coherent case, the path taken is the same as
+in the cited reference. As the degree of polarization is reduced so too is degree of beam bending, reducing
+to propagation in a straight line in the fully incoherent case. In the second example, we consider both
+the bending and diffracting beam. For that example we chose an initial polarization distribution that
+would mitigate the effects of diffraction over a predictable distance. The result suggests new class of
+“non-diffracting” beam. The effects of depolarization can be countered in this case by simply increasing
+the strength of the polarization gradient applied across the transverse dimension of the beam.
+In short, the model we have developed can be used to predict vector beam trajectories in a variety of
+propagation scenarios of interest, including through free-space and a potentially turbulent atmosphere.
+As such it provides a powerful tool in forecasting the utility of the newly discovered vector beam bending
+effect in application. We note that the model rests on the same two assumptions as were used in the
+coherent model development [20], namely, the slowly varying envelope approximation and a weakly
+inhomogeneous medium.
+VII.
+ACKNOWLEDGMENTS
+The authors would like to thank the Office of Naval Research Code 33, for support under
+PE#0601153N, award #N0001422WX01660
+Appendix A: Interpretation of Transport Velocity
+In this section we present a more traditional optics interpretation of the transverse velocity ⃗v =
+k−1
+0 ∇Xφ for coherent light. In particular, we show how this quantity can be related to the familiar
+concept of “optical path length” (OPL). This allows us to properly view the transverse phase gradient
+21
+
+107
+106
+105
+(w)
+104
+103
+102
+10-2
+10-1
+100
+DOP (P)of our electric field as the rate at which intensity is moved in the transverse plane. The interpretation
+will remain valid so long as the paraxial assumption holds.
+To begin, we note that the OPL in the context of a propagating wave is defined (see, for example,
+Saleh [27]) as
+Φ(⃗x, z) = z + φ(⃗x, z)/(2k0)
+(A1)
+that is, as the phase argument of the wave normalized by the wavenumber. The quantity φ/(2k0) can
+be viewed as a perturbation to the optical path resulting from refractive index fluctuations, diffraction,
+and, in this context, from polarization angle gradients as well.
+Consider now the expression for total path length L(⃗xz) in Lagrangian coordinates. For a differential
+length element parameterized by propagation distance, dℓ(z)
+L(⃗xz) =
+� z
+0
+dℓ(ζ)
+=
+� z
+0
+(dζ2 + dx2
+ζ + dy2
+ζ)1/2 =
+� z
+0
+�
+1 +
+�dxζ
+dζ
+�2
++
+�dyζ
+dζ
+�2�1/2
+dζ
+≈
+� z
+0
+dζ + 1
+2
+� z
+0
+�dxζ
+dζ
+�2
+dζ + 1
+2
+� z
+0
+�dyζ
+dζ
+�2
+dζ
+(A2)
+where in the final step we have made use of the fact that for ϵ1, ϵ2 ≪ 1, (1 + ϵ1 + ϵ2)1/2 ≈ 1 + 1
+2ϵ1 + 1
+2ϵ2
+which is equivalent to the paraxial assumption. Equating this expression to the OPL given in Eqn. (A1)
+gives
+L(⃗xz) = z + φ(⃗xz)
+2k0
+=
+� z
+0
+dζ + 1
+2
+� z
+0
+�dxζ
+dζ
+�2
+dζ + 1
+2
+� z
+0
+�dyζ
+dζ
+�2
+dζ
+(A3)
+so that
+φ(⃗xz)
+2k0
+= 1
+2
+� z
+0
+�dxζ
+dζ
+�2
+dζ + 1
+2
+� z
+0
+�dyζ
+dζ
+�2
+dζ
+(A4)
+Differentiating with respect to z yields
+1
+k0
+�∂φ(⃗xz)
+∂xz
+∂xz
+∂z + ∂φ(⃗xz)
+∂yz
+∂yz
+∂z
+�
+=
+�dxz
+dz
+�2
++
+�dyz
+dz
+�2
+.
+(A5)
+which can be written
+1
+k0
+∇Xzφ(⃗xz) · ⃗v(⃗xz) = ⃗v(⃗xz) · ⃗v(⃗xz)
+(A6)
+thus
+⃗v(⃗xz) = 1
+k0
+∇Xzφ(⃗xz).
+(A7)
+This demonstrates that the change in optical path length in the transverse plane per unit change in ˆz
+(i.e. the transverse “velocity”) is equal to the transverse phase gradient normalized by the wavenumber.
+Eq. (A7) was presented in [23] (Eq. 11 of that work) and is referred to appropriately as the “flow vector
+of spectral density”. The connection between ⃗v(⃗xz) and transverse coordinate changes was also leveraged
+in [11] although not explicitly derived as we have here. The key assumption used to arrive at this result
+is that changes in the transverse direction are much smaller than changes in the direction of propagation
+and is tantamount to the same paraxial assumption we have used throughout our model development.
+While the above analysis is performed for the coherent case, we have demonstrated that one can re-
+define the model quantities (amplitude, phase, and polarization angle) as appropriate averages in the
+partially coherent case. Thus, the above interpretation still holds and the transverse phase gradient can
+be interpreted as the average change in optical path in the transverse direction per unit change in the
+direction of propagation.
+22
+
+Appendix B: Derivation of Equation (55)
+The identity required of Eqn.
+(55) requires relating the determinant of the Jacobian of the La-
+grangian coordinate mappings xz(x0, y0), yz(x0, y0) to the divergence of the associated velocity field
+uz(xz, yz), vz(xz, yz). Begin with the determinant
+det(J⃗x0(⃗xz)) = dxz
+dx0
+dyz
+dy0
+− dyz
+dx0
+dxz
+dy0
+,
+(B1)
+take the derivative with respect to z and recognize that uz ≡ dxz/dz, vz ≡ dyz/dz. Then
+d
+dz det(J⃗x0(⃗xz)) = duz
+dx0
+dyz
+dy0
++ dvz
+dy0
+dxz
+dx0
+− dvz
+dx0
+dxz
+dy0
+− duz
+dy0
+dyz
+dx0
+(B2)
+Both uz(xz, yz), vz(xz, yz) are functions of the Lagrangian coordinates, hence we can apply the chain
+rule to obtain
+duz
+dx0
+= ∂uz
+∂xz
+∂xz
+∂x0
++ ∂uz
+∂yz
+∂yz
+dx0
+duz
+dy0
+= ∂uz
+∂xz
+∂xz
+dy0
++ duz
+∂yz
+∂yz
+∂y0
+dvz
+dx0
+= ∂vz
+∂xz
+∂xz
+∂x0
++ ∂vz
+∂yz
+∂yz
+∂x0
+dvz
+dy0
+= ∂vz
+dxz
+∂xz
+∂y0
++ ∂vz
+∂yz
+∂yz
+∂y0
+.
+(B3)
+Substituting (B3) into (B2) and simplifying yields the ordinary differential equation
+d det(J⃗x0(⃗xz))
+dz
+= (∇Xs · ⃗v(⃗xs) det(J⃗x0(⃗xz)),
+(B4)
+with solution
+det (J⃗x0(⃗xz)) = exp
+�� z
+s=0
+∇Xs · ⃗v(⃗xs)ds
+�
+(B5)
+This relationship allows (54) to be written as (55) thus completing the derivation.
+Appendix C: Derivation of Equation (79)
+To derive Equation (79) we begin with Eqn. (71)
+∂z
+�
+ρ0⃗Ω
+�
++ ∇X ·
+�
+ρ0⃗v ⊗ ⃗Ω + ρ0⃗Ω ⊗ ⃗v
+�
+= 0
+(C1)
+Using two applications of the vector identity ∇X ·
+�
+⃗B ⊗ ⃗A
+�
+= ⃗A
+�
+∇X · ⃗B
+�
++
+�
+⃗B · ∇X
+�
+⃗A and grouping
+terms we have
+ρ0[∂z⃗Ω + (⃗v · ∇X)⃗Ω] + ⃗Ω
+�
+((((((((
+∂z(ρ0) + ∇X · ρ0⃗v
+�
++ ⃗v
+�
+∇X · [ρo⃗Ω]
+�
++
+�
+ρ0⃗Ω · ∇X
+�
+⃗v = 0
+(C2)
+where Eqn. (48) has allowed us to cancel the second to last term while continuity of the first Stokes
+parameter (i.e., the intensity) cancels the third term.
+Noting the first term in brackets is the total
+derivative of ⃗Ω, allows us to write Eqn. (C2) in Eulerian coordinates as
+D⃗Ω
+Dz +
+�
+⃗Ω · ∇X
+�
+⃗v = 0
+(C3)
+However, further simplification is possible by re-writing (C2) as
+∂z⃗Ω +
+�
+(⃗v · ∇X) Ω +
+�
+⃗Ω · ∇X
+�
+⃗v
+�
+= 0
+∂z⃗Ω + ∇X
+�
+⃗Ω · ⃗v
+�
+= 0.
+(C4)
+23
+
+where we have leveraged the identity ∇X
+�
+⃗A · ⃗B
+�
+= ( ⃗A·∇X) ⃗B+( ⃗B·∇X) ⃗A+ ⃗A×(∇X × ⃗B)+ ⃗B×(∇X × ⃗A)
+and note that both ⃗Ω and ⃗v are expressible as gradients of scalars, hence the cross-product terms vanish.
+Recalling that ⃗Ω ≡ k−1
+0 ∇Xγ we can write
+k−1
+0
+[∂z(∇Xγ) + ∇X(∇Xγ · ⃗v)] = 0
+= k−1
+0 ∇X [∂zγ + ∇Xγ · ⃗v] = 0
+= k−1
+0 ∇X
+Dγ
+Dz = 0.
+(C5)
+If we now make the switch to Lagrangian coordinates, the total derivatives become ordinary derivatives
+d⃗Ω(⃗xz, ω)
+dz
+= 0.
+(C6)
+which is Eqn. (79).
+[1] J.-D. Benamou and Y. Brenier. A computational fluid mechanics solution to the Monge-Kantorovich mass
+transfer problem. Numerische Mathematik, 84:375–393, 2000.
+[2] B. Boashash. Estimating and interpreting the instantaneous frequency of a signal – part 1: Fundamentals.
+In PROCEEDINGS OF THE IEEE, pages 520–538, 1992.
+[3] T. Boykin. Derivatives of the Dirac delta function by explicit construction of sequences. American Journal
+of Physics, 71(5):462–468, 2003.
+[4] Z. Cai, Y. Fan, R. Li, T. Lu, and Y. Wang. Quantum hydrodynamic model by moment closure of Wigner
+equation. Journal of Mathematical Physics, 53:103503, 2012.
+[5] M. Charnotskii. Propagation of polarized waves in inhomogeneous media. Journal of the Optical Society of
+America – A, 33(7):1385–1394, 2016.
+[6] P. Constantin and G. Iyer. A stochastic lagrangian representation of the three-dimensional incompressible
+navier-stokes equations. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 61(3):330–
+345, 2008.
+[7] P. Degond and C. Ringhofer.
+Quantum moment hydrodynamics and the entropy principle.
+Journal of
+Statistical Physics, 112(3/4):587–628, 2003.
+[8] A. C. Fannjiang and K. Solna. Propagation and time reversal of wave beams in atmospheric turbulence.
+SIAM, 3(3):522–558, 2005.
+[9] R. L. Fante. Electromagnetic beam propagation in turbulent media. In Proceedings of the IEEE, volume 63,
+pages 1669–1692, 1975.
+[10] A. T. Friberg. Energy transport in optical systems with partially coherent light. Applied Optics, 25(24):4547–
+4556, 1986.
+[11] T. H. Emerson J. M. Nichols and G. K. Rohde. A transport model for broadening of a linearly polarized,
+coherent beam due to inhomogeneities in a turbulent atmosphere. Journal of Modern Optics, 66(8):835–849,
+2019.
+[12] A. J¨ungel, D. Mattes, and J. P. Miliˇsi´c. Derivation of new quantum hydrodynamic equations using entropy
+minimization. SIAM Journal on Applied Mathematics, 67(1):46–68, 2006.
+[13] O. Korotkova. Conservation laws for stochastic electromagnetic free fields. Journal of Optics A: Pure and
+Applied Optics, 10:025003, 2008.
+[14] O. Korotkova, M. Salem, and E. Wolf. The far-zone behavior of the degree of polarization of electromagnetic
+beams propagating through atmospheric turbulemce. Optics Communications, 233:225–230, 2004.
+[15] O. Korotkova and E. Wolf. Generalized Stokes parameters of random electromagnetic beams. Optics Letters,
+30(2):198–200, 2005.
+[16] A. Luis. Polarization and coherence for vectorial electromagnetic waves and the ray picture of light propa-
+gation. Journal of the European Optical Society - Rapid Publications, 2:07030, 2007.
+[17] G. Manfredi, P.-A. Herieux, and J. Hurst.
+Fluid descriptions of quantum plasmas.
+Reviews of Modern
+Plasma Physics, 5(7):https://doi.org/10.1007/s41614–021–00056–y, 2021.
+[18] N. Marcuvitz. Quasiparticle view of wave propagation. Proceedings of the IEEE, 68(11):1380–1395, 1980.
+[19] M. Nedjalkov, D. Querlioz, P. Dollfus, and H. Kosina. Wigner function approach. In D. Vasileska D and
+S. Goodnick, editors, Nano-Electronic Devices: Semiclassical and Quantum Transport Modeling. Springer,
+New York, NY, 2011.
+[20] J. M. Nichols, D. V. Nickel, and F. Bucholtz. Vector beam bending via a polarization gradient. Optics
+Express, 30(21):38907–38929, 2022.
+[21] D. Paganin and K. A. Nugent. Noninterferometric phase imaging with partially coherent light. Physical
+Review Letters, 80(12):2586–2589, 1998.
+[22] G. C. Papanicolaou and R. Burridge. Transport equations for the stokes parameters from Maxwell’s equations
+in a random medium. Journal of Mathematical Physics, 16(10):2074–2085, 1975.
+24
+
+[23] J. C. Petruccelli, L. Tian, and G. Barbastathis. The transport of intensity equation for optical path length
+recovery using partially coherent illumination. Optics Express, 21(12):14430–14441, 2013.
+[24] M. B. Priestly. Spectral Analysis and Time Series. Probability and Mathematical Statistics. Elsevier Aca-
+demic Press, London, 1981.
+[25] H. Roychowdhury, S. A. Ponomarenko, and E. Wolf. Change in the polarization of partially coherent elec-
+tromagnetic beams propagating through the turbulent atmosphere. Journal of Modern Optics, 52(11):1611–
+1618, 2005.
+[26] L. Ryzhik, G. Papanicolaou, and J. B. Keller. Transport equations for elastic and other waves in random
+media. Wave Motion, 24:327–370, 1996.
+[27] B. E. A. Saleh and M. C. Teich. Fundamentals of Photonics. John Wiley & Sons, Inc., New York, 1991.
+[28] M. Salem, O. Korotkova, A. Dogariu, and E. Wolf. Polarization changes in partially coherent electromagnetic
+beams propagating through turbulent atmosphere. Waves in Random Media, 14:513–523, 2004.
+[29] B. Schaefer, E. Collett, R. Smyth, D. Barrett, and B. Fraher. Measuring the Stokes polarization parameters.
+American Journal of Physics, 75(2):163–168, 2007.
+[30] V. I. Tatarskii. Light propagation in a medium with random refractive index inhomogeneities in the Markov
+random process approximation. Sov. Phys. JETP, 29:1133–1138, 1969.
+[31] C. Villani. Optimal Transport: Old and New. Springer-Verlag, Berlin, 2008.
+[32] E. P. Wigner. On the quantum correction for thermodynamic equilibrium. Physical Review, 40:749–759,
+1932.
+[33] D. Yin, M. Tang, and S. Jin.
+The Gaussian beam method for the Wigner equation with discontinuous
+potentials. Inverse Problems and Imaging, 7(3):1051–1074, 2013.
+[34] J. Zhou, Y. Liu, Y. Ke, H. Luo, and S. Wen. Generation of Airy vortex and Airy vector beams based on the
+modulation of dynamic and geometric phases. Optics Letters, 40(13):3193–3196, 2015.
+[35] C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi. Transport of intensity phase retrieval and computational
+imaging for partially coherent fields: The phase space perspective. Optics and Lasers in Engineering, 71:20–
+32, 2015.
+25
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+Cold plasma waves in the chiral Maxwell-Carroll-Field-Jackiw electrodynamics
+Filipe S. Ribeiro
+a,∗ Pedro D. S. Silva
+a,† and Manoel M. Ferreira Jr.
+b‡
+aPrograma de P´os-gradua¸c˜ao em F´ısica, Universidade Federal do Maranh˜ao,
+Campus Universit´ario do Bacanga, S˜ao Lu´ıs (MA), 65080-805, Brazil and
+bDepartamento de F´ısica, Universidade Federal do Maranh˜ao,
+Campus Universit´ario do Bacanga, S˜ao Lu´ıs (MA), 65080-805, Brazil
+In this work, we study the propagation and absorption of plasma waves in the chiral Maxwell-
+Carroll-Field-Jackiw electrodynamics (MCJF). The Maxwell equations are rewritten for a cold,
+uniform, and collisionless fluid plasma model, allowing us to determine the new refractive indices and
+propagating modes. The case of transversal propagation is examined considering a purely timelike
+CFJ background that plays the role of the magnetic conductivity chiral parameter. We find four
+distinct refractive indices associated with RCP and LCP waves. For each index, the propagation
+and absorption zones are illustrated for some specific parameter values. The optical behavior is
+investigated by means of the rotatory power (RP) and dichroism coefficient. The existence of a
+negative refraction zone enhances the rotatory power. It is also observed RP sign reversal, a feature
+of rotating plasmas.
+PACS numbers: 11.30.Cp, 41.20.Jb, 41.90.+e, 42.25.Lc
+I.
+INTRODUCTION
+The study of electromagnetic (EM) waves propagation
+[1, 2] in cold magnetized plasma is based on magneto-
+ionic theory [3–8], developed by E. Appleton [9] and D.
+Hartree [10] between 1929 and 1932 to describe the radio
+waves propagation in the ionosphere, in the context of the
+usual electrodynamics [11]. EM waves in plasmas have
+been studied in other scenarios recently, as in logarithmic
+nonlinear electrodynamics [12].
+The chiral magnetic effect (CME) is the macroscopic
+generation of an electric current in the presence of a mag-
+netic field, stemming from an asymmetry between the
+number density of left- and right-handed chiral fermions
+[13–17]. It has been extensively investigated in several
+distinct contexts, such as quark-gluon plasmas [18–20],
+cosmology [21], neutron stars [22, 23], and electroweak
+interactions [24].
+The CME plays a very relevant role
+in Weyl semimetals, where it is usually connected to
+the chiral anomaly associated with Weyl nodal points
+[25], the absence of the Weyl nodes [26], anisotropic ef-
+fects stemming from tilted Weyl cones [27], the CME
+and anomalous transport in Weyl semimetals [28], quan-
+tum oscillations arising from the CME [29], computa-
+tion of the electromagnetic fields produced by an elec-
+tric charge near a topological Weyl semimetal with two
+Weyl nodes [30], renormalization evaluations for Weyl
+semimetals and Dirac materials [31], and solutions of ax-
+ion electrodynamics [32].
+The CME current can be classically described by the
+axion Lagrangian [32–38],
+L = −1
+4F µνFµν + θ(E · B),
+(1)
+∗ fi[email protected], fi[email protected]
+† [email protected], [email protected]
+‡ [email protected], [email protected]
+where θ is the axion field. In this context, the Maxwell
+equations are
+∇ · E = ρ − ∇θ · B,
+(2)
+∇ × B − ∂tE = j + (∂tθ)B + ∇θ × E,
+(3)
+where the terms involving θ derivatives find association
+with condensed matter effects [38]. Indeed, ∇θ · B repre-
+sents an anomalous charge density, while ∇θ×B appears
+in the anomalous Hall effect, and (∂tθ)B plays the role
+of the chiral magnetic current. In the case the axion field
+does not depend on the space coordinates, ∇θ = 0, the
+Maxwell equations (2) and (3) read
+∇ · E = ρ,
+∇ × B − ∂tE = j + (∂tθ)B,
+(4)
+where (∂tθ)B, the chiral magnetic current, may also
+be addressed as a term of Maxwell-Carroll-Field-Jackiw
+(MCFJ) theory. A classical electrodynamics scenario en-
+dowed with a chiral magnetic current has been investi-
+gated considering symmetric and antisymmetric conduc-
+tivity [39]. The latter case has also been addressed in
+Ref. [40].
+The MCFJ model [41] is the CPT-odd part of the U (1)
+gauge sector of the Standard Model Extension (SME)
+[42]. It is described by the Lagrangian density
+L = −1
+4F µνFµν − 1
+4ϵµναβ (kAF )µ AνFαβ − AµJµ,
+(5)
+with (kAF )µ being the 4-vector background which con-
+trols the Lorentz violation. This theory has been investi-
+gated in multiple respects [43], encompassing radiative
+evaluations [44, 45], topological defects solutions [46],
+supersymmetric generalizations [47], classical solutions,
+quantum aspects and unitarity analysis [48]. It may also
+be connected with the CME in the sense that it provides
+a modified Amp`ere’s law,
+∇ × B − ∂E
+∂t = J + k0
+AF B + kAF × E,
+(6)
+arXiv:2301.02183v1  [physics.plasm-ph]  5 Jan 2023
+
+ID2
+containing the magnetic current, JB = k0
+AF B, with the
+component k0
+AF playing the role of the magnetic conduc-
+tivity.
+The SME photon sector is also composed of a CPT-
+even term constituted of a rank 4 Lorentz-violating tensor
+[49], whose components may be properly parametrized in
+terms of dimensionless 3 × 3 matrices, κDE, κDB, κHE,
+and κHB, which allow to write generalized constitutive
+relations between the fields (D, E) and (H, B),
+�
+D
+H
+�
+=
+�
+�
+ϵ1 + κDE
+κDB
+κHE
+µ−11 + κHB
+�
+�
+�
+E
+B
+�
+,
+(7)
+similar to the ones that hold in continuous medium elec-
+trodynamics, see Eqs. (8a) and (8b). Here, D is the elec-
+tric displacement, while H is the magnetic field. This
+CPT-even electrodynamics was investigated in several
+contexts, involving consistency aspects [50], finite tem-
+perature and boundary effects [51].
+Lorentz-violating
+electrodynamics in continuous matter [52, 53] has been
+a topic of interest in the latest years due to its potential
+to describe interesting effects of the phenomenology of
+new materials, such as Weyl semimetals [54]. A classical
+field theory description of wave propagation, refractive
+indices, and optical effects in a continuous medium de-
+scribed by the MCFJ electrodynamics (with usual consti-
+tutive relations), including its Lorentz-violating higher-
+order derivative version [55], was discussed in Ref. [56].
+Chiral media are endowed with parity violation [57–
+60], being described by parity-odd models, as bi-isotropic
+[61] and bi-anisotropic electrodynamics [62–67], whose
+constitutive relations read
+D = ˆϵ E + ˆα B,
+(8a)
+H = ˆβ E + ˆζ B,
+(8b)
+and ˆϵ = [ϵij], ˆα = [αij], ˆβ = [βij], and ˆζ = [ζij] represent,
+in principle, 3 × 3 complex matrices.
+The bi-isotropic
+relations involve the diagonal isotropic tensors, ϵij = ϵδij,
+αij = αδij, βij = βδij.
+In chiral scenarios, LCP and
+RCP waves travel at distinct phase velocities, implying
+birefringence and optical rotation [68]. This phenomenon
+stems from the natural optical activity of the medium
+or can be induced by the action of external fields (e.
+g., Faraday effect [69–71]), and it is measured in terms
+of the rotation angle per unit length or rotatory power
+(RP) [72]. Magneto-optical effects are used to investigate
+features of new materials, such as topological insulators
+[73–79] and graphene compounds [80].
+The RP is a probe to examine the optical behavior of
+several distinct systems, for instance, crystals [81, 82],
+organic compounds [57, 83], graphene phenomena at ter-
+ahertz band [84], and gas of fast-spinning molecules [85].
+The optical rotation may depend on the frequency (RP
+dispersion) and undergo reversion (anomalous RP dis-
+persion) [86–88]. It also finds interesting applications in
+chiral metamaterials [89–91], chiral semimetals [92, 93],
+in the determination of the rotation direction of pulsars
+[94], and in rotating plasmas, which constitutes a sce-
+nario where RP sign reversal also takes place [95]. Re-
+cently, RP reversal was also reported in a bi-isotropic
+dielectric in the presence of chiral magnetic current [96].
+Furthermore, in the presence of absorption, dichroism
+is another useful tool for the optical characterization of
+matter. It occurs when LCP and RCP light waves are
+absorbed by the medium at different degrees. It has been
+used to distinguish between Dirac and Weyl semimetals
+[97], perform enantiomeric discrimination [98, 99], and
+for developing graphene-based devices at terahertz fre-
+quencies [100].
+Another feature of chiral systems is the possible oc-
+currence of negative refraction and negative refractive
+index, which was first proposed by Veselago in 1968 [101]
+and experimentally observed in 2000 [102, 103]. Later,
+other experiments confirmed the negative refraction by
+using Snell’s law [104, 105].
+This unusual property
+was achieved in constructed metamaterials with both
+negative electric permittivity and magnetic permeability
+[106, 107]. The negative refractive index also appears in
+quark-gluon plasmas [108, 109], magnetoelectric materi-
+als [110], metasurfaces [111], chiral bi-anisotropic meta-
+materials [112, 113], and new materials, such as Dirac
+semimetals [114, 115].
+In chiral plasmas described by
+generalized bi-isotropic constitutive relations [116, 117],
+the negative refractive index can occur within some fre-
+quency band and is not necessarily associated with si-
+multaneously negative electric permittivity and negative
+magnetic permeability, being attributed to the chirality
+parameter introduced in the constitutive relations,
+Di = εijEj + iξcBi,
+Hi = µ−1Bi + iξcEi,
+(9)
+where εij, µ, and ξc are the plasma electric permit-
+tivity tensor, the magnetic permeability, and the con-
+stant chirality parameter. Plasmas metamaterials have
+been investigated as new media endowed with interesting
+properties, such as negative refraction and nonlinearities
+[118, 119].
+In this work, we are interested in examining the
+wave propagation in a magnetized cold plasma ruled
+by the MCFJ model, a chiral route distinct from the
+bi-isotropic/anisotropic electrodynamics of the relations
+(9). We carry out our analysis considering the timelike
+Lorentz-violating background component, which plays
+the role of chiral magnetic conductivity. The refractive
+indices are evaluated and optical effects, such as bire-
+fringence and dichroism, are examined, which could be
+useful to trace analogies with other material properties.
+We also find that the chiral conductivity yields negative
+refraction in specific frequency bands, enhancing the ro-
+tatory power and dichroism signals.
+This paper is outlined as follows. In Sec. II, we briefly
+review some aspects of the MCFJ model. In Sec. III, the
+main properties of propagation in usual cold magnetized
+plasmas are presented. The dispersion relations and re-
+fractive indices for cold plasmas in chiral electrodynamics
+
+3
+are addressed in Sec. IV. The optical effects are examined
+in Sec. V. Finally, we summarize our results in Sec. VI.
+II.
+BASICS ON MCFJ ELECTRODYNAMICS
+The Carroll-Field-Jackiw model was proposed as a
+gauge invariant CPT-odd electrodynamics constrained
+by birefringence data of distant galaxies [41]. It was later
+incorporated as the CPT-odd sector of the SME [42], and
+it has been investigated in several respects [43, 44]. In
+matter, it is described by the following Lagrangian den-
+sity1 [56]:
+L = −1
+4GµνFµν − 1
+4ϵµναβ (kAF )µ AνFαβ − AµJµ, (10)
+yielding the MCFJ equation of motion,
+∂ρGρκ + ϵβκµν (kAF )β Fµν = Jκ .
+(11)
+Here, (kAF )µ =
+�
+k0
+AF , kAF
+�
+is a constant 4-vector back-
+ground responsible for the Lorentz violation, and
+Fµν = ∂µAν − ∂νAµ,
+Gµν = 1
+2χµναβFαβ,
+(12)
+are the usual U(1) vacuum and continuous matter field
+strength, respectively.
+The 4-rank tensor, χµναβ, de-
+scribes the medium constitutive tensor [120], whose com-
+ponents provide the electric and magnetic responses of
+the medium. Indeed, the electric permittivity and mag-
+netic permeability tensor components are written as
+ϵij ≡ χ0ij0 and µ−1
+lk
+≡
+1
+4ϵijlχijmnϵmnk, respectively.
+For isotropic polarization and magnetization, it holds
+ϵij = ϵδij and µ−1
+ij = µδij, providing the usual isotropic
+constitutive relations,
+D = ϵE,
+H = µB.
+(13)
+A straightforward calculation from Eq. (11) yields
+∇ · D = J0 − kAF · B,
+(14)
+∇ × H − ∂D
+∂t = J + k0
+AF B + kAF × E,
+(15)
+where Gi0 = Di and Gij = −ϵijkHk. The homogeneous
+Maxwell equations are given by
+∇ · B = 0,
+∇ × E + ∂B
+∂t = 0.
+(16)
+By using a plane-wave ansatz for the electromagnetic
+fields, the MCFJ equations (14)-(16) read:
+1 We use natural units h = c = 1 and the Minkowski metric sig-
+nature gµν = diag (1, −1, −1, −1).
+ik · D + kAF · B = J0,
+(17a)
+ik × H + iωD − k0
+AF B − kAF × E = J,
+(17b)
+k · B = 0,
+k × E − ωB = 0,
+(17c)
+where k is the wave vector and ω is the (angular) wave
+frequency.
+In the presence of anisotropy, the permittivity and per-
+meability are represented by rank 2 tensors, εij and µij,
+which may also depend on the frequency (for a dispersive
+medium). For an anisotropic medium, the constitutive
+relations (13) are replaced by [1, 2],
+Di = εij(ω)Ej,
+Bi = µij(ω)Hj.
+(18)
+For non-magnetic media with isotropic magnetic perme-
+ability, it holds µij(ω) = µ0, where µ0 is the vacuum
+permeability. Considering the constitutive relations (18),
+the modified Amp`ere-Maxwell’s law, Eq.(17b), and Fara-
+day’s law, Eq.(17c), in the absence of sources, we obtain
+a modified wave equation for the electric field,
+ki �
+kjEj�
+− k2Ei = −ω2µ0¯εij (ω) Ej,
+(19)
+where we define the extended permittivity tensor,
+¯εij(ω) = εij(ω) − ik0
+AF
+ω2 ϵikjkk − iϵikj
+kk
+AF
+ω .
+(20)
+Using the definition to the refractive index, n = k/ω, the
+modified wave equation becomes
+MijEj = 0,
+(21)
+with Mij given by
+Mij = n2δij −ninj − εij
+ε0
+− i
+ω
+�
+V0ϵikjnk + ϵikjV k�
+, (22)
+in which ε0 is the vacuum electric permittivity, and
+V0 = k0
+AF /ε0,
+V k = kk
+AF /ε0.
+(23)
+appear as the components of a redefined background,
+V µ =
+�
+V0, V i�
+.
+The nontrivial solutions for the elec-
+tric field require a vanishing determinant of the matrix
+Mij, det Mij = 0, which provides the dispersion relations
+that describe the wave propagation in the medium.
+In this work, we will study plasma waves propagation
+for a chiral (parity-odd) medium, which means restrain-
+ing our investigation to the case of a purely timelike
+Lorentz-violating background vector, (kAF )µ =
+�
+k0
+AF , 0
+�
+.
+The latter also plays the role of chiral magnetic conduc-
+tivity. In this scenario, the wave equation (21) becomes
+�
+n2δij − ninj − εij
+ε0
+− iV0
+ω ϵikjnk
+�
+Ej = 0.
+(24)
+
+4
+III.
+THE USUAL MAGNETIZED COLD
+PLASMA
+In this work we will adopt the fluid theory approach
+in the cold plasma limit [3–7]:
+∂n
+∂t + ∇ · (nu) = 0,
+(25)
+∂u
+∂t + u · ∇u = q
+m (E + u × B0) ,
+(26)
+where n is the electron number density, u is the electron
+fluid velocity field, q and m are the electron charge and
+mass, respectively, and B0 is the equilibrium magnetic
+field. For simplicity, the ions are supposed to be infinitely
+massive, which is appropriate for high-frequency waves.
+Furthermore, thermal and collisional effects are also dis-
+regarded. The linearized version of the magnetized cold
+plasmas [7] consider fluctuations around average quanti-
+ties, n0 and B0, which are constant in time and space.
+Thus, the plasma quantities read
+n = n0 + δn,
+(27a)
+u = δu,
+(27b)
+E = δE
+(27c)
+B = B0 + δB,
+(27d)
+with δn, δu, δE and δB being first order plane wave
+magnitude perturbations. Following the usual procedure
+[3–6], assuming B0 = B0ˆz, we write the corresponding
+dielectric tensor,
+εij(ω) = ε0
+�
+�
+S
+−iD 0
+iD
+S
+0
+0
+0
+P
+�
+� ,
+(28)
+where
+S = 1−
+ω2
+p
+(ω2 − ω2c), D =
+ωcω2
+p
+ω (ω2 − ω2c), P = 1− ω2
+p
+ω2 , (29)
+and
+ωp = n0q2
+mϵ0
+,
+ωc = |q|B0
+m
+,
+(30)
+are the plasma and cyclotron frequencies, respectively.
+From the Maxwell theory, two distinct refractive in-
+dices are obtained,
+n± =
+�
+1 −
+ω2p
+ω (ω ± ωc),
+(31)
+which provide right-handed circularly polarized (RCP)
+and left-handed circularly polarized (LCP) modes,
+ELCP =
+i
+√
+2
+�
+1
+i
+�
+,
+ERCP =
+i
+√
+2
+�
+1
+−i
+�
+,
+(32)
+for the propagating modes associated to n±, respectively.
+This is the standard result of wave propagation in the
+usual magnetized cold plasma. We recall that a cutoff
+happens whenever the refractive index, n, goes to zero.
+On the other hand, a resonance occurs if n tends to infin-
+ity. From the indices (31), we obtain the following cutoff
+frequencies:
+ω± = 1
+2
+��
+ω2c + 4ω2p ∓ ωc
+�
+,
+(33)
+where ω± is related to n±, respectively.
+A very usual effect in magnetized plasmas is the circu-
+lar birefringence2, which causes the rotation of the plane
+of polarization of a linearly polarized wave that propa-
+gates within the medium.
+Thus the linearly polarized
+wave emerges from the medium with an electric field
+whose polarization is rotated relative to its initial lin-
+ear configuration. Such a phenomenon can be properly
+explained by decomposing the initial wave into two cir-
+cularly polarized waves (RCP and LCP) that travel with
+different phase velocities. In this case, the rotation an-
+gle of the electric field can be expressed as the difference
+between the refractive indices associated with the RCP
+and LCP waves [68, 72]:
+θ = πL
+λ0
+(Re [nRCP ] − Re [nLCP ]) ,
+(34)
+where λ0 is the vacuum wavelength of the incident wave.
+The rotation power δ = θ/L (phase difference per unit
+length), is given as
+δ = −ω
+2 (Re [nLCP ] − Re [nRCP ]) .
+(35)
+In a cold magnetized plasma, the refractive indices (31)
+provide the following rotatory power:
+δ = −ω
+2 Re
+�
+�
+�
+1 −
+ω2p
+ω (ω + ωc) −
+�
+1 −
+ω2p
+ω (ω − ωc)
+�
+� .
+(36)
+The behavior of the RP (36) in terms of the frequency
+ω is depicted in Fig. 1. One notices that there is a di-
+vergence at ωc, being positive for ω < ωc and negative
+for ω > ωc. It tends to zero at the high-frequency limit
+ω >> (ωp, ωc), where it decays as
+δ ≈ −ω2
+pωc
+2ω2 .
+(37)
+Associated with the imaginary part of the refractive in-
+dex, one can also examine dichroism, an optical effect
+2 In plasmas, the birefringence is usually a consequence of the Fara-
+day effect, occurring due to the presence of the external field
+B0, which generates distinct phase velocities for the propagating
+modes [70].
+
+5
+that occurs when circularly polarized waves are absorbed
+by the medium at different degrees [56, 58, 59]. Thus
+dichroism coefficient refers to the difference in absorp-
+tion of LCP and RCP waves, being given by:
+δd = −ω
+2 (Im[nLCP ] − Im[nRCP ]) .
+(38)
+which, for the refractive indices (31), implies
+δd = −ω
+2 Im
+�
+�
+�
+1 −
+ω2p
+ω (ω + ωc) −
+�
+1 −
+ω2p
+ω (ω − ωc)
+�
+� .
+(39)
+ω = ωc
+ω = 2 ωc
+ω = ω-
+ω = ω-
+0
+1
+2
+3
+4
+-2
+-1
+0
+1
+2
+ω (rad s-1)
+δ (rad m-1)
+FIG. 1. Rotatory power (36) in terms of ω. Here, ωc = ωp (red
+line) and ωc = 2ωp (blue line), with the choice ωc = 1 rad s−1.
+Such a quantity is plotted in Fig. 2, which shows sin-
+gularity at the cyclotron frequency ωc.
+For ωc = ωp
+(red curve), the dichroism coefficient (39) is negative for
+ω < ωred
++ , positive for 2ωc < ω < ωred
+−
+and null for other
+frequencies. The case for ωc = ωp/2 (blue curve) differs
+in the fact that ωblue
++
+is greater than ωc, showing that
+(39) is now negative for ω < ωc.
+ω = ωc
+ω = 2 ωc
+ω = ω-
+ω = ω-
+ω = ω+
+ω = ω+
+0.0
+0.5
+1.0
+1.5
+2.0
+-2
+-1
+0
+1
+2
+ω (rad s-1)
+δd (rad m-1)
+FIG. 2. Dichroism coefficient (39) in terms of ω. Here, ωc =
+ωp (red line) and ωc = ωp/2 (blue line), with ωc = 1 rad s−1.
+IV.
+WAVE PROPAGATION IN CHIRAL
+ELECTRODYNAMICS
+Starting from the wave equation (24) and using the ex-
+pression of the cold plasma dielectric permittivity, given
+in Eq. (28), we obtain a linear homogeneous system,
+�
+�
+n2 − n2
+x − S
+iD − nxny + i (V0/ω) nz −nxnz − i (V0/ω) ny
+−iD − nxny − i (V0/ω) nz
+n2 − n2
+x − S
+−nynz + i (V0/ω) nx
+−nxnz + i (V0/ω) ny
+−nynz − i (V0/ω) nx
+n2 − n2
+z − P
+�
+�
+�
+�
+δEx
+δEy
+δEz
+�
+� = 0.
+(40)
+Let us consider, for simplicity, the case the refractive
+index is parallel to the magnetic field, n = nˆz, such that
+one obtains
+�
+�
+n2 − S
+iD + i (V0/ω) n
+0
+−iD − i (V0/ω) n
+n2 − S
+0
+0
+0
+−P
+�
+�
+�
+�
+δEx
+δEy
+δEz
+�
+� = 0,
+(41)
+for which det[Mij] = 0 provides the dispersion relations
+P
+�
+ω2 �
+n2 − S
+�2 − (ωD + nV0)2�
+= 0.
+(42)
+Longitudinal waves, n ∥ δE or δE = (0, 0, δEz), may
+emerge, when P = 0, with non propagating vibration
+at the plasma frequency, ω = ωp. For transverse waves,
+n ⊥ δE or δE = (δEx, δEy, 0), the dispersion relation
+(42) simplifies as
+�
+n2 − S
+�2 − (D + n (V0/ω))2 = 0,
+(43)
+also written as a fourth-order equation in n,
+n4 −
+�
+2S + (V0/ω)2�
+n2 − 2D (V0/ω) n +
+�
+S2 − D2�
+= 0.
+(44)
+Taking into account the relations (29), the dispersion re-
+lation (44) provides the following refractive indices:
+nR,M = − V0
+2ω ±
+�
+1 +
+� V0
+2ω
+�2
+−
+ω2p
+ω(ω − ωc),
+(45)
+nL,E = V0
+2ω ±
+�
+1 +
+� V0
+2ω
+�2
+−
+ω2p
+ω(ω + ωc),
+(46)
+In general, the indices nR, nL, nE, nM may be real,
+imaginary, or complex (presenting both pieces) at some
+frequency ranges. As well-known, the real part is asso-
+ciated with propagation, while the complex piece is con-
+cerned with absorption. Furthermore, these indices may
+
+6
+have positive or negative real pieces.
+The indices nL
+and nM are always positive and negative, respectively,
+the latter one being a negative refractive index. On the
+other hand, the indices nR and nE can be positive or
+negative, depending on the frequency zone examined, in
+such a way the associated modes can manifest negative
+refraction behavior (in a suitable frequency band).
+The propagating modes associated with the refractive
+indices in Eq. (45)) and Eq. (46) are obtained by insert-
+ing each one in Eq. (41) and carrying out the correspond-
+ing eigenvector (with a null eigenvalue). The emerging
+electric field are the ELCP and ERCP , given in Eq. (32),
+where nR, nM are associated with the RCP mode, and
+nL, nE are related to the LCP mode,
+nL, nE �→ ELCP =
+i
+√
+2
+�
+1
+i
+�
+,
+(47)
+nR, nM �→ ERCP =
+i
+√
+2
+�
+1
+−i
+�
+.
+(48)
+From the indices nR, nE, given by Eqs. (45) and (46),
+we obtain the same cutoff frequencies (33) of the standard
+case: in fact, ω− is related to the refractive index nR,
+and ω+ is associated with the refractive index nE. In
+contrast, the refractive indices nL and nM have no real
+root. The behavior of the refractive indices in Eqs. (45)
+and (46) will be examined in the following.
+A.
+About the index nR
+We initiate discussing some properties of the index nR.
+The behavior of nR in terms of the dimensionless param-
+eter ω/ωc is illustrated in Fig. 3, which displays the real
+imaginary pieces of the refractive index nR. We point
+out:
+(i) It takes on a finite value when ω → 0, given by
+nR (0) = 1
+V0
+�
+ω2
+p
+ωc
+�
+,
+(49)
+differing from the behavior of the usual magnetized
+plasma index n−, which provides n → ∞ near the
+origin.
+(ii) For 0 < ω < ωc, nR is positive since the square root
+in (45) is real, positive, and larger than the negative
+piece before it. Such a positivity also holds for the
+usual index n−. See the black line in this frequency
+zone in Fig. 3.
+(iii) For ω → ωc, nR → ∞, and there occurs a resonance
+at the cyclotron frequency.
+(iv) For ωc < ω < ωr, there appears a negative refrac-
+tive index zone with absorption, where Re[nR] < 0
+and Im[nR] ̸= 0, as shown in Fig. 3. The frequency
+ωr is the root of the radicand in Eq. (45),
+R− (ω) = 1 + V 2
+0
+4ω2 −
+ω2
+p
+ω (ω − ωc),
+(50)
+which yields a cubic equation in ω.
+(v) For ωr < ω < ω−, one finds a negative refractive
+index zone without absorption, that is, Re[nR] < 0
+and Im[nR] = 0.
+(vi) For ω > ω−, the quantity nR is always positive,
+corresponding to a propagating zone, with nR → 1
+in the high-frequency limit.
+ω = ω-
+ω = ωr
+ω = ωc
+0
+1
+2
+3
+4
+-2
+-1
+0
+1
+2
+3
+4
+ω/ωc
+n
+FIG. 3. Index of refraction nR in terms of the frequency ω.
+The dashed blue (black) line corresponds to the imaginary
+piece of nR (n−), while the solid blue (black) line represents
+the real piece of nR (n−).
+Here ωc = ωp, V0 = 2ωp, and
+ωc = 1 rad s−1.
+The frequency zone in which Im[nR] ̸= 0, that is,
+ωc < ω < ωr, corresponds to the absorption zone for
+the metamaterial (negative refractive index) RCP wave,
+as already mentioned before. The frequency ranges in
+which Im[nR] = 0 define the propagation zone for the
+RCP wave.
+B.
+About the index nL
+The index nL, given in Eq.
+(46), has no real root,
+presenting the following features:
+(i) For ω → 0, nL → +∞. Then, the presence of the
+term V0 turns the refractive index real and pos-
+itively divergent at the origin, differing from the
+usual index n+ behavior, see Eq. (31), which is
+complex and divergent, Im[n+] → ∞, at the ori-
+gin.
+
+7
+(ii) For ω > 0, it is necessary to analyze the radicand
+in Eq. (46),
+R+ (ω) = 1 + V 2
+0
+4ω2 −
+ω2
+p
+ω (ω + ωc),
+(51)
+since it can be positive or negative, which deter-
+mines the absence or presence of an absorption
+zone, respectively. Note that for ω > ω+ the term
+1 − ω2
+p/ω (ω + ωc) is greater than zero (ω+ is the
+root of such a term), such that R+ is positive.
+Therefore, the possibility of R+ being negative oc-
+curs only in the range 0 < ω < ω+, for which the
+term 1 − ω2
+p/ω (ω + ωc) is less than zero. Hence,
+this positivity for R+ is stated by the condition,
+V 2
+0
+4ω2 >
+�����1 −
+4ω2
+p
+ω(ω + ωc)
+�����
+ω<ω+
+,
+(52)
+for which R+ is always positive and the refractive
+index nL is real for any ω > 0. This corresponds
+to a propagating mode for the entire frequency do-
+main. The behavior of nL in terms of the dimen-
+sionless parameter ω/ωc, considering the condition
+(52), that is, R+ > 0, is shown in Fig. 4.
+(iii) On the other hand, for
+V 2
+0
+4ω2 <
+�����1 −
+4ω2
+p
+ω(ω + ωc)
+�����
+ω<ω+
+,
+(53)
+one has R+
+<
+0 and nL becomes complex,
+Im[nL] ̸= 0, determining the opening of an absorp-
+tion zone located within the interval ωi < ω < ωf,
+as shown in Fig. 5. The frequencies ωi and ωf are
+positive and real roots of R+, a cubic equation in
+the frequency.
+ω = ω+
+0
+1
+2
+3
+4
+-2
+0
+2
+4
+6
+ω/ωc
+n
+FIG. 4. Refractive index nL (blue lines) for the condition (52),
+R+ > 0. Refractive index n+ (black lines) of Eq. (31). The
+dashed (solid) lines correspond to the imaginary (real) pieces
+of nL and n+. Here ωc = ωp, V0 = 2ωp, and ωc = 1 rad s−1.
+ω = ω+
+ω = ωf
+ω = ωi
+0.0
+0.5
+1.0
+1.5
+2.0
+-1
+0
+1
+2
+3
+4
+ω/ωc
+n
+FIG. 5. Refractive index nL (blue lines) for the condition (53),
+R+ < 0. Refractive index n+ (black lines) of Eq. (31). The
+dashed (solid) lines correspond to the imaginary (real) pieces
+of nL and n+. Here ωc = ωp, V0 = 0.7ωp, and ωc = 1 rad s−1.
+C.
+About the index nE
+The quantity nE is a refractive index that only exists
+as a positive quantity due to the presence of the chiral
+Lorentz-violating term. In the case we set V0 = 0, the
+second relation in Eq. (46) yields Re[nE] < 0 (negative
+index of refraction). For V0 ̸= 0, the index nE presents a
+small positivity range, Re[nE] > 0, which provides prop-
+agation for the associated LCP wave. We present below
+some aspects of nE:
+(i) For ω → 0, the index nE tends to a finite value at
+origin,
+nE (0) = 1
+V0
+�
+ω2
+p
+ωc
+�
+,
+(54)
+which is inversely proportional to the magnitude of
+the chiral factor, V0.
+(ii) Since the radicand of nE is the same one of nL, see
+Eq. (46), it holds here the same procedure applied
+for nL. For values of V0 that satisfy the condition
+(52), R+ > 0, nE is always real, Im[nE] = 0, being
+positive within the interval 0 < ω < ω+, and nega-
+tive for ω > ω+, since
+�
+R+ > V0/2ω at this range.
+The real and imaginary parts of nE are represented
+in Fig. 6.
+(iii) Considering the condition (53), nE becomes com-
+plex and exhibits an absorption zone, Im[nE] ̸= 0,
+in the interval ωi < ω < ωf, with ωi, ωf < ω+, as
+shown in Fig. 7. Such a figure depicts the real and
+imaginary pieces of nE (under the condition (53)).
+
+8
+ω = ω+
+0.0
+0.5
+1.0
+1.5
+2.0
+-4
+-3
+-2
+-1
+0
+1
+2
+ω/ωc
+n
+FIG. 6.
+Red line: plot of the index nE for the condition
+(52), R+ > 0. Black line: plot of the index −n+ of Eq. (31).
+Dashed (solid) lines represent the imaginary (real) pieces of
+nE and −n+. Here, we have used ωc = ωp and V0 = 2ωp,
+with the choice ωc = 1 rad s−1.
+ω = ω+
+ω = ωf
+ω = ωi
+0.0
+0.5
+1.0
+1.5
+2.0
+-3
+-2
+-1
+0
+1
+2
+3
+ω/ωc
+n
+FIG. 7.
+Red line: plot of the index nE for the condition
+(53), R+ < 0. Black line: plot of the index −n+ of Eq. (31).
+Dashed (solid) lines represent the imaginary (real) pieces of
+nE and −n+. Here, we have set ωc = ωp, V0 = 0.7ωp, and
+ωc = 1 rad s−1.
+D.
+About the index nM
+The additional index nM, given in Eq. (45), is always
+negative (negative refraction) and has no real root. The
+behavior of nM in terms of the dimensionless parameter
+ω/ωc is shown in Fig. 8. We notice the following features:
+(i) For 0 < ω < ωc, nM is real and negative since
+the square root in (45) is real. This is the same
+behavior of the index −n+. See the black line in
+Fig. (8).
+(ii) For ω → ωc, nM → −∞, and there occurs a reso-
+nance at the cyclotron frequency.
+(iii) For ωc < ω < ωr, there appears an absorption zone
+for metamaterial, Re[nM] < 0 and Im[nM] ̸= 0,
+while the index −n+ is purely imaginary, Re[nM] =
+0 and Im[nM] ̸= 0, as shown in Fig. 8. The fre-
+quency ωr is the root of R−.
+(iv) For ω > ωr, the quantity nM is always negative,
+corresponding to a negative propagation zone, with
+nM → −1 in the high-frequency limit.
+ω = ωc
+ω = ω-
+ω = ωr
+0
+1
+2
+3
+4
+-6
+-4
+-2
+0
+ω/ωc
+n
+FIG. 8. Blue line: plot of the index nM. Black line: plot
+of the real piece of −n− of Eq. (31).
+Dashed (solid) lines
+represent the imaginary (real) pieces of nM and −n−. Here,
+we have used: ωc = ωp, V0 = 2ωp, and ωc = 1 rad s−1.
+E.
+Dispersion relations behavior
+The wave dispersion associated with each refractive in-
+dex is usually visualized in plots ω × k. In the following,
+we work with dimensionless plots, (ω/ωc) × (k/ωc).
+The dispersion relations associated with nR and nM
+are depicted in Fig. 9 for ωc = ωp.
+The propagation
+occurs for 0 < ω < ωc and ω > ω−, while absorption
+takes place in ωc < ω < ωr. The range ωr < ω < ω−
+corresponds to negative refraction propagation zone (k <
+0) for nR. The refractive index nM is negative for k < 0
+and ω > 0.
+Figure 10 depicts the dispersion relations related to nL
+and nE. The wave associated with nL propagates for all
+frequencies. For nE, the conventional propagation zone
+occurs in 0 < ω < ω+. For ω > ω+, there occurs a prop-
+agation zone with negative refraction. For the standard
+indices, ±n+, the absorption zone is 0 < ω < ω+.
+Furthermore, Fig. 11 shows the dispersion relations for
+nL and nE in the case there is a modified absorption zone
+for ωi < ω < ωf, while the free propagation occurs for
+0 < ω < ωi and ω > ωf. The frequencies ωi, ωf and
+ωr define the limits for unusual propagation zones. As
+already discussed, these frequencies are obtained from
+the radicands (50) and (51).
+
+9
+Modified absorption
+Usual absorption zone
+ω = ω-
+ω = ωc
+ω = ωr
+ω = k
+-4
+-2
+0
+2
+4
+0
+1
+2
+3
+4
+k/ωc
+ω
+ωc
+FIG. 9. Plot of the dispersion relations related to refractive
+indices nR (solid red line) and nM (solid blue line).
+The
+dashed black line corresponds to the indices of the usual case
+(±n−). The highlighted area in red (gray) indicates the ab-
+sorption zone for nR,M (±n−). Here, we have used ωc = ωp
+and V0 = 2ωp, with ωc = 1 rad s−1.
+Usual absorption zone
+ω = ω+
+ω = k
+-2
+-1
+0
+1
+2
+0.0
+0.5
+1.0
+1.5
+2.0
+k/ωc
+ω
+ωc
+FIG. 10. Plot of the dispersion relations related to refractive
+indices nL (solid red line) and nE (solid blue line). The dashed
+line corresponds to the indices ±n+ of the usual case. The
+highlighted gray area indicates the absorption zone for ±n+,
+where now also occurs propagation. Here, we have used ωc =
+ωp and V0 = ωp, with ωc = 1 rad s−1.
+Modified absorption zone
+ω = ω+
+ω = ωi
+ω = ωf
+ω = k
+-2
+-1
+0
+1
+2
+0.0
+0.5
+1.0
+1.5
+2.0
+k/ωc
+ω
+ωc
+FIG. 11. Plot of the dispersion relations related to refractive
+indices nL (solid red line) and nE (solid blue line). The dashed
+line corresponds to the usual case with indices ±n+.
+The
+highlighted areas in red (gray) indicate the absorption zone
+for nL,E (±n+). Here, we have used ωc = ωp and V0 = 0.7ωc,
+with ωc = 1 rad s−1.
+V.
+BIREFRINGENCE, ROTATORY POWER
+AND DICHROISM
+The phase velocity in terms of the refractive index n
+is defined (in natural units) as vphase = 1/n.
+Hence,
+the corresponding phase velocities, vR = 1/ (nR), vL =
+1/ (nL), vE = 1/ (nE), vM = 1/ (nM), can be defined
+with the indices nR, nL, nE, nM of Eqs. (45) and (46).
+Accordingly with the previous analysis of the refractive
+indices, in general, the RCP and LCP modes propagate
+at different phase velocities for each frequency value, gen-
+erating circular birefringence in the propagation band,
+expressed in terms of the rotatory power (35). On the
+other hand, in the absorption zones, there occurs dichro-
+ism, measured in terms of the coefficient of Eq. (38).
+A.
+Rotatory power
+In order to write the rotatory power (RP), we need to
+consider the refractive indices nL, nE, associated with
+the LCP wave, and the indices nR, nM, associated to
+the RCP wave. It allows, in principle, to determine four
+distinct RPs at the propagation zones, some of which we
+examine in this section.
+We start by writing the rotation power defined in terms
+of real pieces of the refractive indices nL and nR,
+δLR = −ω
+2 (Re[nL] − Re[nR]) ,
+(55)
+
+10
+or explicitly,
+δLR = −ω
+2 Re
+�
+V0/ω +
+�
+R+ −
+�
+R−
+�
+,
+(56)
+where R+ and R− are given in Eqs. (50) and (51). We
+find a positive frequency,
+ˆω =
+�
+ω2c + ω2p/2 − ω2p
+�
+4ω2c + V 2
+0
+2V0
+,
+(57)
+where the RP (56) undergoes a sign reversal.
+In Fig.
+12, we illustrate the behavior of RP for the condition
+(52). For the interval 0 < ω < ˆω, the RP is negative,
+and for ˆω < ω < ωc, it is positive. The RP reversion
+that occurs at ω = ˆω is not usual in cold plasmas theory.
+However, it is reported in graphene systems [84], rotat-
+ing plasmas [95], and bi-isotropic dielectrics supporting
+chiral magnetic current [96].
+For ω > ωc, the RP is
+always negative. Nevertheless, it is necessary to pay at-
+tention to the interval ωc < ω < ωr, where the refractive
+index nR has an imaginary piece and the RCP wave is
+absorbed. At ω = ωr, the real piece of nR undergoes a
+sharp change (see Fig. 3), which also appears in the RP
+profile of Fig. 12.
+ω = ω
+ω = ωc
+ω = ωr
+ω = ω-
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+-2
+-1
+0
+1
+2
+ω (rad s-1)
+δ (rad m-1)
+FIG. 12. The solid blue line represents the rotatory power
+(56) defined by the refractive index nL and nR, for the con-
+dition (52). The dashed black line corresponds to the usual
+rotatory power (36). Here, we have used ωc = ωp, V0 = ωp,
+and ωc = 1 rad s−1.
+We can safely claim that both modes associated with
+the nL and nR propagate for ω > ω−, range in which
+the RP magnitude decreases monotonically with ω, ap-
+proaching to its asymptotic value, −V0/2 (see Fig. 12).
+Assuming the limit where ω >> (ωp, ωc), we can write
+nL,R ≈ 1 ± V0
+2ω + V 2
+0
+8ω2 −
+ω2
+p
+2ω (ω ± ωc),
+(58)
+so that the rotatory power is
+δLR ≈ −V0
+2 − ω2
+pωc
+2ω2 .
+(59)
+Note that taking the limit V0 → 0, the usual Faraday
+effect RP (37) is recovered for the high-frequency regime.
+It is also interesting to point out that the Faraday effect
+disappears for a null magnetic field, ωc = 0. However,
+the birefringence still remains, due to the presence of the
+chiral term, which yields the following RP:
+δ ≈ −V0/2.
+(60)
+For the condition (53), the RP (56) also exhibits a sign
+reversal and a very similar profile to the one of Fig. 12,
+in such a way that it will not be depicted here.
+Considering now the refractive indices nE and nR, the
+rotatory power is:
+δER = −ω
+2 (Re[nE] − Re[nR]) ,
+(61)
+or,
+δER = −ω
+2 Re
+�
+V0/ω −
+�
+R+ −
+�
+R−
+�
+.
+(62)
+Recalling that the LCP wave associated with nE has a
+conventional free propagation for ω < ω+ and propaga-
+tion with negative refractive index (nE < 0) for ω > ω+
+(with ω+ < ωc), the RP magnitude is enhanced in the
+latter zone. This behavior is depicted in Fig. 13, which
+shows the RP (62) for nE given by the condition (52),
+R+ > 0. The RP is positive for ω < ωc and negative
+for ωc < ω < ω′′, becoming positive again for ω > ω′′,
+where ω′′ is the reversal frequency. For nE given by the
+condition condition (53), the RP is depicted in Fig. 14,
+revealing a small reversion at ω′′ < ωc. Note that the
+increasing RP with ω, depicted in Figs. 13 and 14, is due
+to the negative behavior of the index nE for ω > ω+.
+In the asymptotic limit, where ω >> (ωp, ωc), the RP
+(62) goes as
+δER ≈ ω − V0
+2 ,
+(63)
+presentig a predominant linear behavior in ω, as it ap-
+pears in Figs. 13 and 14. It is also worth mentioning
+that the limit V0 → 0, implying δ ≈ ω, does not stand
+for a valid result for usual magnetized plasma, since the
+RP (62) is not defined for achiral cold plasmas.
+B.
+Dichroism coefficients
+As well known, absorption depends on the magnitude
+of the imaginary parts of the refractive indices. When
+one mode is more absorbed than the other, there occurs
+dichroism. Considering the refractive indices nL and nR,
+the circular dichroism coefficient is
+δdLR = −ω
+2 (Im[nL] − Im[nR]) .
+(64)
+Considering the condition (52), only nR has imaginary
+part (localized in the interval ωc < ω < ω−), while nL is
+
+11
+-0.1
+0
+0.1
+ω
+δ
+ω = ω''
+ω = ω''
+ω = ωc
+0
+1
+2
+3
+4
+-4
+-2
+0
+2
+4
+ω (��� �-�)
+δ (��� �-�)
+FIG. 13.
+Solid blue lines: plot of the rotatory power (62)
+associated to the refractive indices nE and nR for the con-
+dition (52).
+The dashed line represents the usual rotatory
+power (36).
+Here, we have used ωc = ωp, V0 = ωp, and
+ωc = 1 rad s−1. The inset plot highlights the behavior of δ
+around ω = ω′′.
+- 1
+10
+0
+1
+10
+ω
+δ
+ω = ω''
+ω = ω''
+ω = ωc
+0
+1
+2
+3
+4
+-4
+-2
+0
+2
+4
+ω (��� �-�)
+δ (��� �-�)
+FIG. 14. Solid red lines: rotatory power (62) associated to
+the refractive indices nE and nR for the condition (53). The
+dashed line represents the usual rotatory power (36). Here,
+we have used ωc = ωp, V0 = 0.7ωp, and ωc = 1 rad s−1. The
+inset plot highlights the behavior of δ around ω = ω′′.
+real for ω > 0. In this case, the dichroism coefficient is
+given by
+δdLR =
+�
+�
+�
+�
+�
+0,
+for 0 < ω < ωc,
+�
+R−,
+for ωc < ω < ωr,
+0,
+for ω > ωr,
+(65)
+being non null only in the range ωc < ω < ω−, as prop-
+erly shown in Fig 15.
+Considering the condition (53), both nR and nL have
+non-null imaginary parts in the intervals ωc < ω < ωr
+and ωi < ω < ωf, respectively. The dichroism coefficient
+is null for 0 < ω < ωi, ωf < ω < ωc, and ω > ωr, being
+ω = ω+
+ω = ω-
+ωc = ωp
+ω = ωr
+0.0
+0.5
+1.0
+1.5
+2.0
+-0.5
+0.0
+0.5
+1.0
+1.5
+2.0
+ω (rad s-1)
+δd (rad m-1)
+FIG. 15. Plot of the dichroism coefficient (65)(red solid lines)
+associated to the refractive indices nL and nR, under the
+condition (52). The black dashed line represents the usual
+dichroism coefficient (39). Here ωc = ωp, V0 = (3/2) ωc, and
+ωc = 1 rad s−1.
+non-null only for
+δdLR =
+�
+− ω
+2
+�
+R+,
+for ωi < ω < ωf,
++ ω
+2
+�
+R−,
+for ωc < ω < ωr,
+(66)
+whose general behavior is exhibited in Fig. 16.
+ω = ωi
+ω = ωf
+ω = ω+
+ω = ω-
+ωc = ωp
+ω = ωr
+0.0
+0.5
+1.0
+1.5
+2.0
+-0.5
+0.0
+0.5
+1.0
+1.5
+2.0
+ω (rad s-1)
+δd (rad m-1)
+FIG. 16. Plot of the dichroism coefficient (66)(solid red lines)
+associated to the refractive indices nL and nR, under the con-
+dition (53). The dashed line represents the usual dichroism
+coefficient (39). Here, we have set ωc = ωp, V0 = 0.7ωp, and
+ωc = 1 rad s−1.
+For the refractive indices nE and nR, the circular
+dichroism coefficient is
+δdER = −ω
+2 (Im[nE] − Im[nR]) .
+(67)
+If we consider nE under the condition (52), the same
+behavior of Fig. 15 is obtained, since nE is always real,
+not contributing to the dichroism. On the other hand,
+regarding now the condition (53), both nR e nE have
+non-zero imaginary parts in the intervals ωc < ω < ωr
+
+12
+and ωi < ω < ωf, respectively). In this case, we have
+δdER =
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+0,
+for 0 < ω < ωi,
++ ω
+2
+�
+R+,
+for ωi < ω < ωf,
+0,
+for ωf < ω < ωc,
++ ω
+2
+�
+R−,
+for ωc < ω < ωr,
+0,
+for ω > ωr.
+(68)
+The general behavior of the dichroism coefficient (68)
+is illustrated in Fig. 17.
+ω = ωi
+ω = ωf
+ω = ω+
+ω = ω-
+ωc = ωp
+ω = ωr
+0.0
+0.5
+1.0
+1.5
+2.0
+-0.5
+0.0
+0.5
+1.0
+1.5
+2.0
+ω (rad s-1)
+δd (rad m-1)
+FIG. 17. Plot of the dichroism coefficients (68) associated to
+the refractive indices nE and nR (for the condition (53)). The
+dashed line represents the usual dichroism coefficient (39).
+Here, we have used ωc = ωp, V0 = 0.7ωp, and ωc = 1 rad s−1.
+VI.
+FINAL REMARKS
+In this work, we have examined the propagation of
+electromagnetic waves in a cold magnetized plasma in
+the context of the chiral MCFJ electrodynamics, describ-
+ing the implied optical effects as well. We have adopted
+a MCFJ timelike background vector in order to repre-
+sent the chirality factor that breaks the parity. Starting
+from the modified Maxwell equations and employing the
+usual methods, we obtained four modified refractive in-
+dices given by Eqs. (45) and (46), associated with cir-
+cularly polarized propagating modes. Such indices were
+analyzed in detail in the Secs. IV A – IV D, where some
+of them exhibited significant modifications, as the index
+nR, see Fig. 3. It presents a negative refraction behavior
+in the range ωc < ω < ω−, in which it occurs propagation
+with absorption for ωc < ω < ωr and free (metamaterial)
+propagation for ωr < ω < ω−. The usual counterpart in-
+dex presents only pure absorption in this range.
+Optical effects of this system, involving birefringence
+and dichroism, were discussed in Sec. V, considering the
+refractive index nL and nR and nE. In Sec.V A, the RP
+δLR was introduced, see Eq. (56), exhibiting sign rever-
+sion at ω = ˆω, for the conditions (52) and (53). The RP
+δER also exhibits sign change at ω = ω′′ > ωc for the con-
+dition (52), and ω = ω′′ < ωc under the condition (53),
+as shown in Figs. 13 and 14, respectively. Such a RP
+reversal is not usual in cold plasmas, being reported in
+graphene systems [84], rotating plasmas [95], Weyl met-
+als and semimetals with low electron density with chi-
+ral conductivity [92, 93], and bi-isotropic dielectrics with
+magnetic chiral conductivity [96]. Comparing our results
+with the rotating plasma scenario of Ref. [95], there ap-
+pear differences. In the rotating plasma, the RP under-
+goes reversal and decays as 1/ω2 for high frequencies. In
+the present case, the rotatory power tends to the asymp-
+totical value −V0, see Eq. (60), or increases with ω when
+it involves the negative refraction index, see Eq. (63).
+These distinct RP properties may provide a channel to
+optically characterize chiral cold plasmas.
+Besides the nonconventional effect of reversion, the RP
+can also be enhanced when it is defined in the negative
+refraction zone. Such an enhancement occurs for δER,
+given in Eq. (62), for ω > ω+ (zone in which nE is neg-
+ative), being a topic of interest in metamaterial plasmas
+[116–119].
+Dichroism was examined in Sec.V B, where
+the coefficients δdLR and δdER have been shown to be
+non-null only in the range ωc < ω < ωr, for the condi-
+tion (52) - see Figs. 15, and in the intervals ωc < ω < ωr,
+ωi < ω < ωf, for the condition (53), in accordance with
+Figs. 16 and 17.
+ACKNOWLEDGMENTS
+The authors express their gratitude to FAPEMA,
+CNPq, and CAPES (Brazilian research agencies) for
+their invaluable financial support. M.M.F. is supported
+by FAPEMA Universal/01187/18, CNPq/Produtividade
+311220/2019-3
+and
+CNPq/Universal/422527/2021-1.
+P.D.S.S
+is
+supported
+by
+FAPEMA
+BPD-12562/22.
+Furthermore, we are indebted to CAPES/Finance Code
+001 and FAPEMA/POS- GRAD-02575/21.
+[1] A. Zangwill, Modern Electrodynamics (Cambridge Uni-
+versity Press, New York, 2012).
+[2] J.D. Jackson, Classical Electrodynamics, 3rd ed. (John
+Wiley & Sons, New York, 1999).
+[3] D.A. Gurnett and A. Bhattacharjee, Introduction to
+Plasma Physics (Cambridge University Press, Cam-
+bridge, 2005).
+[4] P.A. Sturrock, Plasma Physics:
+An Introduction to
+the theory of Astrophysical, Geophysical and Laboratory
+Plasmas, Cambridge, 1994.
+[5] J. A. Bittencourt, Fundamentals of Plasma Physics, 3rd
+ed. (Springer, New York, 2004).
+[6] T. H. Stix, Waves in Plasmas (Springer, New York,
+1992).
+
+13
+[7] T.J.M. Boyd and J.J. Sanderson, The Physics of plas-
+mas (Cambridge University Press, New York, 2003).
+[8] A. Piel, Plasmas Physics - An Introduction to Labora-
+tory, Space, and Fusion Plasmas, (Springer, Heidelberg,
+2010).
+[9] E. V. Appleton, and G. Builder, The Ionosphere as a
+doubly Refracting Medium. Proc. Phys. Soc. 45 208,
+(1932), E. V. Appleton, Wireless Studies of the Iono-
+sphere, J. Inst. Electr. Eng. 257, (1932).
+[10] D. R. Hartree, The propagation of electromagnetic
+waves in a stratified medium, Mathematical Proceed-
+ings of the Cambridge Philosophical Society, 25:97–120,
+1929.
+[11] J. A. Ratcliff, The formation of the ionosphere. Ideas
+of the early years (1925-1955). J. of Atmospheric and
+Terrestrial Physics, Vol. 36. p 2167-2181, (1974).
+[12] F. Haas, P. Gaete, L. P. R. Ospedal, and Jos´e Abdalla
+Helay¨el-Neto, Modified plasma waves described by a
+logarithmic electrodynamics, Phys. Plasmas 26, 042108
+(2019).
+[13] D.E. Kharzeev, The chiral magnetic effect and anomaly-
+induced transport, Prog. Part. Nucl. Phys. 75, 133
+(2014); D.E. Kharzeev, J. Liao, S.A. Voloshin, and
+G. Wang, Chiral magnetic and vortical effects in high-
+energy nuclear collisions – A status report, Prog. Part.
+Nucl. Phys. 88, 1 (2016);
+[14] D. Kharzeev, K. Landsteiner, A. Schmitt and H.U. Yee,
+Strongly Interacting Matter in Magnetic Fields, Lect.
+Notes Phys. 871 (Springer-Verlag, Berlin · Heidelberg,
+2013).
+[15] K. Fukushima, D.E. Kharzeev, and H.J. Warringa, Chi-
+ral magnetic effect, Phys. Rev. D 78, 074033 (2008);
+D.E. Kharzeev and H. J. Warringa, Chiral magnetic
+conductivity, Phys. Rev. D 80, 034028 (2009).
+[16] Q. Li, D.E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosi´c,
+A.V. Fedorov, R.D. Zhong, J.A. Schneeloch, G.D Gu,
+and T. Valla, Chiral magnetic effect in ZrTe5, Nature
+Phys. 12, 550 (2016).
+[17] A. Vilenkin, Equilibrium parity-violating current in
+a magnetic field,
+Phys. Rev. D 22,
+3080 (1980);
+A. Vilenkin and D.A. Leahy, Parity nonconservation
+and the origin of cosmic magnetic fields, Astrophys. J.
+254, 77 (1982).
+[18] G. Inghirami, M. Mace, Y. Hirono, L. Del Zanna,
+D.E. Kharzeev, and M. Bleicher, Magnetic fields in
+heavy ion collisions: flow and charge transport, Eur.
+Phys. J. C 80, 293 (2020).
+[19] J. Schober, A. Brandenburg and I. Rogachevskii, Chiral
+fermion asymmetry in high-energy plasma simulations,
+Geophys. Astrophys. Fluid Dynamics 114, 106 (2020).
+[20] Y. Akamatsu and N. Yamamoto, Chiral Plasma Insta-
+bilities, Phys. Rev. Lett. 111, 052002 (2013); A. Bo-
+yarsky, O. Ruchayskiy, and M. Shaposhnikov, Long-
+Range Magnetic Fields in the Ground State of the
+Standard Model Plasma, Phys. Rev. Lett. 109, 111602
+(2012).
+[21] M. Dvornikov and V.B. Semikoz, Influence of the tur-
+bulent motion on the chiral magnetic effect in the early
+universe, Phys. Rev. D 95, 043538 (2017).
+[22] G. Sigl and N. Leite, Chiral magnetic effect in protoneu-
+tron stars and magnetic field spectral evolution, JCAP
+01, 025 (2016).
+[23] M. Dvornikov and V.B. Semikoz, Magnetic field in-
+stability in a neutron star driven by the electroweak
+electron-nucleon interaction versus the chiral magnetic
+effect, Phys. Rev. D 91, 061301(R) (2015).
+[24] M. Dvornikov and V.B. Semikoz, Instability of magnetic
+fields in electroweak plasma driven by neutrino asym-
+metries, JCAP 05, 002 (2014); M. Dvornikov, Electric
+current induced by an external magnetic field in the
+presence of electroweak matter, EPJ Web Conf. 191,
+05008 (2018).
+[25] A.A. Burkov, Chiral anomaly and transport in Weyl
+metals, J. Phys. Condens. Matter 27, 113201 (2015).
+[26] M.-C. Chang and M.-F. Yang, Chiral magnetic effect in
+a two-band lattice model of Weyl semimetal, Phys. Rev.
+B 91, 115203 (2015).
+[27] E.C.I van der Wurff and H.T.C. Stoof, Anisotropic chi-
+ral magnetic effect from tilted Weyl cones, Phys. Rev.
+B 96, 121116(R) (2017).
+[28] K. Landsteiner, Anomalous transport of Weyl fermions
+in Weyl semimetals, Phys. Rev. B 89, 075124 (2014).
+[29] S. Kaushik and D.E. Kharzeev, Quantum oscillations
+in the chiral magnetic conductivity, Phys. Rev. B 95,
+235136 (2017).
+[30] A. Mart´ın-Ruiz, M. Cambiaso, and L.F. Urrutia, Elec-
+tromagnetic fields induced by an electric charge near a
+Weyl semimetal, Phys. Rev. B 99, 155142 (2019).
+[31] R. E. Throckmorton, J. Hofmann, E. Barnes, and S. D.
+Sarma, Many-body effects and ultraviolet renormaliza-
+tion in three-dimensional Dirac materials, Phys. Rev. B
+92, 115101 (2015).
+[32] K. Deng, J. S. Van Dyke, D. Minic, J. J. Heremans, and
+E. Barnes, Exploring self-consistency of the equations of
+axion electrodynamics in Weyl semimetals, Phys. Rev.
+B 104, 075202 (2021).
+[33] E. Barnes, J. J. Heremans, and Djordje Minic, Elec-
+tromagnetic Signatures of the Chiral Anomaly in Weyl
+Semimetals, Phys. Rev. Lett. 117, 217204 (2016).
+[34] F. Wilczek, Two Applications of Axion Electrodynam-
+ics, Phys. Rev. Lett. 58, 1799 (1987).
+[35] A. Sekine and K. Nomura, Axion electrodynamics
+in topological materials, J. Appl. Phys. 129, 141101
+(2021).
+[36] M. E. Tobar, B. T. McAllister, and M. Goryachev,
+Modified axion electrodynamics as impressed electro-
+magnetic sources through oscillating background po-
+larization and magnetization, Phys. Dark Universe 26,
+100339 (2019).
+[37] J. M. A. Paix˜ao, L. P. R. Ospedal, M. J. Neves, and
+J. A. Helay¨el-Neto, The axion-photon mixing in non-
+linear electrodynamic scenarios, J. High Energ. Phys.
+2022, 160 (2022).
+[38] Z. Qiu, G. Cao and X.-G. Huang, Electrodynamics of
+chiral matter, Phys. Rev. D 95, 036002 (2017).
+[39] P.D.S. Silva,
+M.M. Ferreira Jr.,
+M. Schreck,
+and
+L.F. Urrutia, Magnetic-conductivity effects on electro-
+magnetic propagation in dispersive matter, Phys. Rev.
+D 102, 076001 (2020).
+[40] S. Kaushik, D.E. Kharzeev, and E.J. Philip, Transverse
+chiral magnetic photocurrent induced by linearly polar-
+ized light in symmetric Weyl semimetals, Phys. Rev.
+Research 2, 042011(R) (2020).
+[41] S.M. Carroll, G.B. Field, and R. Jackiw, Limits on a
+Lorentz- and parity-violating modification of electrody-
+namics, Phys. Rev. D 41, 1231 (1990).
+[42] D. Colladay and V.A. Kosteleck´y, CPT violation and
+the standard model, Phys. Rev. D 55, 6760 (1997);
+
+14
+D. Colladay and V.A. Kosteleck´y, Lorentz-violating ex-
+tension of the standard model, Phys. Rev. D 58, 116002
+(1998); S.R. Coleman and S.L. Glashow, High-energy
+tests of Lorentz invariance, Phys. Rev. D 59, 116008
+(1999).
+[43] A.A. Andrianov and R. Soldati, Lorentz symmetry
+breaking in Abelian vector-field models with Wess-
+Zumino interaction, Phys. Rev. D 51, 5961 (1995);
+A.A. Andrianov and R. Soldati, Patterns of Lorentz
+symmetry breaking in QED by CPT-odd interaction,
+Phys. Lett. B 435, 449 (1998); A.A. Andrianov, R. Sol-
+dati,
+and L. Sorbo,
+Dynamical Lorentz symmetry
+breaking from a (3+1)-dimensional axion-Wess-Zumino
+model, Phys. Rev. D 59, 025002 (1999).
+[44] J. Alfaro, A.A. Andrianov, M. Cambiaso, P. Giacconi,
+and R. Soldati, Bare and induced Lorentz and CPT
+invariance violations in QED, Int. J. Mod. Phys. A
+25, 3271 (2010); A.A. Andrianov, D. Espriu, P. Giac-
+coni, and R. Soldati, Anomalous positron excess from
+Lorentz-violating QED, JHEP 09, 057 (2009).
+[45] L. C. T. Brito, J. C. C. Felipe, A. Yu. Petrov, A. P.
+Baeta Scarpelli, No radiative corrections to the Carroll-
+Field-Jackiw term beyond one-loop order, Int. J. Mod.
+Phys. A36, 2150033 (2021); J. F. Assuncao, T. Mariz,
+A. Yu. Petrov, Nonanalyticity of the induced Carroll-
+Field-Jackiw term at finite temperature, EPL 116,
+31003 (2016); J. C. C. Felipe, A. R. Vieira, A. L. Cher-
+chiglia, A. P. Baˆeta Scarpelli, M. Sampaio, Arbitrariness
+in the gravitational Chern-Simons-like term induced ra-
+diatively, Phys. Rev. D 89, 105034 (2014); T.R.S. San-
+tos, R.F. Sobreiro, Lorentz-violating Yang–Mills theory:
+discussing the Chern–Simons-like term generation, Eur.
+Phys. J. C 77, 903 (2017).
+[46] R. Casana, M. M. Ferreira Jr., E. da Hora, A. B. F.
+Neves, Maxwell-Chern-Simons vortices in a CPT-odd
+Lorentz-violating Higgs Electrodynamics, Eur. Phys. J.
+C 74, 3064 (2014); R. Casana, L. Sourrouille, Self-
+dual Maxwell-Chern-Simons solitons from a Lorentz-
+violating model, Phys. Lett. B 726, 488 (2013).
+[47] H. Belich, L. D. Bernald, Patricio Gaete, J. A. Helay¨el-
+Neto, The photino sector and a confining potential in a
+supersymetric Lorentz-symmetry-violating model, Eur.
+Phys. J. C 73, 2632 (2013); L. Bonetti, L. R. dos Santos
+Filho, J A. Helay¨el-Neto, A. D. A. M. Spallicci, Photon
+sector analysis of Super and Lorentz symmetry break-
+ing: effective photon mass, bi-refringence and dissipa-
+tion, Eur. Phys. J. C 78, 811 (2018).
+[48] L.H. C. Borges,
+A.F. Ferrari,
+External sources in
+a minimal and nonminimal CPT-odd Lorentz vio-
+lating Maxwell electrodynamics,
+Mod. Phys. Lett.
+A 37,
+2250021 (2022);
+Y. M. P. Gomes,
+P. C.
+Malta, Lab-based limits on the Carroll-Field-Jackiw
+Lorentz-violating electrodynamics, Phys. Rev. D 94,
+025031 (2016); M.M. Ferreira Jr, J.A. Helay¨el-Neto,
+C.M. Reyes, M. Schreck, P.D.S. Silva, Unitarity in
+St¨uckelberg electrodynamics modified by a Carroll-
+Field-Jackiw term, Phys. Lett. B 804, 135379 (2020);
+A. Mart´ın-Ruiz and C. A. Escobar, Local effects of the
+quantum vacuum in Lorentz-violating electrodynamics,
+Phys. Rev. D 95, 036011 (2017).
+[49] V.A. Kosteleck´y and M. Mewes, Cosmological Con-
+straints on Lorentz Violation in Electrodynamics, Phys.
+Rev. Lett. 87, 251304 (2001); V.A. Kosteleck´y and
+M. Mewes, Signals for Lorentz violation in electrody-
+namics, Phys. Rev. D 66, 056005 (2002); V.A. Kost-
+eleck´y and M. Mewes, Sensitive Polarimetric Search for
+Relativity Violations in Gamma-Ray Bursts, Phys. Rev.
+Lett. 97, 140401 (2006).
+[50] F.R. Klinkhamer, M. Schreck, Consistency of isotropic
+modified Maxwell theory: Microcausality and unitarity,
+Nucl. Phys. B 848, 90 (2011); M. Schreck, Analysis of
+the consistency of parity-odd nonbirefringent modified
+Maxwell theory, Phys. Rev. D 86, 065038 (2012).
+[51] C.A. Escobar and M.A.G. Garcia, Full CPT-even pho-
+ton sector of the standard model extension at finite tem-
+perature, Phys. Rev. D 92, 025034 (2015); A. Mart´ın-
+Ruiz and C.A. Escobar, Casimir effect between ponder-
+able media as modeled by the standard model exten-
+sion, Phys. Rev. D 94, 076010 (2016); L.H.C. Borges,
+A.F. Ferrari, Semi-transparent boundaries in CPT-even
+Lorentz violating electrodynamics, Nucl. Physics B 980,
+115829 (2022).
+[52] Q.G. Bailey and V.A. Kosteleck´y, Lorentz-violating
+electrostatics and magnetostatics, Phys. Rev. D 70,
+076006 (2004).
+[53] A. Gomez, A. Mart´ın-Ruiz, Luis F. Urrutia, Effective
+electromagnetic actions for Lorentz violating theories
+exhibiting the axial anomaly, Phys. Lett. B 829, 137043
+(2022).
+[54] A. V. Kostelecky, R. Lehnert, N. McGinnis, M. Schreck,
+B. Seradjeh,
+Lorentz violation in Dirac and Weyl
+semimetals, Phys. Rev. Research 4, 023106 (2022).
+[55] M.M. Ferreira Jr., L. Lisboa-Santos, R.V. Maluf, and
+M. Schreck, Maxwell electrodynamics modified by a
+CPT-odd dimension-five higher-derivative term, Phys.
+Rev. D 100, 055036 (2019).
+[56] P. D. S. Silva, L. L. Santos, M. M. Ferreira, Jr., and M.
+Schreck, Effects of CPT-odd terms of dimensions three
+and five on electromagnetic propagation in continuous
+matter, Phy. Rev. D 104, 116023 (2021).
+[57] L. D. Barron, Molecular Light Scattering and Optical
+Activity, 2nd ed. (Cambridge University Press, New
+York, 2004).
+[58] E. Hecht, Optics, 4nd ed. (Addison Wesley, San Fran-
+cisco, 2002).
+[59] G. H. Wagniere, On Chirality and the Universal Asym-
+metry: Reflections on Image and Mirror Image, (Wiley-
+Vch, Zurich) (2007).
+[60] Y. Tang and A. E. Cohen, Optical Chirality and Its
+Interaction with Matter, Phys. Rev. Lett. 104, 163901
+(2010).
+[61] A. H. Sihvola and I. V. Lindell, Bi-isotropic constitutive
+relations, Microw. Opt. Technol. Lett., 4 (8), 295-297
+(1991); A. H. Sihvola and I. V. Lindell, Properties of bi-
+isotropic Fresnel reflection coefficients, Optics Commu-
+nications 89, 11992); S. Ougier, I. Chenerie, A. Sihvola,
+and A. Priou, Propagation in bi-isotropic media: ef-
+fect of different formalisms on the propagation analysis,
+Progress In Electromagnetics Research 09, 19 (1994).
+[62] P. Hillion, Manifestly covariant formalism for electro-
+magnetism in chiral media, Phys. Rev. E 47, 1365
+(1993); I. Yakov, Dispersion relation for electromag-
+netic waves in anisotropic media, Phys. Lett. A 374,
+1113 (2010); N.J. Damaskos, A.L. Maffett and P.L.E.
+Uslenghi, Dispersion relation for general anisotropic
+media, IEEE Trans. Antennas Propagat. AP-30, 991
+(1982).
+[63] J. A. Kong, Electromagnetic Wave Theory (Wiley, New
+
+15
+York, 1986).
+[64] Y. T. Aladadi and M. A. S. Alkanhal, Classification and
+characterization of electromagnetic materials, Sci. Rep.
+10, 11406 (2020).
+[65] W. Mahmood and Q. Zhao, The Double Jones Birefrin-
+gence in Magneto-electric Medium, Sci. Rep. 5, 13963
+(2015).
+[66] V. A. De Lorenci and G. P. Goulart, Magnetoelectric
+birefringence revisited, Phys. Rev. D 78, 045015 (2008).
+[67] P. D. S. Silva, R. Casana, and M. M. Ferreira Jr., Sym-
+metric and antisymmetric constitutive tensors for bi-
+isotropic and bi-anisotropic media, Phys. Rev. A 106,
+042205 (2022).
+[68] G. R. Fowles,
+Introduction to modern optics,
+2nd
+ed. (Dover Publications, INC., New York, 1975); A.
+K. Bain, Crystal optics:
+properties and applications
+(Wiley-VCH Verlag GmbH & Co. KGaA, Germany,
+2019).
+[69] H. S. Bennett, E. A. Stern, Faraday effect in solids.
+Phys. Rev. 137, A448–A461 (1965); L. M. Roth. Theory
+of the Faraday effect in solids, Phys. Rev. 133, A542–
+A553 (1964).
+[70] W. S. Porter and E. M. Bock Jr., Faraday effect in a
+plasma, Am. J. Phys. 33, 1070 (1965).
+[71] J. Shibata, A. Takeuchi, H. Kohno, and G. Tatara,
+Theory of electromagnetic wave propagation in ferro-
+magnetic Rashba conductor, J. App. Phy. 123, 063902
+(2018).
+[72] E. U. Condon, Theories of Optical Rotatory Power, Rev.
+Mod. Phys. 9, 432 (1937).
+[73] Ming-Che Chang and Min-Fong Yang, Optical signa-
+ture of topological insulators, Phys. Rev. B 80, 113304
+(2009); L. Ohnoutek et. al., Strong interband Faraday
+rotation in 3D topological insulator Bi2Se3, Sci. Rep.6,
+19087 (2016).
+[74] A. Mart´ın-Ruiz, M. Cambiaso, and L. F. Urrutia, The
+magnetoelectric coupling in Electrodynamics. Int. J.
+Mod. Phys. A 34, 1941002 (2019); A. Mart´ın-Ruiz,
+M. Cambiaso, and L.F. Urrutia, Electro- and magne-
+tostatics of topological insulators as modeled by planar,
+spherical, and cylindrical θ boundaries: ForestGreen’s
+function approach, Phys. Rev. D 93, 045022 (2016).
+[75] A. Lakhtakia and T. G. Mackay, Classical electromag-
+netic model of surface states in topological insulators,
+J. Nanophoton. 10 (3), 033004 (2016).
+[76] T. M. Melo, D. R. Viana, W. A. Moura-Melo, J. M.
+Fonseca, A. R. Pereira, Topological cutoff frequency in
+a slab waveguide: Penetration length in topological in-
+sulator walls, Phys, Lett. A 380, 973 (2016).
+[77] Z.-X. Li, Yunshan Cao, Peng Yan, Topological insula-
+tors and semimetals in classical magnetic systems, Phys.
+Report 915, 1 (2021).
+[78] R. Li, J. Wang, Xiao-Liang Qi and S.-C. Zhang, Dy-
+namical axion field in topological magnetic insulators,
+Nature Phys. 6, 284 (2010).
+[79] W.-K. Tse and A. H. MacDonald, Giant magneto-
+optical Kerr effect and universal Faraday effect in thin-
+film topological insulators, Phys. Rev. Lett. 105, 057401
+(2010); Magneto-optical and magnetoelectric effects of
+topological insulators in quantizing magnetic fields,
+Phys. Rev. B 82, 161104 (2010); Magneto-optical Fara-
+day and Kerr effects in topological insulator films and
+in other layered quantized Hall systems, Phys. Rev. B
+84, 205327 (2011).
+[80] I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bost-
+wick, E. Rotenberg, T. Seyller, D. van der Marel, and
+A. B. Kuzmenko, Giant Faraday rotation in single- and
+multilayer graphene, Nature Phys. 7, 48 (2011); R. Shi-
+mano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe,
+H. Hibino, T. Morimoto and H. Aoki, Quantum Fara-
+day and Kerr rotations in graphene, Nature Comm. 4,
+1841 (2013).
+[81] D. G. Dimitriu, D. O. Dorohoi, New method to deter-
+mine the optical rotatory dispersion of inorganic crystals
+applied to some samples of Carpathian Quartz, Spec-
+trochimica Acta Part A: Molecular and Biomolecular
+Spectroscopy 131, 674-677 (2014).
+[82] L.A. Pajdzik and A.M. Glazer, Three-dimensional bire-
+fringence imaging with a microscope tilting-stage. I.
+Uniaxial crystals, J. Appl. Cryst. 39, 326 (2006).
+[83] X. Liu, J. Yang, Z. Geng, and H. Jia, Simultaneous mea-
+surement of optical rotation dispersion and absorption
+spectra for chiral substances, Chirality 8, 32, 1071-1079
+(2022).
+[84] J.-M.
+Poumirol,
+P.
+Q.
+Liu,
+T.
+M.
+Slipchenko,
+A. Y. Nikitin,
+L. Martin-Morento,
+J. Faist,
+and
+A.
+B.
+Kuzmenko,
+Electrically
+controlled
+terahertz
+magneto-optical phenomena in continuous and pat-
+terned graphene, Nat Commun 8, 14626 (2017).
+[85] I. Tutunnikov, U. Steinitz, E. Gershnabel, J-M. Hart-
+mann, A. A. Milner, V. Milner, and I. Sh. Averbukh,
+Rotation of the polarization of light as a tool for inves-
+tigating the collisional transfer of angular momentum
+from rotating molecules to macroscopic gas flows, Phys.
+Rev. Research 4, 013212 (2022); U. Steinitz and I. Sh.
+Averbukh, Giant polarization drag in a gas of molecular
+super-rotors, Phys. Rev. A 101, 021404(R) (2020).
+[86] L. Tschugaeff, Anomalous rotatory dispersion, Trans.
+Faraday Soc., 10, 70-79 (1914).
+[87] R. E. Newnham, Properties of Materials - anisotropy,
+symmetry, structure (Oxford University Press, New
+York, 2005).
+[88] N. Tischler, M. Krenn, R. Fickler, X. Vidal, A. Zeilinger,
+and G. Molina-Terriza, Quantum optical rotatory dis-
+persion, Sci. Adv. 2, e1601306 (2016).
+[89] J. H. Woo, B. K. M. Gwon, J. H. Lee, D-W. Kim, W.
+Jo, D. H. Kim, and J. W. Wu, Time-resolved pump-
+probe measurement of optical rotatory dispersion in
+chiral metamaterial, Adv. Optical Mater. 5, 1700141
+(2017).
+[90] Q. Zhang, E. Plum, J-Y. Ou, H. Pi, J. Li, K. F. Mac-
+Donald, and N. I. Zheludev, Electrogyration in metama-
+terials: chirality and polarization rotatory power that
+depend on applied electric field, Adv. Optical Mater. 9,
+2001826 (2021).
+[91] J. Mun, et al. Electromagnetic chirality: from funda-
+mentals to nontraditional chiroptical phenomena. Light
+Sci. Appl. 9, 139 (2020).
+[92] J. Ma, and D. A. Pesin, Dynamic chiral magnetic ef-
+fect and Faraday rotation in macroscopically disordered
+helical metals, Phys. Rev. Lett. 118, 107401 (2017).
+[93] U. Dey, S. Nandy, and A. Taraphder, Dynamic chiral
+magnetic effect and anisotropic natural optical activity
+of tilted Weyl semimetals, Sci Rep 10, 2699 (2020).
+[94] R. Gueroult, Y. Shi, J-M. Rax, and N. J. Fisch, Deter-
+mining the rotation direction in pulsars, Nat. Commun.
+10, 3232 (2019).
+[95] R. Gueroult, J.-M. Rax, and N. J. Fisch, Enhanced
+
+16
+tuneable rotatory power in a rotating plasma, Phys.
+Rev. E 102, 051202(R) (2020).
+[96] P. D. S.Silva and M. M. Ferreira Jr., Rotatory power
+reversal induced by magnetic current in bi-isotropic me-
+dia, Phys. Rev. B 106, 144430 (2022).
+[97] P. Hosur, and X-L. Qi, Tunable circular dichroism due
+to the chiral anomaly in Weyl semimetals, Phys. Rev.
+B 91, 081106(R) (2015).
+[98] M. Nieto-Vesperinas, Optical theorem for the conserva-
+tion of electromagnetic helicity: Significance for molec-
+ular energy transfer and enantiomeric discrimination by
+circular dichroism, Phys. Rev. A 92, 023813 (2015).
+[99] Y. Tang and A. E. Cohen, Enhanced Enantioselectivity
+in Excitation of Chiral Molecules by Superchiral Light,
+Science 332, 333 (2011).
+[100] M. Amin, O. Siddiqui, and M. Farhat, Linear and cir-
+cular dichroism in graphene-based reflectors for polar-
+ization control, Phys. Rev. Applied 13, 024046 (2020).
+[101] V. G. Veselago, The electrodynamics of substances with
+simultaneously negative values of ϵ and µ, Sov. Phys.
+Usp. 10, 509 (1968).
+[102] D. R. Smith, W. J. Padilla, D. C. vier, S. C. Nemat-
+Nasser, and S. Schultz, Composite medium with simul-
+taneously negative permeability and permittivity, Phys.
+Rev. Lett. 84, 4184 (2000).
+[103] R. A. Shelby, D. R. Smith, and S. Schultz, Experimental
+verification of a negative index of refraction, Science
+292, 77 (2001).
+[104] C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C.
+Koltenbah, and M. Tanielian, Experimental verifica-
+tion and simulation of negative index of refraction using
+Snells’ law, Phys. Rev. Lett. 90, 107401 (2003).
+[105] A. A. Houck, J. B. Brock, and I. L. Chuang, Experi-
+mental observations of a left-handed material that obeys
+Snell’s law, Phys. Rev. Lett. 90, 137401 (2003).
+[106] M. Kadic, G. W. Milton, M. van Hecke, and M. We-
+gener, 3D metamaterials, Nat. Rev. Phys. 1, 198-210
+(2019).
+[107] N. Engheta and R. W. Ziolkowski (editors), Metama-
+terials: Physics and Engineering Explorations (Wiley-
+Interscience, New Jersey, 2006).
+[108] J. Liu, M. J. Luo, Q. Wang, and H.-J. Xu, Refrac-
+tive index of light in the quark-gluon plasma with the
+hard-thermal-loop perturbation theory, Phys. Rev. D
+84, 125027 (2011).
+[109] M. Y. Jamal, S. Mitra, and V. Chandra, Optical prop-
+erties of an anisotropic hot QCD medium, J. Phys. G:
+Nucl. Part. Phys. 47, 035107 (2020).
+[110] C.-W. Qiu, H.-Y. Yao, L.-W. Li, S. Zouhdi, and T.-S.
+Yeo, Routes to left-handed materials by magnetoelectric
+couplings, Phys. Rev. B 75, 245214 (2007).
+[111] L. Zhang, T. Koschny, and C. M. Soukoulis, Creating
+double negative index materials using the Babinet prin-
+ciple with one metasurface, Phys. Rev. B 87, 045101
+(2013).
+[112] S. Zhang, Y.-S. Park, J. Li, X. Lu, W. Zhang, and X.
+Zhang, Negative refractive index in chiral metamateri-
+als, Phys. Rev. Lett. 102, 023901 (2009).
+[113] J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki
+and C. M. Soukoulis, Negative refractive index due to
+chirality Phys. Rev. D 79, 121104 (2009).
+[114] C.-Y. Chen, M.-C. Hsu, C. D. Hu, and Y. c. Lin, Natu-
+ral negative-refractive-index materials, Phys. Rev. Lett.
+127, 237401 (2021).
+[115] P. Ball, Bending the rules, naturally, Nat. Mater. 21, 2
+(2022).
+[116] B. Guo, Chirality-induced negative refraction in mag-
+netized plasma, Phys. Plasmas 20, 093596 (2013).
+[117] M. X. Gao, B. Guo, L. Peng, and X. Cai, Dispersion
+relations for electromagnetic wave propagation in chiral
+plasmas, Phys. Plasmas 21, 114501 (2014).
+[118] O. Sakai and K. Tachibana, Plasmas as metamateri-
+als: a review, Plasma Sources Sci. Technol. 21, 013001
+(2012).
+[119] O. Sakai, A. Iwai, Y. Omura, S. Lio, and T. Naito, Wave
+propagation in and around negative-dielectric-constant
+discharge plasma, Phys. Plasmas 25, 03191 (2018).
+[120] E. J. Post, Formal Structure of Electromagnetics: Gen-
+eral Covariance and Electromagnetics, (Norht-Holland
+Publishing Company, Amsterdam, Dover Publications,
+1997).
+

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+VS-Net: Multiscale Spatiotemporal Features for
+Lightweight Video Salient Document Detection
+1st Hemraj Singh
+Dept. of Computer Sc. & Engg.
+National Institute of Technology
+Warangal, Telangana, India
+[email protected]
+2nd Mridula Verma
+Institute for Development and Research
+in Banking Technology
+Hyderabad, Telangana, India
+[email protected]
+3rd Ramalingaswamy Cheruku
+Dept. of Computer Sc. & Engg.
+National Institute of Technology
+Warangal, Telangana, India
+[email protected]
+Abstract—Video Salient Document Detection (VSDD) is an es-
+sential task of practical computer vision, which aims to highlight
+visually salient document regions in video frames. Previous tech-
+niques for VSDD focus on learning features without considering
+the cooperation among and across the appearance and motion
+cues and thus fail to perform in practical scenarios. Moreover,
+most of the previous techniques demand high computational
+resources, which limits the usage of such systems in resource-
+constrained settings. To handle these issues, we propose VS-Net,
+which captures multi-scale spatiotemporal information with the
+help of dilated depth-wise separable convolution and Approxi-
+mation Rank Pooling. VS-Net extracts the key features locally
+from each frame across embedding sub-spaces and forwards
+the features between adjacent and parallel nodes, enhancing
+model performance globally. Our model generates saliency maps
+considering both the background and foreground simultaneously,
+making it perform better in challenging scenarios. The immense
+experiments regulated on the benchmark MIDV-500 dataset show
+that the VS-Net model outperforms state-of-the-art approaches
+in both time and robustness measures.
+Index Terms—Separable convolution, Approximation Rank
+Pooling, Variational Autoencoder, Multi-scale features
+I. INTRODUCTION
+Video Salient Document Detection (VSDD) is an essential
+task in several real-world applications, such as video document
+recognition [1], video document compression [2], video doc-
+ument captioning [3] and many more. In real-life scenarios,
+a number of challenges appear due to an unconstrained envi-
+ronment (as shown in Fig.1). Current state-of-the-art (SOTA)
+models [4], [1] utilize non-selective attentional resources in the
+dynamic scenes. They employ limited static features and thus
+face difficulties in detecting the intended object in multiple
+real-world scenarios.
+Most of the existing VSDD models [6], [7], [8] extract
+the spatial features separately using a computationally costly
+process and then integrate them to generate a spatial saliency
+map. Later, they use a different method to extract the refined
+spatial-temporal features. Segregating these two steps reduces
+the quality of the generated frame. This segregation also fails
+to capture the longer-term motion arrangement, which links
+with some actions.
+Supported by Ministry of Electronics and Information Technology (MeiTy),
+Government of India and IIT Bhilai Innovation and Technology Foundation
+(IBITF) under the project entitled ”Blockchain and Machine Learning Pow-
+ered Unified Video KYC Framework”
+(a) Complex Scene
+(b) Keyboard Scene
+(c) Partial Scene
+(d) Noise
+(e) Motion Blur
+(f) Illumination
+Fig. 1. Challenging scenarios from MIDV-500 [5] dataset.
+One of the most popular model for video analytics is U-
+Net [9], which extends the temporal dimension for substituting
+2D filters with 3D filters and produces a little benediction of
+annotated videos to help the 3D convolution layers. Sebastian
+et al. [3] proposed DeepDeSRT, an end-to-end system for
+table understanding in document images and detecting PDF
+documents. But it failed in the video datasets due to poor
+handling of temporal features. To solve these problems, Recur-
+rent Neural Networks (RNNs) [7] used memory cells for the
+long-term pattern, which parses the video frames sequentially
+and encodes the information. The LSTMs use convolutional
+neural networks [10] and output in the form of action labels
+or video specifications. The Autoencoder LSTM model [4] is
+proposed to use either an instant or the next frame for accurate
+reconstruction. Tenet model in [11] acquired salient object de-
+tection metrics and performed unsupervised training on CNN.
+Sheshkus et al. [2] proposed HoughEncoder neural network
+architecture and performed Fast Hough Transform to calculate
+low-level features for the image semantic segmentation task,
+however, failed to resolve challenges due to an unconstrained
+environment. In [12] a spatiotemporal conditional random
+field is proposed to establish the relationships between local
+and global context regions, but the method failed to extract
+the high-level features. Wujie Zhou et al. [13] designed a
+convolution residual module to send equally distributed feature
+maps between the encoder and the decoder but failed due to
+long-range skip connections. The recent method [14] proposed
+Vnet to optimize the skip connection but failed to combine
+arXiv:2301.04447v1  [cs.CV]  11 Jan 2023
+
+D
+Mustermann
+Erika
+3
+12.08.64
+4a.
+22.01.15
+MUSTER
+Berlln
+Musterhausen
+4o,Landratsent
+21.01.30
+B072RRE2155
+am see%
+5
+ni
+FUHRERSCHEIN BUNDESRERUBLK DEUTSCHLAND
+D
+Mustermann
+MUSTER
+Erika
+1.15
+3.
+12.08.64
+Berlin
+4a.22.01.15
+4c.Landratsamt
+Musterhausen
+am See
+4b.21.01.30
+B072RRE2155
+A
+9.CM/B/LP
+D
+C01X0006H
+MUSTERMANN
+ERIKA
+DEUTSCH
+12.08.1964
+BERLIN
+01.11.2007
+31.10.2017
+D6H1D<<6408125F1710319<<<<<<<<<<<<<0FUHRERSCMEINEARE究
+ETIKS
+12.06.54
+22.01:15
+Mueterpnuoen
+21-01.39
+B672RRE2159
+PA/B1Hustermann
+Erlka
+MUSTERmultilevel feature information.
+We propose a novel VS-Net model to overcome these
+problems, which utilizes the separable convolution in the
+combination of the variational encoder to extract the key
+features from each frame across embedding sub-spaces and
+forward the features between adjacent and parallel nodes.
+Our model extracts the spatiotemporal features locally and
+makes better predictions globally. The main contributions of
+our paper are given below: noitemsep, nolistsep
+• We design a novel spatiotemporal-based VS-Net model
+with separable convolutions in variational autoencoder ar-
+chitecture (VAE) [15], which reduces the skip-connection
+between two nodes and generates the generalized latent
+space vector.
+• We utilize the Approximation Rank Pooling (ARP) [16],
+which takes input features from separable convolutions
+intermediate layers to train the VS-Net model. It pro-
+vides low-rank approximation features to preserve their
+temporal locality.
+• We have conducted experiments with MIDV-500 [5]
+dataset and demonstrated that VS-Net performs better in
+terms of both efficiency and time.
+II. PROPOSED METHODOLOGY
+A. VS-Net Architecture
+Based on prior knowledge, spatial and temporal-based
+methods can capture better location information and preserve
+location boundaries than pixel-wise CNN methods. Therefore,
+we design a novel spatial and temporal-based VS-Net model
+with separable convolutions [17] in variational auto-encoder
+architecture (VAE) [15], which reduces the skip-connection
+between two nodes and generates the generalized latent space
+vector (shown in fig.2).
+Given a sequence of input frames (Sn|n = 1, 2, 3, · · ·, N),
+and corresponding ground-truth maps (Gn|n = 1, 2, 3, · · ·, N)
+are first passed into the VS-Net model to extract the spatial and
+temporal features, which uses pretrained weights of ResNet50
+[7]. Our proposed model has two branches with different
+purposes. The first is the down-sampling operation performing
+top to bottom, extracting the spatial and temporal features from
+each node and reducing the feature vectors’ dimension. The
+second is upsampling operation from bottom to top, which
+decodes the spatial-temporal latent space and enhances the
+feature vectors. At last, we combine feature vectors from
+previous nodes and parallel nodes.
+During the down-sampling, we perform separable convolu-
+tion operation with 3 × 3 filters on input frames to extract
+spatial and temporal features, which have rich spatial and
+temporal information. Then max-pooling operation with 2 × 2
+filters succeeded by a ReLU activation operation performs to
+downgrade the dimension of the features vectors and generate
+the latent spatial and temporal map.
+Sd ∼ Down(Sn) = SConv(S1, S2, S3, S4, · · ·, Sn),
+(1)
+where SConv is a separable convolution operation.
+Before the up-sampling, we perform a convolution operation
+using 1 × 1 filters with learnable weight θ and applied the
+ReLU activation function to reduce the dimension of the latent
+features vectors and apply a dropout operation to dropout the
+50% neurons for generating the latent space of spatial and
+temporal features vectors.
+Sl = Dropout(ReLU(Conv(Sd, θ))).
+(2)
+During the up-sampling operation from bottom to top, we
+decode the latent space vectors using separable convolution
+layers with 3× 3 filters, succeeded by up-sampling layers and
+ReLU activation operation to reconstruct the dimension of the
+features vectors.
+Sup ∼ UP(Sl) = SConv(S1, S2, S3, S4, · · ·, Sn),
+(3)
+where SConv is a separable convolution layers with 3×3 filters.
+We extract the spatial and temporal features from latent space
+during the upsampling. The extracted spatial and temporal
+features of each parallel node and adjacent node both are
+concatenated, i.e.,
+Sc = Conc(Sup, Sd),
+(4)
+where Conc is concatenation operation. Then we perform
+separable convolution layers with 3 × 3 filters succeeded by
+the ReLU activation function to enhance the quality of the
+spatial-temporal feature vectors and reconstruct the original
+dimension of latent features vectors. Further, we apply the
+Sigmoid function using the convolution layer with 1×1 filters
+to simplify the spatial and temporal features, i.e.,
+Sm = Sigmoid(Sc).
+(5)
+The network has approximately 3.5 million trainable pa-
+rameters. We notice that each layer of the VS-Net generates
+a feature map with a spatial structure in places of the video
+frames. Max Pooling layers use to increase the feature’s map
+generation speed, which updates the weight matrix of the
+backbone models during the feature extraction from every
+separable convolution layer. During the bottom-up extraction
+of features from high to low resolution, upsampling operations
+with 2×2 filters are used to distribute the latent feature space
+and combine them with the previous layer and parallel layer’s
+nodes’ features.
+We used Approximation Rank Pooling (ARP) [16], which
+takes input features from the intermediate layers of a VS-
+Net, trains on sub-sequences, and generates the output of
+a subspace. ARP not only gives low-rank approximation
+features, but it also conserves temporal order. The low-rank
+approximation differentiated and captured important character-
+istics of the data, which summarizes the document’s position
+and orientation. Further, a quadratic ranking function captured
+the temporal order, which handles non-linear dependencies of
+the input features. Generally, the temporal order deals with the
+protuberances of the input channels onto the substance.
+Due to the low-rank approximation, the down-sampling
+generates the generalized latent space vector. The sampling of
+
+Input Frame
+Saliency Map
+UpSampling
+Down Sampling
+SConv1
+SConv2
+SConv+MaxPool+ReLU
+SConv+MaxPool+ReLU
+SConv+MaxPool+ReLU
+SConv+MaxPool+ 
+ReLU
+SConv6
+SConv7
+SConv8
+SConv9
+SConv10
+SConv14
+SConv15
+Fig. 2. Architecture of the proposed VS-Net.
+mean and variance gives the efficient latent distribution of the
+VS-Net architecture. Based on the latent Gaussian distribution,
+the latent vector is generalized. The down-sampling and up-
+sampling are performed based on the variational encoder and
+decoder. For handling the over-fitting of the proposed model,
+the latent space of the down-sampling is normalized with the
+help of convolution layers and passed to up-sampling layers.
+After concatenating all the spatial and temporal features, we
+applied a convolution layer with 1×1 filters at the last node to
+generate feature vectors. At last, the previous node and parallel
+node features are aggregated and provide the saliency map.
+TABLE I
+PERFORMANCE COMPARISON OF THE SOTA AND PROPOSED MODEL
+(VS-NET) IN TERMS OF BCE+IOU LOSS(%), AND TESTING SPEED (FPS)
+Input frame
+Model
+Output frame
+Loss (BCE+IoU)
+Testing speed (FPS)
+RNN+LSTM [7]
+0.032
+12.34
+U-Net [9]
+0.028
+10.45
+FCNN [18]
+0.038
+12.36
+HE [2]
+0.041
+14.45
+STCRF [12]
+0.039
+13.54
+AED [13]
+0.035
+12.89
+CNN+LSTM [10]
+0.036
+12.63
+RCNN [19]
+0.025
+11.54
+VS-Net
+0.021
+8.36
+B. Loss function
+During training, we use input frames Sk with the corre-
+sponding ground-truth Gk at frame t. The binary cross-entropy
+loss Lbce [20] is used to calculate the dissimilarity of the
+output and target, which is given as follows,
+lbce(Sk, Gk) = −
+�
+i,j
+[Gk(i, j)log(Sk(i, j))+
+(1 − Gk(i, j))log(1 − Sk(i, j))]
+(6)
+where (i,j) represents a coordinate of the frames. The IoU
+loss [21] is computed as:
+lIoU(Sk, Gk) = 1 −
+�w
+i=1
+�h
+j=1 Sk(i, j)Gk(i, j)
+�w
+i=1
+�h
+j=1[Sk(i, j) + Gk(i, j) − Sk(i, j)Gk(i, j)]
+(7)
+The total loss function is derived as,
+Totalloss = lbce(Sk, Gk) + αlIoU(Sk, Gk),
+(8)
+where α is the weighting parameter for the IoU. For the final
+saliency map prediction, we utilize Sk and Gk since it shows
+that our experiments better utilized spatial-temporal cues.
+III. EXPERIMENTAL SETUP AND RESULT ANALYSIS
+A. MIDV-500 Dataset
+We have considered the MIDV-500 dataset [5], which con-
+tains video clips of 50 different identity documents (seventeen
+Id cards, fourteen passports, six identity documents, and
+thirteen driving licenses) of various countries. It has eight
+different variations of background and foreground scenes. The
+attributes of the dataset are TS (Table Scene), TA (Table
+Action), KS (Keyboard Scene), KA (Keyboard Action), HS
+(Hand Scene), HA (Hand Action), PS (Partial Scene), PA
+(Partial Action), CS (Complex Scene), CA (Complex Action).
+Thus a total of 500 videos are generated (50 documents× 5
+desperation×2 devices). Each video has a duration of three
+seconds, which is split into ten frames per second and the
+corresponding annotation. The dataset contains examples of
+multiple challenging scenarios, such as complex scenes, small
+
+FUHRERSCHEIN BUNDESREPUBLKDEUTSCHLAND
+D
+Mustermann
+Erika
+12.08.64
+MUSTER
+4a.22.01.15
+Berlin
+Musterhausen
+4c.Landratsant
+21.0:.30
+B072RRE2155
+am See
+M/B/LFUHRERSCHEIN BUNDESREPUBLKDEUTSCHLAND
+D
+Mustermann
+Erika
+12.08.64
+MUSTER
+4a.22.01.15
+Berlin
+Musterhausen
+4c.Landratsant
+21.0:.30
+B072RRE2155
+am See
+M/B/Lobjects with different variations of frames, appearances of
+background and foreground, cluttered background, etc. (a
+few examples are shown in Fig: 1). The ground truth is
+prepared for each extracted video frame with various document
+locations in JSON format. It has 48 photo patches, 40 signature
+patches, and 546 text patches. The patches convert Cyrillic,
+Greek, Chinese, Japanese, Arabic, and Persian with singular
+Latin characters.
+B. Optimization and Propagation
+For preparing the VS-Net model, the Adaptive Moment Esti-
+mation (ADAM) optimizer is used to facilitate the computation
+of learning rates of each parameter using the first and second
+moment of the gradient. The saliency map optimization is cast
+as a “label propagation” problem, where uncertain labels are
+propagated based on background and foreground seeds. Fur-
+ther, we perform shift and rotation invariance robustly to the
+deformation of gray value variations. These random variations
+of deformation are sampled from the Gaussian distribution.
+Drop-out layers are used at the bottom stop and the previous
+level to normalize the latent space vectors. The proposed VS-
+Net model optimizes the loss of saliency maps from top-to-
+bottom and bottom-to-top and propagative seeds sequentially
+interact. The sequential seeding procedure optimizes feature
+map loss and improves the robustness to construct a saliency
+map.
+C. Evaluation Metrics
+We used Intersection Over Union (IoU) loss as an evaluation
+metric, which is defined as the intersection over the predicted
+boundary box (bbox), and the actual bbox and divided with
+their union. A prediction considers True Positive if Inter-
+section over union (IoU)>threshold, and False Positive If
+IoU<threshold [21].
+IoU = Area
+of
+Overlap
+Area
+of
+Union
+(9)
+The smaller the IoU value, the better the performance. In our
+experiments, the threshold is set as 0.5. The comparison results
+in terms of accuracy are shown in Tab. II).
+TABLE II
+COMPARISON RESULTS WITH SOTA MODELS AND PROPOSED MODEL ON
+MIDV-500 DATASET
+Comparison of document detection accuracy (%)
+Model
+TS,
+KS,
+HS,
+PS,
+CS
+TA
+KA
+HA
+PA
+CA
+U-Net (2019) [9]
+96.44
+97.43
+97.12
+96.64
+97.40
+RNN+LSTM (2021) [7]
+97.12
+96.33
+97.56
+95.56
+96.59
+FCNN (2017)[18]
+97.78
+98.39
+98.89
+96.43
+97.43
+HE (2020) [2]
+96.86
+97.58
+97.54
+96.32
+96.45
+STCRF (2018) [12]
+97.43
+96.98
+97.56
+96.43
+97.98
+AED (2020)[13]
+96.97
+98.54
+98.74
+96.78
+97.69
+CNN+LSTM (2019)[10]
+97.56
+98.54
+98.74
+96.78
+97.69
+RCNN (2019)[19]
+98.43
+98.69
+97.78
+97.19
+98.56
+VS-Net
+99.25
+99.67
+99.62
+99.45
+99.74
+D. Implementation Details
+1) Training Setup: The experiments are accomplished on
+Intel Xeon(R) CPU E5-2640 v4 @ 2.40GHz X40 processor
+with 32GB RAM. We used Tensorflow-gpu2.0, Keras as the
+backend, and Python3.6 accelerated by NVIDIA RTX Graphic
+card (Quadro P5000 / PCIe /SSE2). Input frames are of size
+256×256. The ADAM optimizer, weight decay of 0.006, batch
+size of 128, and learning rate of 0.001 are used to train the
+model, and BCE +IoU loss function is used to calculate the
+loss of the VS-Net model. The running time comparison is
+given in Tab. III.
+2) Testing Setup and Runtime: We resize the frame 256 ×
+256 to feed into the corresponding branch for testing. The
+distribution of the dataset is in the ratio of 3:7. The average
+testing speed of our model is 9.46 fps which is less than the
+existing models. Additionally, we do not perform any pre-
+/post-processing [19]. For validating purpose, the 5-fold cross-
+validation are used to check the overfitting (see Fig.3).
+Fig. 3.
+5-fold cross-validation comparison result of VS-Net and SOTA
+models.
+Ablation Study - The qualitative evaluation shows that
+our VS-Net model gives the best results on MIDV-500 [5]
+datasets but is an extremely lightweight setting that has fewer
+parameters and FLOPs (see in Table. IV).
+Speed Comparison The speed performance is calculated
+on a 64-bit Linux Ubuntu-18.04 operating system with Intel
+Core i7-4590 CPU @ 3.3 GHz. It has 32GB RAM and 1 TB
+Hard disk. The average speed is computed on all frame images
+of MIDV-500 datasets and does not include I/O file time. The
+parallel processing of multiple images is not allowed. Priorly,
+SOTA models require high computational powerful GPU sys-
+tem. For a fair comparison, the recent unsupervised models
+compare the speed on a normal CPU and the speed of deep
+learning methods reported on GPU. The speed comparison is
+given in Table III. We show the trade-off between loss and
+testing speed in Table I. Further, the average time cost of
+each step is examined. VS-Net consumes 256 ms and SOTA
+models 270 ms, respectively, while saliency prediction and
+global optimization use 8.36 ms and 10.0 ms.
+IV. CONCLUSION AND FUTURE WORK
+In this paper, we proposed a novel efficient and fast VS-Net
+model that fully leverages the spatiotemporal features to detect
+
+100
+99
+98
+Accuracy
+97
+96
+95
+94
+HE
+AED
+STCRF
+VS-Net
+RNN+LSTM
+CNN+LSTMTABLE III
+RUNTIME COMPARISON OF SOTA MODELS AND VS-NET MODEL
+U-Net[9]
+RNN+LSTM[7]
+FCNN[18]
+HE [2]
+STCRF[12]
+AED[13]
+CNN+LSTM[10]
+RCNN[19]
+VS-Net
+Runtime (s)
+188
+191
+190
+198
+200
+199
+196
+189
+175
+Step (ms)
+265
+266
+273
+278
+275
+268
+267
+260
+256
+TABLE IV
+ABLATION STUDY WITH RESNET-50 AS BACKBONE.
+# Param(M)
+FLOPS(G)
+Runtime (s)
+Steps(ms)
+Accuracy
+5.42
+10.2
+200
+285
+97.98
+3.54
+7.3
+185
+275
+98.85
+1.20
+3.7
+175
+265
+99.75
+0.95
+2.5
+165
+255
+96.45
+the video identity document. The proposed model used sep-
+arable convolutions with variational autoencoder architecture,
+which performs downsampling for extracting the features and
+upsampling operation for decoding the latent space features.
+The Approximation Rank Pooling (ARP) is used low-rank
+approximation on frames to preserve the temporal locality. The
+bottom-end the generalized latent space is generated. Further,
+These features are combined to generate in fuse spatial and
+temporal characteristics. We validated each module of the
+proposed model with the help of extensive experiments, which
+can be considered as the unified solution advancing VSDD.
+REFERENCES
+[1] J.-C. Burie, A. Forn´es, K. Santosh, and M. M. Luqman, “Deep learning
+for graphics recognition: document understanding and beyond,” pp. 1–2,
+2021.
+[2] A. Sheshku, D. Nikolaev, and V. L. Arlazaro, “Houghencoder: neural
+network architecture for document image semantic segmentation,” in
+2020 IEEE International Conference on Image Processing (ICIP).
+IEEE, 2020, pp. 1946–1950.
+[3] S. Schreiber, S. Agne, I. Wolf, A. Dengel, and S. Ahmed, “Deepdesrt:
+Deep learning for detection and structure recognition of tables in
+document images,” in 2017 14th IAPR international conference on
+document analysis and recognition (ICDAR), vol. 1.
+IEEE, 2017, pp.
+1162–1167.
+[4] X. Sun, X. Yang, S. Wang, and M. Liu, “Content-aware rate control
+scheme for hevc based on static and dynamic saliency detection,”
+Neurocomputing, vol. 411, pp. 393–405, 2020.
+[5] V. V. Arlazarov, K. B. Bulatov, T. S. Chernov, and V. L. Arlazarov,
+“Midv-500: a dataset for identity document analysis and recognition on
+mobile devices in video stream,” Computer Optics, vol. 43, no. 5, pp.
+818–824, 2019.
+[6] B. Liu, K. Mu, M. Xu, F. Wang, and L. Feng, “A novel spatiotempo-
+ral attention enhanced discriminative network for video salient object
+detection,” Applied Intelligence, pp. 1–16, 2021.
+[7] A. Kompella and R. V. Kulkarni, “A semi-supervised recurrent neural
+network for video salient object detection,” Neural Computing and
+Applications, vol. 33, no. 6, pp. 2065–2083, 2021.
+[8] H. Huang, C. Liu, L. Tian, J. Mu, and X. Jing, “A novel fcns-convlstm
+network for video salient object detection,” International Journal of
+Circuit Theory and Applications, vol. 49, no. 4, pp. 1050–1060, 2021.
+[9] H. Liu and J. Jiang, “U-net based multi-instance video object segmen-
+tation,” arXiv preprint arXiv:1905.07826, 2019.
+[10] M. Rhanoui, M. Mikram, S. Yousfi, and S. Barzali, “A cnn-bilstm
+model for document-level sentiment analysis,” Machine Learning and
+Knowledge Extraction, vol. 1, no. 3, pp. 832–847, 2019.
+[11] S. Ren, C. Han, X. Yang, G. Han, and S. He, “Tenet: Triple excitation
+network for video salient object detection,” in European Conference on
+Computer Vision.
+Springer, 2020, pp. 212–228.
+[12] T.-N. Le and A. Sugimoto, “Video salient object detection using spa-
+tiotemporal deep features,” IEEE Transactions on Image Processing,
+vol. 27, no. 10, pp. 5002–5015, 2018.
+[13] W. Zhou, J. Wu, J. Lei, J.-N. Hwang, and L. Yu, “Salient object
+detection in stereoscopic 3d images using a deep convolutional residual
+autoencoder,” IEEE Transactions on Multimedia, 2020.
+[14] R. Huang, Y. Zhang, S. Vatankhah, S. Liu, and R. Qi, “Inversion of
+large-scale gravity data with application of vnet,” Geophysical Journal
+International, 2022.
+[15] B. Li, Z. Sun, and Y. Guo, “Supervae: Superpixelwise variational
+autoencoder for salient object detection,” in Proceedings of the AAAI
+Conference on Artificial Intelligence, vol. 33, no. 01, 2019, pp. 8569–
+8576.
+[16] H. Bilen, B. Fernando, E. Gavves, and A. Vedaldi, “Action recognition
+with dynamic image networks,” IEEE transactions on pattern analysis
+and machine intelligence, vol. 40, no. 12, pp. 2799–2813, 2017.
+[17] Y. Liu, X.-Y. Zhang, J.-W. Bian, L. Zhang, and M.-M. Cheng, “Samnet:
+Stereoscopically attentive multi-scale network for lightweight salient
+object detection,” IEEE Transactions on Image Processing, vol. 30, pp.
+3804–3814, 2021.
+[18] W. Wang, J. Shen, and L. Shao, “Video salient object detection via
+fully convolutional networks,” IEEE Transactions on Image Processing,
+vol. 27, no. 1, pp. 38–49, 2017.
+[19] V. Sharma and R. N. Mir, “Saliency guided faster-rcnn (sgfr-rcnn) model
+for object detection and recognition,” Journal of King Saud University-
+Computer and Information Sciences, 2019.
+[20] G.-P. Ji, K. Fu, Z. Wu, D.-P. Fan, J. Shen, and L. Shao, “Full-duplex
+strategy for video object segmentation,” in Proceedings of the IEEE/CVF
+International Conference on Computer Vision, 2021, pp. 4922–4933.
+[21] F. Ahmed, D. Tarlow, and D. Batra, “Optimizing expected intersection-
+over-union with candidate-constrained crfs,” in Proceedings of the IEEE
+international conference on computer vision, 2015, pp. 1850–1858.
+

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+page_content='  National Institute of Technology  Warangal, Telangana, India  rmlswamy@nitw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='in  Abstract—Video Salient Document Detection (VSDD) is an es-  sential task of practical computer vision, which aims to highlight  visually salient document regions in video frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Previous tech-  niques for VSDD focus on learning features without considering  the cooperation among and across the appearance and motion  cues and thus fail to perform in practical scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Moreover,  most of the previous techniques demand high computational  resources, which limits the usage of such systems in resource-  constrained settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' To handle these issues, we propose VS-Net,  which captures multi-scale spatiotemporal information with the  help of dilated depth-wise separable convolution and Approxi-  mation Rank Pooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' VS-Net extracts the key features locally  from each frame across embedding sub-spaces and forwards  the features between adjacent and parallel nodes, enhancing  model performance globally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Our model generates saliency maps  considering both the background and foreground simultaneously,  making it perform better in challenging scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The immense  experiments regulated on the benchmark MIDV-500 dataset show  that the VS-Net model outperforms state-of-the-art approaches  in both time and robustness measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Index Terms—Separable convolution, Approximation Rank  Pooling, Variational Autoencoder, Multi-scale features  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' INTRODUCTION  Video Salient Document Detection (VSDD) is an essential  task in several real-world applications, such as video document  recognition [1], video document compression [2], video doc-  ument captioning [3] and many more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' In real-life scenarios,  a number of challenges appear due to an unconstrained envi-  ronment (as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Current state-of-the-art (SOTA)  models [4], [1] utilize non-selective attentional resources in the  dynamic scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' They employ limited static features and thus  face difficulties in detecting the intended object in multiple  real-world scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Most of the existing VSDD models [6], [7], [8] extract  the spatial features separately using a computationally costly  process and then integrate them to generate a spatial saliency  map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Later, they use a different method to extract the refined  spatial-temporal features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Segregating these two steps reduces  the quality of the generated frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' This segregation also fails  to capture the longer-term motion arrangement, which links  with some actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Supported by Ministry of Electronics and Information Technology (MeiTy),  Government of India and IIT Bhilai Innovation and Technology Foundation  (IBITF) under the project entitled ”Blockchain and Machine Learning Pow-  ered Unified Video KYC Framework”  (a) Complex Scene  (b) Keyboard Scene  (c) Partial Scene  (d) Noise  (e) Motion Blur  (f) Illumination  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Challenging scenarios from MIDV-500 [5] dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  One of the most popular model for video analytics is U-  Net [9], which extends the temporal dimension for substituting  2D filters with 3D filters and produces a little benediction of  annotated videos to help the 3D convolution layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Sebastian  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' [3] proposed DeepDeSRT, an end-to-end system for  table understanding in document images and detecting PDF  documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' But it failed in the video datasets due to poor  handling of temporal features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' To solve these problems, Recur-  rent Neural Networks (RNNs) [7] used memory cells for the  long-term pattern, which parses the video frames sequentially  and encodes the information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The LSTMs use convolutional  neural networks [10] and output in the form of action labels  or video specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The Autoencoder LSTM model [4] is  proposed to use either an instant or the next frame for accurate  reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Tenet model in [11] acquired salient object de-  tection metrics and performed unsupervised training on CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Sheshkus et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' [2] proposed HoughEncoder neural network  architecture and performed Fast Hough Transform to calculate  low-level features for the image semantic segmentation task,  however, failed to resolve challenges due to an unconstrained  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' In [12] a spatiotemporal conditional random  field is proposed to establish the relationships between local  and global context regions, but the method failed to extract  the high-level features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
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+page_content=' [13] designed a  convolution residual module to send equally distributed feature  maps between the encoder and the decoder but failed due to  long-range skip connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
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+page_content='  We propose a novel VS-Net model to overcome these  problems, which utilizes the separable convolution in the  combination of the variational encoder to extract the key  features from each frame across embedding sub-spaces and  forward the features between adjacent and parallel nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Our model extracts the spatiotemporal features locally and  makes better predictions globally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The main contributions of  our paper are given below: noitemsep, nolistsep  We design a novel spatiotemporal-based VS-Net model  with separable convolutions in variational autoencoder ar-  chitecture (VAE) [15], which reduces the skip-connection  between two nodes and generates the generalized latent  space vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  We utilize the Approximation Rank Pooling (ARP) [16],  which takes input features from separable convolutions  intermediate layers to train the VS-Net model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' It pro-  vides low-rank approximation features to preserve their  temporal locality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  We have conducted experiments with MIDV-500 [5]  dataset and demonstrated that VS-Net performs better in  terms of both efficiency and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' PROPOSED METHODOLOGY  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' VS-Net Architecture  Based on prior knowledge, spatial and temporal-based  methods can capture better location information and preserve  location boundaries than pixel-wise CNN methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Therefore,  we design a novel spatial and temporal-based VS-Net model  with separable convolutions [17] in variational auto-encoder  architecture (VAE) [15], which reduces the skip-connection  between two nodes and generates the generalized latent space  vector (shown in fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Given a sequence of input frames (Sn|n = 1, 2, 3, · · ·, N),  and corresponding ground-truth maps (Gn|n = 1, 2, 3, · · ·, N)  are first passed into the VS-Net model to extract the spatial and  temporal features, which uses pretrained weights of ResNet50  [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Our proposed model has two branches with different  purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The first is the down-sampling operation performing  top to bottom, extracting the spatial and temporal features from  each node and reducing the feature vectors’ dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The  second is upsampling operation from bottom to top, which  decodes the spatial-temporal latent space and enhances the  feature vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' At last, we combine feature vectors from  previous nodes and parallel nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  During the down-sampling, we perform separable convolu-  tion operation with 3 × 3 filters on input frames to extract  spatial and temporal features, which have rich spatial and  temporal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Then max-pooling operation with 2 × 2  filters succeeded by a ReLU activation operation performs to  downgrade the dimension of the features vectors and generate  the latent spatial and temporal map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Sd ∼ Down(Sn) = SConv(S1, S2, S3, S4, · · ·, Sn),  (1)  where SConv is a separable convolution operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Before the up-sampling, we perform a convolution operation  using 1 × 1 filters with learnable weight θ and applied the  ReLU activation function to reduce the dimension of the latent  features vectors and apply a dropout operation to dropout the  50% neurons for generating the latent space of spatial and  temporal features vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Sl = Dropout(ReLU(Conv(Sd, θ))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  (2)  During the up-sampling operation from bottom to top, we  decode the latent space vectors using separable convolution  layers with 3× 3 filters, succeeded by up-sampling layers and  ReLU activation operation to reconstruct the dimension of the  features vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Sup ∼ UP(Sl) = SConv(S1, S2, S3, S4, · · ·, Sn),  (3)  where SConv is a separable convolution layers with 3×3 filters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  We extract the spatial and temporal features from latent space  during the upsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The extracted spatial and temporal  features of each parallel node and adjacent node both are  concatenated, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=',  Sc = Conc(Sup, Sd),  (4)  where Conc is concatenation operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Then we perform  separable convolution layers with 3 × 3 filters succeeded by  the ReLU activation function to enhance the quality of the  spatial-temporal feature vectors and reconstruct the original  dimension of latent features vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Further, we apply the  Sigmoid function using the convolution layer with 1×1 filters  to simplify the spatial and temporal features, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=',  Sm = Sigmoid(Sc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  (5)  The network has approximately 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='5 million trainable pa-  rameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' We notice that each layer of the VS-Net generates  a feature map with a spatial structure in places of the video  frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Max Pooling layers use to increase the feature’s map  generation speed, which updates the weight matrix of the  backbone models during the feature extraction from every  separable convolution layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' During the bottom-up extraction  of features from high to low resolution, upsampling operations  with 2×2 filters are used to distribute the latent feature space  and combine them with the previous layer and parallel layer’s  nodes’ features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  We used Approximation Rank Pooling (ARP) [16], which  takes input features from the intermediate layers of a VS-  Net, trains on sub-sequences, and generates the output of  a subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' ARP not only gives low-rank approximation  features, but it also conserves temporal order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The low-rank  approximation differentiated and captured important character-  istics of the data, which summarizes the document’s position  and orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Further, a quadratic ranking function captured  the temporal order, which handles non-linear dependencies of  the input features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Generally, the temporal order deals with the  protuberances of the input channels onto the substance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Due to the low-rank approximation, the down-sampling  generates the generalized latent space vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The sampling of  Input Frame  Saliency Map  UpSampling  Down Sampling  SConv1  SConv2  SConv+MaxPool+ReLU  SConv+MaxPool+ReLU  SConv+MaxPool+ReLU  SConv+MaxPool+  ReLU  SConv6  SConv7  SConv8  SConv9  SConv10  SConv14  SConv15  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Architecture of the proposed VS-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  mean and variance gives the efficient latent distribution of the  VS-Net architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Based on the latent Gaussian distribution,  the latent vector is generalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The down-sampling and up-  sampling are performed based on the variational encoder and  decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' For handling the over-fitting of the proposed model,  the latent space of the down-sampling is normalized with the  help of convolution layers and passed to up-sampling layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  After concatenating all the spatial and temporal features, we  applied a convolution layer with 1×1 filters at the last node to  generate feature vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' At last, the previous node and parallel  node features are aggregated and provide the saliency map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  TABLE I  PERFORMANCE COMPARISON OF THE SOTA AND PROPOSED MODEL  (VS-NET) IN TERMS OF BCE+IOU LOSS(%), AND TESTING SPEED (FPS)  Input frame  Model  Output frame  Loss (BCE+IoU)  Testing speed (FPS)  RNN+LSTM [7]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='032  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='34  U-Net [9]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='028  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='45  FCNN [18]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='038  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='36  HE [2]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='041  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='45  STCRF [12]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='039  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='54  AED [13]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='035  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='89  CNN+LSTM [10]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='036  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='63  RCNN [19]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='025  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='54  VS-Net  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='021  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='36  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Loss function  During training, we use input frames Sk with the corre-  sponding ground-truth Gk at frame t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The binary cross-entropy  loss Lbce [20] is used to calculate the dissimilarity of the  output and target, which is given as follows,  lbce(Sk, Gk) = −  �  i,j  [Gk(i, j)log(Sk(i, j))+  (1 − Gk(i, j))log(1 − Sk(i, j))]  (6)  where (i,j) represents a coordinate of the frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The IoU  loss [21] is computed as:  lIoU(Sk, Gk) = 1 −  �w  i=1  �h  j=1 Sk(i, j)Gk(i, j)  �w  i=1  �h  j=1[Sk(i, j) + Gk(i, j) − Sk(i, j)Gk(i, j)]  (7)  The total loss function is derived as,  Totalloss = lbce(Sk, Gk) + αlIoU(Sk, Gk),  (8)  where α is the weighting parameter for the IoU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' For the final  saliency map prediction, we utilize Sk and Gk since it shows  that our experiments better utilized spatial-temporal cues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' EXPERIMENTAL SETUP AND RESULT ANALYSIS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' MIDV-500 Dataset  We have considered the MIDV-500 dataset [5], which con-  tains video clips of 50 different identity documents (seventeen  Id cards, fourteen passports, six identity documents, and  thirteen driving licenses) of various countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' It has eight  different variations of background and foreground scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The  attributes of the dataset are TS (Table Scene), TA (Table  Action), KS (Keyboard Scene), KA (Keyboard Action), HS  (Hand Scene), HA (Hand Action), PS (Partial Scene), PA  (Partial Action), CS (Complex Scene), CA (Complex Action).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Thus a total of 500 videos are generated (50 documents× 5  desperation×2 devices).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Each video has a duration of three  seconds, which is split into ten frames per second and the  corresponding annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The dataset contains examples of  multiple challenging scenarios, such as complex scenes, small  FUHRERSCHEIN BUNDESREPUBLKDEUTSCHLAND  D  Mustermann  Erika  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='64  MUSTER  4a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='15  Berlin  Musterhausen  4c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='Landratsant  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='0:.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='30  B072RRE2155  am See  M/B/LFUHRERSCHEIN BUNDESREPUBLKDEUTSCHLAND  D  Mustermann  Erika  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='64  MUSTER  4a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='15  Berlin  Musterhausen  4c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='Landratsant  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='0:.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='30  B072RRE2155  am See  M/B/Lobjects with different variations of frames, appearances of  background and foreground, cluttered background, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' (a  few examples are shown in Fig: 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The ground truth is  prepared for each extracted video frame with various document  locations in JSON format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' It has 48 photo patches, 40 signature  patches, and 546 text patches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The patches convert Cyrillic,  Greek, Chinese, Japanese, Arabic, and Persian with singular  Latin characters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Optimization and Propagation  For preparing the VS-Net model, the Adaptive Moment Esti-  mation (ADAM) optimizer is used to facilitate the computation  of learning rates of each parameter using the first and second  moment of the gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The saliency map optimization is cast  as a “label propagation” problem, where uncertain labels are  propagated based on background and foreground seeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Fur-  ther, we perform shift and rotation invariance robustly to the  deformation of gray value variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' These random variations  of deformation are sampled from the Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Drop-out layers are used at the bottom stop and the previous  level to normalize the latent space vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The proposed VS-  Net model optimizes the loss of saliency maps from top-to-  bottom and bottom-to-top and propagative seeds sequentially  interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The sequential seeding procedure optimizes feature  map loss and improves the robustness to construct a saliency  map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Evaluation Metrics  We used Intersection Over Union (IoU) loss as an evaluation  metric, which is defined as the intersection over the predicted  boundary box (bbox), and the actual bbox and divided with  their union.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' A prediction considers True Positive if Inter-  section over union (IoU)>threshold, and False Positive If  IoU<threshold [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  IoU = Area  of  Overlap  Area  of  Union  (9)  The smaller the IoU value, the better the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' In our  experiments, the threshold is set as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The comparison results  in terms of accuracy are shown in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  TABLE II  COMPARISON RESULTS WITH SOTA MODELS AND PROPOSED MODEL ON  MIDV-500 DATASET  Comparison of document detection accuracy (%)  Model  TS,  KS,  HS,  PS,  CS  TA  KA  HA  PA  CA  U-Net (2019) [9]  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='44  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='43  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='12  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='64  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='40  RNN+LSTM (2021) [7]  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='12  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='33  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='56  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='56  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='59  FCNN (2017)[18]  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='78  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='39  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='89  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='43  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='43  HE (2020) [2]  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='86  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='58  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='54  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='32  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='45  STCRF (2018) [12]  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='43  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='98  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='56  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='43  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='98  AED (2020)[13]  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='97  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='54  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='74  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='78  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='69  CNN+LSTM (2019)[10]  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='56  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='54  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='74  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='78  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='69  RCNN (2019)[19]  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='43  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='69  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='78  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='19  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='56  VS-Net  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='25  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='67  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='62  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='45  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='74  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Implementation Details  1) Training Setup: The experiments are accomplished on  Intel Xeon(R) CPU E5-2640 v4 @ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='40GHz X40 processor  with 32GB RAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' We used Tensorflow-gpu2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='0, Keras as the  backend, and Python3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='6 accelerated by NVIDIA RTX Graphic  card (Quadro P5000 / PCIe /SSE2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Input frames are of size  256×256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The ADAM optimizer, weight decay of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='006, batch  size of 128, and learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='001 are used to train the  model, and BCE +IoU loss function is used to calculate the  loss of the VS-Net model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The running time comparison is  given in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  2) Testing Setup and Runtime: We resize the frame 256 ×  256 to feed into the corresponding branch for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The  distribution of the dataset is in the ratio of 3:7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The average  testing speed of our model is 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='46 fps which is less than the  existing models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Additionally, we do not perform any pre-  /post-processing [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' For validating purpose, the 5-fold cross-  validation are used to check the overfitting (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  5-fold cross-validation comparison result of VS-Net and SOTA  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Ablation Study - The qualitative evaluation shows that  our VS-Net model gives the best results on MIDV-500 [5]  datasets but is an extremely lightweight setting that has fewer  parameters and FLOPs (see in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' IV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Speed Comparison The speed performance is calculated  on a 64-bit Linux Ubuntu-18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='04 operating system with Intel  Core i7-4590 CPU @ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='3 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' It has 32GB RAM and 1 TB  Hard disk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The average speed is computed on all frame images  of MIDV-500 datasets and does not include I/O file time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The  parallel processing of multiple images is not allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Priorly,  SOTA models require high computational powerful GPU sys-  tem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' For a fair comparison, the recent unsupervised models  compare the speed on a normal CPU and the speed of deep  learning methods reported on GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The speed comparison is  given in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' We show the trade-off between loss and  testing speed in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Further, the average time cost of  each step is examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' VS-Net consumes 256 ms and SOTA  models 270 ms, respectively, while saliency prediction and  global optimization use 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='36 ms and 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='0 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' CONCLUSION AND FUTURE WORK  In this paper,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' we proposed a novel efficient and fast VS-Net  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='model that fully leverages the spatiotemporal features to detect  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='99  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='98  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='Accuracy  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='97  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='96  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='95  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='94  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='HE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='AED  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='STCRF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='VS-Net  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='RNN+LSTM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='CNN+LSTMTABLE III  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='RUNTIME COMPARISON OF SOTA MODELS AND VS-NET MODEL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='U-Net[9]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='RNN+LSTM[7]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='FCNN[18]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='HE [2]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='STCRF[12]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='AED[13]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='CNN+LSTM[10]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='RCNN[19]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='VS-Net  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='Runtime (s)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='188  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='191  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='190  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='198  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='199  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='196  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='189  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='175  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='Step (ms)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='265  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='266  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='273  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='278  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='275  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='268  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='267  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='260  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='256  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='TABLE IV  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='ABLATION STUDY WITH RESNET-50 AS BACKBONE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  # Param(M)  FLOPS(G)  Runtime (s)  Steps(ms)  Accuracy  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='42  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='2  200  285  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='98  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='54  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='3  185  275  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='85  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='7  175  265  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='95  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='5  165  255  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='45  the video identity document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The proposed model used sep-  arable convolutions with variational autoencoder architecture,  which performs downsampling for extracting the features and  upsampling operation for decoding the latent space features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  The Approximation Rank Pooling (ARP) is used low-rank  approximation on frames to preserve the temporal locality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' The  bottom-end the generalized latent space is generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Further,  These features are combined to generate in fuse spatial and  temporal characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' We validated each module of the  proposed model with the help of extensive experiments, which  can be considered as the unified solution advancing VSDD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  REFERENCES  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Burie, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Forn´es, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Santosh, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Luqman, “Deep learning  for graphics recognition: document understanding and beyond,” pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 1–2,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Sheshku, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Nikolaev, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Arlazaro, “Houghencoder: neural  network architecture for document image semantic segmentation,” in  2020 IEEE International Conference on Image Processing (ICIP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 1946–1950.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Schreiber, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Agne, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Wolf, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Dengel, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Ahmed, “Deepdesrt:  Deep learning for detection and structure recognition of tables in  document images,” in 2017 14th IAPR international conference on  document analysis and recognition (ICDAR), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  IEEE, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  1162–1167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [4] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Sun, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Wang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Liu, “Content-aware rate control  scheme for hevc based on static and dynamic saliency detection,”  Neurocomputing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 411, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 393–405, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [5] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Arlazarov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Bulatov, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Chernov, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Arlazarov,  “Midv-500: a dataset for identity document analysis and recognition on  mobile devices in video stream,” Computer Optics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 43, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  818–824, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [6] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Mu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Xu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Wang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Feng, “A novel spatiotempo-  ral attention enhanced discriminative network for video salient object  detection,” Applied Intelligence, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 1–16, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Kompella and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Kulkarni, “A semi-supervised recurrent neural  network for video salient object detection,” Neural Computing and  Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 33, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 2065–2083, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [8] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Tian, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Mu, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Jing, “A novel fcns-convlstm  network for video salient object detection,” International Journal of  Circuit Theory and Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 49, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 1050–1060, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [9] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Liu and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Jiang, “U-net based multi-instance video object segmen-  tation,” arXiv preprint arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='07826, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Rhanoui, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Mikram, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Yousfi, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Barzali, “A cnn-bilstm  model for document-level sentiment analysis,” Machine Learning and  Knowledge Extraction, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 1, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 832–847, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Ren, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Han, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Yang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Han, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' He, “Tenet: Triple excitation  network for video salient object detection,” in European Conference on  Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  Springer, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 212–228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Le and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Sugimoto, “Video salient object detection using spa-  tiotemporal deep features,” IEEE Transactions on Image Processing,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 5002–5015, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [13] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Lei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Hwang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Yu, “Salient object  detection in stereoscopic 3d images using a deep convolutional residual  autoencoder,” IEEE Transactions on Multimedia, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [14] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Vatankhah, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Liu, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Qi, “Inversion of  large-scale gravity data with application of vnet,” Geophysical Journal  International, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [15] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Sun, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Guo, “Supervae: Superpixelwise variational  autoencoder for salient object detection,” in Proceedings of the AAAI  Conference on Artificial Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 33, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 01, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 8569–  8576.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [16] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Bilen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Fernando, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Gavves, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Vedaldi, “Action recognition  with dynamic image networks,” IEEE transactions on pattern analysis  and machine intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 40, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 2799–2813, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [17] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Bian, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Zhang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Cheng, “Samnet:  Stereoscopically attentive multi-scale network for lightweight salient  object detection,” IEEE Transactions on Image Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 30, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  3804–3814, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [18] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Shen, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Shao, “Video salient object detection via  fully convolutional networks,” IEEE Transactions on Image Processing,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 38–49, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [19] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Sharma and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Mir, “Saliency guided faster-rcnn (sgfr-rcnn) model  for object detection and recognition,” Journal of King Saud University-  Computer and Information Sciences, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [20] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Ji, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Fu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Wu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Fan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Shen, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Shao, “Full-duplex  strategy for video object segmentation,” in Proceedings of the IEEE/CVF  International Conference on Computer Vision, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 4922–4933.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content='  [21] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Ahmed, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Tarlow, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' Batra, “Optimizing expected intersection-  over-union with candidate-constrained crfs,” in Proceedings of the IEEE  international conference on computer vision, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}
+page_content=' 1850–1858.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtE3T4oBgHgl3EQfUAqQ/content/2301.04447v1.pdf'}

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+1
+Universal Multimodal Representation for
+Language Understanding
+Zhuosheng Zhang#, Kehai Chen, Rui Wang#, Masao Utiyama, Eiichiro Sumita, Zuchao Li, Hai Zhao*
+Abstract—Representation learning is the foundation of natural language processing (NLP). This work presents new methods to employ
+visual information as assistant signals to general NLP tasks. For each sentence, we first retrieve a flexible number of images either
+from a light topic-image lookup table extracted over the existing sentence-image pairs or a shared cross-modal embedding space that
+is pre-trained on out-of-shelf text-image pairs. Then, the text and images are encoded by a Transformer encoder and convolutional
+neural network, respectively. The two sequences of representations are further fused by an attention layer for the interaction of the two
+modalities. In this study, the retrieval process is controllable and flexible. The universal visual representation overcomes the lack of large-
+scale bilingual sentence-image pairs. Our method can be easily applied to text-only tasks without manually annotated multimodal parallel
+corpora. We apply the proposed method to a wide range of natural language generation and understanding tasks, including neural
+machine translation, natural language inference, and semantic similarity. Experimental results show that our method is generally effective
+for different tasks and languages. Analysis indicates that the visual signals enrich textual representations of content words, provide fine-
+grained grounding information about the relationship between concepts and events, and potentially conduce to disambiguation.
+Index Terms—Artificial Intelligence, Natural Language Understanding, Vision-Language Modeling, Multimodal Machine Translation.
+!
+1
+INTRODUCTION
+L
+EARNING contextualized representations of human lan-
+guages is one of the major themes in natural language
+processing (NLP), which is also fundamental to training
+machines to understand human languages and handle ad-
+vanced tasks, such as machine translation, question an-
+swering, and human-computer conversations. Text repre-
+sentation learning has evolved from standard distributed
+representations [1, 2] to contextualized language represen-
+tation from deep pre-trained representation models (PRMs)
+[3, 4, 5, 6]. Despite the success of PRMs, NLP models
+commonly model the world knowledge (e.g, commonsense,
+rules, events, assertions extracted from raw texts) solely
+from textual features without grounding of the outside
+world, such as visual conception [7]. Languages are abstract
+•
+Z. Zhang, R. Wang, Z. Li, H. Zhao are with the Department of
+Computer Science and Engineering, Shanghai Jiao Tong University,
+China and also with Key Laboratory of Shanghai Education Com-
+mission for Intelligent Interaction and Cognitive Engineering, Shang-
+hai Jiao Tong University, China. K. Chen is with the School of
+Computer Science and Technology, Harbin Institute of Technology,
+Shenzhen, China. M. Utiyama and E. Sumita are with the Na-
+tional Institute of Information and Communications Technology (NICT),
+Japan. E-mail: {zhangzs, charlee}@sjtu.edu.cn; [email protected];
+{mutiyama, eiichiro.sumita}@nict.go.jp; [email protected]; zhao-
+[email protected].
+•
+H. Zhao is supported by Key Projects of National Natural Science
+Foundation of China (U1836222 and 61733011). R. Wang is supported
+by National Natural Science Foundation of China (No. 6217020129),
+Shanghai Pujiang Program (No. 21PJ1406800), Shanghai Municipal
+Science and Technology Major Project (No. 2021SHZDZX0102), Beijing
+Academy of Artificial Intelligence (BAAI) (No. 4), CCF-Baidu Open
+Fund (No. CCF-BAIDU OF2022018). K. Chen is supported by National
+Natural Science Foundation of China (No. 62276077) and Shenzhen
+College Stability Support Plan (No. GXWD20220811170358002 and
+GXWD20220817123150002).
+•
+Z. Zhang and R. Wang contribute equally to this work. Part of this work
+was finished when Z. Zhang and Z. Li visited NICT, and R. Wang was
+with NICT. Corresponding author: Hai Zhao.
+and rather difficult for the brain to retain, whereas visuals
+are concrete and, as such, more easily remembered [8, 9].
+Adopting multimodality would be essential for better back-
+ground perception. Therefore, a trend of research has been
+motivated to apply non-linguistic modalities to language
+representations [7, 10, 11, 12, 13, 14].
+Most of previous works focus on joint modeling im-
+ages and texts, involving vision-language (VL) pre-training
+[15, 16, 17, 18, 19, 20] and multimodal (MM) application
+tasks [14, 21, 22, 23, 24]. However, these studies rely on
+large-scale text-image annotations as the paired input and
+thus are confined to VL or MM tasks, such as image cap-
+tioning and visual question answering. It is natural to boost
+the performance on VL and MM tasks as the concerned
+datasets are human-labeled with high quality. However, the
+essential challenge lies with the real-world scenario as there
+is no such high-quality annotated text-image aligned corpus
+for text-only NLP applications. Therefore, it is critical to
+investigate a general method to take advantage of visual
+information in a wide range of mono-modal (e.g., text-only)
+tasks. In addition, it is still not clear the role of images
+in language representation, as well as how to apply the
+multimodality in the standard NLP scenario.
+Taking multimodal machine translation (MMT) as an
+example, the starting point is to leverage visual information
+to improve the quality of the translation from the source
+to the target languages. However, the effectiveness heavily
+relies on the availability of bilingual parallel sentence pairs
+with manual image annotations, which hinders the image
+applicability to neural machine translation (NMT). As a re-
+sult, the visual information is only applied to the translation
+task over specific multimodal datasets [25, 26, 27, 28, 29], in-
+stead of general text-only NMT [30, 31, 32] and low-resource
+text-only NMT [33, 34, 35, 36]. In addition, because of the
+high cost of annotation, the content of one bilingual parallel
+Copyright © 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media,
+including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists,
+or reuse of any copyrighted component of this work in other works.
+arXiv:2301.03344v1  [cs.CL]  9 Jan 2023
+
+2
+sentence pair is paired with a single image, which is weak in
+capturing the diversity of visual information. Therefore, the
+current study of introducing visual information falls into a
+bottleneck in the multimodal NMT and is not feasible for
+text-only NMT and low-resource NMT.
+Our previous work [37] finds that using monolingual
+corpora with image annotations can overcome the lack of
+large-scale bilingual sentence-image pairs, thereby extend-
+ing image applicability in NMT, with performance gains.
+The method of using a lookup table is task-agnostic. This
+work stimulates our further thinking, and we are interested
+in answering the three major aspects of questions:
+(i) Global Multimodality: Can we apply the multi-
+modality to standard text-only NLP tasks to enhance the
+language representations (Section 5.4), e.g., natural lan-
+guage generation (Section 5.1.1) and natural language un-
+derstanding (Section 5.1.2)?
+(ii) Interpretability: Why does the universal representa-
+tion method work (Section 6.2)? How does multimodality
+improve language representation, and what is the network
+learned(Section 6.2-6.6)?
+(iii) Quality: How to control the quality of visual-text
+alignment to reduce noise (Section 6.9)?
+In this paper, we present a universal visual represen-
+tation (UVR) method relying only on a seed set of task-
+independent annotations, instead of the existing approach
+that depends on large-scale task-specific image-text anno-
+tation, thus breaking the bottleneck of using visual infor-
+mation in standard text-only NLP tasks. For each sentence,
+we retrieve diverse images from either a light topic-image
+lookup table or pre-trained shared text-visual embedding
+space that is pre-trained on a large-scale of text-image
+pairs, to connect both the mono-modal paths of text and
+image embeddings. The text and images are encoded by
+Transformer language model (LM) and a pre-trained convo-
+lutional neural network (CNN), respectively. A simple and
+effective attention layer is then designed to fuse the two
+sequences of representations.
+Our approach can be easily applied to text-only tasks
+without manually annotated multimodal parallel corpora.
+Therefore, our method is universal in terms of the task re-
+quirements, in contrast to the recent vision-language models
+that require large-scale and expensive annotation datasets
+for each downstream task. The proposed method is eval-
+uated on 14 NLP benchmark datasets involving natural
+language inference (NLI), semantic similarity, text classifica-
+tion, and machine translation. The experiments and analysis
+verify the effectiveness of the proposed method. To summa-
+rize, our contributions are primarily three-fold:
+(i) This work studies the universal visual representa-
+tion for language representation in a broader view of the
+natural language processing scenario. Besides neural ma-
+chine translation, this work leverages visual information
+as assistant signals for general NLP tasks, with the focus
+on investigating the global multimodality for general NLP,
+interpretability of effectiveness, and quality control of using
+universal visual representation.
+(ii) For the technical side, this work proposes new meth-
+ods of semantic sentence-image matching from a shared
+cross-modal space to give more accurately paired images
+as topic information. We also present a new multimodal
+representation framework and systematically study the two
+main instances, including the model with the original TF-
+IDF topic-image lookup table and the newly proposed one
+from the retrieval from cross-modal retrieval.
+(iii) Experiments are extended to 14 representative NLP
+tasks, which show the effectiveness of the proposed method.
+A series of in-depth analyses indicate that the visual signals
+enrich textual representations of content words, provide
+fine-grained grounding information about the relationship
+between concepts and events, and potentially conduce to
+disambiguation.
+2
+BACKGROUND
+2.1
+Vision-Language Integration
+This study is related to that of VL methods (VLMs). Re-
+cently, there has been a great deal of interest in integrating
+image presentations in pre-trained Transformer architec-
+tures [15, 16, 17, 18, 19, 20, 38]. The common strategy is
+to take a Transformer model [32], such as BERT, as the back-
+bone and learn aligned representations of visual and lan-
+guage in a pre-training manner inspired by the masked lan-
+guage modeling mechanism in pre-trained language models
+[5]. These studies require the annotation of task-dependent
+sentence-image pairs, which are limited to VL tasks, such as
+image captioning and visual question answering.
+Two studies [22, 37] are closely related to general image-
+enhanced LM. Glyce [22] proposes incorporating glyph
+vectors for Chinese character representations. However, it
+can only be used for Chinese and only involves single
+image enhancement. Regarding the technical part, previous
+methods only benefit from one image per sentence. We
+propose taking advantage of a group of similar images using
+a filtering mechanism to form a more fine-grained visual-
+aware context. Our early version of this work [37] proposes
+using multiple images for NMT, based on a text-image
+lookup table trained over a sentence-image pair corpus.
+However, the number of images is fixed because of the lack
+of similarity measurement in the simple lookup method,
+which possibly makes the resulting model suffer from the
+noise of irrelevant images. This work is improved from the
+perspectives of motivation and technique. It is motivated
+by cross-modal semantic retrieval in the shared embedding
+space. It adopts a neural matching method with a similarity
+threshold to control the expected matching degree flexibly,
+which is generally applicable to a broader range of NLP
+tasks. In addition, we conduct an in-depth analysis to inves-
+tigate how the visual modality helps text representation.
+2.2
+Visual-Semantic Embeddings
+Another research line is language grounding for images
+whose major topic is multimodality and cross-modality be-
+tween images and text. The major focus is to bridge the gap
+between text and images through building visual-semantic
+embeddings [39, 40, 41, 42, 43].
+Prior studies have verified that representations of images
+and text can be jointly leveraged to build visual-semantic
+embeddings in a shared representation space [39, 40, 41, 44].
+To this end, a popular approach is to connect both the mono-
+modal text and image encoding paths using fully connected
+
+3
+layers [45, 46]. The shared deep embedding can be used
+for cross-modal retrieval; thus, it can associate sentence
+text with associated images. Partly inspired by this line of
+research, we are motivated to incorporate visual awareness
+into sentence modeling by retrieving a group of images for
+a given sentence.
+One of the first techniques to align two views of hetero-
+geneous data is the canonical correlation analysis method
+[47], in which linear projections defined on both sides are
+optimized to maximize the cross-correlation. Recent studies
+have followed the two-path architecture [45, 46], in which
+the encoder consists of a joint embedding of textual and
+image representations extracted from both the images and
+corresponding caption. Notably, Engilberge et al. [46] adopts
+RNN to encode sentence embeddings in the same space
+with extracted image representations from CNN. Portaz
+et al. [48] enhances cross-modal retrieval using multilingual
+text. Inspired by the previous success of visual-semantic
+embeddings, we apply neural image retrieval from the joint
+space to fetch a group of associated images.
+3
+UNIVERSAL REPRESENTATION FRAMEWORK
+This section overviews our universal representation frame-
+work. Given a sentence, we first fetch a group of matched
+images from our retrieval methods (details of our retrieval
+methods will be given in the next section). The text and
+images are encoded, respectively, by the text feature extrac-
+tor and image feature extractor. Then the two sequences of
+representations are integrated using multi-head attention to
+form a joint representation, which is passed to downstream
+task-specific layers. Figure 1 overviews the whole multi-
+modal representation model.
+3.1
+Encoding Layer
+3.1.1
+Text Encoder
+We pair each sentence with the top matched m images
+according to the retrieval method above. Following [5], the
+sentence is fed into the multi-layer Transformer encoder [32]
+to learn the text representation H ∈ Rn×d where n and d are
+the input text length and dimension of hidden states for the
+text representation.
+Let X = {x1, . . . , xn} be the input sentence in length
+n. We feed the sequence to a PRM encoder (e.g., BERT
+[5]). In the encoder, the input sequence is firstly mapped
+to embeddings. Then, the embeddings are passed to multi-
+head attention layers [32] to obtain the contextualized rep-
+resentations, which is defined as
+H = FFN(MultiHead(K, Q, V )),
+(1)
+where K, Q, V are packed from the input sequence repre-
+sentation X. As the common practice, we set K = Q = V
+in the implementation. MultiHead is short for multi-head
+attention.
+3.1.2
+Image Encoder
+Similar to the standard way of retrieving word embeddings,
+the image embeddings are fetched from a lookup table ∈
+Rnm×dm that contains the image features encoded by a pre-
+trained ResNet [49],1 where nm is the number of the total
+number of unique images +1 and dm is the dimension of the
+image features.2 The first row of the lookup table is filled by
+all-zero vectors, which will be used when no image is paired
+for the sentence.
+After the feature lookup process, we obtain the image
+embeddings E ∈ Rm×dm for the m input images. Then, the
+embeddings are passed to a feedforward layer, to produce
+the image representation M ∈ Rm×d with the same hidden
+dimension as H:
+M = FFN(ResNet(E)).
+(2)
+There may exist cases when no word in the sentence can
+be found in the topic-image lookup table. When there is no
+paired image retrieved, we use the first-row all-zero vectors
+of the image lookup table as the “blank features” in the
+intuition to tell the model to ignore them.
+3.2
+Multimodal Integration Layer
+We connect the visual and text modalities by calculating the
+attention between image and text features:
+α = softmax(H(WgM + bg)⊤),
+(3)
+H′ = αM,
+(4)
+where Wg and bg are parameters to learn. α ∈ Rn×m
+denotes the weights assigned to the different hidden states
+in the sentence and the image sequences. H′ ∈ Rn×d is the
+weighted sum of all the hidden states and it represents how
+the sentence can be aligned to each hidden state in the image
+representation.
+The retrieval process may possibly introduce noise of
+irrelevant images. To alleviate the influence, we use a neural
+gating mechanism for information filtering. In detail, we
+compute λ ∈ [0, 1]n×d to weight the expected importance
+of image representation for each source word:
+λ = sigmoid(WλH′ + UλH),
+(5)
+where Wλ and Uλ are model parameters. We then fuse
+H and H′ and pass the resulting representation to layer
+normalization and learn an effective source representation:
+ˆH = LayerNorm(H + λH′).
+(6)
+The text and image representations are jointly encoded
+as ˆH, which is fed to the task-specific layers for downstream
+decoding or predictions depending on task settings.
+3.3
+Task-specific Layer
+In this section, we show how the joint representation ˆH is
+used for downstream tasks by considering NMT and NLU
+tasks as examples, generally following the standard proce-
+dure of the concerned tasks. For NMT, ˆH is directly fed to
+the decoder to learn a dependent-time context vector to pre-
+dict the target translation. For other tasks, ˆH is directly fed
+1. Note that this is the standard lookup table in embedding imple-
+mentations, which is not our topic-image lookup table.
+2. We used the maxpooling layer of ResNet, which is in the size of
+Rnm×2400.
+
+4
+Add & Norm
+Feed Forward
+Add & Norm
+Multi-head
+Attention
+Add & Norm
+Multi-head
+Attention
+Feed Forward
+ResNet
+Text 
+Embedding
+Sentence
+Text Encoder
+Image
+Corpus
+Image Retrieval
+Pooling
+Linear
+Downstream Adaption
+(NLU, NMT, etc)
+Image Encoder
+Integration
+L×
+Fig. 1. Overview of the universal representation framework. Given a sentence as input, a group of related images will be retrieved by our image
+retrieval methods. The text and images are encoded by the text feature extractor and image feature extractor, respectively. Then the two sequences
+of representations are integrated using multi-head attention to form a joint representation in the same shape as the original text sequence
+representation. Finally, the joint representation is passed to downstream task-specific layers to give predictions.
+to a feed-forward layer to make the prediction, which fol-
+lows the same downstream procedure as the Transformer-
+based LMs, like BERT [5] and RoBERTa [50]. Specifically,
+for sentence-pair tasks, we maintain the pairwise input as
+that in LMs and separate the encoded text representation
+into two individual sentence representations {H1, H2}, ac-
+cording to the positions. The two text representations are
+integrated with the corresponding image representations
+respectively {M 1, M 2}, and then the resulting sequences
+are concatenated for prediction, ˆH = ˆH1 ◦ ˆH2.
+4
+IMAGE RETRIEVAL METHODS
+In this section, we describe our two visual retrieval models
+used for image retrieval given sentence text:
+(i) UVR-TILT: retrieval by topic-image lookup table;
+(ii) UVR-CMRM: retrieval from cross-modal embed-
+ding.
+4.1
+Model-I: Retrieval by Topic-Image Lookup Table
+4.1.1
+Topic-image Lookup Table Conversion
+In this section, we will introduce the proposed universal
+visual representation method. Our basic intuition is to trans-
+form the existing sentence-image pairs into a topic-image
+lookup table,3 which assumes the topic words in a sentence
+should be relevant to the paired image. The procedure can
+be seen as the inverted index where a topic word is mapped
+to a list of images. Consequently, a sentence can possess a
+group of images by retrieving the topic-image lookup table.
+To focus on the major part of the sentence and suppress
+the noise such as stopwords and low-frequency words, we
+design a filtering method to extract the “topic” words of
+the sentence through the term frequency-inverse document
+3. We use the training set of the Multi30K dataset to build the topic-
+image lookup table.
+Algorithm 1 Topic-image Lookup Table Conversion
+Require: Input sentences, S = {X1, X2, . . . XI} and paired
+images E = {e1, e2, . . . , eI}
+Ensure: Topic-image lookup table Q where each word is asso-
+ciated with a group of images
+1: Obtain the TF-IDF dictionary F = TF-IDF(S)
+2: Transform sentence-image pair to topic-image lookup table
+Q = LookUp(S, E, F)
+3: procedure TF-IDF(S)
+4:
+for each sentence in S do
+5:
+Filter stop-words in the sentence
+6:
+Calculate the TF-IDF weight for each word
+7:
+end for
+8:
+return TF-IDF dictionary F
+9: end procedure
+10: procedure LOOKUP(S, E, F)
+11:
+for For each pair {Xi, ei} ∈ zip{S, E} do
+12:
+Rank and pick out the top-w “topic” words in the
+sentence according to the TF-IDF score in the dictionary F,
+and each sentence is reformed as T = {t1, t2, . . . , tw}
+13:
+for For each word tjin T do
+14:
+if ei not in Q[tj] then
+15:
+Add ej to the corresponding image set Q[tj]
+for word tj
+16:
+end if
+17:
+end for
+18:
+end for
+19:
+return Topic-image lookup table Q
+20: end procedure
+frequency (TF-IDF),4 inspired by [51]. Specifically, given an
+original input sentence X = {x1, x2, . . . , xI} of length I
+and its paired image e, X is first filtered by a stopword list,5
+and then the sentence is treated as a document g. We then
+4. We describe our methods by regarding the processing unit as word
+though this method can also be applied to a subword-based sentence
+for which the subword is considered to be the processing unit.
+5. https://github.com/stopwords-iso/stopwords-en.
+
+UBS
+SOONERS
+MEGA
+OMEGA
+0
+SOON5
+   dog is playing in the snow
+dog (1,512)
+playing (1,531)
+snow (439)
+(a) a black dog and a spotted dog are fighting
+(b) a dog is running in the snow
+(c) a dog is playing with a hose
+(d) a family playing on a tractor on a beautiful day
+(e) two people working on removing snow from a roof 
+(f) a black dog and a white dog are standing on snow 
+corpus (29,000)
+(a)
+(b)
+(c)
+(d)
+(e)
+(f)
+sentence-image pairs
+topic-image lookup table
+associated images for input sentence
+tokenize, filtering
+word-image transform
+sampling
+ranking
+Fig. 2. Illustration of the TILT method. We first transform the existing sentence-image pairs from seed small-scale sentence-image datasets into a
+topic-image lookup table. For a given sentence, we extract its topic words and the associated images will be retrieved from the lookup table.
+compute TF-IDF TIi,j for each word xi in g,
+TIi,j =
+oi,j
+�
+k ok,j
+× log
+|G|
+1 + |j : xi ∈ g|,
+(7)
+where oi,j represents the number of occurrences of the word
+xi in the input sentence g, |G| the total number of source
+language sentences in the training data, and |j : xi ∈ g|
+the number of source sentences including word xi in the
+training data. We then select the top-w high TF-IDF words as
+the new image description T = {t1, t2, . . . , tw} for the input
+sentence. After the preprocessing, each filtered sentence T
+is paired with an image e, and each word ti ∈ T is regarded
+as the topic word for image e. After processing the whole
+corpus (i.e., Multi30K), we form a topic-image lookup table
+Q as described in Algorithm 1, in which each topic word ti
+would be paired with dozens of images.
+4.1.2
+Image Retrieval
+For the input sentence, we first obtain its topic words
+according to the text preprocessing method described above.
+Then we retrieve the associated images for each topic word
+from the lookup table Q and group all the retrieved images
+together to form an image list G. We observe that an image
+might be associated with multiple topic words so that it
+would occur multiple times in the list G. Thus, we sort the
+images according to the frequency of occurrences in G to
+maintain the same total number of images for each sentence
+at m.
+Figure 2 illustrates the retrieval process. In the left block,
+we show six examples of sentence-image pairs in which the
+topic words are in boldface. Then we process the corpus
+using the topic-image transformation method demonstrated
+above and obtain the topic-image lookup table. For example,
+the word dog is associated with 1,512 images. For an input
+source sentence, we obtain the topic words (in boldface)
+using the same preprocessing. Then we retrieve the corre-
+sponding images from the lookup table for each topic word.
+Now we have a list of images, and some images appear
+multiple times as they have various topics (like the boxed
+image in Figure 2). So we sort the retrieved image list by the
+count of occurrence to pick out the top-m images that cover
+the most topics of the sentence.
+At test time, the process of getting images is done using
+the image lookup table built by the training set, so we do
+not need to use the images from the validation and test sets
+in Multi30K dataset.6 Intuitively, we do not strictly require
+the manual alignment of the word (or concept) and image
+but rely on the co-occurrence of the topic word and image,
+which is simpler and more general. In this way, we call our
+method universal visual retrieval.
+4.2
+Model-II: Retrieval from Cross-modal Embedding
+Following Engilberge et al. [46], we train a semantic-visual
+embedding on a text-image corpus, which is then used for
+image retrieval. The semantic-visual embedding architec-
+ture comprises two paths to encode the text and images into
+vectors. Based on our preliminary experiments, we maintain
+the same settings in Engilberge et al. [46] by using the simple
+recurrent unit as text encoder, and the fully convolutional
+residual ResNet-152 [52] with Weldon pooling [53] as image
+encoder for our cross-modal retrieval model.
+During training, each text X is paired with (i) a posi-
+tive image Y that is paired with the text and (ii) a hard
+negative Z, which is selected as the image that has the
+6. The lookup table can be easily adapted to a wide range of other
+NLP tasks even without any paired image, and therefore opens our
+proposed model to generalization.
+
+6
+highest similarity to the text while not being associated
+with it. Triplet loss [54, 55, 56] is used to enable the images
+to converge correctly to improve the performance of the
+proposed method:
+loss(X, Y, Z) = max(0, γ − E(X) · E(Y ) + E(X) · E(Z)),
+(8)
+where E(X), E(Y ), and E(Z) are the embeddings of X, Y ,
+and Z, respectively. γ is the minimum margin between the
+similarity of the correct caption and the unrelated caption.
+The loss function enables the sentence X to be closer to the
+corresponding image Y than the unrelated image Z. During
+the prediction time, the relationship between the text and
+images is calculated using the cosine similarity.
+For general use, it is reasonable that some sentences,
+such as social constructs or metaphorical usage, are not
+paired with images after retrieval and have a low similarity
+score. In these cases, visual information might not be help-
+ful. To measure how similar the retrieved images should be,
+we set a threshold δ to choose the top-ranked images for
+each sentence.
+5
+EXPERIMENTS
+5.1
+Task Settings
+Our evaluation is performed on the widely-used natural
+language generation and understanding tasks involving 14
+NLP benchmark datasets that involve machine translation,
+natural language inference (NLI), semantic similarity, and
+text classification. Part of the NLU tasks is available from
+the GLUE benchmark [57], which is a collection of nine NLU
+tasks.
+5.1.1
+Neural Machine Translation
+Five widely-used translation tasks are used for model eval-
+uation, including WMT’16 English-to-Romanian (En-Ro),
+WMT’14 English-to-German (En-De), WMT’14 English-to-
+French (En-Fr), and Multi30K dataset for WMT’16 and
+WMT’17, which are standard corpora for NMT and MMT
+evaluation.
+(i) For the En-Ro task, we experiment with the officially
+provided parallel corpus: Europarl v7 and SETIMES2 from
+WMT’16 with 0.6M sentence pairs. We use newsdev2016 as
+the validation set and newstest2016 as the test set.
+(ii) The En-De task has 4.43M bilingual sentence pairs
+of the WMT14 dataset used as training data, including
+Common Crawl, News Commentary, and Europarl v7. The
+newstest2013 and newstest2014 datasets are used as the vali-
+dation set and test set, respectively.
+(iii) The En-Fr task has 36M bilingual sentence pairs
+from the WMT14 dataset used as training data. Newstest12
+and newstest13 are combined for validation and newstest14
+is used as the test set, following the setting of [31].
+(iv) Multi30K dataset contains 29K English→{German,
+French} parallel sentence pairs with visual annotations.
+The 1,014 English→{German, French} sentence pairs with
+visual annotations serve as the validation set. For WMT’16
+and WMT’17 tasks, we have two test sets, test2016 and
+test2017, with 1,000 pairs for each.
+5.1.2
+Natural Language Understanding
+The NLU task involves natural language inference, semantic
+similarity, and classification subtasks.
+Natural Language Inference involves reading a pair of sen-
+tences and assessing the relationship between their mean-
+ings, such as entailment, neutral, and contradiction. We
+evaluate the proposed method on four diverse datasets:
+SNLI [58], MNLI [59], QNLI [60], and RTE [61].
+Semantic Similarity aims to predict whether two sentences
+are semantically equivalent. Three datasets are used: Mi-
+crosoft Paraphrase Corpus (MRPC) [62], Quora Question
+Pairs (QQP) dataset [63], and Semantic Textual Similarity
+benchmark (STS-B) [64].
+Classification CoLA [65] is used to predict whether an
+English sentence is linguistically acceptable. SST-2 [66] pro-
+vides a dataset for sentiment classification that needs to
+determine whether the sentiment of a sentence extracted
+from movie reviews is positive or negative.
+5.2
+Retrieval Setup
+This part describes the implementation of the image re-
+trieval by the topic-image lookup table (TILT) and cross-
+modal retrieval model (CMRM):
+TILT: We segment the sentences using the same BPE
+vocabulary as that for each source language. We select top-
+8 (w = 8) high TF-IDF words, and the default number of
+images m is set to 5.7 The detailed case study is shown in
+Section 6.9. Image features are extracted from the averaged
+pooled features of a pre-trained ResNet50 CNN [49]. The
+dimension of the feature maps is V ∈ R2048.
+CMRM: The cross-modal retrieval model is trained on
+the MS-COCO dataset [67], which contains 123,287 images
+with five English captions per image. It is split into 82,783
+training images, 5,000 validation images, and 5,000 test
+images. We use the Karpathy split [40] that forms 113,287
+training, 5,000 validation and 5,000 test images. The model
+is implemented following the same settings as Engilberge
+et al. [46], and produces state-of-the-art results (94.0% R@10)
+for cross-modal retrieval. To ensure that each task can enjoy
+enough images, we set the similarity threshold δ to 0.4 and
+rank the paired images according to the similarity score. The
+maximum number of retrieved images m for each sentence
+is set to eight according to our preliminary experiments.
+Multi30K and COCO datasets are used as the candidate
+seed image retrieval corpus for our downstream tasks.
+5.3
+Model Implementation
+Since our task involves text generation and understanding,
+we have two kinds of baselines, the NLG model for transla-
+tion and the NLU model for the other tasks.
+5.3.1
+NLG Model
+Our baseline for NLG is encoder-decoder Transformer [32].
+We use six layers for the encoder and the decoder. The
+number of dimensions of all input and output layers is set to
+512 and 1024 for base and big models. For MMT experiments
+7. In some cases when there is no paired image retrieved, we use
+the first-row all-zero vectors of the image lookup table as the “blank
+features”.
+
+7
+TABLE 1
+Results for the NMT tasks. “++/+” after the BLEU score indicates that the proposed method (base: 5-8; large:9-12) was significantly better than the
+corresponding baseline Transformer (base or big) at significance level p <0.01/0.05.
+#
+Model
+En→Ro
+En→De
+En→Fr
+BLEU
+#Param
+BLEU
+#Param
+BLEU
+#Param
+Text-only Transformer
+1
+Transformer-Base
+32.66
+61.54M
+27.31
+63.44M
+38.52
+63.83M
+2
+Transformer-Big
+33.85
+207.02M
+28.45
+210.88M
+41.10
+211.66M
+Our MMT systems
+3
+UVR-TILTMulti30K
+33.78++
+63.04M
+28.14++
+64.94M
+39.64++
+65.33M
+4
+UVR-TILTCOCO
+34.08++
+63.04M
+27.79+
+64.94M
+39.84++
+65.33M
+5
+UVR-CMRMMulti30K
+34.38++
+63.04M
+27.82+
+64.94M
+39.76++
+65.33M
+6
+UVR-CMRMCOCO
+34.40++
+63.04M
+27.86+
+64.94M
+40.24++
+65.33M
+7
+UVR-TILTMulti30K
+34.46+
+211.02M
+29.14++
+214.89M
+41.83+
+215.66M
+8
+UVR-TILTCOCO
+34.51+
+211.02M
+29.18++
+214.89M
+41.76+
+215.66M
+9
+UVR-CMRMMulti30K
+34.60++
+211.02M
+28.96+
+64.94M
+41.79+
+215.66M
+10
+UVR-CMRMCOCO
+34.62++
+211.02M
+29.21++
+64.94M
+41.82+
+215.66M
+TABLE 2
+Results (BLEU) from the test2016 and test2017 for the MMT task. “++/+” after the BLEU score indicates that the proposed method (base: 5-8;
+large: 9-12) was significantly better than the corresponding baseline Transformer (base or big) at significance level p <0.01/0.05.
+#
+Model
+En-De
+En-Fr
+Test2016
+Test2017
+#Param
+Test2016
+Test2017
+#Param
+Text-only Transformer
+1
+Transformer-Base
+35.59
+26.31
+49.15M
+57.88
+48.55
+49.07M
+2
+Transformer-Big
+36.86
+27.62
+186.38M
+56.97
+48.17
+186.23M
+Standard MMT systems
+3
+MMT-Base
+35.09
+27.10
+50.72M
+57.40
+48.02
+50.65M
+4
+MMT-Big
+35.60
+28.02
+190.58M
+57.87
+49.63
+190.43M
+Our MMT systems
+5
+UVR-TILTMulti30K
+35.72
+26.87+
+50.72M
+58.32+
+48.69
+50.65M
+6
+UVR-TILTCOCO
+35.67
+26.89+
+50.72M
+58.21+
+48.73
+50.65M
+7
+UVR-CMRMMulti30K
+36.38+
+27.34++
+50.72M
+58.53+
+49.28+
+50.65M
+8
+UVR-CMRMCOCO
+35.78
+26.92+
+50.72M
+58.46+
+48.58
+50.65M
+9
+UVR-TILTMulti30K
+37.02
+28.63++
+190.58M
+57.53+
+48.46
+190.43M
+10
+UVR-TILTCOCO
+36.94
+28.69++
+190.58M
+57.62+
+48.39
+190.43M
+11
+UVR-CMRMMulti30K
+37.16
+28.82++
+190.58M
+58.37++
+48.77+
+190.43M
+12
+UVR-CMRMCOCO
+37.28+
+28.71++
+190.58M
+57.60+
+48.42
+190.43M
+on the Multi30K dataset, we also use the tiny setting where
+the dimension of the input and output layer is 128. The inner
+feed-forward neural network layer is set to 2048. The heads
+of all multi-head modules are set to eight in both the encoder
+and decoder layers. For the Multi30K dataset, we further
+evaluate a multimodal baseline (denoted as MMT) where
+each source sentence was paired with an original image.
+The other settings were the same as our proposed model.
+The byte pair encoding algorithm is adopted to segment
+sentences into subword sequences, with the vocabulary size
+set to 40,000. In each training batch, a set of sentence pairs
+contains approximately 4096×4 source tokens and 4096×4
+target tokens. During training, the value of label smoothing
+is set to 0.1, and the attention dropout and residual dropout
+rates are p = 0.1. We used Adam optimizer [74] to tune the
+parameters of the model. The learning rate is varied under
+a warm-up strategy with 8,000 steps. For evaluation, we
+validate the model with an interval of 1,000 batches on the
+validation set. For the Multi30K dataset, we train the model
+up to 10,000 steps, and the training will be early-stopped
+if the validation set BLEU score does not improve for ten
+epochs. For the En-De, En-Ro, and En-Fr tasks, following
+the training of 200,000 batches, the model with the highest
+BLEU score of the validation set is selected to evaluate
+the test sets. During the decoding, the beam size is set to
+five. Multi-bleu.perl is used to compute case-sensitive 4-
+gram BLEU scores for all test sets.8 We follow the model
+configurations of [32] to train big models for WMT En-Ro,
+En-De, and En-Fr translation tasks. The experiments of NLG
+are conducted with fairseq [75].9
+For the statistical tests, we perform the paired bootstrap
+resampling test [76] to measure the reliability of the con-
+clusion that our system is better than the baseline. Our im-
+8. https://github.com/moses-smt/mosesdecoder/tree/
+RELEASE-4.0/scripts/generic/multi-bleu.perl.
+9. https://github.com/pytorch/fairseq.
+
+8
+TABLE 3
+Comparison with public methods on the Multi30K MMT dataset. The results of existing methods are from [68]. “++/+” after the BLEU score
+indicates that the proposed method was significantly better than the corresponding baseline Transformer (tiny) at significance level p <0.01/0.05.
+#
+Model
+En-De
+En-Fr
+Test2016
+Test2017
+#Param
+Test2016
+Test2017
+#Param
+Text-only Transformer
+1
+Transformer-Tiny
+40.38
+32.86
+2.6M
+61.00
+52.42
+2.6M
+Existing MMT systems
+2
+GMNMT [69]
+39.8
+32.2
+4.0M
+60.9
+53.9
+-
+3
+DCCN [70]
+39.7
+31.0
+17.1M
+61.2
+54.3
+16.9M
+Our MMT systems
+4
+UVR-TILTTiny
+41.27++
+33.62++
+2.9M
+61.60+
+54.83++
+2.9M
+5
+UVR-CMRMTiny
+40.94+
+33.11+
+2.9M
+61.50+
+53.64++
+2.9M
+TABLE 4
+Test results on the GLUE benchmark. The best results are marked in boldface.
+#
+Model
+Classification
+Semantic Similarity
+Language Inference
+Average
+CoLA
+SST-2
+MRPC
+STS-B
+QQP
+MNLI
+QNLI
+RTE
+SNLI
+Public Systems
+1
+BERT [5]
+60.5
+94.9
+85.4
+87.6
+89.3
+86.7
+92.7
+70.1
+-
+83.4
+2
+MT-DNN [71]
+62.5
+95.6
+88.2
+89.5
+89.6
+86.7
+93.1
+81.4
+91.6
+86.4
+3
+BERT + Voken-cls [72]
+-
+92.2
+-
+-
+88.6
+82.6
+88.6
+-
+-
+-
+4
+UniT [73]
+-
+91.5
+-
+-
+88.4
+79.8
+88.0
+-
+-
+-
+-
+Our Systems
+5
+Baseline (BERTWWM)
+63.6
+93.6
+87.0
+90.2
+88.8
+87.2
+93.9
+77.3
+91.6
+85.9
+6
+UVR-TILTMulti30K
+62.5
+94.7
+87.7
+89.8
+89.4
+87.2
+94.1
+84.5
+91.7
+86.8
+7
+UVR-TILTCOCO
+62.8
+94.9
+87.4
+90.2
+89.7
+86.9
+94.0
+83.6
+91.7
+86.8
+8
+UVR-CMRMMulti30K
+63.0
+94.3
+87.8
+90.2
+89.6
+87.3
+93.8
+83.8
+91.6
+86.8
+9
+UVR-CMRMCOCO
+63.2
+94.6
+87.9
+90.3
+89.8
+87.4
+94.2
+83.9
+91.7
+87.0
+plementation is based on the public toolkit.10 Two thousand
+bootstrap samples are used for each significance test.
+5.3.2
+NLU Model
+For the NLU tasks, the baseline is encoder-only BERT [5].11
+We use the whole-word-mask (WWM) version of the pre-
+trained weights due to its more stable, reproducible, and
+slightly better performance than the original large version
+[5]. The initial learning rate is set in the range {2e-5, 3e-5}
+with a warm-up rate of 0.1 and L2 weight decay of 0.01.
+The batch size is selected from {16, 24, 32}. The maximum
+number of epochs is set in the range [2, 5]. Texts are
+tokenized using SentencePiece,12 with a maximum length
+of 128.
+5.4
+Main Results
+Tables 1-4 show the results for the 14 NMT, MMT, and NLU
+tasks, respectively. According to the results, we have the
+following observations:
+(i) According to the machine translation results in Tables
+1-2, the proposed UVR methods significantly outperform
+the baselines according to the statistical test, demonstrating
+10. https://github.com/neubig/util-scripts/blob/master/
+paired-bootstrap.py
+11. https://github.com/huggingface/transformers.
+12. https://github.com/google/sentencepiece.
+the effectiveness of modeling visual information for text-
+only NMT. In particular, the superiority is observed in
+the translation tasks of three language pairs with different
+training data scales, verifying that the proposed approach is
+a universal method for improving translation performance.
+(ii) Our method introduces only 1.5M and 4.0M param-
+eters for the base and big Transformers, respectively. The
+number is less than 3% of the baseline parameters as we use
+the fixed image embeddings from the pre-trained ResNet
+feature extractor. Besides, the training time is basically the
+same as the baseline model (Section 6.10).
+(iii) Results in Tables 2-3 show that our model can
+generally outperform the Transformer baseline in multi-
+modal settings that could benefit from the gold sentence-
+image annotations. Compared with the results in text-only
+NMT, we find that the image enhancement sometimes gives
+marginal contribution, which is consistent with the findings
+in previous work [77, 78, 79]. The most plausible reason
+might be that the sentences in Multi30K are quite simple,
+short, and repetitive, so that the source text itself is sufficient
+to perform the translation [10, 79]. We also see that the big
+models sometimes show inferior results. The possible reason
+is that the dataset is too small to effectively train such big
+models, which easily suffer from over-fitting issues. The
+hypothesis is also supported by our superior results with
+the tiny model setting in Table 3. The observation verifies
+our assumption of the current bottleneck of MMT due to
+
+9
+0.4
+0.5
+Percentage
+D-value
+Coverage
+CoLA
+SST-2
+MRPC
+STS-B
+QQP
+MNLI
+QNLI
+RTE
+SNLI
+0
+5
+10
+Accuracy
+Fig. 3. Accuracy difference between our method and baseline compared
+with the coverage percentage of tokens that can be paired with images
+in each dataset.
+TABLE 5
+Validation results on GLUE datasets in different sizes: small datasets
+with less than 10k examples (RTE and STS-B), and a large dataset
+with more than 10k examples (QNLI). The MT-DNN results are
+reproduced using the released weights [71].
+Model
+RTE
+STS-B
+QNLI
+MT-DNNbase
+78.94±0.83
+88.14±0.40
+90.32±0.12
+w/ UVR-TILT
+81.59±0.63
+90.16±0.07
+91.31±0.19
+MT-DNNlarge
+78.70±1.65
+90.16±0.17
+92.04±0.27
+w/ UVR-TILT
+82.19±1.37
+91.32±0.12
+92.78±0.12
+the limitation of Multi30K and shows the necessity of our
+new methodology of transferring multimodality into more
+standard and mature text-only NMT tasks.
+(iv) Table 4 shows our method is generally helpful for a
+wide range of NLU tasks in the GLUE benchmark, which
+verifies the effectiveness of modeling visual information
+for language understanding. We are interested in whether
+public methods, such as MT-DNN, can be further enhanced
+by our method, we apply our UVR-TILT method to the MT-
+DNN model based on the same implementation in BERT.
+According to the results in Table 5, both the base and
+large models are enhanced, and we observe consistent gains
+in different datasets, especially the small datasets. For the
+results in Tables 4-5, we notice a few inferior or marginally
+better performances in the CoLA, MNLI, and QNLI tasks.
+We calculate the accuracy difference (D-value) between our
+method and baseline compared with the coverage percent-
+age of tokens that can be paired with images in each dataset
+using UVR-TILTMulti30K. From Figure 3, we see that those
+datasets are commonly paired with a relatively small num-
+ber of images so that the visual signals can enhance only a
+small proportion of token representations. In addition, some
+datasets, i.e., ColA, mainly require linguistic knowledge for
+solving the tasks, so introducing visual modality might not
+benefit such tasks, which corresponds to the common short-
+coming of vision injection for language tasks. For MNLI and
+QNLI, the possible reason for the marginal improvements
+would be that both of the datasets are quite large. Still, the
+task is relatively simple, so the model might well solve the
+tasks directly via the text representations. In this scenario,
+the visual features might only provide the regularization
+effect to improve the model robustness [80, 81, 82].
+0
+5
+10
+15
+20
+epoch
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+0.7
+0.8
+value
+Fig. 4. Illustration of the gate values λ with the UVR-TILT method on
+Multi30K En-De Test2016.
+(v) For the two retrieval methods, we observe that UVR-
+CMRM is slightly better than UVR-TILT in general, and
+the results of the two methods are pretty close for the
+MMT task. We find a performance tradeoff between them:
+there might be more accurate similarity calculation after
+cross-modal pre-training than the direct topic extraction.
+However, controlling the proper similarity threshold would
+be a heuristic for each dataset. In contrast, the advantage of
+UVR-TILT is the simple preprocessing, which only requires
+TF-IDF-based topic extraction and matching.
+(vi) We also compare the results using different seed cor-
+pora, i.e., Multi30K and COCO. For the MMT task in Table
+2, using Multi30k is basically similar to or slightly better
+than COCO in general, as the task could enjoy the images
+in the same domain. For the out-of-domain evaluations in
+Table 1 and Table 4, we obverse that using COCO generally
+achieves better results because the size of COCO images
+is three times that of Multi30K, which could provide more
+diverse image features.
+6
+ANALYSIS
+This section presents our exploration on the role of visual
+contexts, which involves two aspects, when the visual con-
+text helps and how the visual context helps language repre-
+sentations. In the following analysis part, we use Multi30K
+for UVR-TILT and COCO for UVR-CMRM by default.
+6.1
+Dynamics of the visual information
+To explore the role of visual context in the training process,
+we illustrate the gate values λ (defined in Eq. 5) in Figure
+4 where a larger value indicates more dependence on the
+visual context in the fusion process. We observe that the
+model relies on the visual context in the early stages, and
+the role of visual information changes dynamically across
+training. When the training starts, the model accommodates
+the visual information to a large extent (λ ≥ 0.6), indicating
+that the model tends to trust the visual context, which could
+provide useful information in the early stages. With more
+knowledge captured as the training continues, the contribu-
+tions of the visual contexts appeal to decay. In the following
+parts, we will further discuss the specific effectiveness of
+visual representations in language modeling.
+
+10
+A girl in a purple tutu dances in the yard.
+A little girl is walking over a path of numbers.
+A girl jumping rope on a sidewalk near a parking garage.
+A young girl washes an automobile.
+Fig. 5. Examples of sentences that share the same retrieved images, in which the common topic is about “girl”. Sentences with similar topics tend to
+be paired with similar or even the same images, and vice versa. This means that images may provide topic information, which benefits the modeling
+of similar sentences.
+6.2
+Pairwise relationship across modalities
+The benefits of the universal representation method could
+be two folds: (i) the content connection of the sentences and
+images; (ii) the topic-aware co-occurrence of similar images
+and sentences. According to Distributional Hypothesis [83],
+which states that words that occur in similar contexts tend to
+have similar meanings, we are inspired to extend the concept
+in the multimodal world, the sentences with similar meanings
+would be likely to pair with similar even the same images. There-
+fore, the consistent images (with a related topic) could play
+the role of topic or type hints for similar sentence modeling.
+After using our image retrieval method, sentences with
+similar topics tend to be paired with similar or even the
+same images, and vice versa. Figure 5 shows examples in
+which the common topic is about “girl”. This means that
+images may provide topic information, which benefits the
+modeling of similar sentences. Thus, aside from the image
+embeddings’ inner meaning (vectors), there is a mapping
+relationship between the sentence and images after the
+retrieval process.
+For the image embeddings, as described in Section 3.1.2,
+we adopt the embedding lookup to fetch the embedding
+features for each image, which is very similar to the way of
+using word embedding by treating each image as a “word”.
+The weights of the embedding features are derived from
+the average pooled output of ResNet, where each image is
+represented as a 2400-d vector. For all the 29,000 images
+(e.g., using Multi30K), we have an embedding layer with
+size (29000, 2400). The “content” of the image can be seen
+as embedding initialization. The pre-initialized embedding
+weights might yield slight improvement gains. However,
+the neural network can also be effectively trained with
+random initialization [84, 85]. In contrast, whether to use
+the embedded feature is more critical. In other words, the
+mapping relationship of the sentences and images in image
+embedding would be essential, i.e., similar sentences (with
+the same topic words) tend to map the same or similar
+image after the word-image lookup process.
+To verify the hypotheses, we conduct the following
+ablations: we replace the ResNet50 feature extractor in our
+UVR-TILT model with (1) ResNet101 and (2) ResNet152;
+additionally, we compare the results with the following
+operations: (3) Shuffle: shuffle the image features but retain
+TABLE 6
+Ablation for the image embedding operation on En-Ro. The scores are
+reported by means and standard deviations for three random seeds.
+Method
+BLEU Score
+Baseline
+32.75±0.10
+UVR-TILT
+33.72±0.08
+w/ (1) Res101
+33.65±0.06
+w/ (2) Res152
+33.82±0.07
+w/ (3) Shuffle
+33.40±0.14
+w/ (4) Random Init
+33.08±0.17
+w/ (5) Random Mapping
+32.05±0.14
+the lookup table; (4) Random Init: randomly initialize the
+image embedding but keep the lookup table; (5) Random
+Mapping: randomly retrieve unrelated images.
+Table 6 shows the ablation results. The BLEU scores
+of models 1-4 are close to the proposed UVR method,
+and those ablated methods still outperform the baseline,
+indicating that using image features generally yields better
+performance than the baseline. In addition, either replacing
+the trained image features (model 4) or disturbing the
+mapping information (model 5) leads to a performance
+drop (↓0.64/↓1.67, respectively), which indicates that both
+the image features and mapping information are contribut-
+ing factors. Compared with image features, the mapping
+information has a larger impact, which verifies our prior
+hypothesis that the consistent images with a related topic
+could play the role of topic or type hints for similar sentence
+modeling in the whole training process. With the mapping
+information, the same images will be assigned to the same
+context. During training, the image features will be learned
+just like word embeddings. Therefore, it does not mean that
+the image features are not very helpful, but the mapping
+information in the lookup table reduces the dependence on
+the trained image features.
+From the view of an individual image, image content
+(embedding) has an effect. If we maintain the pairwise
+relationship between the sentence and image, the result is
+still higher than the baseline, even with shuffled or random
+image embeddings. This indicates that the pairwise rela-
+tionship is a vital contributor. From the macro perspective
+of sentence-image co-occurrence, image information plays
+the role of topic information, where similar sentences tend
+
+11
+a) baseline method without visual features
+b) our method with visual features
+Fig. 6. Visualization of (a) attention weights of the input tokens with regards to the probed token “lock” across different layers (Y-axis) using the
+BERT baseline; (b) image-to-word attention from our model. The illustration shows that the images provide fine-grained grounding information about
+the relationship between concepts and events, e.g., “lock”, “door”, “fancy”, “hotel”.
+TABLE 7
+Results of MMT with incomplete source texts by removing visually
+grounded tokens in the Multi30K dataset. The scores are reported by
+means and standard deviations for three random seeds.
+Model
+En-De
+En-Fr
+Test2016
+Test2017
+Test2016
+Test2017
+Baseline
+10.94±0.21
+7.75±0.24
+18.61±0.16
+15.01±0.15
+UVR-TILT
+12.80±0.18
+9.15±0.19
+19.60±0.17
+15.77±0.20
+to pair with similar images. The observation corresponds
+to the distributional hypothesis. This explains the potential
+effects of the pairwise relationship.
+This finding may potentially facilitate future research
+because most existing studies focus on the content of the
+individual image itself. We highlight the pairwise relation-
+ship across modalities as a different research line to bridge
+the gap between language and image modeling.
+6.3
+Handling incomplete source texts
+Content words are naturally related to specific content, such
+as car, room, play. We collect a list of tokens that have
+more than ten occurrences in the Multi30K training set
+after removing all stop words following [72]. We remove
+those tokens in the source sentence, which occupy 42.87%
+of tokens in the token dictionary. Table 7 shows the results
+of the baseline model and our model with the incomplete
+source texts. We observe that our model achieves noticeable
+gains over the baseline. The results verify that the visual
+representation can reduce the gap of the missing informa-
+tion from the content words in the source texts.
+6.4
+Knowledge grounding with the visual context
+To gain an insight into the process of multimodal integra-
+tion by our model, we analyze the attention distributions
+(α in Eq.3) at the multimodal integration layer. Figure 6
+shows the attention distributions of (a) the baseline and
+(b) our model 13 for an example randomly selected from
+13. Our model is the UVR-TILT trained on the CoLA dataset.
+TABLE 8
+Results (BLEU score) of the multimodal disambiguation experiments
+on WAT’19 English to Hindi dataset. The scores are reported by means
+and standard deviations for three random seeds.
+Model
+Validation
+Test
+Challenge
+Baseline
+47.04±0.27
+39.33±0.24
+20.52±0.14
+UVR-CMRM
+47.49±0.06
+39.81±0.12
+21.62±0.08
+our GLUE validation sets, “You should always lock your door,
+no matter how fancy the hotel might be.” For comparison,
+the baseline is implemented following Abnar and Zuidema
+[86]. Concretely, we collect the attention weights of all the
+input tokens with regards to a targeted token “lock” across
+different layers (i.e., {2, 4, . . . , 24}). As the baseline uses the
+representation of the last layer for prediction, we focus on
+the attention distributions of the last layer.
+Compared with the baseline that only captures partial
+relations in the last layer, e.g., with a lack of relationship
+among {“lock”, “door”, “hotel”}, our model provides more
+fine-grained connections. In detail, two generic patterns are
+observed in these examples.
+(i) the images appear to match the concepts and actions
+with the texts, in other words, the images tend to provide
+fine-grained grounding information about the relationship
+between concepts and events, e.g., {”lock”, ”door”, ”fancy”,
+”hotel”}.
+(ii) our model can resist irrelevant information from
+noisy images. For example, the second and third images
+yield low attention scores for the texts.
+6.5
+Disambiguation
+A natural intuition of using visual clues for text represen-
+tation is the advantage of alleviating the ambiguation of
+language. To evaluate the model performance for disam-
+biguation, we use a dataset from the HVG [88], which serves
+as a part of the WAT’19 Multimodal Translation Task.14 The
+dataset consists of a total of 31525 randomly selected images
+14. http://lotus.kuee.kyoto-u.ac.jp/WAT/WAT2019/index.html
+
+1.0
+always
+lock
+0.8
+Joop
+0.6
+0.4
+how
+fancy
+ 0.2
+might
+be
+0.0Toilet
+f1忆
+2
+0.175
+0.150
+8
+0.125
+4
+0.100
+2
+0
+0.075
+8
+0.050
+9
+4
+0.025
+2
+2
+matt12
+a) baseline method without visual features
+b) our method with visual features
+Fig. 7. Visualization of (a) attention weights of the input tokens with regards to the ambiguous token “apple” across different layers (Y-axis) using the
+BERT baseline; b) image-to-word attention from our model. The illustration shows that the images bridge the connection between “apple”, “watch”,
+“time”, helping disambiguate the meaning of “apple”.
+TABLE 9
+Selected eight probing tasks [87] to study what syntactic and semantic properties are captured by the encoders.
+Probing Tasks
+Content
+Syntactic
+TrDep
+Checking whether an encoder infers the hierarchical structure of sentence
+ToCo
+Sentences should be classified in terms of the sequence of top constituents immediately below the
+sentence node
+BShif
+Testing whether two consecutive tokens within the sentence have been inverted
+Semantic
+Tense
+Asking for the tense of the main clause verb
+SubN
+Focusing on the number of the main clause’s subject
+ObjN
+Testing for the number of the direct object of the main clause
+SoMo
+Some sentences are modified by replacing a random noun or verb with another one and the classifier
+should tell whether a sentence has been modified
+CoIn
+Containing sentences made of two coordinate clauses
+TABLE 10
+Classification accuracy on eight probing tasks of evaluating linguistics embedded in the encoder outputs.
+Model
+Syntactic
+Semantic
+TrDep
+ToCo
+BShif
+Tense
+SubN
+ObjN
+SoMo
+CoIn
+Baseline
+28.34
+58.33
+76.34
+80.66
+72.02
+68.57
+64.42
+67.51
+UVR-CMRM
+28.53
+58.64
+77.72
+80.97
+73.79
+69.66
+65.44
+67.23
+from Visual Genome [89] and a parallel image caption
+corpus in English-Hindi for selected image segments. The
+training part consists of 29K English and Hindi short cap-
+tions of rectangular areas in photos of various scenes, and
+it is complemented by three evaluation subsets: validation,
+test, and challenge test set (Challenge). The challenge test set
+is created by searching for (particularly) ambiguous English
+words based on the embedding similarity and manually
+selecting those where the image helps to resolve the am-
+biguity. We do not use the images but follow the same
+settings as the experiments on Multi30K. As the results
+shown in Table 8, we observe that our UVR model works
+effectively on the challenge disambiguation set, indicating
+that the visual information induced by retrieved images
+allows disambiguation of translation.
+Figure 7 shows a heatmap of the attention visualization
+on an ambiguous sentence, “apple watch keeps telling me
+the time”. In Figure 7(a), the baseline model fails to capture
+the relationship between “apple” with “time”. In Figure
+7(b), the retrieved images bridge the connection among
+“apple”, “watch” and “time”, which helps disambiguate the
+meaning of “apple”.
+6.6
+Linguistic Analysis
+We are interested in what knowledge is learned in the
+universal representations. In this section, we select eight
+widely-used language probing tasks [87] (see Table 9) to
+study what kind of syntactic and semantic properties are
+captured by the encoders. Specifically, we use the encoders
+of the baseline BERT-based SNLI model,15 and our UVR-
+CMRM visual representation model to generate the sentence
+representations of input, which are used to carry out the
+above eight probing tasks. The results are as shown in Table
+10.
+15. We select the SNLI model because NLI models show good
+generalization capacity for language representation [90, 91], which is
+supposed to be a strong test-bed for the evaluation.
+
+1.0
+apple
+watch
+ 0.8
+0.6
+telling
+0.4
+the
+ 0.2
+time
+0.0AppleWatchEdition
+WATCHEDITIONWATCHWATCH7AppStore&iTunes忆
+0.25
+2
+0.20
+4
+ 0.15
+2
+0
+ 0.10
+8
+6
+0.05
+4
+2
+me
+the
+telling13
+0
+1
+3
+5
+7
+9
+15 20 30
+33
+33.5
+Number of images per sentence
+BLEU
+Fig. 8. Influence of the number of images on the BLEU score.
+TABLE 11
+Experiments on different source languages using the Multi30K dataset.
+The baseline is Transformer-Tiny.
+Model
+De-En
+Fr-En
+Test2016
+Test2017
+Test2016
+Test2017
+Baseline
+42.88
+40.57
+54.60
+48.45
+UVR-TILT
+43.10
+40.07
+54.92
+49.10
+Concerning semantic properties, our model gains the
+most significant improvement on the SubN and ObjN tasks.
+The result indicates that visual information helps NMT to
+identify and represent the subject and object information,
+which is consistent with our hypotheses.
+6.7
+Effectiveness across languages
+Table 11 shows the experiment results on different source
+languages. We observe that our method is applicable when
+the source texts are in other languages such as German
+and French. Our proposed methods are supposed to be
+independent of languages because the calculation for image
+retrieval only relies on the light lookup table, which can be
+extracted from an off-the-shelf seed corpus that is available
+for many languages.
+6.8
+Joint Training and Fine-tuning
+Since the multimodal and text-only machine translation
+tasks can benefit from the visual modality after retrieving
+images from the seed corpus, it is possible to bridge both
+tasks to train an even more powerful model. The connec-
+tions between the texts and images inside the Multi30K
+datasets could be strong indications to bridge the gap be-
+tween text and image modalities.
+Therefore, we train a unified model based on UVR-
+CMRM by using the joint En-De datasets of Multi30K and
+WMT’14 (Joint Model), and respectively train the Multi30K
+(Fine-tuned Multi30K) and WMT’14 (Fine-tuned WMT) mod-
+els by initializing the trainable model parameters using the
+joint model. According to the results shown in Table 12, we
+summarize the following observations:
+(i) Two-stage training (joint training and fine-tuning) can
+boost the performance on the two concerned datasets, which
+indicates that the highly relevant Multi30K dataset can play
+the role of the seed data for training a text-only NMT model
+using our topic-image lookup table.
+0
+50
+100
+Percentage
+BLEU
+Data Size
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+0.6
+33.5
+34
+34.5
+35
+Percentage
+BLEU
+Fig. 9. BLEU score for different similarity thresholds.
+TABLE 12
+Results of joint training and fine-tuning.
+Model
+Multi30K Task
+WMT Task
+Joint training baseline
+37.28
+27.68
++ Fine-tuned Multi30K
+-
+27.96
++ Fine-tuned WMT
+43.13
+-
+(ii) The major gain is achieved by fine-tuning the smaller
+dataset, showing that the large-scale text-only dataset with
+our lookup table can also provide valuable complementary
+information for training a multimodal model on a much
+smaller dataset. The result further verifies the effectiveness
+of our method in low-resource settings.
+6.9
+Parameter Sensitivity Analysis
+In this section, we analyze our model sensitivity against
+parameter settings, including similarity threshold, number
+of images, and gating weight.
+Influence of the similarity threshold. We investigate the
+influence of the similarity threshold δ that is set to filter the
+top-ranked images for each sentence in UVR-CMRM. Figure
+9 shows the performance for thresholds in [0.0, 0.1, 0.2, 0.3,
+0.4, 0.5, 0.6] on the En-Ro test set. We observe that setting
+the threshold around 0.4 can yield a good balance of data
+size and BLEU score. It is reasonable that the best thresholds
+vary for different datasets because of the domain divergence
+of the image corpus for pre-training.
+Influence of the number of images. To evaluate the
+influence of the number of paired images m for UVR-TILT,
+we constrain m in {0, 1, 3, 5, 7, 9, 15, 20, 30} for experiments
+on the En-Ro test set, as shown in Figure 8. When m = 0,
+the model is the baseline NMT model, whose BLEU score
+is lower than all the models with images. As the number
+of images increases, the BLEU score also increases at the
+beginning (from 32.66 to 33.78) and then slightly decreases
+when m exceeds 5. The reason might be that too many
+images for a sentence would have a higher chance of noise.
+Therefore, we set m = 5 in our models.
+Influence of gating weight λ. In our model, the weight
+λ of the gated aggregation method is learned automatically
+to measure the importance of the visual information. We
+compare by manually setting the weight λ to scalar values
+in {0.1, 0.3, 0.5, 0.7, 0.9} for experiments of UVR-TILT on the
+En-Ro test set. Figure 10 shows that all models with manual
+
+14
+0.1
+0.3
+0.5
+0.7
+0.9
+33
+33.5
+Weight λ
+BLEU
+Manual weight
+Transformer-Base
+Ours
+Fig. 10. Quantitative study of the gating weight λ.
+λ outperform the baseline Transformer-base, indicating the
+effectiveness of image information. In contrast, they are in-
+ferior to the performance of our model. This means that the
+degree of dependency for image information varies for each
+source sentence, indicating the necessity of automatically
+learning the gating weights of image representations.
+6.10
+Computation Efficiency
+There are mainly two extra computation costs using our
+method, including (i) obtaining image data for sentences
+and (ii) learning image representations, which are negligible
+compared with training an NMT model. The time of retriev-
+ing image data for MT sentences for the En-Ro dataset is
+less than 1 minute using GPU. The lookup table is formed
+as the mapping of the token (only topic words) index to
+the image id. Then, the retrieval method is applied as the
+tensor indexing from the sentence token indices (only topic
+words) to image ids, which is the same as the procedure of
+word embedding. The retrieved image ids are then sorted
+by frequency. Learning image representations takes about
+2 minutes for all the 29,000 images in Multi30K using 6G
+GPU memory for feature extraction and eight CPU threads
+for transforming images. The extracted features are formed
+as the “image embedding layer” in the size of (29000, 2400)
+for quick access in the neural network.
+7
+CONCLUSIONS
+This work investigates a flexible framework to incorporate
+visual information into sentence modeling by image re-
+trieval from a light lookup table and learned cross-modal
+embedding space. Extensive empirical experiments on 14
+benchmark datasets verify the effectiveness of the proposed
+method. A series of case studies are conducted to evaluate
+visual benefits and influence factors. Our method is general
+and can be easily implemented in existing deep-learning
+NLP systems for different languages. Through the proposed
+retrieval methods, we can provide a group of images that
+disclose a diversity of implicit topics that might be entailed
+in sentences, yielding better context grounding with fine-
+grained information. We show that our method enriches
+the representation of content words, provide fine-grained
+grounding information about the relationship between con-
+cepts and events, and potentially enhances the accuracy
+of disambiguation. Besides incorporating images to build
+the pairwise relationship across modalities, it is potential
+to incorporate various extra knowledge as alignment topic
+information in the future, such as audio, not only images.
+ACKNOWLEDGEMENT
+Part of this study has been published as “Neural Machine
+Translation with Universal Visual Representation” [37] in
+the Eighth International Conference on Learning Represen-
+tations (ICLR 2020). The extension includes three sides: (i)
+general tasks: this work studies the universal visual rep-
+resentation for language representation in a broader view
+of the natural language processing scenario, with experi-
+ments on 14 representative NLP tasks; (ii) new method: this
+work investigates new methods of semantic sentence-image
+matching from a shared cross-modal space, to give more
+accurately paired images as topic information; (iii) in-depth
+analysis to interpret the benefits from the visual modality.
+REFERENCES
+[1]
+T. Mikolov, I. Sutskever, K. Chen, G. S. Corrado, and
+J. Dean, “Distributed representations of words and
+phrases and their compositionality,” in Advances in
+Neural Information Processing Systems 26: 27th Annual
+Conference on Neural Information Processing Systems 2013.
+Proceedings of a meeting held December 5-8, 2013, Lake
+Tahoe, Nevada, United States, 2013, pp. 3111–3119.
+[2]
+J. Pennington, R. Socher, and C. Manning, “GloVe:
+Global vectors for word representation,” in Proceedings
+of the 2014 Conference on Empirical Methods in Natural
+Language Processing (EMNLP), 2014, pp. 1532–1543.
+[3]
+M. E. Peters, M. Neumann, M. Iyyer, M. Gardner,
+C. Clark, K. Lee, and L. Zettlemoyer, “Deep contextu-
+alized word representations,” in Proceedings of the 2018
+Conference of the North American Chapter of the Association
+for Computational Linguistics: Human Language Technolo-
+gies, Volume 1 (Long Papers), 2018, pp. 2227–2237.
+[4]
+A.
+Radford,
+K.
+Narasimhan,
+T.
+Salimans,
+and
+I. Sutskever, “Improving language understanding by
+generative pre-training,” Technical report, 2018.
+[5]
+J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova,
+“BERT: Pre-training of deep bidirectional transformers
+for language understanding,” in Proceedings of the 2019
+Conference of the North American Chapter of the Association
+for Computational Linguistics: Human Language Technolo-
+gies, Volume 1 (Long and Short Papers), 2019, pp. 4171–
+4186.
+[6]
+Z. Yang, Z. Dai, Y. Yang, J. G. Carbonell, R. Salakhut-
+dinov, and Q. V. Le, “Xlnet: Generalized autoregres-
+sive pretraining for language understanding,” in Ad-
+vances in Neural Information Processing Systems 32: An-
+nual Conference on Neural Information Processing Systems
+2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC,
+Canada, 2019, pp. 5754–5764.
+[7]
+K. Zhang, G. Lv, L. Wu, E. Chen, Q. Liu, H. Wu, and
+F. Wu, “Image-enhanced multi-level sentence represen-
+tation net for natural language inference,” in 2018 IEEE
+International Conference on Data Mining (ICDM).
+IEEE,
+2018, pp. 747–756.
+
+15
+[8]
+M. A. McDaniel and G. O. Einstein, “Bizarre imagery
+as an effective memory aid: The importance of distinc-
+tiveness.” Journal of experimental psychology: Learning,
+memory, and cognition, vol. 12, no. 1, p. 54, 1986.
+[9]
+D. Meier, The accelerated learning handbook: A creative
+guide to designing and delivering faster, more effective train-
+ing programs, 2000.
+[10] J. Ive, P. Madhyastha, and L. Specia, “Distilling trans-
+lations with visual awareness,” in Proceedings of the
+57th Annual Meeting of the Association for Computational
+Linguistics, 2019, pp. 6525–6538.
+[11] H. Shi, J. Mao, K. Gimpel, and K. Livescu, “Visually
+grounded neural syntax acquisition,” in Proceedings of
+the 57th Annual Meeting of the Association for Computa-
+tional Linguistics, 2019, pp. 1842–1861.
+[12] T. Baltruaitis, C. Ahuja, and L.-P. Morency, “Multi-
+modal machine learning: A survey and taxonomy,”
+IEEE Transactions on Pattern Analysis and Machine In-
+telligence, vol. 41, no. 2, pp. 423–443, 2019.
+[13] R. Hong, D. Liu, X. Mo, X. He, and H. Zhang, “Learning
+to compose and reason with language tree structures
+for visual grounding,” IEEE Transactions on Pattern
+Analysis and Machine Intelligence, vol. 44, no. 2, pp. 684–
+696, 2022.
+[14] B. A. Plummer, K. J. Shih, Y. Li, K. Xu, S. Lazeb-
+nik, S. Sclaroff, and K. Saenko, “Revisiting image-
+language networks for open-ended phrase detection,”
+IEEE Transactions on Pattern Analysis and Machine Intel-
+ligence, vol. 44, no. 4, pp. 2155–2167, 2022.
+[15] W. Su, X. Zhu, Y. Cao, B. Li, L. Lu, F. Wei, and J. Dai,
+“VL-BERT: pre-training of generic visual-linguistic rep-
+resentations,” in 8th International Conference on Learning
+Representations, ICLR 2020, Addis Ababa, Ethiopia, April
+26-30, 2020, 2020.
+[16] J. Lu, D. Batra, D. Parikh, and S. Lee, “Vilbert: Pre-
+training task-agnostic visiolinguistic representations
+for vision-and-language tasks,” in Advances in Neural
+Information Processing Systems 32: Annual Conference
+on Neural Information Processing Systems 2019, NeurIPS
+2019, December 8-14, 2019, Vancouver, BC, Canada, 2019,
+pp. 13–23.
+[17] H. Tan and M. Bansal, “LXMERT: Learning cross-
+modality encoder representations from transformers,”
+in Proceedings of the 2019 Conference on Empirical Methods
+in Natural Language Processing and the 9th International
+Joint Conference on Natural Language Processing (EMNLP-
+IJCNLP), 2019, pp. 5100–5111.
+[18] G. Li, N. Duan, Y. Fang, M. Gong, and D. Jiang,
+“Unicoder-vl: A universal encoder for vision and lan-
+guage by cross-modal pre-training,” in The Thirty-
+Fourth AAAI Conference on Artificial Intelligence, AAAI
+2020, The Thirty-Second Innovative Applications of Artifi-
+cial Intelligence Conference, IAAI 2020, The Tenth AAAI
+Symposium on Educational Advances in Artificial Intelli-
+gence, EAAI 2020, New York, NY, USA, February 7-12,
+2020, 2020, pp. 11 336–11 344.
+[19] L. Zhou, H. Palangi, L. Zhang, H. Hu, J. Corso, and
+J. Gao, “Unified vision-language pre-training for image
+captioning and vqa,” in Proceedings of the AAAI Confer-
+ence on Artificial Intelligence, vol. 34, no. 07, 2020, pp.
+13 041–13 049.
+[20] C. Sun, A. Myers, C. Vondrick, K. Murphy, and
+C. Schmid, “Videobert: A joint model for video and
+language representation learning,” in 2019 IEEE/CVF
+International Conference on Computer Vision, ICCV 2019,
+Seoul, Korea (South), October 27 - November 2, 2019, 2019,
+pp. 7463–7472.
+[21] E. Zablocki, B. Piwowarski, L. Soulier, and P. Gallinari,
+“Learning multi-modal word representation grounded
+in visual context,” in Proceedings of the Thirty-Second
+AAAI Conference on Artificial Intelligence, (AAAI-18), the
+30th innovative Applications of Artificial Intelligence (IAAI-
+18), and the 8th AAAI Symposium on Educational Ad-
+vances in Artificial Intelligence (EAAI-18), New Orleans,
+Louisiana, USA, February 2-7, 2018, 2018, pp. 5626–5633.
+[22] Y. Meng, W. Wu, F. Wang, X. Li, P. Nie, F. Yin, M. Li,
+Q. Han, X. Sun, and J. Li, “Glyce: Glyph-vectors for
+chinese character representations,” in Advances in Neu-
+ral Information Processing Systems 32: Annual Conference
+on Neural Information Processing Systems 2019, NeurIPS
+2019, December 8-14, 2019, Vancouver, BC, Canada, 2019,
+pp. 2742–2753.
+[23] K. Han, Y. Wang, H. Chen, X. Chen, J. Guo, Z. Liu,
+Y. Tang, A. Xiao, C. Xu, Y. Xu, Z. Yang, Y. Zhang,
+and D. Tao, “A survey on vision transformer,” IEEE
+Transactions on Pattern Analysis and Machine Intelligence,
+pp. 1–1, 2022.
+[24] X. Wang, Q. Huang, A. Celikyilmaz, J. Gao, D. Shen,
+Y.-F. Wang, W. Y. Wang, and L. Zhang, “Vision-
+language navigation policy learning and adaptation,”
+IEEE Transactions on Pattern Analysis and Machine Intel-
+ligence, vol. 43, no. 12, pp. 4205–4216, 2021.
+[25] D. Elliott, S. Frank, K. Sima’an, and L. Specia,
+“Multi30K: Multilingual English-German image de-
+scriptions,” in Proceedings of the 5th Workshop on Vision
+and Language, 2016, pp. 70–74.
+[26] X. Li, C. Xu, X. Wang, W. Lan, Z. Jia, G. Yang, and J. Xu,
+“Coco-cn for cross-lingual image tagging, captioning,
+and retrieval,” IEEE Transactions on Multimedia, vol. 21,
+no. 9, pp. 2347–2360, 2019.
+[27] Y. Yoshikawa, Y. Shigeto, and A. Takeuchi, “STAIR cap-
+tions: Constructing a large-scale Japanese image cap-
+tion dataset,” in Proceedings of the 55th Annual Meeting
+of the Association for Computational Linguistics (Volume 2:
+Short Papers), 2017, pp. 417–421.
+[28] T. Miyazaki and N. Shimizu, “Cross-lingual image
+caption generation,” in Proceedings of the 54th Annual
+Meeting of the Association for Computational Linguistics
+(Volume 1: Long Papers), 2016, pp. 1780–1790.
+[29] J. Hewitt, D. Ippolito, B. Callahan, R. Kriz, D. T. Wijaya,
+and C. Callison-Burch, “Learning translations via im-
+ages with a massively multilingual image dataset,” in
+Proceedings of the 56th Annual Meeting of the Association
+for Computational Linguistics (Volume 1: Long Papers),
+2018, pp. 2566–2576.
+[30] D. Bahdanau, K. Cho, and Y. Bengio, “Neural machine
+translation by jointly learning to align and translate,” in
+3rd International Conference on Learning Representations,
+ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Confer-
+ence Track Proceedings, 2015.
+[31] J. Gehring, M. Auli, D. Grangier, and Y. Dauphin,
+“A convolutional encoder model for neural machine
+
+16
+translation,” in Proceedings of the 55th Annual Meeting
+of the Association for Computational Linguistics (Volume 1:
+Long Papers), 2017, pp. 123–135.
+[32] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit,
+L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin,
+“Attention is all you need,” in Advances in Neural
+Information Processing Systems 30: Annual Conference on
+Neural Information Processing Systems 2017, December 4-
+9, 2017, Long Beach, CA, USA, 2017, pp. 5998–6008.
+[33] M. Fadaee, A. Bisazza, and C. Monz, “Data augmen-
+tation for low-resource neural machine translation,” in
+Proceedings of the 55th Annual Meeting of the Association
+for Computational Linguistics (Volume 2: Short Papers),
+2017, pp. 567–573.
+[34] G. Lample, M. Ott, A. Conneau, L. Denoyer, and
+M. Ranzato, “Phrase-based & neural unsupervised ma-
+chine translation,” in Proceedings of the 2018 Conference
+on Empirical Methods in Natural Language Processing,
+2018, pp. 5039–5049.
+[35] X. Ma, C. Zhou, X. Li, G. Neubig, and E. Hovy,
+“FlowSeq: Non-autoregressive conditional sequence
+generation with generative flow,” in Proceedings of the
+2019 Conference on Empirical Methods in Natural Lan-
+guage Processing and the 9th International Joint Conference
+on Natural Language Processing (EMNLP-IJCNLP), 2019,
+pp. 4282–4292.
+[36] C. Zhou, X. Ma, J. Hu, and G. Neubig, “Handling syn-
+tactic divergence in low-resource machine translation,”
+in Proceedings of the 2019 Conference on Empirical Methods
+in Natural Language Processing and the 9th International
+Joint Conference on Natural Language Processing (EMNLP-
+IJCNLP), 2019, pp. 1388–1394.
+[37] Z. Zhang, K. Chen, R. Wang, M. Utiyama, E. Sumita,
+Z. Li, and H. Zhao, “Neural machine translation with
+universal visual representation,” in 8th International
+Conference on Learning Representations, ICLR 2020, Addis
+Ababa, Ethiopia, April 26-30, 2020, 2020.
+[38] X. Li, X. Yin, C. Li, P. Zhang, X. Hu, L. Zhang, L. Wang,
+H. Hu, L. Dong, F. Wei et al., “Oscar: Object-semantics
+aligned pre-training for vision-language tasks,” in Eu-
+ropean Conference on Computer Vision.
+Springer, 2020,
+pp. 121–137.
+[39] A. Frome, G. S. Corrado, J. Shlens, S. Bengio, J. Dean,
+M. Ranzato, and T. Mikolov, “Devise: A deep visual-
+semantic embedding model,” in Advances in Neural In-
+formation Processing Systems 26: 27th Annual Conference
+on Neural Information Processing Systems 2013. Proceed-
+ings of a meeting held December 5-8, 2013, Lake Tahoe,
+Nevada, United States, 2013, pp. 2121–2129.
+[40] A. Karpathy and F. Li, “Deep visual-semantic align-
+ments for generating image descriptions,” in IEEE Con-
+ference on Computer Vision and Pattern Recognition, CVPR
+2015, Boston, MA, USA, June 7-12, 2015, 2015, pp. 3128–
+3137.
+[41] Z. Ren, H. Jin, Z. L. Lin, C. Fang, and A. L. Yuille, “Joint
+image-text representation by gaussian visual-semantic
+embedding,” in Proceedings of the 2016 ACM Conference
+on Multimedia Conference, MM 2016, Amsterdam, The
+Netherlands, October 15-19, 2016, 2016, pp. 207–211.
+[42] A. Karpathy and L. Fei-Fei, “Deep visual-semantic
+alignments for generating image descriptions,” IEEE
+Transactions on Pattern Analysis and Machine Intelligence,
+vol. 39, no. 4, pp. 664–676, 2017.
+[43] C. Gao, Q. Zhu, P. Wang, H. Li, Y. Liu, A. Van den
+Hengel, and Q. Wu, “Structured multimodal attentions
+for textvqa,” IEEE Transactions on Pattern Analysis and
+Machine Intelligence, 2021.
+[44] T. Mukherjee and T. Hospedales, “Gaussian visual-
+linguistic embedding for zero-shot recognition,” in Pro-
+ceedings of the 2016 Conference on Empirical Methods in
+Natural Language Processing, 2016, pp. 912–918.
+[45] L. Wang, Y. Li, J. Huang, and S. Lazebnik, “Learning
+two-branch neural networks for image-text matching
+tasks,” IEEE Transactions on Pattern Analysis and Ma-
+chine Intelligence, vol. 41, no. 2, pp. 394–407, 2018.
+[46] M. Engilberge, L. Chevallier, P. P´erez, and M. Cord,
+“Finding beans in burgers: Deep semantic-visual em-
+bedding with localization,” in 2018 IEEE Conference on
+Computer Vision and Pattern Recognition, CVPR 2018, Salt
+Lake City, UT, USA, June 18-22, 2018, 2018, pp. 3984–
+3993.
+[47] H. Hotelling, “Relations between two sets of variates,”
+in Breakthroughs in statistics, 1992, pp. 162–190.
+[48] M. Portaz, H. Randrianarivo, A. Nivaggioli, E. Maudet,
+C. Servan, and S. Peyronnet, “Image search using mul-
+tilingual texts: a cross-modal learning approach be-
+tween image and text maxime portaz qwant research,”
+arXiv preprint arXiv:1903.11299, 2019.
+[49] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual
+learning for image recognition,” in 2016 IEEE Confer-
+ence on Computer Vision and Pattern Recognition, CVPR
+2016, Las Vegas, NV, USA, June 27-30, 2016, 2016, pp.
+770–778.
+[50] Y. Liu, M. Ott, N. Goyal, J. Du, M. Joshi, D. Chen,
+O. Levy, M. Lewis, L. Zettlemoyer, and V. Stoyanov,
+“RoBERTa: A robustly optimized bert pretraining ap-
+proach,” arXiv preprint arXiv:1907.11692, 2019.
+[51] K. Chen, R. Wang, M. Utiyama, E. Sumita, and T. Zhao,
+“Neural machine translation with sentence-level topic
+context,” IEEE/ACM Transactions on Audio, Speech, and
+Language Processing, 2019.
+[52] S. Xie, R. B. Girshick, P. Doll´ar, Z. Tu, and K. He,
+“Aggregated residual transformations for deep neural
+networks,” in 2017 IEEE Conference on Computer Vision
+and Pattern Recognition, CVPR 2017, Honolulu, HI, USA,
+July 21-26, 2017, 2017, pp. 5987–5995.
+[53] T. Durand, N. Thome, and M. Cord, “WELDON:
+weakly supervised learning of deep convolutional neu-
+ral networks,” in 2016 IEEE Conference on Computer
+Vision and Pattern Recognition, CVPR 2016, Las Vegas,
+NV, USA, June 27-30, 2016, 2016, pp. 4743–4752.
+[54] J. Wang, Y. Song, T. Leung, C. Rosenberg, J. Wang,
+J. Philbin, B. Chen, and Y. Wu, “Learning fine-grained
+image similarity with deep ranking,” in 2014 IEEE
+Conference on Computer Vision and Pattern Recognition,
+CVPR 2014, Columbus, OH, USA, June 23-28, 2014, 2014,
+pp. 1386–1393.
+[55] F. Schroff, D. Kalenichenko, and J. Philbin, “Facenet:
+A unified embedding for face recognition and cluster-
+ing,” in IEEE Conference on Computer Vision and Pattern
+Recognition, CVPR 2015, Boston, MA, USA, June 7-12,
+2015, 2015, pp. 815–823.
+
+17
+[56] A. Gordo, J. Almazan, J. Revaud, and D. Larlus, “End-
+to-end learning of deep visual representations for im-
+age retrieval,” International Journal of Computer Vision,
+vol. 124, no. 2, pp. 237–254, 2017.
+[57] A. Wang, A. Singh, J. Michael, F. Hill, O. Levy, and S. R.
+Bowman, “GLUE: A multi-task benchmark and analy-
+sis platform for natural language understanding,” in
+7th International Conference on Learning Representations,
+ICLR 2019, New Orleans, LA, USA, May 6-9, 2019, 2019.
+[58] S. R. Bowman, G. Angeli, C. Potts, and C. D. Manning,
+“A large annotated corpus for learning natural lan-
+guage inference,” in Proceedings of the 2015 Conference on
+Empirical Methods in Natural Language Processing, 2015,
+pp. 632–642.
+[59] N. Nangia, A. Williams, A. Lazaridou, and S. Bowman,
+“The RepEval 2017 shared task: Multi-genre natural
+language inference with sentence representations,” in
+Proceedings of the 2nd Workshop on Evaluating Vector
+Space Representations for NLP, 2017, pp. 1–10.
+[60] P. Rajpurkar, J. Zhang, K. Lopyrev, and P. Liang,
+“SQuAD: 100,000+ questions for machine comprehen-
+sion of text,” in Proceedings of the 2016 Conference on
+Empirical Methods in Natural Language Processing, 2016,
+pp. 2383–2392.
+[61] L. Bentivogli, P. Clark, I. Dagan, and D. Giampiccolo,
+“The fifth pascal recognizing textual entailment chal-
+lenge.” in ACL-PASCAL, 2009.
+[62] W. B. Dolan and C. Brockett, “Automatically construct-
+ing a corpus of sentential paraphrases,” in Proceed-
+ings of the Third International Workshop on Paraphrasing
+(IWP2005), 2005.
+[63] Z. Chen, H. Zhang, X. Zhang, and L. Zhao, “Quora
+question pairs,” 2018.
+[64] D. Cer, M. Diab, E. Agirre, I. Lopez-Gazpio, and L. Spe-
+cia, “SemEval-2017 task 1: Semantic textual similarity
+multilingual and crosslingual focused evaluation,” in
+Proceedings of the 11th International Workshop on Semantic
+Evaluation (SemEval-2017), 2017, pp. 1–14.
+[65] A. Warstadt, A. Singh, and S. R. Bowman, “Neural
+network acceptability judgments,” Transactions of the
+Association for Computational Linguistics, vol. 7, pp. 625–
+641, 2019.
+[66] R. Socher, A. Perelygin, J. Wu, J. Chuang, C. D. Man-
+ning, A. Ng, and C. Potts, “Recursive deep models for
+semantic compositionality over a sentiment treebank,”
+in Proceedings of the 2013 Conference on Empirical Methods
+in Natural Language Processing, 2013, pp. 1631–1642.
+[67] T.-Y. Lin, M. Maire, S. Belongie, J. Hays, P. Perona,
+D. Ramanan, P. Doll´ar, and C. L. Zitnick, “Microsoft
+coco: Common objects in context,” in European confer-
+ence on computer vision.
+Springer, 2014, pp. 740–755.
+[68] Z. Wu, L. Kong, W. Bi, X. Li, and B. Kao, “Good
+for misconceived reasons: An empirical revisiting on
+the need for visual context in multimodal machine
+translation,” in Proceedings of the 59th Annual Meeting
+of the Association for Computational Linguistics and the
+11th International Joint Conference on Natural Language
+Processing (Volume 1: Long Papers), 2021, pp. 6153–6166.
+[69] Y. Yin, F. Meng, J. Su, C. Zhou, Z. Yang, J. Zhou,
+and J. Luo, “A novel graph-based multi-modal fusion
+encoder for neural machine translation,” in Proceedings
+of the 58th Annual Meeting of the Association for Compu-
+tational Linguistics, 2020, pp. 3025–3035.
+[70] H. Lin, F. Meng, J. Su, Y. Yin, Z. Yang, Y. Ge, J. Zhou,
+and J. Luo, “Dynamic context-guided capsule network
+for multimodal machine translation,” in MM ’20: The
+28th ACM International Conference on Multimedia, Virtual
+Event / Seattle, WA, USA, October 12-16, 2020, 2020, pp.
+1320–1329.
+[71] X. Liu, P. He, W. Chen, and J. Gao, “Multi-task deep
+neural networks for natural language understanding,”
+in Proceedings of the 57th Annual Meeting of the Associa-
+tion for Computational Linguistics, 2019, pp. 4487–4496.
+[72] H. Tan and M. Bansal, “Vokenization: Improving
+language understanding via contextualized, visually-
+grounded supervision,” in Proceedings of the 2020 Con-
+ference on Empirical Methods in Natural Language Process-
+ing (EMNLP), 2020, pp. 2066–2080.
+[73] R. Hu and A. Singh, “Unit: Multimodal multitask learn-
+ing with a unified transformer,” in Proceedings of the
+IEEE/CVF International Conference on Computer Vision,
+2021, pp. 1439–1449.
+[74] D. P. Kingma and J. Ba, “Adam: A method for stochastic
+optimization,” in 3rd International Conference on Learn-
+ing Representations, ICLR 2015, San Diego, CA, USA, May
+7-9, 2015, Conference Track Proceedings, 2015.
+[75] M. Ott, S. Edunov, A. Baevski, A. Fan, S. Gross, N. Ng,
+D. Grangier, and M. Auli, “fairseq: A fast, extensible
+toolkit for sequence modeling,” in Proceedings of the
+2019 Conference of the North American Chapter of the As-
+sociation for Computational Linguistics (Demonstrations),
+2019, pp. 48–53.
+[76] P. Koehn, “Statistical significance tests for machine
+translation evaluation,” in Proceedings of the 2004 confer-
+ence on empirical methods in natural language processing,
+2004, pp. 388–395.
+[77] J. Zhang, M. Utiyama, E. Sumita, G. Neubig, and
+S. Nakamura, “NICT-NAIST system for WMT17 mul-
+timodal translation task,” in Proceedings of the Second
+Conference on Machine Translation, 2017, pp. 477–482.
+[78] S.-A. Gr¨onroos, B. Huet, M. Kurimo, J. Laakso-
+nen, B. Merialdo, P. Pham, M. Sj¨oberg, U. Suluba-
+cak, J. Tiedemann, R. Troncy, and R. V´azquez, “The
+MeMAD submission to the WMT18 multimodal trans-
+lation task,” in Proceedings of the Third Conference on
+Machine Translation: Shared Task Papers, 2018, pp. 603–
+611.
+[79] O. Caglayan, P. Madhyastha, L. Specia, and L. Barrault,
+“Probing the need for visual context in multimodal
+machine translation,” in Proceedings of the 2019 Confer-
+ence of the North American Chapter of the Association for
+Computational Linguistics: Human Language Technologies,
+Volume 1 (Long and Short Papers), 2019, pp. 4159–4170.
+[80] W. M. Brown, T. D. Gedeon, and D. I. Groves, “Use
+of noise to augment training data: a neural network
+method of mineral–potential mapping in regions of
+limited known deposit examples,” Natural Resources
+Research, vol. 12, no. 2, pp. 141–152, 2003.
+[81] H. Noh, T. You, J. Mun, and B. Han, “Regularizing
+deep neural networks by noise: Its interpretation and
+optimization,” in Advances in Neural Information Process-
+ing Systems 30: Annual Conference on Neural Information
+
+18
+Processing Systems 2017, December 4-9, 2017, Long Beach,
+CA, USA, 2017, pp. 5109–5118.
+[82] J. Brownlee, “Train neural networks with noise to re-
+duce overfitting,” Machine Learning Mastery, 2019.
+[83] Z. S. Harris, “Distributional structure,” Word, vol. 10,
+no. 2-3, pp. 146–162, 1954.
+[84] M. Neishi, J. Sakuma, S. Tohda, S. Ishiwatari, N. Yoshi-
+naga, and M. Toyoda, “A bag of useful tricks for
+practical neural machine translation: Embedding layer
+initialization and large batch size,” in Proceedings of the
+4th Workshop on Asian Translation (WAT2017), 2017, pp.
+99–109.
+[85] T. Kocmi and O. Bojar, “An exploration of word em-
+bedding initialization in deep-learning tasks,” in Pro-
+ceedings of the 14th International Conference on Natural
+Language Processing (ICON-2017), 2017, pp. 56–64.
+[86] S. Abnar and W. Zuidema, “Quantifying attention flow
+in transformers,” in Proceedings of the 58th Annual Meet-
+ing of the Association for Computational Linguistics, 2020,
+pp. 4190–4197.
+[87] A. Conneau, G. Kruszewski, G. Lample, L. Barrault,
+and M. Baroni, “What you can cram into a single
+$&!#* vector: Probing sentence embeddings for linguis-
+tic properties,” in Proceedings of the 56th Annual Meeting
+of the Association for Computational Linguistics (Volume 1:
+Long Papers), 2018, pp. 2126–2136.
+[88] S. Parida, O. Bojar, and S. R. Dash, “Hindi visual
+genome: A dataset for multimodal english-to-hindi
+machine translation,” arXiv preprint arXiv:1907.08948,
+2019.
+[89] R. Krishna, Y. Zhu, O. Groth, J. Johnson, K. Hata,
+J. Kravitz, S. Chen, Y. Kalantidis, L.-J. Li, D. A. Shamma
+et al., “Visual genome: Connecting language and vision
+using crowdsourced dense image annotations,” Inter-
+national Journal of Computer Vision, vol. 123, no. 1, pp.
+32–73, 2017.
+[90] Z. Zhang, Y. Wu, H. Zhao, Z. Li, S. Zhang, X. Zhou,
+and X. Zhou, “Semantics-aware BERT for language
+understanding,” in The Thirty-Fourth AAAI Conference
+on Artificial Intelligence, AAAI 2020, The Thirty-Second
+Innovative Applications of Artificial Intelligence Conference,
+IAAI 2020, The Tenth AAAI Symposium on Educational
+Advances in Artificial Intelligence, EAAI 2020, New York,
+NY, USA, February 7-12, 2020, 2020, pp. 9628–9635.
+[91] K. Clark, M. Luong, Q. V. Le, and C. D. Manning,
+“ELECTRA: pre-training text encoders as discrimina-
+tors rather than generators,” in 8th International Confer-
+ence on Learning Representations, ICLR 2020, Addis Ababa,
+Ethiopia, April 26-30, 2020, 2020.
+Zhuosheng Zhang received his Bachelor’s de-
+gree in internet of things from Wuhan University
+in 2016, his M.S. degree in computer science
+from Shanghai Jiao Tong University in 2020. He
+is working towards his Ph.D. degree in computer
+science with the Center for Brain-like Computing
+and Machine Intelligence of Shanghai Jiao Tong
+University. He was an internship research fellow
+at NICT from 2019-2020. His research interests
+include natural language processing, machine
+reading comprehension, dialogue systems, and
+machine translation.
+Kehai Chen is an Assistant Professor at Harbin
+Institute of Technology (Shenzhen) since 2022.
+Before that, he was a researcher at Japan Na-
+tional Institute of Information and Communica-
+tions Technology (NICT) from 2018 to 2021. He
+received the Ph.D. degree in computer science
+from Harbin Institute of Technology in 2018. His
+research interests include machine translation
+and natural language processing.
+Rui Wang is an associate professor at Shanghai
+Jiao Tong University since 2021. Before that, he
+was a researcher (tenured in 2020) at Japan
+National Institute of Information and Communi-
+cations Technology (NICT) from 2016 to 2020.
+He received his B.S. degree from Harbin Institute
+of Technology in 2009, his M.S. degree from the
+Chinese Academy of Sciences in 2012, and his
+Ph.D. degree from Shanghai Jiao Tong Univer-
+sity in 2016, all of which are in computer science.
+He was a joint Ph.D. at Centre Nationnal de
+la Recherche Scientifique, France in 2014. His research interests are
+machine translation and natural language processing.
+Masao Utiyama is a research manager of the
+National Institute of Information and Communi-
+cations Technology, Japan. He completed his
+doctoral dissertation at the University of Tsukuba
+in 1997. His main research field is machine
+translation.
+Eiichiro Sumita received the Bachelor and Mas-
+ter degree in computer science from The Univer-
+sity of Electro-Communications, Japan in 1980
+and 1982 and the Ph.D degree in Engineering
+from Kyoto University, Japan in 1999. He is cur-
+rently Director of Multilingual Translation Labora-
+tory of National Institute of Information and Com-
+munication Technology from 2006. He worked
+at Advanced Telecomunications Research Insti-
+tute International from 1992 to 2009 and IBM
+Research-Tokyo from 1980 to 1991. His re-
+search interests include machine translation and e-Learning.
+Zuchao Li received the B.S. degree from Wuhan
+University, Wuhan, China, in 2017. Since 2017,
+he has been a Ph.D. student with the Center for
+Brain-like Computing and Machine Intelligence
+of Shanghai Jiao Tong University, Shanghai,
+China. His research focuses on natural language
+processing, especially syntactic and semantic
+parsing.
+Hai Zhao received the BEng degree in sensor
+and instrument engineering, and the MPhil de-
+gree in control theory and engineering from Yan-
+shan University in 1999 and 2000, respectively,
+and the PhD degree in computer science from
+Shanghai Jiao Tong University, China in 2005.
+He is currently a full professor at department
+of computer science and engineering, Shanghai
+Jiao Tong University after he joined the university
+in 2009. He was a research fellow at the City
+University of Hong Kong from 2006 to 2009, a
+visiting scholar in Microsoft Research Asia in 2011, a visiting expert in
+NICT, Japan in 2012. He is an ACM professional member, and served as
+area co-chair in ACL 2017 on Tagging, Chunking, Syntax and Parsing,
+(senior) area chairs in ACL 2018, 2019 on Phonology, Morphology and
+Word Segmentation. His research interests include natural language
+processing and related machine learning, data mining and artificial
+intelligence.
+

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+arXiv:2301.01282v1  [cs.CR]  31 Dec 2022
+RSA+: AN ALGORITHM AT LEAST AS SECURE AS RSA
+KRISHNAN SHANKAR
+Introduction
+The RSA algorithm has been around for nearly five decades ([RSA78]) and remains one
+of the most studied public key cryptosystems. Many attempts have been made to break
+it or improve it and questions remain about the equivalence of the strength of its security
+to well known hard problems in computational number theory. A basic question which has
+received much attention (cf. [AM09], [BV98]1) is: Is breaking RSA equivalent to factoring?
+In this note we propose a modified version which we call RSA+ which is at least as secure as
+RSA and show that breaking RSA+ is probably computationally equivalent to factoring n,
+the public modulus. The motivation came from wanting to obscure the encryption exponent
+in RSA.
+1. The RSA+ Algorithm
+RSA: Bob wishes to send a message m to Alice whose RSA public key is (n, e) and private
+key is (p, q, d) where n = pq and de ≡ 1 (mod ϕ(n)).
+In the usual implementation of
+RSA Bob computes c ≡ me (mod n) and sends it to Alice. Decryption is straightforward:
+cd ≡ (md)e ≡ mde ≡ m (mod n) since de ≡ 1 (mod ϕ(n)).
+RSA+: We start with the same setup as above namely that Bob has a message m to
+transmit to Alice whose RSA public key is (n, e).
+Encryption:
+1. Bob finds a random number x (mod n) and computes y ≡ x2 (mod n).
+2. Bob computes c ≡ mx (mod n) and r ≡ ye (mod n).
+3. Bob transmits the pair (c, r) to Alice.
+Decryption:
+1. Alice computes y ≡ (ye)d (mod n). This step is similar to decrypting in RSA.
+2. Alice then writes down the equation y ≡ x2 (mod n). She uses her knowledge of
+the factorization of n = pq to compute all four square roots of y (see Section 4).
+3. For each square root, say {x1, x2, x3, x4}, Alice sequentially computes the inverse
+ui ≡ x−1
+i
+(mod ϕ(n)) and evaluates cui (mod n) until she sees an intelligible mes-
+sage m (but see 1.2 below).
+Theorem A. Breaking RSA+ is probably computationally equivalent to factoring n = pq.
+1In [BV98] there seems to be an issue in the proof of Lemma 3.2, where it is assumed that a cyclotomic
+polynomial Φd(x) is irreducible over Fp, which is not always true.
+
+2
+KRISHNAN SHANKAR
+1.1.
+Similar to RSA care must be taken in choosing the random integer x in Step 1 of
+encryption. If Bob chooses x < √n, then y = x2 as integers and it is easy to find the square
+root if one knows y. In this case the system is as secure as RSA since y is RSA-encrypted.
+It is also important that gcd(x, ϕ(n)) = 1 since otherwise Alice cannot decrypt the message
+even if she can find x (Euler’s theorem). So, Bob could choose x to be a prime of at least
+150 digits assuming n is around 300 digits.
+1.2.
+In Step 3 of decryption as stated Alice must compute all four square roots and then
+try to uncover an intelligible message by sequentially decrypting each mxi (mod n) which is
+onerous in practice. We describe a way around this problem as long as both primes dividing
+n are congruent to 3 mod 4 (this is the workaround suggested by Blum and Williams).
+Consider the setup with y ≡ x2 (mod n), where Bob chooses x, y. Then y has four square
+roots mod n which come from combining the two square roots each mod p and mod q using
+the Chinese Remainder Theorem (CRT). Suppose both primes p, q in the factorization of n
+are chosen (by Alice) to be congruent to 3 mod 4. Now Bob chooses x, y such that x itself
+is a square mod n. Then solving the equation X2 ≡ y (mod n) has solutions (say) X ≡ ±a
+(mod p) and X ≡ ±b (mod q). These are combined using CRT to yield X ≡ xi (mod n),
+for i = 1, 2, 3, 4 and let us suppose x = x1. Note that p, q ≡ 3 (mod 4) so
+�
+−1
+p
+�
+= −1 and
+�
+−1
+q
+�
+= −1 i.e., −1 is not a quadratic residue mod p nor mod q. This implies that exactly
+one of the roots ± (mod p) and one of the roots ±b (mod q) is a quadratic residue (mod the
+respective primes) and the other is not. Since Bob picked x to be a square mod n, it follows
+that the congruences that yielded x1 must also be squares i.e., suppose X ≡ a (mod p)
+and X ≡ b (mod q) yields X ≡ x1 (mod n), then it follows that
+�
+a
+p
+�
+= +1,
+�
+b
+q
+�
+= +1 and
+�
+−a
+p
+�
+= −1,
+�
+−b
+q
+�
+= −1. From this it follows that none of x2, x3, x4 is a square mod n. We
+summarize this via the following
+Proposition 1.1. Suppose n = pq, where p and q are congruent to 3 mod 4. Given x, y
+such that y ≡ x2 (mod n), gcd(x, n) = 1. Then y has four square roots mod n exactly one
+of which is a square mod n.
+This suggests a way to pinpoint x without having to search all square roots, namely, Bob
+picks x to be a square mod n and then computes y ≡ x2 (mod n). By the above Proposition
+this will be the only square root of y mod n. It also follows from the discussion above that:
+(i) If one of the primes is congruent to 1 mod 4, then the number of square roots that are
+themselves perfect squares is either 0 or 2; (ii) If both primes are congruent to 1 mod 4,
+then the number of square roots that are themselves perfect squares is 0 or 4.
+1.3.
+Decryption is more involved if at least one of the primes dividing n is congruent to 1
+(mod 8). Nevertheless, the overall algorithm’s security is tied to the difficulty of factoring
+and as such lies in class NP, although it is unknown whether it is in P.
+
+RSA+: AN ALGORITHM AT LEAST AS SECURE AS RSA
+3
+2. RSA+ is at least as secure as RSA
+In this section we show that RSA+ is at least as secure as RSA. We will show this via
+the use of a so-called black box i.e., an unknown machine or method or algorithm that
+takes in a specified input and returns an output that is otherwise currently computationally
+intractable.
+Theorem B. RSA+ is at least as secure as RSA.
+Proof. Suppose we have a black box that is able to decrypt RSA+ messages i.e., this black
+box takes as input (n, e, mx (mod n), ye (mod n)) and returns m. Here y ≡ x2 (mod n).
+Given an RSA ciphertext c ≡ me (mod n) one would then input (n, e, c, (e2)e (mod n))
+which should generate the output of m.
+This shows that any system that can decrypt
+RSA+ ciphertexts can also decrypt RSA ciphertexts.
+Conversely, suppose there is a black box that is able to decrypt RSA messages i.e., this
+black box takes as input (n, e, c ≡ me (mod n)) and returns m. Given an RSA+ ciphertext
+(mx (mod n), ye (mod n)) one can only decrypt y. In order to get to m one would need to
+know the exponent x for input into this black box, i.e., one would now need x in order to
+input (n, x, mx (mod n)) into the black box. This means computing a square root of y. It
+is not known whether this black box which can decrypt RSA ciphertexts can also compute
+square roots (but see Theorem C).
+□
+3. Computational Black Boxes
+In this section we explore further computational black boxes which may circumvent known
+methods like factoring. Suppose one is able to decrypt y by ascertaining d. One needs to
+compute the particular square root x used to encrypt m. Is it possible to compute just one
+(pair of) square root(s) without knowledge of the factors? If there exists a computational
+black box that can produce one square root when the input is (y, n), then there are two
+possibilities.
+3.1.
+Suppose the black box spits out a random square root mod n for the equation y ≡ x2
+mod n. In this case one simply inputs the same pair (y, n) repeatedly until we get two
+distinct square roots that do not add up to zero mod n. By Lemma 4.1 this will yield a
+factorization of n.
+3.2.
+Suppose the black box spits out a random square root mod n but always the same
+square root for the equation y ≡ x2 mod n i.e., for a given input (y, n), the output is
+always the same x rather than one of the four distinct square roots at random. In this case
+we start with some known x and square it to obtain y ≡ x2 (mod n). Now input (y, n)
+into the black box; if the output is ±x, then discard and try again with a different x. If
+the output, say x′ is different from ±x (mod n), then by Lemma 4.1 we can factor n by
+computing gcd(x − x′, n).
+
+4
+KRISHNAN SHANKAR
+3.3.
+If the adversary has instead a black box that computes d given the input (n, e),
+then ϕ(n) | (de − 1). Therefore, for any x we have xde−1 ≡ 1 (mod ϕ(n)). Since ϕ(n) =
+(p−1)(q−1) is divisible by 4, we may compute y ≡ x(de−1)/2 (mod n). Then, by construction
+y2 ≡ 1 (mod n) which means n | (y − 1)(y + 1). Then either y ≡ ±1 (mod n) or by Lemma
+2.1 gcd(y ± 1, n) yields a factor of n. Again, we can repeat this for several different x as
+needed to factor n with high probability.
+Whether RSA+ is computationally equivalent to factoring depends on the following
+thought experiment. Suppose we have a black box like the one in the previous Section
+which takes as input (n, e, mx (mod n), ye (mod n)), where y ≡ x2 (mod n) and produces
+as output m. Does this allow us to factor n?
+Theorem C. A black box with input (n, e, mx (mod n), ye (mod n)) and output m can
+probably factor n.
+Proof. Start with a known pair (x, y), where y ≡ x2 (mod n). Then note that:
+yx ≡ (x2)x ≡ x2x ≡ (xx)2
+(mod n)
+xy ≡ xx2 ≡ xx·x ≡ (xx)x
+(mod n)
+If we were to input (n, e, xy (mod n), ye (mod n)) into the black box, then this is the same
+as the input (n, e, (xx)x (mod n), ye (mod n)). The output should therefore be xx (mod n)
+which is a square root of yx (mod n). From 3.1 and 3.2 above, repeating this procedure for
+several different x should yield a factorization of n.
+□
+3.4. Remark. The above proof carries over for RSA as well i.e., if we had a black box for
+RSA, then the same argument above yields a procedure to compute square roots mod n.
+3.5. Remark. The only caveat in Theorem C above is the nature of the black box. Suppose
+the black box were to always return the distinguished square root xx (mod n) for the square
+yx ≡ (xx)2 (mod n), then this will not allow us to factor n.
+4. Computing square roots and factoring
+In the absence of a black box an adversary Eve would need y and then a square root
+of y to attempt to decrypt m. Computing y ≡ (ye)d mod n without (p, q, d) is as hard
+as breaking RSA. Even if Eve can deduce d without factoring n, she would next have to
+solve the equation y ≡ x2 (mod n). See Section 3 for a discussion on black boxes that may
+compute square roots.
+Lemma 4.1. Given n = pq if we can solve the (generic) equation y ≡ x2 (mod n) and find
+all four roots ±a, ±b mod n, then we can factor n.
+Conversely, if one can solve the equation y ≡ x2 (mod p) and y ≡ x2 (mod q), then one
+can combine the roots using the Chinese Remainder Theorem to produce (in general) four
+square roots mod pq.
+
+RSA+: AN ALGORITHM AT LEAST AS SECURE AS RSA
+5
+Proof. Since a ̸≡ ±b (mod n) and a2 ≡ b2 mod n implies that n | (a − b)(a + b). Thus,
+computing gcd(a ± b, n) yields a non-trivial factor of n.
+□
+Lemma 4.2. If p ≡ 3 (mod 4) is prime, then one can solve y ≡ x2 (mod p) by computing
+x ≡ y(p+1)/4 (mod p). Then (±x)2 ≡ y (mod p).
+Lemma 4.3. If p = 8k + 5 is prime, i.e., p ≡ 5 (mod 8), then one can solve y ≡ x2
+(mod p).
+Proof. Since y is a square mod p, we have that y(p−1)/2 ≡ 1 (mod p). Since (p − 1)/4 is an
+integer we can take a square root and we obtain that y(p−1)/4 ≡ ±1 (mod p).
+Case 1: If y(p−1)/4 ≡ 1 (mod p) and p = 8k + 5, then x ≡ yk+1 ≡ y(p+3)/8 (mod p) is a
+desired square root. This is because
+x2 ≡ y(p+3)/4 ≡ y(p−1)/4 · y ≡ y
+(mod p)
+Case 2: If y(p−1)/4 ≡ −1 (mod p), then x ≡ 22k+1yk+1 ≡ 2(p−1)/4y(p+3)/8 (mod p) is a
+desired square root. This is because
+x2 ≡ 2(p−1)/2y(p+3)/4 ≡ (−1) · y(p−1)/4 · y ≡ (−1)(−1)y ≡ y
+(mod p)
+Note that 2(p−1)/2 ≡ −1 (mod p) since p ≡ 5 (mod 8).
+□
+Lemma 4.4. If p ≡ 1 (mod 8) is prime, then there exists an algorithm terminating in at
+most r steps to compute y ≡ x2 (mod p), where p − 1 = 2rs.
+Proof. This is the most involved case of the Tonelli–Shanks algorithm, which covers all the
+above Lemmas; see [Sh73], [Ton1891]. See [Tur94] for a nice exposition.
+□
+Now we can prove Theorem A.
+Proof of Theorem A. If an adversary Eve can factor n, then she can certainly decrypt the
+message m: compute ϕ(n) = (p−1)(q −1), find d using the Extended Euclidean Algorithm
+and use this to find y ≡ (ye)d mod n. Now using Lemmas 4.2, 4.3, 4.4, depending on
+whether p, q are congruent to 1 (mod 4) or 3 (mod 4), Eve can find the square roots of y
+mod p and mod q. Then she can combine them to obtain all square roots mod n using the
+Chinese Remainder Theorem. Finally Eve solves for x−1 (mod ϕ(n)) to decrypt m.
+If Eve possesses a black box as described in Theorem C, then Eve can probably factor n
+(with the caveat introduced in Remark 3.5). If Eve has instead a black box or method to
+find square roots mod n, then by Lemma 4.1 she can factor n.
+□
+5. Similar cryptosystems
+A search of the literature by the author yielded similar cryptosystems and these are
+described briefly here. Any other omissions are entirely accidental. To the author’s knowl-
+edge this particular protocol has not been described before. For each protocol below the
+description is brief and only intended to serve as a reference or comparison.
+
+6
+KRISHNAN SHANKAR
+5.1. The Rabin Cryptosystem. This cryptosystem ([Rab79]) is the closest in spirit to
+the method proposed here. Its security is tied to square roots and factoring. Alice finds
+primes p, q both congruent to 3 mod 4 and computes n = pq and exponents e, d with de ≡ 1
+(mod ϕ(n)) same as in RSA.
+Bob encrypts his message m as c ≡ m2 (mod n) and transmits c.
+To decrypt Alice
+computes the square root mod p and mod q by the method outlined in Lemma 4.2. Then
+she combines them using the Chinese Remainder Theorem to obtain all four square roots
+and then examines which of these is intelligible. This latter disambiguation problem was
+addressed by Blum and Williams. The Rabin cryptosystem was shown to be vulnerable
+to a chosen ciphertext attack. This attack can be thwarted by adding redundancies to the
+message.
+5.2. D–RSA (Dependent RSA). This cryptosystem, described in [Po99], was in re-
+sponse to finding a so-called semantically secure cryptosystem as efficient as RSA. Similar
+to RSA Alice has public key (n, e). Then Bob picks a random k ∈ (Zn)∗ and computes
+A ≡ ke (mod n) and B ≡ m · (k + 1)e (mod n). Decryption is via computing k ≡ (ke)d
+(mod n) and then B · (k + 1)−e (mod n). This is also similar in spirit to what we have
+described in that Bob picks a random number during the encryption process. Among the
+theorems in the paper it is shown that a slight modification of this protocol is semantically
+secure against adaptive chosen ciphertext attacks relative to the Decision D–RSA Problem
+in the random oracle model.
+5.3. RSA–CRT. This is a variant of RSA ([Vig08]) in which the public key is the same,
+namely (n, e), but the private key is split up as dp ≡ d (mod p − 1), dq ≡ d (mod q − 1),
+qinv ≡ q−1 (mod p). The encrypted message c ≡ me (mod n) is then decrypted as m1 ≡
+mdp (mod p), m2 ≡ mdq (mod q), h ≡ qinv(m1 − m2) (mod p) and finally, m = m2 + hq.
+This variant runs faster than RSA in practice but it was found in 1996 to be vulnerable to
+a differential fault attack by the Bellcore Institute.
+5.4. Multi-prime RSA. In this variant more than two primes are used in the public
+modulus. The system yields some advantages in efficiency but may be more vulnerable to
+attacks to factor n.
+5.5. Multi-power RSA. In this variant one considers public moduli of the form n = prqs,
+where gcd(r, s) = 1 (when s = 1 this is also called Takagi’s variant; [Ta98]). The method
+offers advantages in speedier decryption using Hensel’s lemma and the Chinese Remainder
+theorem mod pr and mod qs.
+5.6. More RSA variants. Several other variants exist: Dual RSA (using two distinct
+moduli that share the same d, e), Batch RSA (encrypting using two different small expo-
+nents; [F89]) etc. Most RSA variants are vulnerable to small private exponent attacks first
+described by Boneh and Durfee; [BD00]. A fairly exhaustive survey of RSA variants and
+their cryptanalysis can be found in the book by Hinek; [Hin09].
+
+RSA+: AN ALGORITHM AT LEAST AS SECURE AS RSA
+7
+5.7. Hofheinz–Kiltz–Shoup Cryptosystem. This more recent system is described as a
+so-called Key Exchange Mechanism (KEM); [HKS13]. The precise details would take up a
+few pages so an abbreviated version is outlined here. To set up Alice picks two safe primes
+P, Q i.e., Sophie Germain primes, P = 2p + 1, Q = 2q + 1. Moreover, P, Q ≡ 3 (mod 4).
+Then N = PQ is a so-called Blum integer.
+Let QRN ⊆ (ZN)∗ denote the subset of quadratic residues mod N; this has pq elements.
+A signed quadratic residue is an element of QRN which is normalized to lie in the set,
+[− (N−1)
+2
+, (N−1)
+2
+]; this normalized set is denoted QR+
+N. We also a target collision resistant
+function (also known as universal one way hash function), say T. The desired key to be
+transmitted is K and the notation ℓK denotes the number of bits in K. Finally, for u ∈ ZN
+(thought of as an element in [− (N−1)
+2
+, (N−1)
+2
+]) define the function LBSN(u) = u (mod 2) and
+then use this to define bits of the key using the Blum–Blum–Shub pseudorandom number
+generator ([BBS86]):
+BBSN(u) := (LBSN(u), LBSN(u2), . . . , LBSN(u2ℓK −1)) ∈ {0, 1}ℓK
+Public and Private keys: Given N, Alice picks a signed quadratic residue g ∈ QR+
+N
+and an element α ∈ {1, 2, . . . , (N−1)
+4
+}. Let X ≡ gα2ℓK +ℓT (mod N). Then the public key is
+(N, g, X) and the private key is (N, g, α).
+Encapsulation: Bob chooses r ∈ {1, 2, . . . , (N−1)
+4
+} and computes
+R ≡ gr2ℓK +ℓT
+(mod N),
+t = T(R),
+S ≡ (gtX)r
+(mod N)
+The ciphertext is C = (R, S) and the key transmitted is K = BBSN(gr·2ℓT ) ∈ {0, 1}ℓK .
+Decapsulation: The receiver computes t = T(R) and verifies whether
+S2ℓK +ℓT
+?≡ Rt+α2ℓK +ℓT
+(mod N)
+Assuming this equality is satisfied the receiver (Alice) computes integers a, b, c such that
+2c = gcd(t, 2ℓK+ℓT ) = at + b2ℓK+ℓT . Alice then derives
+U ≡ (SaRb−aα)2ℓT −c (mod N),
+=⇒
+K = BBSN(U)
+We don’t add any more details; the reason for describing this algorithm is to point out
+that the ciphertext has the same flavor of the algorithm presented in this paper. Note that
+decapsulation here does not require knowing the factorization of N.
+6. Remarks
+6.1.
+The method proposed is probably computationally equivalent to factoring.
+To be
+certain one would have to solve the following thought exercise: Suppose there is a black box
+which takes in input (c, r, n, e) in the proposed algorithm and returns m. Can one factor n
+given this information? A similar formulation can be made for RSA itself: Suppose there is
+a black box which takes input (c, n, e) and outputs m; can one factor m? This is similar in
+spirit to a chosen plaintext attack on either system. While Theorem C indicates this may
+be true the caveat of Remark 3.4 suggests uncertainty.
+
+8
+KRISHNAN SHANKAR
+Acknowledgments
+The author is grateful to Kimball Martin, Steven Miller and Larry Washington for their
+careful reading of early drafts and for providing valuable comments that helped greatly
+improve this paper.
+References
+[AM09] D. Aggarwal and U. Maurer, Breaking RSA generically is equivalent to factoring, In A. Joux, editor,
+EUROCRYPT 2009, volume 5479 of LNCS, pages 36–53. Springer, Heidelberg, April 2009.
+[BBS86] L. Blum, M. Blum and M. Shub, A simple unpredictable pseudo-random number generator, SIAM
+J. Comput. 15(2), 364–383 (1986).
+[BD00] D. Boneh and G. Durfee, Cryptanalysis of RSA with Private Key d Less than n0.292, IEEE Trans.
+Information Theory, 46(4):1339–1349, July 2000.
+[BDH-G99] D. Boneh, G. Durfee, and N. Howgrave-Graham, Factoring N = prq for Large r, In M. Weiner,
+ed., Proceedings of Crypto ’99, vol. 1666 of LNCS, pp. 326–337. Springer–Verlag, Aug. 1999.
+[BV98] D. Boneh and R. Venkatesan, Breaking RSA may not be equivalent to factoring, In K. Nyberg, editor,
+EUROCRYPT’98, volume 1403 of LNCS, pages 59–71. Springer, Heidelberg, May / June 1998.
+[F89] A. Fiat., Batch RSA, In G. Brassard, ed., Proceedings of Crypto 1989, vol. 435 of LNCS, pp. 175–185.
+Springer–Verlag, Aug. 1989.
+[Hin09] M. J. Hinek, Cryptanalysis of RSA and its variants, Cryptography & Network Security series,
+Chapman and Hall publishers, 2009.
+[HKS13] D. Hofheinz, E. Kiltz and V. Shoup, Practical Chosen Ciphertext Secure Encryption from Factoring,
+J. of Cryptology (2013) vol. 26, 102–118.
+[Po99] D. Pointcheval, New Public Key Cryptosystems based on the Dependent RSA-Problems, EURO-
+CRYPT ’99, Lecture Notes in Computer Science 1592, 239–254.
+[RSA78] R. Rivest, A. Shamir, L. Adleman, A method for obtaining digital signatures and public-key cryp-
+tosystems, Communications of the Association for Computing Machinery, 21(2):120–126.
+[Rab79] M. Rabin, Digital signatures and public key functions as intractable as factorization., Technical
+Report MIT/LCS/TR-212, Massachusetts Institute of Technology, January 1979.
+[Sh73] D. Shanks, Five Number Theoretic Algorithms, Proceedings of the Second Manitoba Conference on
+Numerical Mathematics. Pp. 51–70, 1973.
+[Ta98] T. Takagi, Fast RSA-type Cryptosystem Modulo pkq, In H. Krawczyk, ed., Proceedings of Crypto
+1998, vol. 1462 of LNCS, pp. 318–326. Springer-Verlag, Aug. 1998
+[Ton1891] A. Tonelli, Bemerkung ¨uber die Aufl¨osung quadratischer Congruenzen, Nachrichten von der
+K¨oniglichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universit¨at zu G¨ottingen, 344–
+346, 1891.
+[Tur94] S. Turner, Square roots mod p, The American Mathematical Monthly, May 1994, vol. 101, no. 5,
+443–449.
+[Vig08] D. Vigilant, RSA with CRT: A New Cost-Effective Solution to Thwart Fault Attacks, In: Cryp-
+tographic Hardware and Embedded Systems – CHES 2008. CHES 2008. Lecture Notes in Computer
+Science, vol 5154.
+[Wie90] M. Wiener, Cryptanalysis of Short RSA Secret Exponents, IEEE Trans. Information Theory
+36(3):553–558. May 1990.
+Department of Mathematics & Statistics, James Madison University, 60 Bluestone Drive,
+Harrisonburg VA 22807.
+Email address: [email protected]
+

JdAzT4oBgHgl3EQfVPzH/content/tmp_files/load_file.txt

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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf,len=380
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='01282v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='CR]  31 Dec 2022  RSA+: AN ALGORITHM AT LEAST AS SECURE AS RSA  KRISHNAN SHANKAR  Introduction  The RSA algorithm has been around for nearly five decades ([RSA78]) and remains one  of the most studied public key cryptosystems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Many attempts have been made to break  it or improve it and questions remain about the equivalence of the strength of its security  to well known hard problems in computational number theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' A basic question which has  received much attention (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' [AM09], [BV98]1) is: Is breaking RSA equivalent to factoring?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  In this note we propose a modified version which we call RSA+ which is at least as secure as  RSA and show that breaking RSA+ is probably computationally equivalent to factoring n,  the public modulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The motivation came from wanting to obscure the encryption exponent  in RSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The RSA+ Algorithm  RSA: Bob wishes to send a message m to Alice whose RSA public key is (n, e) and private  key is (p, q, d) where n = pq and de ≡ 1 (mod ϕ(n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  In the usual implementation of  RSA Bob computes c ≡ me (mod n) and sends it to Alice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Decryption is straightforward:  cd ≡ (md)e ≡ mde ≡ m (mod n) since de ≡ 1 (mod ϕ(n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  RSA+: We start with the same setup as above namely that Bob has a message m to  transmit to Alice whose RSA public key is (n, e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Encryption:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Bob finds a random number x (mod n) and computes y ≡ x2 (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Bob computes c ≡ mx (mod n) and r ≡ ye (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Bob transmits the pair (c, r) to Alice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Decryption:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Alice computes y ≡ (ye)d (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This step is similar to decrypting in RSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Alice then writes down the equation y ≡ x2 (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' She uses her knowledge of  the factorization of n = pq to compute all four square roots of y (see Section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' For each square root, say {x1, x2, x3, x4}, Alice sequentially computes the inverse  ui ≡ x−1  i  (mod ϕ(n)) and evaluates cui (mod n) until she sees an intelligible mes-  sage m (but see 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='2 below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Breaking RSA+ is probably computationally equivalent to factoring n = pq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  1In [BV98] there seems to be an issue in the proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='2, where it is assumed that a cyclotomic  polynomial Φd(x) is irreducible over Fp, which is not always true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  2  KRISHNAN SHANKAR  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Similar to RSA care must be taken in choosing the random integer x in Step 1 of  encryption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' If Bob chooses x < √n, then y = x2 as integers and it is easy to find the square  root if one knows y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' In this case the system is as secure as RSA since y is RSA-encrypted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  It is also important that gcd(x, ϕ(n)) = 1 since otherwise Alice cannot decrypt the message  even if she can find x (Euler’s theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' So, Bob could choose x to be a prime of at least  150 digits assuming n is around 300 digits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  In Step 3 of decryption as stated Alice must compute all four square roots and then  try to uncover an intelligible message by sequentially decrypting each mxi (mod n) which is  onerous in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' We describe a way around this problem as long as both primes dividing  n are congruent to 3 mod 4 (this is the workaround suggested by Blum and Williams).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Consider the setup with y ≡ x2 (mod n), where Bob chooses x, y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then y has four square  roots mod n which come from combining the two square roots each mod p and mod q using  the Chinese Remainder Theorem (CRT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Suppose both primes p, q in the factorization of n  are chosen (by Alice) to be congruent to 3 mod 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Now Bob chooses x, y such that x itself  is a square mod n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then solving the equation X2 ≡ y (mod n) has solutions (say) X ≡ ±a  (mod p) and X ≡ ±b (mod q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' These are combined using CRT to yield X ≡ xi (mod n),  for i = 1, 2, 3, 4 and let us suppose x = x1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Note that p, q ≡ 3 (mod 4) so  �  −1  p  �  = −1 and  �  −1  q  �  = −1 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', −1 is not a quadratic residue mod p nor mod q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This implies that exactly  one of the roots ± (mod p) and one of the roots ±b (mod q) is a quadratic residue (mod the  respective primes) and the other is not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Since Bob picked x to be a square mod n, it follows  that the congruences that yielded x1 must also be squares i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', suppose X ≡ a (mod p)  and X ≡ b (mod q) yields X ≡ x1 (mod n), then it follows that  �  a  p  �  = +1,  �  b  q  �  = +1 and  �  −a  p  �  = −1,  �  −b  q  �  = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' From this it follows that none of x2, x3, x4 is a square mod n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' We  summarize this via the following  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Suppose n = pq, where p and q are congruent to 3 mod 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Given x, y  such that y ≡ x2 (mod n), gcd(x, n) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then y has four square roots mod n exactly one  of which is a square mod n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  This suggests a way to pinpoint x without having to search all square roots, namely, Bob  picks x to be a square mod n and then computes y ≡ x2 (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' By the above Proposition  this will be the only square root of y mod n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' It also follows from the discussion above that:  (i) If one of the primes is congruent to 1 mod 4, then the number of square roots that are  themselves perfect squares is either 0 or 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' (ii) If both primes are congruent to 1 mod 4,  then the number of square roots that are themselves perfect squares is 0 or 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Decryption is more involved if at least one of the primes dividing n is congruent to 1  (mod 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Nevertheless, the overall algorithm’s security is tied to the difficulty of factoring  and as such lies in class NP, although it is unknown whether it is in P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  RSA+: AN ALGORITHM AT LEAST AS SECURE AS RSA  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' RSA+ is at least as secure as RSA  In this section we show that RSA+ is at least as secure as RSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' We will show this via  the use of a so-called black box i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', an unknown machine or method or algorithm that  takes in a specified input and returns an output that is otherwise currently computationally  intractable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' RSA+ is at least as secure as RSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Suppose we have a black box that is able to decrypt RSA+ messages i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', this black  box takes as input (n, e, mx (mod n), ye (mod n)) and returns m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Here y ≡ x2 (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Given an RSA ciphertext c ≡ me (mod n) one would then input (n, e, c, (e2)e (mod n))  which should generate the output of m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  This shows that any system that can decrypt  RSA+ ciphertexts can also decrypt RSA ciphertexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Conversely, suppose there is a black box that is able to decrypt RSA messages i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', this  black box takes as input (n, e, c ≡ me (mod n)) and returns m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Given an RSA+ ciphertext  (mx (mod n), ye (mod n)) one can only decrypt y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' In order to get to m one would need to  know the exponent x for input into this black box, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', one would now need x in order to  input (n, x, mx (mod n)) into the black box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This means computing a square root of y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' It  is not known whether this black box which can decrypt RSA ciphertexts can also compute  square roots (but see Theorem C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Computational Black Boxes  In this section we explore further computational black boxes which may circumvent known  methods like factoring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Suppose one is able to decrypt y by ascertaining d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' One needs to  compute the particular square root x used to encrypt m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Is it possible to compute just one  (pair of) square root(s) without knowledge of the factors?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' If there exists a computational  black box that can produce one square root when the input is (y, n), then there are two  possibilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Suppose the black box spits out a random square root mod n for the equation y ≡ x2  mod n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' In this case one simply inputs the same pair (y, n) repeatedly until we get two  distinct square roots that do not add up to zero mod n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1 this will yield a  factorization of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Suppose the black box spits out a random square root mod n but always the same  square root for the equation y ≡ x2 mod n i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', for a given input (y, n), the output is  always the same x rather than one of the four distinct square roots at random.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' In this case  we start with some known x and square it to obtain y ≡ x2 (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Now input (y, n)  into the black box;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' if the output is ±x, then discard and try again with a different x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' If  the output, say x′ is different from ±x (mod n), then by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1 we can factor n by  computing gcd(x − x′, n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  4  KRISHNAN SHANKAR  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  If the adversary has instead a black box that computes d given the input (n, e),  then ϕ(n) | (de − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Therefore, for any x we have xde−1 ≡ 1 (mod ϕ(n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Since ϕ(n) =  (p−1)(q−1) is divisible by 4, we may compute y ≡ x(de−1)/2 (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then, by construction  y2 ≡ 1 (mod n) which means n | (y − 1)(y + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then either y ≡ ±1 (mod n) or by Lemma  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1 gcd(y ± 1, n) yields a factor of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Again, we can repeat this for several different x as  needed to factor n with high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Whether RSA+ is computationally equivalent to factoring depends on the following  thought experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Suppose we have a black box like the one in the previous Section  which takes as input (n, e, mx (mod n), ye (mod n)), where y ≡ x2 (mod n) and produces  as output m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Does this allow us to factor n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Theorem C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' A black box with input (n, e, mx (mod n), ye (mod n)) and output m can  probably factor n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Start with a known pair (x, y), where y ≡ x2 (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then note that:  yx ≡ (x2)x ≡ x2x ≡ (xx)2  (mod n)  xy ≡ xx2 ≡ xx·x ≡ (xx)x  (mod n)  If we were to input (n, e, xy (mod n), ye (mod n)) into the black box, then this is the same  as the input (n, e, (xx)x (mod n), ye (mod n)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The output should therefore be xx (mod n)  which is a square root of yx (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' From 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='2 above, repeating this procedure for  several different x should yield a factorization of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Remark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The above proof carries over for RSA as well i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', if we had a black box for  RSA, then the same argument above yields a procedure to compute square roots mod n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Remark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The only caveat in Theorem C above is the nature of the black box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Suppose  the black box were to always return the distinguished square root xx (mod n) for the square  yx ≡ (xx)2 (mod n), then this will not allow us to factor n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Computing square roots and factoring  In the absence of a black box an adversary Eve would need y and then a square root  of y to attempt to decrypt m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Computing y ≡ (ye)d mod n without (p, q, d) is as hard  as breaking RSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Even if Eve can deduce d without factoring n, she would next have to  solve the equation y ≡ x2 (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' See Section 3 for a discussion on black boxes that may  compute square roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Given n = pq if we can solve the (generic) equation y ≡ x2 (mod n) and find  all four roots ±a, ±b mod n, then we can factor n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Conversely, if one can solve the equation y ≡ x2 (mod p) and y ≡ x2 (mod q), then one  can combine the roots using the Chinese Remainder Theorem to produce (in general) four  square roots mod pq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  RSA+: AN ALGORITHM AT LEAST AS SECURE AS RSA  5  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Since a ̸≡ ±b (mod n) and a2 ≡ b2 mod n implies that n | (a − b)(a + b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Thus,  computing gcd(a ± b, n) yields a non-trivial factor of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  □  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' If p ≡ 3 (mod 4) is prime, then one can solve y ≡ x2 (mod p) by computing  x ≡ y(p+1)/4 (mod p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then (±x)2 ≡ y (mod p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' If p = 8k + 5 is prime, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', p ≡ 5 (mod 8), then one can solve y ≡ x2  (mod p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Since y is a square mod p, we have that y(p−1)/2 ≡ 1 (mod p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Since (p − 1)/4 is an  integer we can take a square root and we obtain that y(p−1)/4 ≡ ±1 (mod p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Case 1: If y(p−1)/4 ≡ 1 (mod p) and p = 8k + 5, then x ≡ yk+1 ≡ y(p+3)/8 (mod p) is a  desired square root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This is because  x2 ≡ y(p+3)/4 ≡ y(p−1)/4 · y ≡ y  (mod p)  Case 2: If y(p−1)/4 ≡ −1 (mod p), then x ≡ 22k+1yk+1 ≡ 2(p−1)/4y(p+3)/8 (mod p) is a  desired square root.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This is because  x2 ≡ 2(p−1)/2y(p+3)/4 ≡ (−1) · y(p−1)/4 · y ≡ (−1)(−1)y ≡ y  (mod p)  Note that 2(p−1)/2 ≡ −1 (mod p) since p ≡ 5 (mod 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  □  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' If p ≡ 1 (mod 8) is prime, then there exists an algorithm terminating in at  most r steps to compute y ≡ x2 (mod p), where p − 1 = 2rs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This is the most involved case of the Tonelli–Shanks algorithm, which covers all the  above Lemmas;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' see [Sh73], [Ton1891].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' See [Tur94] for a nice exposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  □  Now we can prove Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Proof of Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' If an adversary Eve can factor n, then she can certainly decrypt the  message m: compute ϕ(n) = (p−1)(q −1), find d using the Extended Euclidean Algorithm  and use this to find y ≡ (ye)d mod n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Now using Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='2, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='3, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='4, depending on  whether p, q are congruent to 1 (mod 4) or 3 (mod 4), Eve can find the square roots of y  mod p and mod q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then she can combine them to obtain all square roots mod n using the  Chinese Remainder Theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Finally Eve solves for x−1 (mod ϕ(n)) to decrypt m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  If Eve possesses a black box as described in Theorem C, then Eve can probably factor n  (with the caveat introduced in Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' If Eve has instead a black box or method to  find square roots mod n, then by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1 she can factor n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  □  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Similar cryptosystems  A search of the literature by the author yielded similar cryptosystems and these are  described briefly here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Any other omissions are entirely accidental.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' To the author’s knowl-  edge this particular protocol has not been described before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' For each protocol below the  description is brief and only intended to serve as a reference or comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  6  KRISHNAN SHANKAR  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The Rabin Cryptosystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This cryptosystem ([Rab79]) is the closest in spirit to  the method proposed here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Its security is tied to square roots and factoring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Alice finds  primes p, q both congruent to 3 mod 4 and computes n = pq and exponents e, d with de ≡ 1  (mod ϕ(n)) same as in RSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Bob encrypts his message m as c ≡ m2 (mod n) and transmits c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  To decrypt Alice  computes the square root mod p and mod q by the method outlined in Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then  she combines them using the Chinese Remainder Theorem to obtain all four square roots  and then examines which of these is intelligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This latter disambiguation problem was  addressed by Blum and Williams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The Rabin cryptosystem was shown to be vulnerable  to a chosen ciphertext attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This attack can be thwarted by adding redundancies to the  message.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' D–RSA (Dependent RSA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This cryptosystem, described in [Po99], was in re-  sponse to finding a so-called semantically secure cryptosystem as efficient as RSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Similar  to RSA Alice has public key (n, e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then Bob picks a random k ∈ (Zn)∗ and computes  A ≡ ke (mod n) and B ≡ m · (k + 1)e (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Decryption is via computing k ≡ (ke)d  (mod n) and then B · (k + 1)−e (mod n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This is also similar in spirit to what we have  described in that Bob picks a random number during the encryption process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Among the  theorems in the paper it is shown that a slight modification of this protocol is semantically  secure against adaptive chosen ciphertext attacks relative to the Decision D–RSA Problem  in the random oracle model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' RSA–CRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This is a variant of RSA ([Vig08]) in which the public key is the same,  namely (n, e), but the private key is split up as dp ≡ d (mod p − 1), dq ≡ d (mod q − 1),  qinv ≡ q−1 (mod p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The encrypted message c ≡ me (mod n) is then decrypted as m1 ≡  mdp (mod p), m2 ≡ mdq (mod q), h ≡ qinv(m1 − m2) (mod p) and finally, m = m2 + hq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  This variant runs faster than RSA in practice but it was found in 1996 to be vulnerable to  a differential fault attack by the Bellcore Institute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Multi-prime RSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' In this variant more than two primes are used in the public  modulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The system yields some advantages in efficiency but may be more vulnerable to  attacks to factor n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Multi-power RSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' In this variant one considers public moduli of the form n = prqs,  where gcd(r, s) = 1 (when s = 1 this is also called Takagi’s variant;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' [Ta98]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The method  offers advantages in speedier decryption using Hensel’s lemma and the Chinese Remainder  theorem mod pr and mod qs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' More RSA variants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Several other variants exist: Dual RSA (using two distinct  moduli that share the same d, e), Batch RSA (encrypting using two different small expo-  nents;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' [F89]) etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Most RSA variants are vulnerable to small private exponent attacks first  described by Boneh and Durfee;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' [BD00].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' A fairly exhaustive survey of RSA variants and  their cryptanalysis can be found in the book by Hinek;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' [Hin09].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  RSA+: AN ALGORITHM AT LEAST AS SECURE AS RSA  7  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Hofheinz–Kiltz–Shoup Cryptosystem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This more recent system is described as a  so-called Key Exchange Mechanism (KEM);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' [HKS13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The precise details would take up a  few pages so an abbreviated version is outlined here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' To set up Alice picks two safe primes  P, Q i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', Sophie Germain primes, P = 2p + 1, Q = 2q + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Moreover, P, Q ≡ 3 (mod 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Then N = PQ is a so-called Blum integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Let QRN ⊆ (ZN)∗ denote the subset of quadratic residues mod N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' this has pq elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  A signed quadratic residue is an element of QRN which is normalized to lie in the set,  [− (N−1)  2  , (N−1)  2  ];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' this normalized set is denoted QR+  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' We also a target collision resistant  function (also known as universal one way hash function), say T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' The desired key to be  transmitted is K and the notation ℓK denotes the number of bits in K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Finally, for u ∈ ZN  (thought of as an element in [− (N−1)  2  , (N−1)  2  ]) define the function LBSN(u) = u (mod 2) and  then use this to define bits of the key using the Blum–Blum–Shub pseudorandom number  generator ([BBS86]):  BBSN(u) := (LBSN(u), LBSN(u2), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' , LBSN(u2ℓK −1)) ∈ {0, 1}ℓK  Public and Private keys: Given N, Alice picks a signed quadratic residue g ∈ QR+  N  and an element α ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' , (N−1)  4  }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Let X ≡ gα2ℓK +ℓT (mod N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Then the public key is  (N, g, X) and the private key is (N, g, α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Encapsulation: Bob chooses r ∈ {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' , (N−1)  4  } and computes  R ≡ gr2ℓK +ℓT  (mod N),  t = T(R),  S ≡ (gtX)r  (mod N)  The ciphertext is C = (R, S) and the key transmitted is K = BBSN(gr·2ℓT ) ∈ {0, 1}ℓK .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Decapsulation: The receiver computes t = T(R) and verifies whether  S2ℓK +ℓT  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='≡ Rt+α2ℓK +ℓT  (mod N)  Assuming this equality is satisfied the receiver (Alice) computes integers a, b, c such that  2c = gcd(t, 2ℓK+ℓT ) = at + b2ℓK+ℓT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Alice then derives  U ≡ (SaRb−aα)2ℓT −c (mod N),  =⇒  K = BBSN(U)  We don’t add any more details;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' the reason for describing this algorithm is to point out  that the ciphertext has the same flavor of the algorithm presented in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Note that  decapsulation here does not require knowing the factorization of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Remarks  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  The method proposed is probably computationally equivalent to factoring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  To be  certain one would have to solve the following thought exercise: Suppose there is a black box  which takes in input (c, r, n, e) in the proposed algorithm and returns m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Can one factor n  given this information?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' A similar formulation can be made for RSA itself: Suppose there is  a black box which takes input (c, n, e) and outputs m;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' can one factor m?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' This is similar in  spirit to a chosen plaintext attack on either system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' While Theorem C indicates this may  be true the caveat of Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='4 suggests uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  8  KRISHNAN SHANKAR  Acknowledgments  The author is grateful to Kimball Martin, Steven Miller and Larry Washington for their  careful reading of early drafts and for providing valuable comments that helped greatly  improve this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  References  [AM09] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Aggarwal and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Maurer, Breaking RSA generically is equivalent to factoring, In A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Joux, editor,  EUROCRYPT 2009, volume 5479 of LNCS, pages 36–53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Springer, Heidelberg, April 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [BBS86] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Blum, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Blum and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Shub, A simple unpredictable pseudo-random number generator, SIAM  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 15(2), 364–383 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [BD00] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Boneh and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Durfee, Cryptanalysis of RSA with Private Key d Less than n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='292, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Information Theory, 46(4):1339–1349, July 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [BDH-G99] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Boneh, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Durfee, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Howgrave-Graham, Factoring N = prq for Large r, In M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Weiner,  ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', Proceedings of Crypto ’99, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 1666 of LNCS, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 326–337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Springer–Verlag, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [BV98] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Boneh and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Venkatesan, Breaking RSA may not be equivalent to factoring, In K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Nyberg, editor,  EUROCRYPT’98, volume 1403 of LNCS, pages 59–71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Springer, Heidelberg, May / June 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [F89] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Fiat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', Batch RSA, In G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Brassard, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', Proceedings of Crypto 1989, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 435 of LNCS, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 175–185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Springer–Verlag, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [Hin09] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Hinek, Cryptanalysis of RSA and its variants, Cryptography & Network Security series,  Chapman and Hall publishers, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [HKS13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Hofheinz, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Kiltz and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Shoup, Practical Chosen Ciphertext Secure Encryption from Factoring,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' of Cryptology (2013) vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 26, 102–118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [Po99] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Pointcheval, New Public Key Cryptosystems based on the Dependent RSA-Problems, EURO-  CRYPT ’99, Lecture Notes in Computer Science 1592, 239–254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [RSA78] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Rivest, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Shamir, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Adleman, A method for obtaining digital signatures and public-key cryp-  tosystems, Communications of the Association for Computing Machinery, 21(2):120–126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [Rab79] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Rabin, Digital signatures and public key functions as intractable as factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', Technical  Report MIT/LCS/TR-212, Massachusetts Institute of Technology, January 1979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [Sh73] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Shanks, Five Number Theoretic Algorithms, Proceedings of the Second Manitoba Conference on  Numerical Mathematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 51–70, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [Ta98] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Takagi, Fast RSA-type Cryptosystem Modulo pkq, In H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Krawczyk, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=', Proceedings of Crypto  1998, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 1462 of LNCS, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 318–326.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Springer-Verlag, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 1998  [Ton1891] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Tonelli, Bemerkung ¨uber die Aufl¨osung quadratischer Congruenzen, Nachrichten von der  K¨oniglichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universit¨at zu G¨ottingen, 344–  346, 1891.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [Tur94] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Turner, Square roots mod p, The American Mathematical Monthly, May 1994, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 101, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' 5,  443–449.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [Vig08] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Vigilant, RSA with CRT: A New Cost-Effective Solution to Thwart Fault Attacks, In: Cryp-  tographic Hardware and Embedded Systems – CHES 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' CHES 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Lecture Notes in Computer  Science, vol 5154.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  [Wie90] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Wiener, Cryptanalysis of Short RSA Secret Exponents, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' Information Theory  36(3):553–558.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content=' May 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Department of Mathematics & Statistics, James Madison University, 60 Bluestone Drive,  Harrisonburg VA 22807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='  Email address: shankakx@jmu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}
+page_content='edu' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/JdAzT4oBgHgl3EQfVPzH/content/2301.01282v1.pdf'}

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