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+{"text":"\\section{Introduction}\nVarious approaches to quantum gravity, such as string theory and\nloop quantum gravity as well as black hole physics, predict a\nminimum measurable length of the order of the Planck length,\n$\\ell_{p}=\\sqrt{\\frac{G\\hbar}{c^{3}}}\\sim10^{-35}m$. In the presence\nof this minimal observable length, the standard Heisenberg\nUncertainty Principle attains an important modification leading to\nthe so-called Generalized Uncertainty Principle (GUP). As a result,\ncorresponding commutation relations between position and momenta are\ngeneralized too \\cite{1}. In recent years a lot of attention has\nbeen attracted to extend the fundamental problems of physics in this\nframework (see for instance\n\\cite{21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,p,PRD,PhysA,PLB}).\nSince in the GUP framework one cannot probe distances smaller than\nthe minimum measurable length at finite time, we expect it modifies\nthe Hamiltonian of systems too. Recently it has been shown that the\nGUP affects Lamb shift, Landau levels, reflection and transmission\ncoefficients of a potential step and potential barrier \\cite{9}. In\naddition, they speculated on the possibility of extracting\nmeasurable predictions of GUP in the future experiments. In this\nwork we will follow the procedure introduced in the Ref. \\cite{9},\nbut we are going to address the effect of GUP on the\nRamsauer-Townsend (RT) effect. The RT effect can be observed as long\nas the scattering does not become inelastic by excitation of the\nfirst excited state of the atom. This condition is best fulfilled by\nthe closed shell noble gas atoms. Physically, the RT effect may be\nthought of as a diffraction of the electron around the rare-gas\natom, in which the wave function inside the atom is distorted in\nsuch a way that it fits on smoothly to an undistorted wave function\noutside. The effect is analogous to the perfect transmission found\nat particular energies in one-dimensional scattering from a square\nwell. The one-dimensional treatment of scattering from a square well\nand also three-dimensional treatment using the partial waves\nanalysis can be found in \\cite{14}. We generalize the\none-dimensional treatment of the scattering from a square well to\nthe GUP framework. We also address the condition for interference in\nthe Fabry-Perot interferometer in the framework of GUP.\n\n\n\\section{A Generalized Uncertainty Principle}\nQuantum mechanics with modification of the usual canonical\ncommutation relations has been investigated intensively in the last\nfew years (see \\cite{PRD} and references therein). Such works which\nare motivated by several independent streamlines of investigations\nin string theory and quantum gravity, suggest the existence of a\nfinite lower bound to the possible resolution $\\Delta X$ of\nspacetime points. The following deformed commutation relation has\nattracted much attention in recent years \\cite{1}\n\\begin{equation}\n[X, P]=i\\hbar(1+\\beta P^2),\n\\label{eq1}\n\\end{equation}\nand it was shown that it implies the existence of a minimal\nresolution length $\\Delta X=\\sqrt{\\langle X^2 \\rangle -\\langle X\n\\rangle^2}\\ge\\hbar\\sqrt\\beta$. This means that there is no\npossibility to measure coordinate $X$ with accuracy smaller than\n$\\hbar\\sqrt\\beta$. Since in the context of the string theory the\nminimum observable distance is the string length, we conclude that\n$\\sqrt{\\beta}$ is proportional to this length. If we set $\\beta=0$,\nthe usual Heisenberg algebra is recovered. The use of the deformed\ncommutation relation (\\ref{eq1}) brings new difficulties in solving\nthe quantum problems. A part of difficulties is related to the break\ndown of the notion of locality and position space representation in\nthis framework \\cite{1}. The above commutation relation results in\nthe following uncertainty relation:\n\\begin{eqnarray}\n \\Delta X \\Delta P \\geq \\frac{\\hbar}{2}\n\\left( 1 +\\beta (\\Delta P)^2 +\\gamma \\right),\n\\label{eq2}\n\\end{eqnarray}\nwhere $\\beta$ is the GUP parameter and $\\gamma$ is a positive\nconstant that depends on the expectation value of the momentum\noperator. In fact, we have $\\beta=\\beta_0\/(M_{Pl} c)^2$ where\n$M_{Pl}$ is the Planck mass and $\\beta_0$ is of the order of unity.\nWe expect that these quantities are only relevant in the domain of\nthe Planck energy $M_{Pl} c^2\\sim 10^{19}$GeV. Therefore, in the low\nenergy regime, the parameters $\\beta$ and $\\gamma$ are irrelevant\nand one recovers the well-known Heisenberg uncertainty principle.\nThese parameters, in principle, can be obtained from the underlying\nquantum gravity theory such as string theory. Moreover, the\ncomparison between Eqs.~(\\ref{eq1}) and (\\ref{eq2}) shows that\n$\\gamma=\\beta\\langle P\\rangle^2$. Now, let us define \\cite{9}\n\\begin{eqnarray}\n\\left\\{\n\\begin{array}{ll}\nX = x,\\\\\\\\ P = p \\left( 1 + \\frac{1}{3}\\beta\\, p^2 \\right),\n\\end{array}\n\\right.\n\\label{eq4}\n\\end{eqnarray}\nwhere $x$ and $p$ obey the canonical commutation relations\n$[x,p]=i\\hbar$. One can check that using Eq.~(\\ref{eq4}),\nEq.~(\\ref{eq1}) is satisfied up to ${\\cal{O}}(\\beta)$. Also, from\nthe above equation we can interpret $p$ as the momentum operator at\nlow energies ($p=-i\\hbar \\partial\/\\partial{x}$) and $P$ as the\nmomentum operator at high energies. Now, consider the following form\nof the Hamiltonian:\n\\begin{eqnarray}\nH=\\frac{P^2}{2m} + V(x),\n\\label{eq5}\n\\end{eqnarray}\nwhich using Eq.~(\\ref{eq4}) can be written as\n\\begin{eqnarray}\nH=H_0+\\beta H_1+{\\cal{O}}(\\beta^2),\n\\label{eq6}\n\\end{eqnarray}\nwhere $H_0=\\frac{\\displaystyle p^2}{\\displaystyle2m} + V(x)$ and\n$H_1=\\frac{\\displaystyle p^4}{\\displaystyle3m}$.\n\nIn the quantum domain, this Hamiltonian results in the following\ngeneralized Schr\\\"odinger equation in the quasi-position\nrepresentation\n\\begin{eqnarray}\n-\\frac{\\hbar^2}{2m}\\frac{\\partial^2\\psi(x)}{\\partial\nx^2}+\\beta\\frac{\\hbar^{4}}{3m}\\frac{\\partial^{4}\\psi(x)}{\\partial\nx^{4}} +V(x)\\psi(x)=E\\psi(x),\n\\label{eq7}\n\\end{eqnarray}\nwhere the second term in the left side is due to the generalized\ncommutation relation (\\ref{eq1}). This equation is a fourth-order\ndifferential equation which in principle admits four independent\nsolutions. Therefore, solving this equation in $x$ space and\nseparating the physical solutions is not an easy task. With these\npreliminaries, in the next section we solve equation (\\ref{eq7}) for\na quantum well to address the RT effect and the Fabry-Perot\ninterferometer resonance condition in the presence of the minimal\nobservable length.\n\n\\section{The Ramsauer-Townsend effect with GUP}\nWe choose the following geometry of the quantum well (see\nFig.~\\ref{fig1})\n\\begin{equation}\nV(x)=\\left\\{\\begin{array}{ll} -V_{0}&\\quad \\quad0< x < a,\\\\ \\\\\n\\quad0&\\quad\\quad{\\rm elsewhere},\\end{array}\\right. \\label{eq8}\n\\end{equation}\nwhere $V_{0}$ is a positive constant and we assume $E>0$.\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=8cm]{gup3.eps}\n\\caption{ The geometry of a quantum well.}\\label{fig1}\n\\end{figure}\n\nThe eigenfunctions of a particle in this potential well satisfy the\ngeneralized Schr\\\"{o}dinger equation (\\ref{eq7}). We need to find\nthe solutions in three different regions which are indicated in\nFig.~(\\ref{fig1}). To proceed further, we rewrite Eq.~(\\ref{eq7}) in\nthese regions separately as\n\\begin{equation}\nd^{2}\\psi(x)+q^{2}\\psi(x)-\\ell_{p}^{2}d^{4}\\psi(x)=0,  \\label{eq12}\n\\end{equation}\nfor $0<x<a$, and\n\\begin{equation}\nd^{2}\\psi(x)+k^{2}\\psi(x)-\\ell_{p}^{2}d^{4}\\psi(x)=0,  \\label{eq13}\n\\end{equation}\nelsewhere, where by definition\n$d^{n}\\equiv\\frac{\\partial^{n}}{\\partial x^{n}}$,\n$k=\\sqrt{\\frac{2mE}{\\hbar^{2}}}$,\n$q=\\sqrt{\\frac{2m(E+V_{0})}{\\hbar^{2}}}$, and\n$\\ell_{p}=\\hbar\\sqrt{\\frac{2\\beta}{3}}$. As state before, the above\nequations are forth-order differential equations which in general\nadmit four independent solutions. However, some solutions would be\nunphysical which should be removed upon imposing the boundary\nconditions. As it is shown in Ref.~\\cite{p}, alternatively, we can\nfind the equivalent physical solutions by adding the following\nconstraint: the physical solutions should also satisfy the ordinary\nSchr\\\"{o}dinger equation but with different eigenenergy. In fact,\nfor the cases of a free particle and a particle in a box, this\nadditional condition prevents us from doing equivalent but lengthy\ncalculations \\cite{p}. Therefore, we demand that the eigenfunctions\nalso satisfy the following second-order differential equations:\n\\begin{equation}\nd^{2}\\psi(x)+q'^{2}\\psi(x)=0,  \\label{eq12a}\n\\end{equation}\nfor $0<x<a$, and\n\\begin{equation}\nd^{2}\\psi(x)+k'^{2}\\psi(x)=0,  \\label{eq13a}\n\\end{equation}\nelsewhere, where $k'=\\sqrt{\\frac{2mE'}{\\hbar^{2}}}$ and\n$q'=\\sqrt{\\frac{2m(E'+V_{0})}{\\hbar^{2}}}$. The solutions of\nEqs.~(\\ref{eq12a}) and (\\ref{eq13a}) in regions $\\mathrm{I}$,\n$\\mathrm{II}$ and $\\mathrm{III}$ are\n\\begin{eqnarray}\\left\\{\n\\begin{array}{l}\n\\psi_{\\mathrm{I}}=e^{ik'x}+Ae^{-ik'x},\\\\\\\\\n\\psi_{\\mathrm{II}}=Be^{iq'x}+Ce^{-iq'x},\\\\\\\\\n\\psi_{\\mathrm{III}}=De^{ik'x},\n\\end{array}\\right.\n\\end{eqnarray}\nrespectively. These solutions should also satisfy Eqs.~(\\ref{eq12})\nand (\\ref{eq13}) which result in\n\\begin{equation}\\label{kq}\nk^2=k'^2+\\ell_{p}^{2}k'^4,\\hspace{2cm} q^2=q'^2+\\ell_{p}^{2}q'^4.\n\\end{equation}\nThese solutions are similar to the solutions of the ordinary quantum\nmechanics but with modified wavenumbers. Now the boundary conditions\nare the continuity of the wave functions and their first derivatives\nat the boundaries. The resulting equations can be solved\nanalytically to obtain the coefficients $A$, $B$, $C$, and $D$. For\nour purposes, the solution for $A$ is as follows\n\\begin{equation}\nA=\\frac{(k'^{2}-q'^{2})\\sin(q'a)}{(k'^2+q'^2)\\sin(q'a)+2ik'q'\\cos(q'a)}\\,.\n\\label{eq30}\n\\end{equation}\nSo the reflection coefficient is given by\n\\begin{eqnarray}\nR_a(k',q')&\\equiv&|A|^{2},\\nonumber \\\\ &=&\n\\frac{(k'^{2}-q'^{2})^2\\sin^2(q'a)}{(k'^2+q'^2)^{2}\\sin^2(q'a)+4k'^2q'^2\\cos^2(q'a)}.\n\\label{eq31}\n\\end{eqnarray}\nBecause of the smallness of the Planck length, we can obtain\n$k'\\simeq k\\left(1-\\frac{1}{2}\\ell_{p}^{2}k^2\\right)$ and $q'\\simeq\nq\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)$ from Eq.~(\\ref{kq}) and\nwrite the reflection coefficient in terms of the physical\nwavenumbers\n\\begin{equation}\nR_a(k,q)=\\frac{(k^{2}-q^{2})^2\\left[1-2\\ell_{p}^{2}(k^2+q^2)\\right]\n\\sin^2\\left[q\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)a\\right]}{\\left[(k^2+q^2)^{2}-\n2\\ell_{p}^{2}(k^4+q^4)\\right]\\sin^2\\left[q\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)a\\right]\n+4k^2q^2\n\\left[1-\\ell_{p}^{2}(k^2+q^2)\\right]\\cos^2\\left[q\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)a\\right]}.\\label{wide}\n\\end{equation}\nFigure \\ref{fig2} shows the variation of the reflection coefficient\nversus the energy. This figure compares also the ordinary quantum\nmechanical result with corresponding result in the presence of a\nminimal observable length.\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=8cm]{R.eps}\n\\caption{The reflection coefficient $R$ versus the energy $E$ for\n$\\beta=0$ (solid line), $\\beta=0.005$ (dashed line), $\\beta=0.01$\n(dot-dashed line), $V_0=8$, $a=\\pi$, and $\\hbar=2m=1$.}\\label{fig2}\n\\end{figure}\n\nAt this point, it is worth to mention that the rectangular potential\nwell is an idealization, and it would be desirable to evaluate the\nadmitted deviations of a real potential from this ideal one. Indeed,\nin reality, the sharp edges are changed to the smoothed out edges. A\nproper candidate for this case is the Woods-Saxon potential which\nhas the following functional form \\cite{r1}:\n\\begin{equation}\nV(x)=-V_0\\left[\\frac{\\theta(-x+L\/2)}{1+e^{-\\alpha\nx}}+\\frac{\\theta(x-L\/2)}{1+e^{\\alpha (x-L\/2)}}\\right],\n\\end{equation}\nwhere $\\alpha$ and $L$ are real and positive, and $\\theta(x)$ is the\nHeaviside step function. For $\\alpha L\\gg1$ this potential closely\nresembles a rectangular well with smooth edges and size $L$\n(Fig.~\\ref{fig3}). This potential is exactly solvable in\nrelativistic and non-relativistic cases and the solutions can be\nwritten in terms of the hypergeometric functions \\cite{r1,r2,r3}.\nSince these solutions smoothly converge to the plane wave solutions\nfor $\\alpha L\\gg1$, we expect that the GUP-corrected reflection\ncoefficient of this system also continuously tends to\nEq.~(\\ref{wide}) at this limit. However, for this case the wave\nfunction cannot satisfy both the ordinary and GUP-corrected\nSchr\\\"odinger equations simultaneously. This is due to the fact that\nthe potential is not constant inside the well. This problem needs\nfurther investigation and we are going to study it in a separate\nprogram.\n\n\\begin{figure}\n\\centering\n\\includegraphics[width=8cm]{WS.eps}\n\\caption{The Woods-Saxon potential well for $L = 10$ with $\\alpha\n=10$ (solid line) and $\\alpha = 1$ (dashed line).}\\label{fig3}\n\\end{figure}\n\nFor the particular case where\n$\\sin[q\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)a]=0$, there is no\nreflection, that is $R=0$ and therefore we will have maximum\ntransmission. This is the Ramsauer-Townsend effect. In this case\n\\begin{equation}\nq\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)=\\frac{n\\pi}{a}.\n\\label{eq32}\n\\end{equation}\nIn ordinary quantum mechanics this effect occurs at those\nwavenumbers that satisfy the condition\n$q_{\\mbox{\\footnotesize{ord}}}=n\\pi\/a$. This feature shows that\nthere is a shift\n($\\Delta_q=q_{\\mbox{\\tiny{GUP}}}-q_{\\mbox{\\footnotesize{ord}}}$) in\nthe wavenumber of the transmission resonance and this shift itself\nis wavenumber-dependent. Up to the first-order in the GUP parameter,\nwe find\n\\begin{equation}\n\\Delta_q\\simeq\\frac{1}{2}\\ell_{p}^{2}\\left(\\frac{n\\pi}{a}\\right)^3.\n\\end{equation}\nWe also note that in ordinary quantum mechanical description, the\ncondition for resonance is\n$\\lambda_{\\mbox{\\footnotesize{ord}}}=2\\pi\/q=2a\/n$ which is the same\ncondition as in Fabry-Perot interferometer. In the presence of the\nminimal observable length, this condition modifies as follows\n\\begin{equation}\n\\lambda'=\\frac{2\\pi}{q'}\\simeq\\frac{2\\pi}{q}\\left(1+\\frac{1}{2}\\ell_{p}^{2}q^{2}\\right)=\n\\lambda_{\\mathrm{ord}}\\left(1+\\frac{1}{2}\\ell_{p}^{2}q^{2}\\right).\n\\label{eq34}\n\\end{equation}\nTherefore, in the presence of the minimal length, the condition for\ninterference in Fabry-Perot interferometer will change too.\nAmazingly, this change is itself wavelength-dependent.\n\nUp to this point, we have addressed the RT effect and the\nFabry-Perot interferometer resonance condition in the GUP framework.\nTo complete our treatment of this interesting quantum mechanical\nproblem, let us consider the negative energy case $-V_0<E<0$ which\nresults in the quantized energy spectrum. In this case,\nEqs.~(\\ref{eq12a}) and (\\ref{eq13a}) cast into the following\nequations:\n\\begin{equation}\nd^{2}\\psi(x)+q'^{2}\\psi(x)=0,  \\label{eq12b}\n\\end{equation}\nfor $0<x<a$, and\n\\begin{equation}\nd^{2}\\psi(x)-\\kappa'^{2}\\psi(x)=0,  \\label{eq13b}\n\\end{equation}\nelsewhere, where by definition\n$\\kappa=\\sqrt{\\frac{2m|E'|}{\\hbar^2}}$ and\n$q=\\sqrt{\\frac{2m(V_0-|E'|)}{\\hbar^2}}$. So the solutions are\n\\begin{eqnarray}\\left\\{\n\\begin{array}{l}\n\\psi_{\\mathrm{I}}=Ae^{\\kappa'x},\\\\\\\\\n\\psi_{\\mathrm{II}}=Be^{iq'x}+Ce^{-iq'x},\\\\\\\\\n\\psi_{\\mathrm{II}}=De^{-\\kappa'x}.\n\\end{array}\\right.\n\\end{eqnarray}\nIf we choose the center of the well as the center of the coordinate\nsystem, it is straightforward to check that the energy eigenvalues\nare given by the roots of equations\n\\begin{eqnarray}\n\\left\\{\n\\begin{array}{l}\n\\tan(q'a\/2)=\\kappa'\/q', \\\\\\\\\n\\cot(q'a\/2)=-\\kappa'\/q',\n\\end{array}\\right.\n\\end{eqnarray}\nfor even and odd eigenstates, respectively. These eigenvalues can\nalso be written in terms of physical quantities $k$ and $q$ as\n\\begin{eqnarray}\n\\tan\\left[q\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)a\/2\\right]&=&\n\\frac{\\sqrt{\\frac{2mV_0}{\\hbar^2}-q^2}\\left[1-\\frac{1}{2}\\ell_{p}^{2}\n\\left(\\frac{2mV_0}{\\hbar^2}-q^2\\right)\\right]}{q\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)},\\\\\n\\cot\\left[q\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)a\/2\\right]&=&\n-\\frac{\\sqrt{\\frac{2mV_0}{\\hbar^2}-q^2}\\left[1-\\frac{1}{2}\\ell_{p}^{2}\n\\left(\\frac{2mV_0}{\\hbar^2}-q^2\\right)\\right]}{q\\left(1-\\frac{1}{2}\\ell_{p}^{2}q^2\\right)}.\n\\label{eq030}\n\\end{eqnarray}\nSo, for the negative energy case, the energy eigenvalues are the\nroots of Eq.~(\\ref{eq030}). We note that there is no trace of the RT\neffect for $-V_0<E<0$ case.\n\n\\section{Conclusions}\nThe scattering cross section of electrons in noble gas atoms\nexhibits a minimum value at electron energies of approximately\n$1$eV, an effect of which is called the Ramsauer-Townsend effect. We\nstudied the RT effect in the presence of the minimal observable\nlength in the framework of the generalized uncertainty principle. We\nhave shown that in the presence of the minimal observable length\nthere is a shift\n$\\Delta_q=q_{\\mathrm{GUP}}-q_{\\mathrm{ord}}\\simeq\\frac{1}{2}\\ell_{p}^{2}\\left(\\frac{n\\pi}{a}\\right)^3\n$ in the wavenumber of the transmission resonance and this shift\nitself is wavenumber dependent. This shift also affects the\nresonance in the Fabry-Perot interferometer in such a way that this\nchange is itself wavelength dependent. If in the future experiments\none finds a similar shift in Fabry-Perot interferometer resonance\nwavelength, it would be an explicit trace of underlying quantum\ngravity scenario. We note also that the RT effect is in principle a\n3-dimensional effect that needs a 3-dimensional analysis. However,\ncorresponding calculations in 3-dimensions are so lengthy and the\nessential ingredients and outcomes are the same as presented in this\none-dimensional analysis. Finally, we note that this problem can be\ntreated with more real potentials such as the Woods-Saxon potential\nto have more realistic situation. This potential is exactly solvable\nin relativistic and non-relativistic cases and the solutions can be\nwritten in terms of the hypergeometric functions. Since these\nsolutions smoothly converge to the plane wave solutions in\nappropriate limit, we expect that the GUP-corrected reflection\ncoefficient of this system also continuously tends to our result at\nthis limit. We are going to treat this more real situation in a\nseparate research program.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\nCore-collapse supernovae (CCSNe) became the first extra-solar multimessenger objects when SN 1987A was detected by the Kamiokande II experiment and Irvine-Michigan-Brookhaven water Cerenkov detector in 1987 \\citep{bionta:1987,hirata:1987} along with concurrent electromagnetic (EM) observations \\citep[see][]{arnett:1989}. With the recent detection of a neutron star merger--GW170817--in both photons and gravitational waves (GWs) by the LIGO and Virgo collaborations \\citep{abbott:2016}, we have entered the era of GW multimessenger astronomy.  \nSo far, only the mergers of black hole binaries and a neutron star binary have been detected in GWs, but CCSNe are also predicted to be prodigious GW sources, although not quite as ``loud'' as compact object binary mergers.\nAccurate predictions of the expected GW signal from CCSNe is key to increasing the likelihood of detection by GW observatories such as Advanced LIGO (aLIGO) and Advanced Virgo (AdV) and will be crucial in our ability to extract physical meaning from a future CCSN GW detection \\citep{abdik:2014,gossan:2016}.\n\nCCSNe are routinely observed in the EM window, and the data-collecting power of synoptic surveys such as the Large Synoptic Survey Telescope and Zwicky Transient Facility may increase the volume of such data for CCSNe by orders of magnitude \\citep{ivezic:2019,bellm:2019}.\nStill, until the late nebular phase, which is often too dim to be easily observed for distant CCSNe, the EM emission arises from the very outermost layers of the progenitor star and the central core regions, where the explosion is driven, are obscured. \nThis makes it challenging to connect EM emission from CCSNe directly to the mechanism that powers them.\nDue to their relatively small interaction probabilities with matter, both neutrinos and GWs offer windows through which to peer directly into the heart of a CCSN explosion.  \nMoreover, these observations have broader astrophysical applications: restricting nuclear equations of state, verifying angular momentum transport in plasmas, and better understanding stellar rotation.\n\nAn observation of either GWs or neutrino emission from a nearby CCSN combined with multiband observations would allow us to place unique constraints on the physics of the explosion mechanism and key nuclear physics, such as the nuclear equation of state (EOS).  \nThere has yet to be a single astrophysical object detected via all three of these messengers.  \nAlbeit a rare event, a Galactic CCSN offers the perfect opportunity to observe such a multimessenger ``trifecta.''  \nIn order to increase our chances of ``hearing'' such an event in GWs, and in order to be able to extract the greatest scientific meaning from them, we need accurate predictions for CCSN GW signals from the wide range of initial conditions that give rise to these stellar explosions.\n\nModeling GWs from CCSNe incurs all of the challenges of simulating the CCSN mechanism itself, along with a heightened emphasis on the importance of the general relativistic (GR) treatment of gravity. \nThe increased expense of including a fully dynamical spacetime evolution coupled to GR dynamics \\citep[see][]{ott:2009, ott:2012} can further reduce the size of the parameter space that it is feasible to explore. \nApproximations that maintain sufficient numerical accuracy become necessary in order to reduce computational cost.  \nA common approach for CCSNe, particularly in 2D, is the conformal flatness condition (CFC) approximation wherein the spatial three-metric is obtained approximately from the flat spacetime three-metric.\nCFC has been shown to accurately reproduce prebounce and early postbounce signals from CCSNe to within a few percent when compared with direct solutions to Einstein's field equations  \\citep{ott:2007}.  Likewise, while some differences appear, \\citet{shibata:2004} find good qualitative agreement between the effective GR potential and CFC.  This conformal flatness approach has also been extended to an ``augmented CFC\" scheme as introduced by \\citet{saijo:2004}, refined by \\citet{cordero-carrion:2009}, and utilized by \\citet{bmuller:2019}.\nA further approximation, also common in simulations of the CCSN mechanism, is to couple an effective GR gravitational potential to otherwise Newtonian dynamics \\citep{rampp:2002, marek:2006, bruenn:2016,  moro:2018, oconnor:2018}.  \nThis relativistic effective potential empirically satisfies the solution to hydrostatic equilibrium according to a modified Tolman-Oppenheimer-Volkoff equation \\citep{rampp:2002, marek:2006}.\nThis approach further reduces the computational expense of CCSN simulations relative to the CFC approach and reproduces fairly accurately gross features of CCSN simulations \\citep{marek:2006, muller:2012,oconnor:2018}.  \n\nAfter the infalling matter from collapse reaches nuclear densities, the core nuclei dissolve into nucleons and, eventually, the strong force becomes repulsive, halting the material infall.  On the time scale of tens of microseconds, the subsonic inner core encounters the supersonic outer core, forming a shock front.  As this shock front photodissociates overlying material and releases an enormous neutrino flux, it leaves behind a negative entropy gradient \\citep{mazurek:1982,bruenn:1985,bruenn:1989}.  This scenario is unstable according to the Ledoux criterion, causing prompt convection in the postshock region \\citep{burrows:1992}, therefore creating an associated emission of gravitational radiation \\citep{marek:2009b,ott:2009}.  This prompt convection is an important feature that occurs in simulations that incorporate either GR or Newtonian treatments of gravity during the early postbounce phase \\citep{muller:2017,richers:2017,nagakura:2018}.\n\nEarly research into GW emission from CCSNe focused on the bounce and early postbounce phase of the explosion in rotating progenitors.\nThese investigations found that increasing the angular momentum of the core leads to a larger strain peak at bounce \\citep{muller:1982,moench:1991,yamada:1995,zwerger:1997,dimm:2002,kotake:2003,shibata:2004}.  \nMore recent investigations of rotating core collapse examine the role of the angular momentum distribution within the supernova progenitor and find it is only important in the rapid rotation regime, where the ratio of kinetic to gravitational potential energy ($T\/|W|$) $ \\gtrsim 8\\%$ at bounce \\citep{abdik:2014}. In order to examine GW emission at later times, different groups have considered other factors for nonrotating cases---for example, convection in the postshock region \\citep{burrows:1996,muller:1997,muller:2004,marek:2009b,murphy:2009}, the standing accretion shock instability (SASI) \\citep{blondin:2003,blondin:2006,ohnishi:2006,foglizzo:2007,scheck:2008,iwakami:2009,fernandez:2010}, and protoneutron star (PNS) vibrational modes \\citep{cerda-duran:2013,torres-forne:2018,torres-forne:2019}.  \\citet{moro:2018} investigate GW emission for moderate rotational speeds ($\\Omega_{\\mathrm{core}} = 0.2$ rad s$^{-1}$) for a single progenitor mass ($13 M_\\odot$) over 1 second postbounce.  \\citet{pan:2018}, \\citet{kuroda:2018}, \\citet{cerda-duran:2013}, and \\citet{ott:2011} investigate the relationship between black hole formation and GW emission, for a nonrotating 40 $M_\\odot$, a nonrotating  70 $M_\\odot$, a rotating 35 $M_\\odot$, and a rotating 75 $M_\\odot$ progenitor, respectively.  These studies also find stronger GW emission at bounce with increased progenitor angular momentum and loud GW emission at later times for nonrotating CCSNe.\n \n\nIn this work, we present 15 axisymmetric (2D) neutrino radiation-hydrodynamic CCSN simulations.  \nOur parameter space spans four progenitor masses ranging from $12\\,M_\\odot$ to $60\\,M_\\odot$ \\citep{Suk:2016} and four peak core rotation speeds: $0-3 \\text{ rad s}^{-1}$.  \nWe examine the variation in key features of the GW emission from CCSNe at these different masses and rotation rates.\nRapid rotation rates up to 2 and 3 rad s$^{-1}$ are likely rare in typical massive stars at solar metallicity due to efficient transport and loss of angular momentum \\citep{heger:2005}.\nWhile \\citet{woosley:2006} observe that only 1\\% of massive stars may reach the rapid rotation regime, there are high uncertainties in the stellar mass loss and magnetic braking calculations \\citep{smith:2014}.  Moreover, albeit a small percentage, \\citet{demink:2013} show the distinct possibility of rapidly rotating stars formed from binary interactions. Thus, there is some likelihood of rapidly rotating supernova progenitors in the mass range we explore.  \n\n\nIn addition to the breadth of parameter space we cover, we also explore the role of rotation up to 300 ms postbounce.  \nWe find that rotation restricts the growth of SASI by centrifugally flattening the shock, leaving it slightly oblate. Likewise, the positive angular momentum gradient created by the rotation stabilizes the postshock convection according to the Solberg-H{\\o}iland stability criterion \\citep{endal:1978,fryer:2000}.  Not only are the SASI and postshock convection contributions to the gravitational radiation diminished, but the PNS vibrational signals are damped because of less turbulent downflows of matter onto the PNS surface.  \nThis results in a ``muting'' of the GW signal with increasing rotation speeds.\nWhile the origins of this muting are physical, such behavior may not be seen in full 3D simulations of CCSNe due to the appearance of spiral modes of the SASI and magnetorotational instabilities (MRI) \\citep{cerda-duran:2007,andresen:2019} . \n\nCompared with previous works, the strength of this project is its ability analyze GWs from multiple progenitors hundreds of milliseconds postbounce while accurately accounting for rotation and neutrinos.  The wide breadth of parameter space we examine allows us to reveal certain rotational effects on the GW signal in the context of a controlled study.\n\nIn the present simulations we use an approximate, effective GR potential \\citep{marek:2006,oconnor:2018}.\nIn order to validate this approximate approach for studying GWs from CCSNe, we compare our results to those of \\citet{richers:2017}, who use a CFC GR approach.  We find that our simulations produce nearly identical GW bounce signals to those of \\citet{richers:2017}.  \n\nThis paper is organized as follows:  in Section \\ref{sec:method} we present our methods and treatment of microphysics within our \\texttt{FLASH} simulations.  We present a new method for applying initial rotation to the progenitor.  Because each progenitor evolves at a different rate and we terminate our simulations at 300 ms postbounce, we refrain from asserting which explode.  Rather, in Section \\ref{sec:results}, we begin by addressing the shock front evolution for each of the progenitor masses and initial rotation velocities.  We then verify our gravitational treatment by comparing our bounce signal to GR simulations.  We explore the effect of rotation on GWs emitted hundreds of milliseconds after core bounce and discuss implications on their detectability.  In Section \\ref{sec:summary} we conclude and summarize the influence of rotation on GWs from initial collapse to 300 ms postbounce. \n\n\n\\section{Methods and Simulation Setup}\n\\label{sec:method}\nWe utilize the \\texttt{FLASH} (version 4) multiscale, multiphysics adaptive mesh refinement simulation framework for our simulations \\citep{fryxell:2000,dubey:2009}.\\footnote[7]{\\url{http:\/\/flash.uchicago.edu\/site\/}}  We employ a modified, GR, effective potential \\citep{marek:2006, oconnor:2018} incorporated into the multipole Poisson solver of \\citet{couch:2013a}, where we retain spherical harmonic orders up through 16.   We utilize the SFHo EOS in all of our 15 simulations \\citep{steiner:2013}.  Our grid setup is a 2D cylindrical geometry with the PARAMESH (v.4-dev) library for adaptive mesh refinement  \\citep{macneice:2000}.  The outer boundary is $10^4$ km in all directions, with nine levels of refinement, yielding a finest grid spacing of about 0.65 km.\nThe maximum allowed level of refinement is decreased as a function of spherical radius, $r$, in order to maintain a resolution aspect ratio, $\\Delta x_i \/ r$, of about 0.01, corresponding approximately to an ``angular'' resolution of $0.5^{\\circ}$.\n\nNeutrinos play a vital role in CCSNe.  Directly after collapse, they provide an avenue through which the PNS can cool.  As the shock propagates outward, they also provide heating in the gain region that is crucial in reviving the explosion, according to the neutrino heating mechanism.  The opacity of the material to these outflowing neutrinos must be carefully accounted for in an energy-dependent way.  We incorporate a multidimensional, multispecies, energy-dependent, two-moment scheme with an analytic closure, or the so-called M1 scheme.  Our implementation is based on \\citet{oconnor:2015}, \\citet{shibata:2011}, and \\citet{cardall:2013}.  A detailed outline of the M1 implementation in \\texttt{FLASH} is in \\citet{oconnor:2018}.  This combination of rotation and the M1 neutrino treatment is similar to the work of \\citet{obergaulinger:2017} and \\citet{obergaulinger:2018}.  In order to reduce computational costs to explore the wide parameter space for our study, we neglect velocity-dependent neutrino transport and do not account for inelastic neutrino-electron scattering.\nWe use 12 energy bins spaced logarithmically up to 250 MeV, and the full set of rates and opacities we use is described in \\citet{oconnor:2017a}. \nSpecifically, we use the effective, many-body, corrected rates\nfor neutrino-nucleon, neutral current scattering of \\citet{horowitz:2017}.  \n\nWe use the 12, 20, 40, and 60 \\ensuremath{\\mathrm{M}_\\odot}\\xspace nonrotating, solar-metallicity progenitors models from \\citet{Suk:2016} for the present work.\n\n\\begin{figure}[t]\n    \\centering\n    \\includegraphics[scale=0.45]{omega_vs_r.pdf}\n    \\caption{The rotation profiles for five of the \\citet{heger:2005} progenitors.  Each solid line represents \\citeauthor{heger:2005}'s (\\citeyear{heger:2005}) model, and the dashed lines are Equation (\\ref{eq:omega}) applied to the respective progenitor, with the appropriate differential rotation parameter.  }\n    \\label{fig:ovsr}\n\\end{figure}\n\n\\subsection{Treatment of Rotation}\n\n\n\n\nThe progenitor models we use are evolved without rotation.\nAt the start of core collapse, when we map the 1D models into our 2D grid, we apply an artificial rotation profile\n\\begin{equation}\n    \\Omega(r) = \\Omega_0 \\bigg[1 + \\bigg(\\frac{r}{A}\\bigg)^2 \\bigg]^{-1}, \n    \\label{eq:omega}\n\\end{equation}\n\nwhere $r = \\sqrt{R^2 + z^2}$ is the spherical radius for a given cylindrical radius $R$ and altitude $z$, $\\Omega_0$ is the central angular speed of the star, and $A$ is the differential rotation parameter \\citep{eriguchi:1985}.  For large values of $A$, the stellar rotation is nearly solid body, whereas small values of $A$ lead to a more differential profile. \nThe {\\it linear} rotational velocity is then calculated by multiplying the angular speed with the distance from the rotation axis, $v_\\phi (R, z) = R \\Omega (r) $. \n\nThe precise rotation rates and profiles of massive stellar cores at collapse are uncertain.\nPrevious work \\citep[e.g.,][]{abdik:2014} treated the differential rotation parameter $A$ as a free parameter and explored the impact of its variation.\nExamining the stellar evolution models of \\citet{heger:2005}, which include angular momentum transport due to the Tayler-Spruit dynamo \\citep{spruit:2002}, we find that $A$ is strongly determined by the {\\it compactness} \\citep{oconnor:2011} of the stellar core.\nIn order to demonstrate this, we fit the rotation profiles of the 20 progenitor models from \\citet{heger:2005} to Equation (\\ref{eq:omega}) in order to determine the best-fit $A$.\nThe models of \\citet{heger:2005} include stars of zero-age main sequence (ZAMS) masses 12, 15, 20, 25, and 35 $M_{\\odot}$, with various angular momentum transport parameters and initial ZAMS rotation rates.  \nUsing the \\texttt{curve\\_fit} function (in the \\texttt{scipy.optimize} library) available in \\texttt{Python}, we obtain $A$ values that correspond to the most accurate fits of Equation (\\ref{eq:omega}) to the rotation profiles of these models.  Figure \\ref{fig:ovsr} displays the radial, rotation profile for five of the aforementioned progenitors, compared with our implementation of Equation (\\ref{eq:omega}), with the best-fit $A$ value.\n\nThe core compactness as introduced by \\citet{oconnor:2011} is defined as\n\\begin{equation}\n    \\xi_M = \\left.\\frac{M\/M_{\\odot}}{R(M_\\mathrm{bary}=M)\/1000 \\text{km}}\\right\\vert_\\mathrm{collapse} ,\n\\end{equation} \nwhere we choose $M = 2.5 M_\\odot$, and $R(M_{\\mathrm{bary}}=M) $ as the radius at which the internal baryonic mass is $2.5M_\\odot$, at collapse.  \nFigure \\ref{fig:a_vs_comp} shows the compactness parameters from the \\citet{heger:2005} models (blue stars) plotted against their best-fit $A$ values.\nA clear linear relation exists between $A$ and $\\xi_{2.5}$.  \n\n\\begin{figure}[t]\n    \\centering\n    \\includegraphics[scale=0.45]{a_vs_compact.pdf}\n    \\caption{Linear relation between differential rotation parameter, $A$, and compactness parameter of the inner 2.5 $M_\\odot$, $\\xi_{2.5}$.  The linear trend is constructed from the \\citet{heger:2005} rotation profiles.  We then apply the relation to the compactness values from \\citet{Suk:2016} to yield the differential rotation parameters.  The progenitor ZAMS masses are labeled in units of $M_\\odot$ for each respective point.}\n    \\label{fig:a_vs_comp}\n\\end{figure}\n\n\\begin{table}[t]\n\\begin{tabular}{c|c|c}\nProgenitor Mass ($M_\\odot$) & Compactness & \\textit{A}(1000 km) \\\\\n\\hline\n12  & 0.0738 &         0.8123             \\\\\n20  & 0.2785 &         1.021            \\\\\n40  & 0.5341 &         1.282           \\\\\n60  & 0.1708 &         0.9112          \n\\end{tabular}\n\\caption{Listed values for ZAMS Mass, Compactness Calculated from \\citet{Suk:2016}, and Differential Rotation Parameter \\textit{A}.}\n\\label{table:compact}\n\\end{table}\n\nUsing this relationship, we calculate optimal $A$ values for the four \\citet{Suk:2016} progenitors we use in this work (orange circles in Figure \\ref{fig:a_vs_comp}).  \nThe full list of progenitor masses, compactness values, and \\textit{A} values we use is given in Table ~\\ref{table:compact}.  \n\nAs a note, we choose to omit the 40 $M_\\odot$ progenitor at $\\Omega_0 = 3$ rad s$^{-1}$ from our following analysis with a numerically motivated rationale.  The $\\xi_{2.5}$ value of this progenitor is nearly double that of the 20 $M_\\odot$ progenitor (the next closest compactness value).  This fact displays that the 40 $M_\\odot$ has a much larger differential rotation parameter compared with the other progenitors, resulting in a nearly solid-body rotation of the core. This endows the core in the 40 \\ensuremath{\\mathrm{M}_\\odot}\\xspace model with drastically more angular momentum than the other models.  The vast amount of angular momentum ultimately led to numerical instabilities in our calculations; thus, we omit the 40 $M_\\odot$, with $\\Omega_0 = 3$ rad s$^{-1}$ from our analysis.  \\\\\n\n\n\n\n\n\n\\section{Results}\n\\label{sec:results}\n\nTo extract the GW signal from our simulations, we adopt the dominant, quadrupole moment formula for the gravitational strain, through the slow motion, weak-field formalism\n\\citep[eg.][]{blanchet:1990,finn:1990}\n\\begin{equation}\n    h_+ \\approx \\frac{2G}{Dc^4}\n    \\frac{d^2I_{zz}}{dt^2},\n\\label{eq:quad}\n\\end{equation}\nwhere $I_{zz}$ is the reduced-mass quadrupole moment, $G$ is the gravitational constant, $c$ is the speed of light, and $D$ is the distance to the source (our fiducial value is $D=10$ kpc) and we assume optimal source orientation---GWs emitted from the equator of the CCSN.\\\\\n\\par When plotting the amplitude spectral density (ASD) of the GW signal we compute the discrete Fourier transform consistent with \\citet{anderson:2004} and LIGO's implementation\n\\begin{equation}\n\\widetilde{h}_{+k} = \\sum^{N-1}_{j=0} h_{+j} e^{-i2\\pi jk\/N}\n\\label{eq:dft}\n\\end{equation}\nwhere $i=\\sqrt{-1}$.\n\nTo quantify the strength of convection within our simulations, we characterize the anisotropic velocity of the fluid motion within the postshock region according to \\citet{takiwaki:2012}:\n\n\\begin{equation}\n    v_{\\mathrm{aniso}} = \\sqrt{\\left<\\rho\\Big((v_r - \\left<v_r\\right>)^2 + v_\\theta^2 + v_\\phi^2\\Big) \\right>\/\\left<\\rho\\right>}\n\\label{eq:vaniso}\n\\end{equation}\nwhere $\\left<\\right>$ represents an angle average, $v_r$ is the radial velocity, $v_\\theta$ is the velocity component in the polar direction, $v_\\phi$ is the velocity component in the azimuthal direction, and $\\rho$ is the density.  \n\nWith the introduction of rotation, a positive angular momentum gradient can be established, leading to inhibited convection, according to the Solberg-H{\\o}iland stability criterion.  To quantify this criterion we calculate the condition at the equator for stability in the vertical direction, $R_{\\mathrm{SH}}$, consistent with \\citet{heger:2000}:\n\n\\begin{equation}\n    R_{\\mathrm{SH}} := \\frac{g}{\\rho}\\Bigg[\\Bigg(\\frac{d\\rho}{dr}\\Bigg)_{\\mathrm{ad}}-\\frac{d\\rho}{dr}\\Bigg] + \\frac{1}{r^3}\\frac{d}{dr}(r^2\\omega)^2 \\geq 0\n\\label{eq:SHI}\n\\end{equation}\nwhere $g$ is the local gravitational acceleration, $\\rho$ is the density, $(d\\rho\/dr)_{\\mathrm{ad}}$ is the radial density gradient at constant entropy and composition, $r$ is the distance from the axis of rotation, and $\\omega$ is the rotational velocity. \n\nTo examine the shape of the shock front, $R_S(\\theta,\\phi)$, we represent it as a linear combination of spherical harmonics, $Y_l^m(\\theta,\\phi)$:\n\n\\begin{equation}\n    R_S(\\theta,\\phi) = \\sum_{l=0}^\\infty \\sum_{m=-l}^{l} a_l^m Y_l^m(\\theta,\\phi)\n\\end{equation}\n\\begin{equation}\n    Y_l^m = \\sqrt{\\frac{2l+1}{4\\pi}\\frac{(l-m)!}{(l+m)!}}P_l^m(\\cos(\\theta)) e^{im\\phi}\n\\end{equation}\nwhere $P_l^m$ are the associated Legendre polynomials \\citep{burrows:2012,takiwaki:2012}.  However, because of the 2D nature of our simulations $\\phi = 0$ and all $m = 0$ as well; thus the coefficients $a_l^0$ are\n\n\\begin{equation}\n    a_l^0 = \\int_0^\\pi d\\theta \\sin(\\theta)R_S(\\theta)Y_l^0(\\theta) .\n\\label{eq:sho_coeff}\n\\end{equation}\nIt follows that $a_0^0$ corresponds to the average shock radius.\n\\subsection{Rotation's Influence on Shock Front Evolution}\n\nWhile our focus in the present work is on the GW signals up to 300 ms postbounce, we briefly discuss the impact of rotation on the evolution of the shock front as it propagates outward.  In certain cases, independent of the mechanism, the shock front may require over 300 ms to revive and complete a successful explosion.  Because our simulations are only run until 300 ms postbounce, we refrain from asserting which progenitors successfully explode.  Rather, we remark on how the average shock radii develop with time.\n\nOf our 15 simulations, only the nonrotating 20 \\ensuremath{\\mathrm{M}_\\odot}\\xspace and 60 \\ensuremath{\\mathrm{M}_\\odot}\\xspace progenitors show substantial shock expansion.  The effect rotation has on reviving the shock is not a simple one. \nIn one respect, one expects greater centrifugal support to lead to a larger shock front.  However, there are two factors that inhibit the shock from propagating outward.  The first is the inhibited convection due to the positive angular momentum gradient within the progenitor. Weaker convection results in less efficient neutrino heating \\citep{dolence:2013, murphy:2013} and less positive support from turbulence in the gain region \\citep{couch:2015a, mabanta:2018}.  The  second rotational element that inhibits explosions is the lack of neutrino production.  Rotation centrifugally supports matter that is infalling during the initial collapse of a star.  As such, the collapsing material does not settle as deeply into the gravitational potential of the stellar core, thereby releasing less gravitational binding energy.  This process results in a lower neutrino luminosity and slower contraction of the PNS \\citep{summa:2018}. \nThese two dominant effects, weaker convection and reduced neutrino luminosity, can create an unfavorable scenario for a supernova explosion that is revived by neutrino heating.\n\nDespite rotation inhibiting certain aspects of a successful explosion, some of our rotating models ($\\Omega_0 = 3$ rad s$^{-1}$, 20 \\ensuremath{\\mathrm{M}_\\odot}\\xspace, and 60 \\ensuremath{\\mathrm{M}_\\odot}\\xspace) have advancing shock radii.  With longer simulation times, these could lead to explosion.  In these cases, it seems that rotation could be sufficiently rapid to overcome the deleterious effects on convection and reduced neutrino luminosity.\nSimilar nonmonotonic behavior is reported by \\citet{summa:2018} in their 2D simulations.\nHence, the introduction of rotation involves competing forces that can enhance or diminish the shock.  Figure \\ref{fig:shock} shows the average shock radius evolution versus time (postbounce) over our entire parameter space.\n\n\\begin{figure}[t]\n    \\centering\n    \\includegraphics[width = 0.5\\textwidth]{M1_shock_mass_raster.pdf}\n    \\caption{Shock radius evolution of the four progenitor models versus time (postbounce).  As different progenitors evolve at different rates, they may not have enough time to revive their shock front within the 300 ms interim.  As such, only the nonrotating 20 \\ensuremath{\\mathrm{M}_\\odot}\\xspace and 60 \\ensuremath{\\mathrm{M}_\\odot}\\xspace progenitors show substantial shock expansion. }\n    \\label{fig:shock}\n\\end{figure} \n\n\\subsection{Comparison with CFC GR}\n\n \\begin{figure}[t]\n    \\centering\n    \\includegraphics[width=0.48\\textwidth]{bounce_richers.pdf}\n    \\caption{GW strain vs. time (postbounce) for a 12 \\(M_\\odot\\) progenitor \\citep{woosley:2007} with $\\Omega_0 = 3$ rad s$^{-1}$.  Plotted in the dashed line is the GW strain from \\citet{richers:2017} using the CFC \\texttt{CoCoNuT} code, and the solid line is our result using the effective relativistic potential coupled with Newtonian dynamics.  While the different grids and treatment of hydrodynamics lead to differences in the strain in the early postbounce phase, we qualitatively verify our gravitational treatment by obtaining a nearly exact bounce signal. }\n    \\label{fig:bounce_cfc}\n\\end{figure}\n\n\\begin{figure*}[t]\n  \\centering    \n  \\includegraphics[width=0.49\\textwidth]{hd3_bounce_test.pdf}\n  \\includegraphics[width=0.49\\textwidth]{hdj_bounce_final.pdf}\n  \\caption{(Left) GW bounce signal from all 10 progenitor masses with $\\Omega_0 = 3 \\text{ rad s}^{-1}$.  By applying Equation (\\ref{eq:omega}), we assign a radially dependent, angular velocity to our progenitors.  Because the central density profiles of each progenitor are different---namely, a less compact $12\\,M_\\odot$ and more compact $40\\,M_\\odot$---the progenitor cores are endowed with different amounts of angular momenta.   (Right) Modified bounce signals after adjusting rotation rates to yield similar angular momenta ($\\sim 2.4\\times10^{49} \\text{erg s}$) of the inner $1.75\\,M_\\odot$ of matter.  As predicted by \\citet{dimm:2008} and \\citet{abdik:2010,abdik:2014}, the GW bounce signals depend on the inner core angular momentum at bounce, not the original ZAMS mass.}\n  \\label{fig:bounce}\n\\end{figure*}\n\nIn multidimensional simulations of CCSNe, the treatment of gravity must offer a balance between numerical accuracy and computational cost.   The CFC offers a nearly identical GW signal, compared with full GR, while reducing simulation time \\citep{ott:2007}.  Figure \\ref{fig:bounce_cfc} offers a qualitative check of our effective GR potential compared with CFC \\citep{richers:2017}.  We incorporate an identical deleptonization profile \\citep{lieb:2005} and SFHo EOS \\citep{steiner:2013} for a 12 \\ensuremath{\\mathrm{M}_\\odot}\\xspace progenitor \\citep{woosley:2007}.  Moreover, we match the differential rotation parameter and rotation profile by selecting an $A = 634$ km and $\\Omega_0 = 3$ rad s$^{-1}$.  For this comparison, we match the neutrino physics of \\citet{richers:2017}'s simulation by using a ray-by-ray, three-species, neutrino leakage scheme \\citep{oconnor:2010,couch:2014}.  We capture a nearly identical bounce signal and similar strain up to 5 ms postbounce. \\par\nHowever, after the initial bounce signal ring-down, it is clear that the different computational treatments of hydrodynamics and grid geometry result in differences in the GW strains.  Although not exact, the efficiency of the effective GR potential offers a reasonable method to accurately model the GW signal from CCSNe to within 10\\% and allows for larger sweeps of parameter space \\citep{muller:2013}.\n\n\n\n\\subsection{ZAMS Influence on Gravitational Bounce Signal}\n\nWhile different progenitors $\\gtrsim$$8\\, M_\\odot$ will experience widely varied evolution, once their iron cores reach the effective Chandrasekhar mass \\citep{baron:1990} and collapse commences, the physics of the collapse becomes somewhat universal.\nIn particular, the mass of the homologously collapsing inner core is fixed more by microphysics than by the macrophysics of varied stellar evolution. \nThis nearly identical inner core mass across the ZAMS parameter space yields similar core angular momenta, for identical rotation rates.  Hence, the core bounce signal is nearly indistinguishable between progenitor masses.  For further verification of our gravitational treatment, we perform 12 additional simulations using neutrino leakage---from collapse---until 8 ms after core bounce, in order to replicate this bounce signal degeneracy, using the \\citet{Suk:2016} progenitors.  Outlined by \\citet{ott:2012}, neutrino leakage has a small effect on the GW bounce and early postbounce signal.  \nMoreover, our results are consistent with 3D, fully GR predictions given by \\citet {ott:2012} that similar core angular momenta yield similar GW bounce signals.  \n\nFigure \\ref{fig:bounce} displays the bounce signals for all 10 progenitor masses, ranging from 12 \\ensuremath{\\mathrm{M}_\\odot}\\xspace to 120 \\ensuremath{\\mathrm{M}_\\odot}\\xspace.  The left panel is for uniform rotational velocity prescriptions at $\\Omega_0 = 3\\text{ rad s}^{-1}$.  As previously highlighted, the angular momentum of the inner core is the main contributor to the gravitational bounce signal.  While many of the waveforms have similar amplitudes, there are two clear outliers: the $12\\,M_\\odot$ and $40\\,M_\\odot$ progenitors.  The $12\\,M_\\odot$ and $40\\,M_\\odot$ progenitors, respectively, have lower and higher compactness values at collapse, by nearly a factor of 2.  Because we endow each progenitor with angular velocity, and not specific angular momentum, the more compact $40\\,M_\\odot$ progenitor will receive more angular momentum, compared with the remaining progenitors, thereby affecting the resulting GW bounce signal.  As outlined by \\citet{dimm:2008}, once a star is sufficiently rotating, the centrifugal support slows the bounce, diminishing the GW bounce amplitude and widening out the bounce peak of the waveform.  \n\nThe inverse is true for the $12\\,M_\\odot$ case.  Because it has a less compact inner core at collapse, using Equation (\\ref{eq:omega}) leads to less initial angular momentum, thereby producing a lower amplitude bounce signal.  After modifying the initial rotation rates of both progenitors, to match the progenitor core angular momenta (right panel of Figure \\ref{fig:bounce}), the change produces nearly identical GW bounce signals.  \n\nHence, our results from exploring the bounce signal over a wide range of progenitor masses support the results of previous studies of the angular momentum dependence of the GW signal \\citep{dimm:2008,abdik:2010,abdik:2014} but also serve as a cautionary note for future groups who perform rotating CCSN simulations with a wide variety of progenitor models.  \nIt is worth noting that other rotational treatments exist beyond the simple angular velocity law, such as specifying a radial, specific angular momentum profile \\citep[eg.,][]{oconnor:2011} or using the rotational profile from the rotating stellar evolution models directly \\citep{summa:2018}.  The profiles used by \\citet{oconnor:2011} lead to a roughly uniform rotation rate within a mass coordinate of 1 $M_\\odot$ and $\\Omega(r)$ decreasing with  $r^{2}$ outside this mass coordinate.  \\citet{summa:2018} utilize two different rotation schemes: one that matches the \\citet{heger:2005} models seen in Figure \\ref{fig:ovsr} and one that is solid body out to $\\sim 1500$ km and then falls as $r^{-3\/2}$.\n\n\\subsection{Rotational Influence on Accretion-phase GW Emission}\n\nOur results in the previous section support the efficacy of our effective GR potential for accurately modeling the GW signals from CCSNe.  While the effective GR potential has been shown to overestimate peak frequency from GWs compared with GR, it produces similar GW amplitudes and accurately captures PNS compactness during the accretion-phase \\citep{muller:2013}.  Thus we now turn to exploring the rotational effects on the GW signal during the accretion-phase, up to 300 ms after bounce.\n\nWhile the consistency of the inner core mass for a collapsing iron core creates a setting where envelope mass has little effect on the bounce signal, the postbounce dynamics of the explosion largely depend on the mass surrounding the PNS.  For nonrotating CCSNe, the shock front propagates outward and loses energy due to dissociation of iron nuclei and neutrino cooling.  In the case of rotation, the initial progenitor and resulting shock front become more oblate.  Rotation can affect the GW emission in three respects: the postshock convection is damped, the SASI becomes restricted, and it slows the rate at which the PNS peak vibrational frequency increases.\n\n\\begin{figure}[]\n    \\centering\n    \\includegraphics[width=0.5\\textwidth]{vaniso_rad.pdf}\n    \\caption{Spherically averaged anisotropic velocity of the postshock region for the 12 \\ensuremath{\\mathrm{M}_\\odot}\\xspace progenitor.  Brighter colors correspond to increased convection in the postshock region according to Equation (\\ref{eq:vaniso}).  As rotational velocity increases, convective activity is inhibited.  Traced in red is the radius of the PNS.}\n    \\label{fig:vaniso}\n\\end{figure}\n\n\\begin{figure}[]\n    \\centering\n    \\includegraphics[width=0.5\\textwidth]{SHI_panel_invert.pdf}\n    \\caption{Slices along the equator of the 12 \\ensuremath{\\mathrm{M}_\\odot}\\xspace progenitor at each rotational velocity.  Colors correspond to the Solberg-H{\\o}iland stability criterion, $R_{\\mathrm{SH}}$, from Equation (\\ref{eq:SHI}).  As rotational velocity increases, not only does the convectively stable band in the core grow (seen in blue), but the amount of convection within the postshock region (seen in red) decreases as well.  The differences in shock radius evolution between Figure \\ref{fig:vaniso} and this figure arise because Figure \\ref{fig:vaniso} uses an angular average over the domain, whereas this figure uses equatorial slices.}\n    \\label{fig:SHI}\n\\end{figure}\n\n \\begin{figure*}[htp]\n  \\centering    \n  \\includegraphics[width=\\textwidth]{tdwf_region_20.pdf}\n  \\caption{Time domain waveforms for the 20 $M_\\odot$ progenitor.  Each panel corresponds to the region from which the GWs are emitted.  The large contribution in the top panel indicates the main source of GWs during the accretion-phase is from the vibrating PNS.  The lower panel displays the inhibited convective signal $\\sim 50$--$100 $ ms postbounce that is characteristic of this quiescent phase.}\n  \\label{fig:region}\n\\end{figure*}\n\n\\begin{figure}\n    \\centering\n    \\includegraphics[width=0.5\\textwidth]{sasi_axis_norm.pdf}\n    \\caption{Coefficients from spherical harmonic decomposition of the shock front, outlined in Equation (\\ref{eq:sho_coeff}).  The $a_1^0\/a_0^0$ and $a_2^0\/a_0^0$ terms describe the overall dipole and quadrupole nature of the shock front, respectively.  As the SASI is one of the main contributors to the creation of asymmetries in the shock front, the lower $a$ values correspond to a less prolate shock, or one with diminished SASI.}\n    \\label{fig:sasi}\n\\end{figure}\n\n  As the $\\Omega_0$ value increases in our models, a positive angular momentum gradient is established within the postshock region, partially stabilizing it to convection via the Solberg-H{\\o}iland instability criterion \\citep{endal:1978,fryer:2000}.  We quantify the reduced convection in Figure \\ref{fig:vaniso}.  Brighter colors correspond to higher values of the anisotropic velocity as outlined in Equation (\\ref{eq:vaniso}).  As expected, the convection in the gain region is reduced with increasing rotational velocity.  To tie this inhibited convection to the Solberg-H{\\o}iland instability criterion, we follow the prescription of Section 2.3.2 of \\citet{heger:2000}.  We quantify this instability criterion as outlined in Equation (\\ref{eq:SHI}) by taking slices along the equator and tracking its evolution.  Figure \\ref{fig:SHI} displays the $R_{\\mathrm{SH}}$ value along the equator of the 12 \\ensuremath{\\mathrm{M}_\\odot}\\xspace progenitor for all four rotational velocities.  As the $\\Omega_0$ increases, the propensity for convection (colored red) within the postshock region clearly decreases.  This inhibited convection results in weakened turbulent mass motion within the gain region, thereby reducing the GW amplitude at later times.\n \nFurthermore, we recast our analysis by focusing on regions within the CCSN that emit GWs.  The lower panel of Figure \\ref{fig:region} displays the inhibited convective signal  with increasing rotation, as the GW signal in the gain region becomes increasingly muted.  The typical convective signals in the early postbounce regime are then quickly washed out by the postbounce ring-down of the PNS, as rotation increases.\n\n\\begin{figure*}[t]\n\\includegraphics[width=\\textwidth]{ccsn2D_M1_all.pdf}\n\\centering\n\\caption{Time domain waveforms over our entire parameter space.  For all four progenitor masses, the rotational muting of the accretion-phase GW signal is clear.  While there is some weak dependence in the character of the accretion-phase GW signals with progenitor ZAMS mass, the rotational muting occurs for all progenitors.}\n\\label{fig:ccsn_all}\n\\end{figure*}\n\n\\begin{figure}[t]\n    \\centering\n    \\includegraphics[trim=80 0 0 0, scale=0.38]{gws_2x2_line_test_size.pdf}\n    \\caption{Spectrograms for the $12 M_\\odot$ progenitor over all four rotational velocities.  The key aspects revealed by the spectrogram are the rotational muting of GWs and the flattening of the signal from the surface g-mode of the PNS.  This flattening is a product of the enlarged radius of the PNS due to centrifugal effects and can be characterized by the dynamical frequency ($f_{dyn} = \\sqrt{G \\overline{\\rho}}$), overlaid in gray.}\n    \\label{fig:2x2}\n\\end{figure}\n\n\\begin{figure*}[t!]\n  \\centering    \n  \\includegraphics[width=\\textwidth]{tbe6tbe300_combined_M1_long_referee.pdf}\n  \\caption{ASD plot of all progenitors for all rotation rates from $t_{be}+6$ ms $\\rightarrow t_{be}+300$ ms, with an assumed distance of 10 kpc.  The rotational muting of the fundamental PNS g-mode is displayed as the peak frequency ($\\sim 800$ Hz) becomes less prevalent, with increasing rotation rate.  Likewise, the low-frequency signals ($\\sim40$ Hz) from the gain region become more audible, with increasing rotational velocity.  The damping of the vibrational modes of the PNS allows the slower postshock convection to contribute more to the overall GW signal.  Plotted in the black dashed line is the design sensitivity curve for aLIGO in the zero-detuning, high-sensitivity configuration \\citep{barsotti:2018}.  The cyan dashed line is the predicted KAGRA detuned, sensitivity curve \\citep{komori:2017}.  The purple dashed line is the design sensitivity curve for AdV \\citep{abbott:2018}.}\n  \\label{fig:spetra_long}\n\\end{figure*}\n\nUnder nonrotating conditions, the shock can grow unstable due to nonradial deformations exciting a vortical-acoustic cycle that leads to the growth of large-scale shock asymmetries, that is, the SASI \\citep{blondin:2003, blondin:2006, scheck:2008,marek:2009a}.\nIn 2D simulations, the SASI excites large, oscillatory flows along both poles that drive changes in entropy capable of causing postshock convection.  It is worth noting in 3D simulations that the SASI can excite `spiral' modes that correspond to nonzero $m$ values \\citep{blondin:2007,kuroda:2016}.  The high degree of nonlinearity among the hydrodynamic flows, neutrino interactions, and gravitational effects can yield matter flow that is quadrupolar, thereby resulting in GW emission.  However, when the shock becomes restricted in the polar direction, due to centrifugal effects, SASI development is inhibited.  To quantify the role of SASI, we decompose the shock front into coefficients based on the spherical harmonics, $Y_l^m$, according to Equation (\\ref{eq:sho_coeff}). Figure \\ref{fig:sasi} illustrates the evolution of the $a_1^0$ and $a_2^0$ coefficients over time.  Both coefficients quantify the deviation of the shock from spherical symmetry.  Specifically, the $a_1^0$ term describes the overall dipole nature of the shock, and the $a_2^0$ term describes its quadrupole nature.  Both coefficients are normalized by the mean shock radius, $a^0_0$.  Clearly, both approach zero with increasing rotational velocity.  Physically, this effect corresponds to a shock that is becoming less prolate.  To further illustrate this transition, we direct the reader to Figures \\ref{fig:vaniso} and \\ref{fig:SHI}.  Figure \\ref{fig:vaniso} takes an angular average to calculate $v_{\\mathrm{aniso}}$, whereas Figure \\ref{fig:SHI}, by contrast, uses equatorial slices  to calculate the Solberg-H{\\o}iland stability criterion.  The boundary between the white and colored region in both panels then acts as a proxy for average shock radius and equatorial shock radius, respectively.  Thus, as rotational velocity increases, average shock radius decreases, while increasing the equatorial shock radius.  Put more simply, the rotation in our 2D simulations acts to create less prolate shock fronts.  Hence, because SASI plays a significant role in creating a shock that is extended along the axis of rotation, we conclude that the effect of SASI is reduced as rotational velocity increases in our 2D simulations.\nWhile we expect the SASI activity to contribute uniquely to the GW spectrum, depending on progenitor mass, the rotational muting of the GWs is universal across ZAMS mass parameter space, as illustrated in Figure \\ref{fig:ccsn_all}. \nBoth \\citet{burrows:2007}  and \\citet{moro:2018} point out the partial suppression of SASI, but the former does not focus on the gravitational radiation emitted and the latter only examines a single, slow rotating, progenitor.  Our work provides strong support for the rotational muting of accretion-phase GWs, over such a wide region of parameter space of 2D CCSN simulations. \n \nWith respect to PNSs, a variety of oscillatory modes exist that could be of interest to current and future GW astronomers: fundamental f-modes, pressure based p-modes, and gravity g-modes---due to chemical composition and temperature gradients \\citep{unno:1989}.  The typical frequency of the PNS f-mode is around 1 kHz, and p-modes have frequencies greater than f-modes, which are of little use to GW astronomers, with the current detector capabilities \\citep{ho:2018}.  \nThe frequencies of g-modes, however, are on the order of hundreds of hertz, falling squarely within the detectability range of current GW detectors \\citep{martynov:2016}.  \nThe top panel of Figure \\ref{fig:region} displays the contribution of the vibrating PNS to the majority of the GW signal during the accretion-phase, with $h_+D$ normalized strain amplitudes around 50 cm.  \nThese g-modes are thought to be excited by downflows from postshock convection or internal PNS convection \\citep{marek:2009b,murphy:2009,muller:2013}.  \nFigure \\ref{fig:2x2} shows a spectrogram for the $12 \\, M_\\odot$ progenitor over all rotational speeds, where lighter colors represent greater strain amplitudes, $h_+$.  The dominant yellow band that extends from 100 to 1000 Hz represents this contribution.  \nOverlaid in gray is the dynamical frequency that is characterized by the average density of the PNS, $\\overline{\\rho}$, and gravitational constant, $G$, $f_\\mathrm{dyn} = \\sqrt{G \\overline{\\rho}}$,  that evolves synchronously with the g-mode contribution.  The synchronized evolution of $f_\\mathrm{dyn}$ and the frequency at which the PNS emits gravitational radiation are no coincidence.  As both are fundamentally related to the mass and radius of the PNS, we expect that both are affected similarly when introducing rotation.  The initial progenitor rotation will centrifugally support the PNS, thereby leaving it with a larger average radius.  Similar to two tuning forks of different lengths, the PNS with a larger radius will emit at a lower frequency, compared with a smaller PNS.  This ``flattening'' of the emitted frequency is displayed in Figure \\ref{fig:2x2}.  Furthermore, Figure \\ref{fig:2x2} provides a different lens through which the rotational muting is displayed, via the progressively darker panels with increasing rotational velocity.  We note that more robust peak GW frequency calculations exist \\citep[e.g.,][]{muller:2013,moro:2018}, but we find that the simple $f_\\mathrm{dyn}$ relation gives a good estimate of the PNS peak frequency.\n\nWe also Fourier transform the accretion-phase GW signal, as displayed in Figure \\ref{fig:spetra_long} and scale the magnitude of the Fourier coefficients by $\\sqrt{f}$ in order to produce ASD plots.  These plots commonly display the sensitivity curves of current and next-generation GW detectors.  We define $t_{\\mathrm{be}}$ similar to \\citet{richers:2017} as the third zero crossing of the gravitational strain.  We focus on the signal later than $t_{\\mathrm{be}} + 6$ ms in order to remove the bounce signal and early postbounce oscillation contribution to the signal.  \nThe dominant contributions are the prompt convection, SASI, and surface g-modes of the PNS---as displayed by a peak frequency ranging from 700 to 1000 Hz.  Universally, the prevalence of the peak frequency decreases with increasing rotational velocity.  It is worth noting this peak could shift to higher frequencies with longer simulation times.\n\nWhen incorporating magnetic fields into CCSN simulations, other instabilities may arise that can compromise stability in the postshock region and possibly affect the behavior of the PNS.  The $\\alpha$--$\\Omega$ dynamo and MRI are two such mechanisms that can reexcite postshock convection; however, work from \\citet{bonanno:2005} suggests that the $\\alpha$--$\\Omega$ dynamo is unimportant on dynamical timescales.   MRI has the potential to drive convection in the postshock region, yet as the strength and geometry of magnetic fields in 3D simulations are largely still unknown, we exclude them from our simulations \\citep{cerda-duran:2007}.\n\n\\subsection{Observability of the Accretion-phase Signal}\n\nOverlaid on our ASD plots is the expected sensitivity of future GW observatories.  \nIn the black, cyan, and purple dashed lines we have plotted the sensitivity curves of design sensitivity for aLIGO in the zero-detuning, high-sensitivity configuration, the predicted KAGRA detuned sensitivity curve, and design sensitivity for AdV, respectively \\citep{komori:2017,abbott:2018,barsotti:2018}.\nThese curves represent the incoherent sum of the principal noise sources to the best understanding of the respective collaborations.  While these curves do not guarantee the performance of the detectors, they act as good guides for their anticipated sensitivities nonetheless. \n\nBeyond the decreased prevalence of the peak frequency, an interesting trend emerges in Figure \\ref{fig:spetra_long} as rotation increases.  \nWe separate the GW signals by region within the star.  The top row of Figure \\ref{fig:spetra_long} corresponds to GWs originating from the inner 50 km of the supernova, and the GW signal in the bottom row originates from radial distances between 50 and 150 km from the supernova center.  In the top row, we note the first peak of emission, around 80 Hz, is independent of rotation.  We point to the bright, higher $v_\\mathrm{aniso}$ region in Figure \\ref{fig:vaniso} within the first 25 ms postbounce that is present for all rotational velocities.\nFocusing on the bottom row, we highlight a noticeable difference in the amplitude of the low-frequency contributions, particularly around 40 Hz.  The nonrotating progenitors have undetectable low-frequency signals for all three detectors, whereas rotating progenitors create measurable signals at low frequencies. \nThis enhanced low-frequency signal may provide an observable feature that can help determine progenitor angular momentum information.  \n\nThe amplitude of low-frequency GWs in the 50--150 km region of the supernova increases with rotational velocity, but this trend does not occur within the inner 50 km.  As such, we restrict the low-frequency GW contribution to the gain region.  We note the two main physical mechanisms in this region correspond to postshock convection and the SASI.  While both mechanisms are reduced in strength due to rotational effects, they do not completely cease.  This fact is displayed in Figure \\ref{fig:vaniso}, as the region between 50 and 150 km is nonzero.  For the nonrotating case, the high convective velocities (bright yellow) create higher frequency GWs within the 100 km region of interest.  As rotation velocity increases, convective velocities decrease enough to cease exciting the vibrational modes of the PNS.  These slower convective flows thereby reduce the total amount of power produced by the GWs and push the peak GW frequency---from the gain region---to lower frequencies.  Performing an order-of-magnitude estimate on the source of the low-frequency signal, from Figure \\ref{fig:vaniso}, we find  $v_{\\mathrm{aniso}} \\sim 1 \\times 10^9$ cm s$^{-1}$ for $\\Omega_0 = 0$ rad s$^{-1}$ and $v_{\\mathrm{aniso}} \\sim 5 \\times 10^8$ cm s$^{-1}$ for $\\Omega_0 = 3$ rad s$^{-1}$.  As the region of interest is $\\sim 10^7$ cm, we yield an estimated frequency of emission $f_{\\mathrm{low}}$ around $\\sim 100$ Hz and $\\sim 50$ Hz, respectively.  These quantitative frequency estimates are reflected in the ASD as the contribution from peak frequency ($\\sim 100$ Hz) from the gain region decreases, while the contribution $\\sim 40$ Hz increases.\n\n\n\n\n\\section{Summary and Conclusion}\n\\label{sec:summary}\n\nThe strength of this project is its ability analyze GWs hundreds of milliseconds postbounce from multiple progenitors while accurately accounting for rotation and neutrinos.  The wide breadth of parameter space we examine allows us to reveal certain rotational effects on the GW signal in the context of a controlled study.  We have explored the influence of rotation on the GW emission from CCSNe for four different progenitors and four different core rotational speeds.  \nWe point out that there exists a roughly linear relation between compactness, $\\xi$, and the differential rotation parameter, $A$, as defined in Equation (\\ref{eq:omega}). \nUsing this relation, we calculate appropriate $A$ values for each progenitor mass, based on their individual compactness parameters of the \\citet{Suk:2016} progenitors.  Of our 15 simulations, only two nonrotating progenitors have average shock radii that show substantial shock expansion, while the remaining rotating progenitors do not because of rotationally inhibited convection in the gain region and less neutrino production.  In agreement with other recent work \\citep[e.g.,][]{summa:2018}, we find a complex interplay between centrifugal support and neutrino heating as successful explosions do not display a monotonic relationship with rotation.\n\nWhile there are more accurate treatments of gravity, we utilize the effective GR potential in order to streamline calculations, granting us the ability to explore larger sections of parameter space. \nWe find that our results utilizing this approximation match very closely the CCSN bounce signal of CFC gravity with GR hydrodynamics \\citep{richers:2017}.  \n\nThe main contributors to the GW signal (10--300 ms postbounce) are postbounce convection, the SASI, and the surface g-modes of the PNS \\citep{moro:2018}.  By establishing a positive angular momentum gradient, the convection is suppressed according to the Solberg-H{\\o}iland stability criterion \\citep{endal:1978,fryer:2000}.  The more oblate shock front inhibits the bipolar sloshing of the SASI.  Since the SASI and convection are the principal drivers exciting the g-modes of the PNS, vibrational emission from the PNS is also inhibited by rotation.  \nWe, therefore, find that rotation in 2D CCSN simulations results in the muting of GW emission.\nThis result is consistent across progenitors with different ZAMS masses. \n\nBefore the PNS g-mode signal is completely muted, as rotation gradually increases, this signal is pushed to lower peak frequencies and can be characterized by its dynamical frequency.  This observation is no coincidence as both  fundamentally depend on the radius and mass of the PNS.  With more centrifugal support, the PNS has a larger radius.  This larger radius causes the surface of the PNS to emit at lower frequencies, thereby producing a ``flatter,'' lower frequency signal.\n\nWe reveal a novel rotational effect on the GW signal during the accretion-phase.  We notice that the nonrotating progenitors all produce low-frequency signals ($\\sim 40$ Hz) that are below the plausible detection threshold of the aLIGO and KAGRA detectors, whereas the progenitors with larger angular velocities produce measurable GW signals in this frequency range.  We attribute this increase of low-frequency emission to the SASI and postshock convection.  For nonrotating progenitors, the convective velocity within the postshock region is high, emitting GWs $\\sim 100$ Hz.  As rotational velocity increases, the PNS GW contribution is reduced.  Likewise, as the convection slows, the mass within the gain region emits at lower GW frequencies.  The slower convective flows reduce the total amount of GW power and push the peak GW frequency from the gain region to lower values.  Whereas previous rotating core-collapse GW studies have focused on the bounce signal as a means to determine rotational features, or have focused on late time signals without rotation, our study unifies both facets and opens the door to measuring GW signals beyond the bounce phase that encode progenitor, angular momentum information. \nWe postpone asserting quantitative relations between low-frequency emission and progenitor angular momentum until we incorporate more detailed microphysics.\n\n\nWhile our approximations have allowed us to make large sweeps of parameter space, they leave room for us to include more robust microphysics.  In an ideal situation, we would compute 3D simulations, including full GR, magnetohydrodynamics, and GR Boltzmann neutrino transport that incorporates velocity dependence and inelastic scattering on electrons and nucleons.  These additions would allow for more accurate gravitational waveforms and allow other phenomena to occur, for example the $m\\ne 0$ (spiral) modes of the SASI. \\citet{andresen:2019} recently highlighted the rotational effects on GWs in 3D.  Inherent to its 3D nature, their study finds the strongest GW amplitudes at high rotation velocities due to these spiral modes.  The 2D geometry of our study, however, allows us to observe the relative strength of the convective signal, without interference from $m\\ne 0$ modes, as we extend beyond the case of a single rotational velocity.\nWhile the physical origin of this muting that damps the convection and the SASI is not constrained only to 2D, in 3D, as \\citet{andresen:2019} point out, other nonaxisymmetric instabilities can contribute to significant GW emission at late times, negating this rotational muting effect.\nThus, once again, we are reminded of the key role of 3D simulations in the study of the CCSN mechanism.\n\n\\acknowledgements\n\nWe would like to thank Jess McIver for pointing us to the aLIGO and AdV sensitivity curves.  M.A.P. was supported by a Michigan State University Distinguished Fellowship. \nS.M.C. is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics,\nunder award Nos. DE-SC0015904 and DE-SC0017955 and the \\textit{Chandra\nX-ray Observatory} under grant No. TM7-18005X.\nThis research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of two U.S. Department of Energy organizations (Office of Science and the National Nuclear Security Administration) that are responsible for the planning and preparation of a capable exascale ecosystem, including software, applications, hardware, advanced system engineering, and early testbed platforms, in support of the nation's exascale computing imperative.\nThe software used in this\nwork was in part developed by the DOE NNSA-ASC OASCR Flash Center at\nthe University of Chicago.  \n\n    \\software{FLASH (see footnote 7) \\citep{fryxell:2000,fryxell:2010}, Matplotlib\\footnote[8]{\\url{https:\/\/matplotlib.org\/}} \\citep{hunter:2007},\n    NuLib\\footnote[9]{\\url{http:\/\/www.nulib.org}}\n    \\citep{oconnor:2015},\n    NumPy\\footnote[10]{\\url{http:\/\/www.numpy.org\/}} \\citep{vanderwalt:2011}, SciPy\\footnote[11]{\\url{https:\/\/www.scipy.org\/}} \\citep{jones:2001}}\n    \n\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{{\\rmfamily \\scshape vitaLITy}}\n\\label{sec:system}\n\n\\begin{figure*}[!t]\n  \\centering\n  \\setlength{\\belowcaptionskip}{-10pt}\n  \\includegraphics[width=\\linewidth]{figures\/vitality-architecture.pdf}\n  \\caption{The {\\rmfamily \\scshape vitaLITy}{} architecture. (1) DBLP data is filtered by relevant venues. (2) Author and title metadata from DBLP is augmented with abstracts, keywords, and citations from custom scrapers. (3) Data is cleaned (e.g., to resolve duplicate keywords, etc). (4) GloVe and Specter document embeddings are created. (5) Data is exported to a variety of formats for subsequent open-source use. (6) The server exposes a RESTful API that can ultimately be called upon in rendering the interactive system.}\n  \\label{fig:architecture}\n\\end{figure*}\n\nWe present {\\rmfamily \\scshape vitaLITy}{}, a system designed to complement existing tooling for conducting academic literature reviews by supporting serendipitous discovery of relevant literature. \n\n\\subsection{Data} \n\\label{sec:data}\nFigure~\\ref{fig:architecture} outlines the pipeline for curating the paper corpus.\n\n\\begin{figure}[t]\n    \\centering\n    \\includegraphics[width=\\linewidth]{figures\/venues.pdf}\n    \\caption{Results from a Twitter survey with \\texttt{24} users on venues where VIS researchers publish; (numbers in parentheses) are aggregated counts of the \\texttt{24} responses; \\st{struckthrough venues} were not in DBLP and hence currently not available in {\\rmfamily \\scshape vitaLITy}{}; * venues were added as also-relevant venues by the authors after the survey; ``Vis.'' is short for Visualization.}\n    \\label{fig:venues}\n\\end{figure}\n\n\n\\noindent\\textbf{1. Filter:} We conducted an open-ended crowd-sourced survey on Twitter asking visualization researchers about venues (e.g., journals, conferences, workshops) where they publish. We received responses from \\texttt{24} users (current roles: 17 Ph.D. students, 4 Faculty, 2 Industry researchers, and 1 Postdoctoral scholar; self-reported visualization literacy out of 5: $\\mu$=4, $\\sigma$=1.142, median=4). We supplemented the list with \\texttt{six} additional venues based on our own knowledge that were not captured in the survey. Figure~\\ref{fig:venues} outlines the final list of \\texttt{38} venues within our corpus. Next, we downloaded the November 2020 release~\\footnote{\\url{https:\/\/dblp.org\/xml\/release\/dblp-2020-11-01.xml.gz}} of DBLP~\\cite{dblp} and filtered it for the aforementioned \\texttt{38} venues. From the resultant subset, we chose the \\attr{Title}, \\attr{Authors}, \\attr{Source} (venue), \\attr{Year} (published), and \\attr{URL} attributes and added a unique \\attr{ID} for tracking. Note that the {\\rmfamily \\scshape vitaLITy}{} dataset and hence the UI show more than 38 venues because DBLP (a) utilizes multiple descriptors to represent different tracks at the same venue (e.g., Eurographics (Area Papers), Eurographics (State of the Art Papers), Eurographics (Short Papers), etc.) and (b) splits some venues across different versions (e.g., Interact, Interact (1), Interact (2), etc.).\n\n\\noindent\\textbf{2. Scrape:} The DBLP dataset does not include abstracts, keywords, and number of citations for papers. Thus, we developed a \\emph{scraper} module that, given a list of publication URLs, scrapes the corresponding publisher's webpage (e.g., IEEE Xplore, ACM Digital Library) and extracts the \\attr{Abstract}, \\attr{Keywords}, and \\attr{CitationCounts} from it.\n\n\\noindent\\textbf{3. Clean:} We performed data cleaning and transformation operations. To aid search, we encoded all text attributes to ASCII and converted \\attr{Authors} and \\attr{Keywords} into a JSON array from a comma separated list. We de-duplicated \\attr{Keywords} by matching their lowercase forms; we combined similar keywords (e.g., HCI \\& Human-Computer Interaction, Visuali\\textbf{z}ation \\& Visuali\\textbf{s}ation) through manual inspection. We dropped \\texttt{1497} papers with \\emph{null} \\{\\attr{Title}, \\attr{Authors}, \\attr{Abstract}\\} values, and very short or very long \\attr{Title} ($<$5, $>$250 characters) and \\attr{Abstract} ($<$50, $>$2500 characters) to create effective word embeddings. We retained DBLP's strategy in disambiguating author names (e.g., \\emph{J. Thompson} and \\emph{J. Thompson 001}). At the end of this step, the dataset has \\texttt{8} attributes (columns) and \\texttt{59,232} papers (rows).\n\n\\noindent\\textbf{4. Embed:} We next curated a dataframe of \\attr{Title}, \\attr{Abstract}, \\attr{Authors}, \\attr{Source}, \\attr{Year}, and \\attr{Keywords} and created the GloVe \\cite{pennington2014glove} and Specter\\cite{cohan2020specter} document embeddings. To create the document embeddings for GloVe, we used TF-IDF weightings (instead of mean vectors) and SIF weightings that have been shown to remove noise through PCA reduction \\cite{arora2017simple}. We used the public API to create the Specter embeddings~\\cite{cohan2020specter}. With these document embeddings, we used UMAP to construct 2-D document representations used in the Visualization Canvas (see Figure \\ref{fig:umap}).\n\n\\noindent\\textbf{5. Export:} We export the consolidated dataset as JSON and a MongoDB dump for different open-source use.\n\n\\noindent\\textbf{6. Serve:} We also developed a server that exposes a RESTful API to (a) load the {\\rmfamily \\scshape vitaLITy}{} document corpus, (b) perform similarity search by a list of seed papers as input, (c) perform similarity search by a working title and abstract as input, and (d) download metadata of (saved) papers as a JSON array. The similarity search by seed papers (b) supports querying by 2-D UMAP as well as n-D document embeddings for both GloVe and Specter. We used MongoDB to maintain the 2-D indexes and Facebook Research's faiss library~\\cite{faiss} to maintain the n-D indexes. \\revised{For one seed paper as input, we utilize existing APIs to compute the Euclidean (2-D; MongoDB) and L2 (n-D; Faiss) distances between the input paper and other papers, compute their reciprocals, and normalize them between 0-1 for use as the similarity scores (1 = most similar). For more than one seed paper as input, we first compute the average vector from all input papers and then follow the same procedure as above to compute the similarity scores. \n} The {\\rmfamily \\scshape vitaLITy}{} UI interfaces with this server, described next.\n\n\\subsection{System Overview}\n\\label{sec:system_overview}\n\nThe system, shown in Figure~\\ref{fig:teaser}, is comprised of a \\emph{Paper Collection View} (A), \\emph{Similarity Search View} (B), \\emph{Visualization Canvas} (C), \\emph{Meta View} (D), and \\emph{Saved Papers View} (E), described in turn below. \n\n\n\\smallskip\n\\noindent\\textbf{Paper Collection View} shows the entire corpus of papers in an interactive tabular layout. (1) shows an overview (number of visible papers) and UI controls to perform a global search (\\faSearch), show hidden columns ([Column~\\faPlus]), add all papers to the input list of papers in the \\emph{Similarity Search} table ([\\faPlusCircle~All]), and save all papers to the ``cart'' in the \\emph{Saved Papers View} ([\\faSave~All]). (2) shows the attributes along with UI controls to filter (range sliders for Quantitative attributes, multiselect dropdowns for Nominal attributes), hide a column (\\faEyeSlash), and define a column on hover (\\faQuestionCircle). (3) shows an interactive table of all papers with options to see detail \n(\\faInfoCircle), \nlocate in the UMAP (\\faMapMarker), add to the input list of papers for similarity search (\\faPlusCircle), and save to the ``cart'' (\\faSave). Search and filter capabilities are designed to be an intuitive entry-point into the dataset of academic articles (\\textbf{DG 2}).\n\n\n\\smallskip\n\\noindent\\textbf{Similarity Search View} shows options to find papers similar to (a) one or more input papers (Figure~\\ref{fig:search-by-papers}, \\textbf{DG 1}) or (b) a work-in-progress title and abstract (Figure~\\ref{fig:search-by-abstract}, \\textbf{DG 3}). {\\rmfamily \\scshape vitaLITy}{} supports setting the dimensions (2-Dimensional, n-Dimensional), number of similar papers to return, and the word embedding approach (e.g., Specter) to compute similarity.\n\n\\smallskip\n\\noindent\\textbf{Visualization Canvas} shows a 2-D UMAP projection of the embedding space of the entire paper collection (Figure~\\ref{fig:umap}, \\textbf{DG 4}): hovering on a point highlights it, shows the corresponding title in a fixed tooltip below, and automatically scrolls the collection (table) to bring the corresponding paper (row) into the viewport; clicking on a point (de)selects it and shows it in the tooltip below with additional options to \\faInfoCircle, \\faPlusCircle, \\faSave; clicking on \\faTimes~deselects all selected points; pressing Shift enables lasso-mode to select multiple points using a free-form lasso operation; zooming and panning support helps navigate the UMAP to specific regions; clicking on \\faDotCircleO~re-centers and fits the UMAP in the viewport. By default, each point in the UMAP is colored based on the state of the corresponding paper (``Default''): Unfiltered (unfiltered and visible in the main paper collection table; dark-grey), Filtered (filtered out and not visible in the paper collection table; light-grey), Similarity Input (added to the \\emph{By Papers} section in the Similarity Search View; pink), Similarity Output (in the \\emph{Output Similar} table; orange), and Saved (added to the Saved Papers table; red). Other options to color include \\attr{Source}, \\attr{Year}, \\attr{CitationCounts}, and \\attr{Similarity Score}.\n\n\\smallskip\n\\noindent\\textbf{Meta View} shows aggregated summaries of \\attr{Keywords}, \\attr{Authors}, \\attr{Source}, \\attr{Year} with respect to the \\emph{Paper Collection View} (A). Figure~\\ref{fig:meta} shows how a filter in the main table (\\attr{Authors}=\\emph{John T. Stasko}) updates the Meta Views with the distribution of keywords (a) associated with their research, their co-authors (b), venues where they have published (c), and in which years (d).\n\n\\smallskip\n\\noindent\\textbf{Saved Papers View} shows a table with the papers added to the ``cart'' with an additional option to export them as a JSON (Figure~\\ref{fig:search-by-papers}d).\n\n\\begin{figure}[!t]\n    \\centering\n    \\setlength{\\belowcaptionskip}{-10pt}\n    \\includegraphics[width=\\columnwidth]{figures\/umap.pdf}\n    \\caption{Interactive 2-D scatterplot of the UMAP projection.}\n    \\label{fig:umap}\n  \\end{figure}\n\n\\begin{figure*}[!t]\n    \\centering\n    \\setlength{\\belowcaptionskip}{-10pt}\n    \\includegraphics[width=\\linewidth]{figures\/meta.pdf}\n    \\caption{The Meta View showing aggregated summaries of (a) \\attr{Keywords}, (b) \\attr{Co-authors}, (c) \\attr{Source}, and (d) \\attr{Year} associated with \\emph{John T. Stasko}.}\n    \\label{fig:meta}\n  \\end{figure*}\n\n\\begin{comment}\n\\begin{figure}[!t]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{figures\/info.pdf}\n    \\caption{Clicking on \\faInfoCircle~opens a modal that describes all attributes and also lets the user to select, save, and open the paper's Google Scholar listing.\\ali{this fig can be removed if we don't have enough space}}\n    \\label{fig:info}\n  \\end{figure}\n\\end{comment}\n\n\\subsection{Implementation}\nThe \\emph{filter}, \\emph{scrape}, \\emph{clean}, \\emph{embed}, \\emph{export}, and \\emph{serve} modules are all implemented in Python. The \\emph{UI} is developed in React and uses the regl-based WebGL library\\footnote{https:\/\/github.com\/flekschas\/regl-scatterplot} to render the UMAP. MongoDB provides the document corpus to the UI and maintains the 2-D indexes while faiss~\\cite{faiss} maintains the n-D indexes for efficient similarity search.\n\\section{Discussion}\n\\label{sec:discussion}\n\n\\medskip\n\\noindent\\textbf{Quality of Search Results. }\nAcross our (relatively small) sample of participants, there was variability in terms of perceived relevance of Similarity Search results. \nSome participants felt that, like Google Scholar, relevant results were lost among a sea of irrelevant papers, while others felt that the results were highly relevant. \nIn general, participants perceived results from SPECTER embeddings to be more relevant than GloVe, suggesting that further exploration of alternative transformer-based approaches (e.g., BERT~\\cite{devlin2018bert}, or training a custom model on the target document corpus) could yield better search results. \nFurthermore, given the disparity in perceived quality and disparity in participants' perception of when this approach could be useful in their literature review process, future work could develop additional guidelines that assess the specific role of document retrieval based on semantic similarity.\n\n\n\n\n\\medskip\n\\noindent\\textbf{Relevance \\& Space. }\nPresuming {\\rmfamily \\scshape vitaLITy}{} is able to provide serendipitous discovery of relevant literature, the process doesn't abruptly come to a successful end. \nAuthors still need to manage goals in their writing that may be at odds with one another: i.e., the tradeoff of relevance or salience of related work and the commodity of space. \nFrom this perspective, {\\rmfamily \\scshape vitaLITy}{} is best viewed as a way to identify critical gaps or serve as kindling for a new literature review. \nIn its current form, {\\rmfamily \\scshape vitaLITy}{} shows (1) similarity score, and (2) citation counts as the primary cues of relevance or salience of a given paper.\nIt still requires substantial knowledge from the author to (1) read an abstract or paper and determine its actual relevance to a given topic, and (2) assess the credibility of the work, author(s), and venue. \nSubsequent versions of {\\rmfamily \\scshape vitaLITy}{} could focus on innovating solutions to support these and other parts of the literature review process.\n\n\n\n\n\\medskip\n\\noindent\\textbf{Future Work. } \nBased on our use of {\\rmfamily \\scshape vitaLITy}{} and participant feedback, we identify a number of potential future directions. \\revised{First, as mentioned in the Related Work, with citation and user activity data, {\\rmfamily \\scshape vitaLITy}{} could expand its functionality to citation or read\/view recommendation using SPECTER.}\n\\revised{Second}, current similarity scores in the projected 2-D space (UMAP) are based on the reciprocal of the distance measure and might yield different results compared to distances in the N-D embedding space.\nThese scores and their context may not be especially intuitive for users. \nHence, future work could refine the similarity score formulation and \/ or presentation in {\\rmfamily \\scshape vitaLITy}{} to provide users an accessible framework to interpret results.\n\\revised{Third}, the Saved Papers Cart currently exports a file in JSON format with the papers. \nAt least two improvements could be made within this view, including exporting files in .bibtex format for easy incorporation in \\LaTeX{} bibliographies.\nFurthermore, it could be useful to users to provide a meta analysis of the saved papers, e.g., via topic modeling. \nHow can these papers be summarized? \n\\revised{Fourth, while our research prototype of {\\rmfamily \\scshape vitaLITy}{} is intended to be complementary to existing search strategies, future work could expand {\\rmfamily \\scshape vitaLITy}{} to a more comprehensive search tool, incorporating the benefits of e.g., citation networks.}\n\\revised{Lastly, {\\rmfamily \\scshape vitaLITy}{} is modular, scalable, and extensible: it applies the virtual scrolling principle in the UI table views (preventing unnecessary rendering of objects not visible in the viewport), renders the UMAP using WebGL, and uses a library (faiss) that performs efficient similarity search of dense vectors with an option to leverage GPUs. The \\emph{scraper} module currently uses DBLP as the source of raw data but can be extended to support other digital libraries, e.g., JSTOR (https:\/\/www.jstor.org\/).\nHence, augmenting the system with additional venues (and allowing users to define which venues are relevant to load in their specific literature review) is a feasible next step to expand {\\rmfamily \\scshape vitaLITy}{} to other research domains.}\n\n\\section{Evaluation}\n\\label{sec:evaluation}\n\nBased on the final form of {\\rmfamily \\scshape vitaLITy}{}, developed from formative feedback with visualization researchers, we next describe the summative evaluation of {\\rmfamily \\scshape vitaLITy}{} in a qualitative study.\nWe recruited 6 Computer Science PhD students (1 female, 5 male; avg. 3.3 yrs. into PhD program) whose primary research area is within the field of visualization.\nNone of the participants were involved in the formative study. \nSessions lasted approximately 45 minutes.\nParticipation was voluntary with no compensation.\n\n\\subsection{Task \\& Procedures}\n\\label{sec:task}\nAfter obtaining informed consent,\nparticipants were asked to reflect on a topic for which they had recently or were currently conducting a literature review. \n{\\rmfamily \\scshape vitaLITy}{} was loaded with all \\texttt{59,232} papers, described in Section~\\ref{sec:data}, running locally on the study investigator's machine. \nParticipants connected to the study virtually via Microsoft Teams. \nThey were asked to \\textbf{recreate or continue their literature review using {\\rmfamily \\scshape vitaLITy}}, which they interacted with by using Microsoft Teams's ``Request Control'' feature on the study investigator's machine.\nWe utilized a think aloud protocol to capture users' impressions and qualitative feedback on the system. \nSessions were screen-recorded for subsequent analysis.\n\nParticipants chose the following topics for their literature reviews: \\emph{multiple comparisons problem}, \\emph{interpretable machine learning}, \\emph{misinformation}, \\emph{network visualization}, \\emph{scrollytelling visualization}, and \\emph{transformation \/ similarity between two visualizations}.\n\n\n\\subsection{Findings}\n\\label{sec:findings}\nIn this section, we discuss qualitative findings from our evaluation of {\\rmfamily \\scshape vitaLITy}{} for each of its primary features (Figure~\\ref{fig:sus-scores-specific}), and lastly summarize participants' general impressions of the system (Figure~\\ref{fig:sus-scores-generic}).\n\n\n\n\\subsubsection{Paper Collection View}\nParticipants felt that the Paper Collection View was a good ``entry point'' into the paper corpus in {\\rmfamily \\scshape vitaLITy}, containing familiar data that users expected to see, e.g., authors, abstracts, etc (S02). \nSearching by keyword was familiar and produced expected outcomes.\nFor instance, S03 identified some papers previously read as well as an interesting new one, which led them to iterate on their search query to find other papers by the same author.\n\nHowever, some users expressed the desire for the keyword search features to support more robust or customizable queries. \nAs a case in point, S01 conducted a global search for multiple keyword variations ``uncertainty visualisations'' $\\rightarrow$ ``uncertainty visualizations'' $\\rightarrow$ ``uncertainty visualization'', which returned 0, 8, and 49 hits respectively.\nFuzzy string matching would be a useful feature to support in subsequent iterations of {\\rmfamily \\scshape vitaLITy}{} (S06).\nAnother small usability issue that arose was lack of feedback upon clearing filters. \nFor instance, some participants would backspace to delete text; however, the system would only remove filters by selecting the `x' icon next to the filter (S01, S05). \nFurthermore, S06 suggested it would be useful for {\\rmfamily \\scshape vitaLITy}{} to expand the searchable text beyond titles and abstracts: \\textit{``Google Scholar searches body text too.''}\n\n\n\n\\subsubsection{Similarity Search}\n\\noindent\\textbf{By Paper. } The ability to start with a seed paper(s) and identify other relevant literature was appreciated, with varying opinions about the quality and relevance of results.\nMany participants were able to identify interesting and relevant papers; e.g., S04 identified a relevant paper from two key authors that they were not aware had collaborated.\nS05 indicated a significant finding of a paper that \\textit{``did something similar to what [they] were considering doing.''}\nCompared to searching by keywords, S05 said \\textit{``the papers [they are] seeing now are a lot more relevant. Some of these papers [they have] been reviewing. Some of them are kind of new.''}\nS05 later acknowledged the utility of the similarity score: \\textit{``It seems reasonable\u2026 Those on top tended to be more relevant to what [they were] looking for.''}\nS06 commented that the similarity score was good feedback on the precision and quality of the search itself: \\textit{``some would return like 0.0001 and [they] could see that [their] search was wrong.''}\n\nNot all feedback about the similarity search was positive, however. \nS01 was uncertain about the quality of the results, stating they \\textit{``could find a few papers that came up that slipped [their] mind, but [they] didn't find any new papers that [they] hadn't already cited. [...] [they] have some confidence that it would work, but for this particular context, [they] did not find anything new.''}\nIn response to some search queries, participants expressed disappointment with the results. \nFor instance, using a single seed paper as input to similarity search, S02 indicated \\textit{``these do not seem to be good results. The 2-D search does not seem to be good with GloVe. The N-D results were much better.''}\nS02 then added additional papers as input to the similarity search and again noted \\textit{``some match, but some do not. [...] [they] could have expected better search results.''} \nS02 ultimately suggested to explore other transformer embeddings, e.g., BERT.\n\n\n\n\n\\smallskip\n\\noindent\\textbf{By Abstract. } While not all participants had an abstract prepared to utilize the Similarity Search by Abstract feature, they nonetheless saw value in it. \nS01, for instance, indicated that if they are \\textit{``starting a new project [...] [they] can write up some words in the form of an abstract to see if this has been done.''}\n\nS06 interestingly appropriated the abstract search in response to perceived shortcomings of traditional search features. \nFor instance, after searching by keyword, applying filters, and iteratively revising queries to try to capture multiple keywords, S06 felt dissatisfied with the limitations of searching by keyword in {\\rmfamily \\scshape vitaLITy}: \\textit{``Maybe [they] should use word embeddings because it might have more flexibility, and [they] can pass more information in [their] search.''}\nThey wrote a quick abstract paragraph during the study session and observed that the results showed \\textit{``a lot of foundational literature.''}\nThey iterated, adding additional details to the abstract and expressed \\textit{``Wow, this shows much better results now than the short abstract.''}\nBy the end of the study session, S06 identified several papers they had already cited as well as a few key new ones: \\textit{``For 15 minutes, [they] found two papers [they] might be interested in. It's a really useful process. Otherwise [they] might spend a lot of time scanning PDFs, which is not a very pleasant experience.''}\n\n\n\n\n\n\\subsubsection{Visualization Canvas}\nMany participants found the projection visualization of the embedded space to be a useful way to identify conceptually ``nearby'' relevant papers. \nS05 suggested the visualization \\textit{``provides a nice overview of the selected papers, and [they] could see to drill down into more details or look for clusters.''}\nS01 appreciated the ability to select nearby papers in the embedded space via lasso, indicating \\textit{``It's like a mystery. [They] feel like if [they] spent some time on this, [they] might stumble upon a paper that was relevant that was published in a different domain [...] It might be especially useful if [they] worked on a different topic that [they] had not worked on in the past.''}\nS04 echoed this sentiment and added that the feature to locate a given paper on the visualization was helpful for orienting.\n\nHowever, this impression was not universal. \nWhile S06 appreciated searching by abstract, they preferred to examine results in tabular format, because \\textit{``personally [they are] not super familiar with these visualizations, dimensionality reduction, so it's harder to interpret how to assess this information.''}\nS03 was skeptical about the accuracy of the projection, stating \\textit{``the algorithm might be bad, or the projection. It doesn't accurately depict similarity between papers.''}\n\nSome participants suggested variations, such as spacing out papers in the visualization and connecting them by edges where the weight reflects the similarity with other papers in the visualization (S04).\nS06 suggested for lasso selection, it would be useful to see \\textit{``factors that can cluster similar papers.''}\nFurthermore, S04 suggested additional interactivity to filter out papers on different ``layers'' in the visualization, e.g., those that are part of similarity search, saved papers, etc. \nS02 suggested a minor tweak: \\textit{``when [they] do this similarity search, it should automatically zoom to show the paper(s) that were the beginning search point and the papers that it found, rather than this zoomed out view where [they] have to look for the orange or red dots.''}\n\n\n\n\n\\subsubsection{Meta View}\nThe Meta View went relatively unused compared to other features of {\\rmfamily \\scshape vitaLITy}.\nHowever, some participants did express ideas to improve its utility. \nFor instance, S03 expressed that they would have preferred if the Meta View \\textit{``[did not display] keywords for the stuff above [Paper Collection View], but for what [they] have selected [Similarity Search input, Saved papers].''}\nS05 suggested that the Meta View could offer additional keyword \\emph{recommendations} based on semantically similar keywords, to help users identify other potential search terms. \nOthers indicated a desire for further integration of the Meta View such that selecting a keyword could highlight papers in the visualization (S04) or filter the Paper Collection View (S06). \n\n\n\n\n\\subsubsection{Saved Papers Cart}\nThe Saved Papers Cart was also not used as often as some of the other views. \nSome preferred their existing workflow of downloading PDFs directly (S06), while others appreciated the ``cart'' analogy and the accompanying mindfulness to \\textit{``fill the cart with relevant papers''} (S02) as an alternative to manually maintaining \\textit{``a word document to keep track of the titles''} (S03). \n\n\\begin{figure}[!t]\n    \\centering\n    \\setlength{\\abovecaptionskip}{4pt}\n    \\includegraphics[width=\\columnwidth]{figures\/sus-scores-features.pdf}\n    \\caption{Usability scores of {\\rmfamily \\scshape vitaLITy}{} features.}\n    \\label{fig:sus-scores-specific}\n  \\end{figure}\n  \n  \n\\begin{figure}[!t]\n    \\centering\n    \\setlength{\\abovecaptionskip}{4pt}\n    \\setlength{\\belowcaptionskip}{-10pt}\n    \\includegraphics[width=\\columnwidth]{figures\/sus-scores.pdf}\n    \\caption{Overall SUS scores of {\\rmfamily \\scshape vitaLITy}{}.}\n    \\label{fig:sus-scores-generic}\n  \\end{figure}\n\n\\subsubsection{Summary \\& Workflow}\n\n\\noindent\\textbf{Overall Impressions. }\nUsers believed that {\\rmfamily \\scshape vitaLITy}{} would be useful in a variety of contexts.\nSeveral users believed {\\rmfamily \\scshape vitaLITy}{} would be helpful in identifying gaps in their literature review (S01, S04). \nFor instance, S04 indicated \\textit{``it's very helpful to actually find a set of papers that are semantically relevant to one paper. If [they] identify a paper that [they] missed in the lit review, [they] can find other papers similar to that one to be sure [they] don't miss anything else.''}\nParticipants felt that it could help avoid ``embarassment'' of reviewers pointing out missing related work (S01, S06). \n\n\\revised{The individual SUS scores per participant were S01=72.5, S02=77.5, S03=45, S04=72.5, S05=70, S06=92.5 for an overall average SUS score=72.5 (Figure~\\ref{fig:sus-scores-generic}).} While participants generally liked using {\\rmfamily \\scshape vitaLITy}{}, several expressed that, given the large number of features, customization of the screen real estate would have been beneficial (S02, S04, S06).\nFor instance, S02 indicated \\textit{``when [they] had already filtered by keywords, [they are] only focusing on this view [Visualization Canvas]. It's very small in the screen space. [They] want to hide the Meta View and maybe even the [Paper Collection View], so [they] can easily zoom and pan and lasso. The Similarity Search panel could also be bigger.''}\nOthers echoed formative feedback, wanting to see the citation network in {\\rmfamily \\scshape vitaLITy}, e.g., which papers cite others (S01, S06).\n\n\n\\smallskip\n\\noindent\\textbf{Workflow. }\nSome participants viewed {\\rmfamily \\scshape vitaLITy}{} as a complementary component to their existing literature review workflow. \nFor instance, S01 indicated they would \\textit{``interleave this with a Google Scholar search. If [they] found a few relevant papers, [they] would go to Google Scholar to see the references in that paper and who has cited that paper.''}\nS06 indicated preference to continue their existing approach of beginning a literature review with Google Scholar and use {\\rmfamily \\scshape vitaLITy}{} at a later stage of the research, e.g., \\textit{``when [they] want to do some sanity checks [...] [after they] have [their] abstract, papers [they] have already cited, and based on that [they] can do a more narrow search for papers [they] might be missing,''} while others preferred to use {\\rmfamily \\scshape vitaLITy}{} as early in the lit review process that you are able to \\textit{``structure the related work sections [...] and [identify] those 2-3 themes''} (S05).\n\nOthers felt that {\\rmfamily \\scshape vitaLITy}{} suffered from many of the same problems that existing tooling has. \nFor instance, S01 said \\textit{``[The] target is one unknown paper among hundreds. A lot of the papers [they] find because coauthors tell [them] about them.''}\nS03 indicated they would use the tool primarily in the same ways as Google Scholar, e.g., \\textit{``[they] would just search for keywords.''}\n\n\n\n\n\n\n\n\\section{Conclusion}\n\\label{sec:conclusion} \n\nWe introduced a visualization system, {\\rmfamily \\scshape vitaLITy}, designed to promote serendipitous discovery of relevant academic literature. \nDesigned and developed with formative input from data visualization researchers, {\\rmfamily \\scshape vitaLITy}{} allows users to search and explore academic literature using a document-level transformer-based approach to identify semantically similar literature.\nIn addition, we contributed a dataset about \\texttt{59,232} academic articles with metadata (titles, abstracts, authors, keywords, citation counts, etc.) across \\texttt{38} venues common in data visualization research, along with open-source scrapers to expand and customize the corpus of literature searchable in {\\rmfamily \\scshape vitaLITy}.\nWe demonstrated how {\\rmfamily \\scshape vitaLITy}{} can complement existing academic literature review practices through a series of usage scenarios and shared feedback from 6 data visualization researchers from a qualitative study. \nParticipants expressed excitement to incorporate {\\rmfamily \\scshape vitaLITy}{} in their workflow, to identify gaps in their academic literature searches or to kickstart the literature review of a new topic. \n\\revised{While our initial prototype and evaluation focused on the data visualization field, we have open-sourced our system and scraper framework to enable expansion of the {\\rmfamily \\scshape vitaLITy}{} approach to other venues and academic communities.\nWe invite those who are interested to augment the {\\rmfamily \\scshape vitaLITy}{} system and data for their academic interests.}\n\\section{Usage Scenarios}\n\\label{sec:case_study}\n\nA common thread among the authors' prior research deals with \\textbf{human bias in data visualization}, and in particular, the authors have focused on defining~\\cite{wall2018four}, detecting~\\cite{cho2017,WallBias,WallFormative,WallMarkov}, and mitigating~\\cite{WallDesign,Lumos,LRG} cognitive biases.\nThus, we find it fitting to demonstrate the usage of {\\rmfamily \\scshape vitaLITy}{} through a series of usage scenarios in the context of a literature review on bias in visualization.\n\n\n\\subsection{Usage Scenario 1: Identifying Missing Papers}\nMaya is a data visualization PhD student working on their dissertation on the topic of ``Mitigating Bias in Data Visualization.''  \nThey are wrapping up the related work and preparing to submit their thesis. \nBefore submitting, Maya wants to check for potential gaps in the literature review and ensure there is no critical missing work. \nMaya decides to use {\\rmfamily \\scshape vitaLITy}{} to explore the visualization literature.\n\nMaya wants to be systematic about their search. \nThey begin by taking some of the key papers related to bias in visualization, including the following~\\cite{dimara2017attraction,dimara2018task,dimara2019mitigating,WallBias,WallDesign,cho2017,wesslen2019investigating,gotz2016adaptive}. \nMaya has already examined the papers cited from these works and written about the relevant ones in their dissertation. They locate these key papers in {\\rmfamily \\scshape vitaLITy}{} and ``select'' them [add them as input to Similarity Search] (Figure~\\ref{fig:search-by-papers}a), then map them in the Visualization (Figure~\\ref{fig:search-by-papers}b).\n\nStarting with N-Dimensional Specter embedding, Maya searches for similar papers (Figure~\\ref{fig:search-by-papers}c). \nThe first result, ``A Formative Study of Interactive Bias Metrics in Visual Analytics Using Anchoring Bias''~\\cite{WallFormative} (similarity score \\texttt{0.4355}), is cited in one of the papers~\\cite{WallDesign} so Maya was already aware. \nScanning down the list, the fourth result is ``CogTool-Explorer: A Model of Goal-Directed User Exploration That Considers Information Layout''~\\cite{teo2012cogtool}, a paper Maya is not aware of. \nPublished at CHI in 2012, this paper describes a method for modeling and predicting user interactive behavior. \nIntrigued by the relevance of precursory work in HCI to predict interactive behavior~\\cite{teo2012cogtool} to work on modeling user bias~\\cite{WallBias}, Maya saves this paper to the ``cart''. \n\nContinuing to examine the list of output papers, the next result also proves relevant with a similarity score of \\texttt{0.2593}: a BELIV paper titled ``Just the Other Side of the Coin? From Error to Insight Analysis''~\\cite{smuc2016just} which models errors and insights in cognitive processing. \nSeveral others also catch Maya's eye relevant to the design of bias mitigation strategies, including research about introducing visualization ``difficulties'' in design to aid comprehension and recall~\\cite{hullman2011benefitting} and even use of so-called ``transparent deception'' in visualization if and when it is aligned with certain user goals~\\cite{ritchie2019lie}.\nMaya saves these papers and exports them for further review (Figure~\\ref{fig:search-by-papers}d). \n\nFurthermore, Maya notices a particularly relevant paper, ``Priming and Anchoring Effects in Visualization''~\\cite{valdez2018priming}, which they forgot about, so adds it to the input similarity search and re-computes the output. \nThey find ``Pushing the (Visual) Narrative: the Effects of Prior Knowledge Elicitation in Provocative Topics''~\\cite{heyer2020pushing}, discussing persuasive visualization designs, which again Maya finds relevant for designing bias mitigation interventions. \nMaya continues iterating on their exploration of the literature, augmenting their dissertation related work section and filling in gaps, especially from the CHI community. \n\n\n\n\n\\subsection{Usage Scenario 2: Analysis of Keyword Quality}\nKatherine is a visualization researcher who focuses on topics related to bias and decision making. \nShe has primarily relied on keyword searches supported by IEEE Xplore, ACM Digital Library, etc. for identifying relevant literature in the past. \nBeginning with a set of known papers about bias in visualization (i.e., the same set from the previous scenario~\\cite{gotz2016adaptive,WallBias,WallDesign,cho2017,wesslen2019investigating,dimara2017attraction,dimara2018task,dimara2019mitigating}), she identifies several relevant keywords, including\n\\emph{human biases}, \\emph{bias mitigation}, \\emph{bias mitigation strategies}, \\emph{bias alleviation}, \\emph{debiasing}, \\emph{cognition}, \\emph{cognitive bias}, \\emph{cognitive biases}, \\emph{cognitive heuristics}, \\emph{heuristics},  \\emph{decision making}, \\emph{decision-making}, \\emph{human decision-making}, \\emph{sensemaking capabilities}, \\emph{uncertainty}, \\emph{anchoring bias}, and \\emph{attraction effect}.\nShe disregards several others that she believes are too broad, e.g., \\emph{visualization}, \\emph{information visualization}, \\emph{data visualization}, \\emph{human-centered computing}, \\emph{visual analytics}, etc. \nShe notes the multiplicity of some keywords defined by authors. \n\nKatherine conducts a similarity search using {\\rmfamily \\scshape vitaLITy}{} (yielding the same output as the previous scenario for Maya's literature review). \nShe notes a number of papers that she would have been unable to identify given only these keyword searches. \nFor instance, ``Designing Information for Remediating Cognitive Biases in Decision-Making''~\\cite{zhang2015designing} contains keywords \\emph{Human Computer Interaction (hci)} and \\emph{Human-centered Computing} and would have been missed by targeted bias-related keywords and likely lost among a sea of other papers by searching for more generic HCI keywords.\nSimilarly, ``A Lie Reveals the Truth: Quasimodes for Task-Aligned Data Presentation''~\\cite{ritchie2019lie} contains very broad keywords, including \\emph{Visualization}, \\emph{Empirical Studies In Visualization}, and \\emph{Human-centered Computing}.\nOther papers not directly related to bias, but still relevant, are even less likely to contain keyword matches. \nFor instance, ``Observation-Level Interaction with Statistical Models for Visual Analytics''~\\cite{Endert2011} describes data- or ``observation''-level interactions users perform with data based on perceived relationships and interests in the data, a topic of precursory relevance to bias research in data visualization. \nHowever, it contains keywords with no overlap to the bias-related search terms: \\emph{Principal Component Analysis}, \\emph{Data Models}, \\emph{Data Visualization}, \\emph{Visual Analytics}, \\emph{Analytical Models}, and \\emph{Layout}.\n\n\nNotably, Katherine observes that some venues expose only index terms from e.g., IEEE or ACM, while others also expose author-defined keywords. \nThis provides different levels of granularity in the ability to search for literature by keyword. \nHence, Katherine finds that alternative approaches based on document-level embeddings can be a fruitful way to identify literature when keyword searches prove insufficient or inconsistent across venues.\n\n\n\\subsection{Usage Scenario 3: Beginning a New Project} \n\\begin{comment}\n\\emily{Remco approved our use of this abstract.\nAlso, need to consider how to frame this; seems odd to use fictional Ella when it's a real paper w\/ real author names... but would also be weird to use real author names since they didn't actually use {\\rmfamily \\scshape vitaLITy}; or maybe the disclaimer before the quote is enough?}\nElla is a big data researcher, new to the area of data visualization. \nShe wants to study how prominent cognitive biases are when people view progressive visualizations of big data.\nShe plans to conduct a series of experiments in which participants will complete tasks using progressive visualizations. \nShe writes out her idea in the form of the abstract below.\nNote: This abstract was used with permission from the authors of a recent 2021 TVCG paper titled ``Impact of Cognitive Biases on Progressive Visualization''~\\cite{procopio2021impact}, which was not yet in our document corpus.\nHence, it serves as a dramatized exemplar of using {\\rmfamily \\scshape vitaLITy}{} with a working abstract. \n\n\\begin{quotation}\n\\textit{Progressive visualization is fast becoming a technique in the visualization community to help users interact with large amounts of data. \nWith progressive visualization, users can examine intermediate results of complex or long running computations, without waiting for the computation to complete. \nWhile this has shown to be beneficial to users, recent research has identified potential risks. \nFor example, users may misjudge the uncertainty in the intermediate results and draw incorrect conclusions or see patterns that are not present in the final results. \nIn this paper, we conduct a comprehensive set of studies to quantify the advantages and limitations of progressive visualization. \nBased on a recent report by Micallef et al., we examine four types of cognitive biases that can occur with progressive visualization: uncertainty bias, illusion bias, control bias, and anchoring bias. \nThe results of the studies suggest a cautious but promising use of progressive visualization \u2013 while there can be significant savings in task completion time, accuracy can be negatively affected in certain conditions. \nThese findings confirm earlier reports of the benefits and drawbacks of progressive visualization and that continued research into mitigating the effects of cognitive biases is necessary.}\n\\end{quotation}\n\\arpit{Is this quotation required to be in-text? We can could come up with a set of figures encompassing either or both of the abtract search + umap stuff discussed in the scenario, e.g.Figure~\\ref{fig:search-by-abstract-remco}.}\n\nElla enters her working title and abstract in {\\rmfamily \\scshape vitaLITy}{} and examines the resulting literature. \nShe maps several of the output papers on the Visualization and realizes they are fairly close together in the Specter embedding space. \nShe selects them on the map and clicks \\faInfoCircle~ to examine them more closely. \nShe finds two recent papers by the author Emanuel Zgraggen: (1) a 2018 CHI paper titled ``Investigating the Effect of the Multiple Comparisons Problem in Visual Analysis''~\\cite{zgraggen2018investigating} that describes an experiment to quantify spurious findings users make from visualizations, and (2) a 2017 TVCG paper titled ``How Progressive Visualizations Affect Exploratory Analysis''~\\cite{zgraggen2016progressive}. \nShe finds these works to be relevant points of comparison and saves them for a closer reading. \n\nAfter reading the saved papers more carefully, Ella believes there is significant innovation in her project with respect to quantifying specific types of bias. \nShe begins writing about the papers she found to form a Related Work section of her paper and continues to refine her experimental design.\n\\emily{surprisingly there weren't that many results that were ultimately cited in Remco's paper. We could leave it at this \/ I can possibly mention a couple other papers; Or this could be a more comprehensive example, where there are a few papers identified from the abstract search, and then maybe move on to keyword \/ author search?}\n\n\\arpit{Yeah, Remco's abstract based search scenario ended abruptly at first read (I was expecting a lot more). Also we are not directly commenting that they did cite vitality recommended papers or that they missed a few relevant ones which is somehow making this exemplar incomplete and hence weakish. this section abruptly ended for me. Based on your points, I think mentioning a couple more and then moving on to keyword\/author search will be nice for the exemplar to stand-out.}\n\n\\arpit{OR, we could stop at what we have here and let the next paragraph take-up that role. I think our own abstract based search scenario should be there since we have control over the resultant citations and vitality is already doing a great job recommending nice relevant citations}\n\n\n\\emily{Yeah, I struggled with this one because there weren't that may {\\rmfamily \\scshape vitaLITy}{} recommended papers that were cited... lots of stuff wasn't cited, and it felt odd to point to a bunch of gaps in someone else's lit review, ya know? Leaning toward just keeping ours instead...}\n\n\\hrule\n\n\n\\emily{version 2: our abstract}\n\\end{comment}\n\n\nIn this scenario, we showcase how {\\rmfamily \\scshape vitaLITy}{} facilitated our own literature review for the present work. \nAfter using traditional approaches based on keyword searches or citations from known papers, we found {\\rmfamily \\scshape vitaLITy}{} helped us identify a plethora of additional literature we were previously unaware of.\nWe used the Similarity Search by Abstract feature of {\\rmfamily \\scshape vitaLITy}{} with our paper title and abstract (Figure~\\ref{fig:search-by-abstract}a). \n\nThe first returned result is a 2011 Computer Graphics Forum paper titled ``PaperVis: Literature Review Made Easy''~\\cite{chou2011papervis} that utilizes a node-link visualization approach to support literature review and creates a topic hierarchy based on semantically meaningful topics (Figure~\\ref{fig:search-by-abstract}b). \nThe next paper similarly focuses on creating iterative citation networks to facilitate creation and sharing of bibliographies~\\cite{dattolo2018visualbib}.\nIn general, after searching the output, a few themes emerge: (1) visualization systems that focus on citation networks (e.g.,~\\cite{wilkins2015evolutionworks,heimerl2015citerivers}), systems that focus on clustering or similarity (typically by matching keywords, e.g.,~\\cite{wang2019vispubcompas}, or using topic modeling, e.g.,~\\cite{alexander2014serendip}), and (3) systems that focus on both citation networks and similarity measures (e.g.,~\\cite{nakazawa2018analytics}).\nOther notable topics also surfaced, including a design space~\\cite{felix2017taking} and analyses of keywords utilized in the visualization community~\\cite{isenberg2016visualization}, a system for supporting dissemination of curated survey results~\\cite{beck2015visual}, analysis of the contextual \\emph{reasons} for citations~\\cite{yoon2020conference}, and an emergent design space for considering visualizations of literature collections~\\cite{hinrichs2015speculative}.\n\nReflecting on these findings, we believe traditional methods for searching literature left many gaps in our literature review for two primary reasons: (1) many of these works are distributed across several publication venues (e.g., IV, PacificVis, Interact, VAST, TVCG), and (2) many of these papers received relatively little traction since their original publication 5-10 years ago. \n\n\n\n\n\n\n\n\\subsection{Usage Scenario 4: Getting to Know VIS}\nRosa is a new PhD student joining a lab that conducts research in data visualization. \nTo become acquainted with the field, her advisor suggests that Rosa browse through some of the prominent literature in {\\rmfamily \\scshape vitaLITy}.\nUpon loading the system, Rosa observes that it contains \\texttt{59,232} papers in the Paper Collection View. \nInspecting the Meta View, she observes those papers are described by \\texttt{49,278} keywords, written by \\texttt{82,391} authors from \\texttt{55} different venues, across \\texttt{47} years.\nAmong the top keywords are \\emph{Human-centered Computing} and \\emph{Human Computer Interaction (hci)}, describing \\texttt{13,833} and \\texttt{8,365} papers respectively. \nThe lineage of data visualization becomes apparent to Rosa when she notices that the fifth most common keyword is \\emph{Computer Graphics}, followed by \\emph{Data Visualization}. \nOther common keywords that catch Rosa's eye describe topics such as \\emph{Machine Learning}, \\emph{Information Retrieval}, \\emph{Artificial Intelligence}, \\emph{Interaction Design}, and \\emph{Animation}, among others. \n\nRosa enters \\emph{Data Visualization} as a filter in the Keywords column of the Paper Collection View, then filters to show only papers in the past 10 years to focus on the \\texttt{2,032} most relevant recent works in the field. \nInterestingly, these papers appear in a fairly dense area near the center of the Visualization. \nIn the Meta View, she notes a few authors whose names she recognizes, including Kwan-liu Ma who authored \\texttt{58} of the papers with the keyword \\emph{Data Visualization} since 2010. \nShe also notices Daniel Keim, John T. Stasko, Niklas Elmqvist, and Hanspeter Pfister, among others. \nShe next filters the Paper Collection View to see only John T. Stasko's papers (\\texttt{80}) and removes the other filters (Figure~\\ref{fig:meta}a-d). \nThe Meta View reveals that his work is associated with the following keywords: \\emph{data visualization, visualization, human-center computing, visual analytics, human computer interaction (hci)} (a). Some of his common co-authors include Zhicheng Liu, Carsten Gorg, and Youn Ah Kang (b).\nHe publishes primarily at TVCG (\\texttt{21}) and VAST (\\texttt{15}) (c), with 2007 his most productive year (\\texttt{11} publications) followed by 2008 (\\texttt{10} publications) then 2011, 2012, and 2014 each with \\texttt{6} publications (d).\n\n\n\n\\begin{figure*}[!t]\n    \\centering\n    \\setlength{\\belowcaptionskip}{-10pt}\n    \\includegraphics[width=\\linewidth]{figures\/search-by-papers.pdf}\n    \\caption{\\textbf{Search by a list of seed papers: Scenario 1}. Based on a list of known relevant bias papers (a), Maya observes the clustering of similar papers in the Visualization (b). She examines the similar papers more closely to gauge their relevance (c) and exports relevant saved papers (d).}\n    \\label{fig:search-by-papers}\n  \\end{figure*}\n\n\\begin{figure}[!t]\n   \n    \\centering\n    \\includegraphics[width=\\linewidth]{figures\/search-by-abstract.pdf}\n    \\caption{\\textbf{Search by Abstract: {\\rmfamily \\scshape vitaLITy}{}'s own Literature Review.} The authors using {\\rmfamily \\scshape vitaLITy}{}'s working title and abstract (a) to find similar papers (b) to assist in its own literature review.}\n    \\label{fig:search-by-abstract}\n  \\end{figure}\n\n \n \n\n\\section{Evaluation}\n\\label{sec:evaluation}\n\n- evaluate the system via a case study comparison of our technique to an existing survey paper, perhaps Dimara's interaction paper~\\cite{dimara2019interaction}\n\n\n\\subsection{Existing Survey Methodology}\n\n- in addition to systematic lit reviews conducted for papers, we also examined several survey papers (e.g., ~\\cite{})\n- these surveys describe their methodology for lit reivew, including collecting an initial set of seed papers, keyword search, inclusion criteria, venues considered, etc.\n\n\n\\subsection{Existing Survey Results}\n\n- total number of papers found, high level topics covered\n\n\n\\subsection{Our Survey Methodology}\n\n- need to give our system a catchy name to refer to it here ;) \n\n- describe our alternative approach, including both keyword and exemplar paper search\n\n\n\\subsection{Our Survey Results}\n\n- total number of papers found, clusters of topics that formed\n\n\n\n\\subsection{Comparing Survey Results}\n\n- using two alternative methodologies, we achieved (hopefully at least close to) comparable results using less manual effort\n\n- set comparison: if the Dimara survey is set A and our survey is set B, how many papers are in the intersection? how many in the set difference A-B and B-A? \n\\section{Usage Scenarios: Bias in Visualization}\n\\label{sec:case_study}\n\n\\subsection{Motivation}\nA common thread among the authors' prior research deals with \\textbf{human bias in data visualization}, and in particular, the authors have focused on defining~\\cite{wall2018four}, detecting~\\cite{cho2017,WallBias,WallFormative,karduni2018can}, and mitigating~\\cite{WallDesign} cognitive biases.\nThrough a number of prior discussions, we identified topics in visualization research that were relevant to our own work: e.g., Bayesian cognitive modeling~\\cite{kim2019bayesian}, guidance~\\cite{ceneda2017characterizing}, and mixed-initiative~\\cite{Horvitz1999} visual analytics (e.g.,~\\cite{BrownDisFunction2012,WallPodium,cook2015mixed}), to name a few.\nHowever, seldom do authors of these topics utilize the language of \\emph{bias}. \n\nKnowledge of these topics motivated the present work.\nHow could we identify these relevant topics in our literature reviews? \nA simple keyword search would not be fruitful due to a lack of common language. \nThus, we find it fitting to put {\\rmfamily \\scshape vitaLITy}{} to the test in the domain of \\textbf{bias in data visualization}.\nIn addition to identifying these known topics of interest, can our approach bring to light any additional topics of interest?\n\n\n\n\\subsection{Topics of Interest}\nPrior to beginning our literature review, we identified three topics of interest we hoped our literature review would uncover: (1) Bayesian cognitive modeling, (2) guidance, and (3) mixed-initiative visual analytics. \n\nBayesian cognitive modeling is often used in data visualization to compare how a user updates their beliefs in the presence of new and uncertain data to a normative benchmark~\\cite{kim2019bayesian,karduni2020bayesian}. \nWith respect to bias, this approach can be one promising direction toward characterization of bias (e.g., it can provide a normative framework in which to interpret observed user decisions).\nWhile this approach has been recently proposed~\\cite{wu2017towards}, to our knowledge it has not been used in empirical studies of bias in data visualization.\n\nThe topics of guidance and mixed-initiative visual analytics can similarly be relevant in the context of bias mitigation. \nThese topics motivated a recent design space of bias mitigation techniques in visualization~\\cite{WallDesign}.\nIn particular, techniques used to generally guide users through knowledge gaps in data analysis~\\cite{ceneda2017characterizing} can be applied to guiding users toward a less biased analysis process. \nIn doing so, systems are likely to employ mixed-initiative techniques~\\cite{Horvitz1999} wherein systems assume some responsibility and control from users. \n\n\n\\subsection{Strategy}\nWe began our search by ``blinding'' ourselves to the topics of interest. \nHence, our search strategies were initially restricted to include use of ``obvious'' keywords (e.g., bias, decision making) and known papers on bias in visualization (e.g., the authors' own papers and select others that utilize the language of bias~\\cite{dimara2017attraction,dimara2018task,dimara2019mitigating,gotz2016adaptive}). \n\n\n\\subsection{Findings}\n\n\\subsubsection{Keyword Search}\nglobal keyword search for ``bias'' returns 1639\/59413 hits\n\ngiven the scope of venues included, this revealed some relevant papers of interest (that likely would have been lost \/ difficult to filter for if searching via google scholar; less common venue, but still important for vis); \n- e.g., Two Implications and Dual-Process Theories of Reasoning. (venue: Diagrams)\n- The Nudge Deck: A Design Support Tool for Technology-Mediated Nudging.(venue: Conference on Designing Interactive Systems)\n\nSome of the usual suspects identified: \n- FairSight: Visual Analytics for Fairness in Decision Making.\n- Selection Bias Tracking and Detailed Subset Comparison for High-Dimensional Data. (follow up paper to Gotz adaptive contextualization paper)\n- Recent work on perceptual bias: Biased Average Position Estimates in Line and Bar Graphs: Underestimation, Overestimation, and Perceptual Pull.\n\n\n\\subsubsection{Similarity Search}\n\nbegin with my own paper~\\cite{WallBias} as a seed\nsome obvious results:\n- A Formative Study of Interactive Bias Metrics in Visual Analytics Using Anchoring Bias\n- lots of DECISIVe hits (Cognitive Biases in Visualization book chapters)\n- Adaptive Contextualization: Combating Bias During High-Dimensional Visualization and Data Selection.\n\nsome less obvious results: \n- Internalization, qualitative methods, and evaluation. (venue: BELIV)\n- An Analysis of Machine- and Human-Analytics in Classification. (interestingly describes machine v. human+machine)\n- Evaluating visualization using cognitive measures.\n- Designing Theory-Driven User-Centric Explainable AI.\n(can explanation techniques be used to mitigate bias in machine reliance?)\n- Taking Development Seriously: Modeling the Interactions in the Emergence of Different Word Learning Biases.\n- Bounded rationality leads to optimal decision-making and learning under uncertainty: Satisficing, prospect theory, and comparative valuation breaking the speed-accuracy tradeoff.\n- BiDots: Visual Exploration of Weighted Biclusters.\n- An Information-theoretic Framework for Visualization.\n\n\n\nthen adding my formative study paper and adaptive contextualization: \n- some weird ones come up: \n- A review of monocular visual odometry.\n- Wall cavitation caused by projectile impact.\n\n(by the end of the 25 output, we are getting similarity scores of 0)\n\nthen adding ~\\cite{cho2017}, we get \n- Measuring Cognitive Load using Eye Tracking Technology in Visual Computing\n\n\nnew query: add all of my own papers as input to similarity search\noutput: User Evaluations of Interactive Multimodal Data Presentation. (suggests vis + sonification is promising...; this was actually rated really similar for some reason, interesting)\n- Towards an instrument for measuring sensemaking and an assessment of its theoretical features. (sensemaking motivated a lot of my early work)\n- Casual Information Visualization: Depictions of Data in Everyday Life. (I have since gone into some recent work on causality...)\n\ntried similar query for each of us -- interestingly, similarity search based on all of our individual papers leads to some sensemaking papers for each of us (except Arpit, just based on the papers that are scraped of yours)\n\n\nif we use ALL of our papers as input (20 in total): \ntop 3 interestingly seem irrelevant: \n- Wall cavitation caused by projectile impact.\n- BiDots: Visual Exploration of Weighted Biclusters.\n- A review of monocular visual odometry.\n\nNext ones seem better: \n- The Impact of User Characteristics and Preferences on Performance with an Unfamiliar Voice User Interface.\n- Towards Deeper Understanding of User Experience with Ubiquitous Computing Systems: Systematic Literature Review and Design Framework.\n- User Evaluations of Interactive Multimodal Data Presentation.\n- Towards an instrument for measuring sensemaking and an assessment of its theoretical features.\n- A Computational Model of the Role of Attention in Subitizing and Enumeration.\n- Casual Information Visualization: Depictions of Data in Everyday Life.\n- Effects of Sensemaking Translucence on Distributed Collaborative Analysis\n- Trust in AutoML: exploring information needs for establishing trust in automated machine learning systems\n- Demonstrational Interaction for Data Visualization.\n\n\n\n\n\\emily{- Not a gold standard by any stretch, but would be interesting to compare to the references captured in my (Emily)'s dissertation; I tried to be reasonably complete. What did I miss?}\n\n\\begin{figure*}[!t]\n    \\centering\n    \\includegraphics[width=\\linewidth]{figures\/search-by-papers.pdf}\n    \\caption{Search by Papers. \\arpit{To tweak to replicate the eventual bias case study.}}\n    \\label{fig:search-by-papers}\n  \\end{figure*}\n\n\\begin{figure*}[!t]\n    \\centering\n    \\includegraphics[width=\\linewidth]{figures\/search-by-abstract.pdf}\n    \\caption{Search by Abstract. \\arpit{For this one, it'll be cool to do a search with our own final abstract that results in some similar papers that we actually cite in our related work.}}\n    \\label{fig:search-by-abstract}\n  \\end{figure*}\n\\subsubsection{Positive Quotes}\n\n- searching nearby papers in the embedded space, after lassoing: S01 said \"This is interesting. It seems there are some papers here that might be useful.\"\n\"I feel like I would spend a lot of time on this. It's like this mystery, I feel like if I spent some time on this, I might stumble upon a paper that was relevant that was published in a different domain. And that's basically like half of the papers that I cite.\"\n\"It might be especially useful if I worked on a different topic that I hadn't worked on in the past.\"\n\n- Search by abstract: S01 said \"If I'm starting a new project and I don't know if this has been done, I can write up some words in the form of an abstract to see if this is done.\"\n\n- would you use this? S01 \"Yeah, I think it could be very useful if I have a gap in my lit search. There are some papers I should cite, and if i don't cite them, then reviewers will be like 'you should cite these papers', and this seems like it would yield such results. I have some confidence. This garden of forking paths paper I had not search for but it came up because of this similarity search. And if I were in a new domain where I didn't have a lot of background knowledge, this would be useful. I would interleave this with a Google Scholar search. If I found a few relevant papers, I would go to Google Scholar to see the references in that paper and who has cited that paper. And that's a workflow that I'm familiar with.\"\n\n- would you use this: S02 \"I can see myself using a tool like this, especially for someone like me who has been in the field for a bit and knows where to begin the search process. But I wish fine tuning search results were more intuitive. I could find some relevant papers, then use the JSON output to reduce the search space within another tool like Google Scholar.\"\n\n- specter embeddings: S02, after less successful 2-D search w\/ glove: \"I'm going to try 2-D search with Specter. This search seems to be a little bit better.\"\n\n- favorite features: S02 \"I think the table view at the top is a really good starting point. It works really well. It shows the authors, etc. that I expect to see. It's a good entry point for the user. The saved paper cart is also a neat addition. I will always be mindful of my goal to fill the cart with relevant papers.\"\n\n- in response to keyword search results, S03 \"I've read this one before [Verifi]. This one I don't care about, it's more machine learning. I'd like to find more social science.\" \n\"Social Media\u2026 sounds interesting, I want to save this paper to read it later.\"\n\"Nudging, this is interesting. I should take a look at the abstract.\"\n\"Now I just want to check out the other papers from this author\" [Zhicong Lu]\n\"I think I'll read some of these.\"\n\n- saved paper cart: S03 \"I liked the fact that I'm able to save some of the papers. Typically I wouldn't do it that way. When I search for papers that might be relevant, I just use a word document or something to keep track of the titles and maybe download the paper as well. It's nice to be able to save the papers.\"\n\n- after doing n-D similarity search, S04: \"Ohhh, interesting, I never knew that these two people had a collaboration.\" -- in response to interesting relevant network paper [Cody Dunne and Ben Shneiderman]\n\n- S04 \"I liked the visualization, especially the lasso select. It's really cool and really helpful.\" \n\"Also, locate is a really good feature, you can actually identify the papers in different colors.\"\n\n- would you use it? S04 \"I definitely see myself using this app. I really like the idea of this visualization, it's really cool, because it's very helpful to actually find a set of papers that are semantically relevant to one paper. Especially when I can randomly identify a paper that I missed in the lit review, and find other papers similar to that one to be sure you aren't missing anything.\"\n\n- relevance of similarity output: S05 \"The papers I'm seeing now are a lot more relevant, some of the papers I've been reviewing. Hmm, some of them are kind of new, but let's see if they're relevant to my topic.\"\n\"I'm trying to find if there are new papers worth exploring.\"\n\"This one seems interesting, so I would like to add this to my list and maybe save it as well.\"\n\n- found something really similar to what she was thinking of writing about: S05 \"I'm noticing some papers that I was considering to review to write my discussion section. I wanted to review other related domains and use this analytical framework to conduct research in that domain. One possibility was to use it for evaluations of different structures of storytelling visualizations. I'm seeing a paper that did something similar to what I was considering doing.\"\n\n- S05 \"I want to see 2-D similarity results now -- ohh, this is interesting: Design Patterns for Data Comics.\"\n\n- distinction between 2-D and n-D similarity: S05 \"I do see a difference, I think 2-D search may be giving me more relevant results.\" \n\"Might be better for more in-depth exploration. If there's a very specific topic you're looking for. For example, I was looking for analytical frameworks within storytelling. And it seemed like 2-D similarity search gave better results.\"\n\"n-D seemed to give better results that were exploratory. I found some interesting papers I would like to read more.\" \n\n- S05 \"This was actually useful, because there were some papers that caught my eye that I hadn't seen before.\"\n\n- similarity search S05 \"I really liked the similarity search. I liked that you showed the similarity score. It seems reasonable\u2026 Those on top tended to be more relevant to what I was looking for.\"\n\n- umap S05 \"I guess this [umap] provides a nice overview of the selected papers, and I could see to drill down into more details or look for clusters.\"\n\n- would you use it? S05 \"Yes. I would probably use it when I have some high-level ideas about how I would structure the related sections -- when I know what those 2-3 themes are. I would use this to find more relevant papers.\"\n\n- S06: Hid author column and resized column to see full titles\u2026 seemed very intuitive to him, he expected it would do this\n\n- Appropriation of abstract search: S06 after searching in abstracts, applying filters for relevant venues, etc. felt unsatisfied by results; so used search by abstract instead: \"Maybe I should use word embedding because it might have more flexibility and I can pass more information in my search.\" \n\"It shows a lot of foundational literature\u2026\"\n[after first iteration results were only ok, added more content to the abstract and was much more satisfied with results]\n\"Wow, this shows much better results now than the short abstract.\"\n\"Presentation-oriented visualization techniques -- hmm looks interesting.\"\n\"Oh this looks interesting, but I haven't looked at.\" [Comparing the Effectiveness of Visualizations of Different Data Distributions]\n\"I should take a note.\" [writes down paper info]\n\"This one, I think I cited this one.\"\n\"I'm also writing down this one. It's look at EEG, wow. It looks interesting because I cited a similar mathematical paper, they want to approximate the same thing.\" [Comparing Similarity Perception in Time Series Visualizations]\n\n- satisfaction w\/ search: S06 \"Yes, I was mostly looking for papers that I haven't looked at before. For 15 minutes, I found two papers I might be interested in. It's a really useful process. Otherwise I might spend a lot of time scanning PDFs, which is not a very pleasant experience.\"\n\n- lots of good features: S06 \"Search by abstract was super useful. Personally I'm not super familiar with these visualizations, dimensionality reduction, so it's harder to interpret how to assess this information.\"\n\"The similarity measures here [in similarity output] were really useful. But some would return like 0.0001 and I could see that my search was wrong.\"\n\"For lasso selection, I want to see factors that can cluster similar papers. I want to just see similarity output, not select everything.\" \n\"Changing columns was useful too, so I can get a better sense of the data. If the search gets improved then search by abstract will be much better. Google Scholar searches body text too. But for Google Scholar the similarity [or relevance?] of results is not so good.\"\n\n- when it's useful (at the end of lit review) S06: \"For searching papers, I would continue to use Google Scholar when I start the lit review. But I think vitaLITy could be super useful at the later stage of your research. You want to do some sanity checks on your literature review. At that point of time, I have my abstract, more details, papers I have already cited, and based on that, I can do a more narrow search for papers I might be missing. When you're finalizing your literature review. It can help people evaluate their process and understand how they are doing, how they can improve. Sometimes you get reviews that you didn't cite this or this or this and it's sort of embarrassing.\"\n\n\n\n\n\n\\subsubsection{Negative Quotes} \n- in reasoning about the quality of similarity output: \"I see why these papers are not giving the best results. It seems in the word embedding space, they are not close together.\" (S01)\n- did you find useful papers: S01 said \"I could find a few papers that came up that slipped my mind. But I didn't find any new papers that I hadn't already cited. I got some sense that the search was giving me useful results. I have some confidence that it would work, but for this particular context, I did not find anything new.\"\n\n- some resistance to doing things a different way: S01 said \"I'm having some of the same difficulties that I have when I do a Google Scholar search. I need to find one paper. My target is one unknown paper among hundreds. It's very rare that I find multiple useful papers when I try random keywords on Google Scholar. A lot of the papers I find because coauthors tell me about a relevant paper. A lot of the papers that we cite are not directly relevant, but it's adjacent. That kind of makes it complicated to search if I had already filtered on a particular keyword.\"\n- S03 \"I prefer Google Scholar. Would I use it? Maybe\u2026 I suspect I would use it just like I use Google Scholar. I wouldn't use similarity search. I would just search for keywords. I'm not sure how Google Scholar does it, but I like this global search to look in abstracts, titles, etc.\"\n\n- didn't use umap much: S01 \"This visualization [scatterplot] was interesting, but I spent very little time on this. I'm not sure why, but it almost seemed like I would need very specific input to find relevant results, so I ended up spending more time on filtering that I would want a similarity search on.\"\n\n- relevance of glove output: S02 \"The original paper I'm looking for Regroup, these do not seem to be good results. The 2-D search does not seem to be good with Glove. The n-D results were much better.\" [switched to specter], \"Maybe if I give a few other papers as examples, it may help.\" [adds 2 more papers]\n\"Some matches, but some do not.\"\n- S05 \"I'm reviewing the results, some seem relevant, some not so much.\"\n\n- quality of similarity search results: S02 \"When I look by author or keywords, I find relevant papers. But when I try to fine tune, it loses track. I could have expected better search results.\"\n\n- accuracy \/ utility of umap projection, S03 \"not sure these are so similar\" -- appear far apart (did n-D search rather than 2-D)\n \"I don't think I need to see all the papers at once. I mostly want to see all the papers I have selected and their geolocation and whether they're similar or not so similar. But the algorithm might be bad. Or the projection. It doesn't accurately depict similarity between papers.\"\n \n - too much packed into one tool: S04 \"The unique part of this interface is the visualization of the space of papers. I wish it could be bigger canvas space so I can select papers. The interface is a little small and too compact that makes me feel like too many things are changing in front of my face and I lost track.\"\n\"I feel like the similarity search and visualization can be a separate thing on its own. And the meta thing and table search can be on its own.\"\n\n- didn't use saved papers cart S06: \"I realized looking at the questions that I never used the saved papers cart. Even using Google Scholar I usually just prefer to save the PDF.\"\n\n\n\n\n\n\\subsubsection{Desired Features} \n\n- citation networks: S01 \"The other thing, in this case, I forgot to mention this, but a way I conduct literature reviews is to look at the cited papers of a relevant paper and then go in a search. That is missing. Google Scholar makes it easier, but it's not great.\"\n- S06 \"I think it's hard to implement, I've tried it before, but maybe it could show the citation map. Sometimes I find a really old paper that has some really core ideas and I want to see more recent papers that cite it.\"\n\n- more embedding options: S02 \n\"Other than Glove, you can consider to use transformer embeddings like BERT. It uses context vectors.\"\n\n- indicators about credibility of venue \/ author: S03 \"If I'm able to get a sense of how credible the source is, e.g., this particular conference. When it comes to some other domains or venues, we have a hard time getting an indicator of whether this is a good conference or not until we read the paper, or if we know the author is highly cited and respected.\"\n\n- alternate way to visualize umap: S04 \"Is there any possible way to visualize this in terms of networks? If you can separate out the nodes in space and add edge weights to reflect similarity. The biggest problem is overlapping nodes, so I don't have a full picture. Or at least put the red dots in the top layer. Now you have three layers: filtered, unfiltered, saved. Maybe I can use the legend as a filter to show only that layer.\"\n\n- metal panel integration: S04 \"I didn't feel like I used the meta panel a lot. Is it possible that I select a keyword that it could query all papers that have this keyword in the search \/ umap?\"\n\n- suggested keywords: S05 \"For keywords, if I could look for multiple keywords\u2026\"\n\"Can it suggest semantically similar keywords?\"\n\n\n\n\\subsubsection{Small Usability Issues}\n\n- fuzzy string search could be useful: S01 searched for \"uncertainty visualisations\" -> \"uncertainty visualizations\" -> \"uncertainty visualization\" \n- S01 also tried multiple keywords; may be beneficial to have more robust and customizable search mechanism\n- SOMEONE used the search by abstract as a workaround (interestingly)\n\n- \"Wall Cavitation\" paper seems to come up frequently (in our usage scenarios and in participant sessions) [I think just for Glove?]; something about abstract length (very short) makes it seem like a good match for lots of searches\n\n- feedback about queries: S01 \"I did find a lack of feedback on the queries.\"\nS05: \"Apart from being a little laggy, it was pretty straightforward. But I kept forgetting to clear out the search [clear filters].\"\n\n- customizable layout: S02 \"I found myself when I had already filtered by keywords, I am only focusing on this view [scatterplot], it's very small in the screen space. I want to hide the meta view and maybe even the main table view, so I can easily zoom and pan and lasso. The similarity search panel could also be bigger.\"\n- S04: \"I wish this interface [umap] could be a little bigger.\"\n- S06 \"I think the window [top table] is a little bit short. Can I expand this?\" [no, could not... although was able to very intuitively resize \/ customize column widths]\n\n- zoom level on umap: S02 \"When I do this similarity search, it should automatically zoom to show the paper(s) that were the beginning search point and the papers that it found, rather than this zoomed out view where I have to look for the orange or red dots.\"\n\n- button layout: S02 \"The glove \/ specter and n-D \/ 2-D buttons should be closer together so it's easier for me to realize where to make changes related to the search process.\"\n\n- keywords in meta view: S03 \"Keyword feature can be useful if it's not displaying keywords for the stuff above but for what I have selected.\"\n\n- S06 \"Most of the features were really good as-is.\" \n\"Maybe the interface might be able to support more natural interactions -- more connected between these panels. E.g., if I filter keyword here [meta view] it would filter here [main table].\"\n\"When I search the abstract, it might be useful to support non-exact match, because you usually don't expect an exact string match.\"\n\"Match the conferences were not matched -- like 20 Eurographics [variations].\"\n\"Some focus on sections. If I'm working on the table, this could be bigger, or let users change the proportion of the panels.\"\n\n\\section{Formative Study}\n\\label{sec:formative}\n\nWe conducted a formative study to better understand the needs of researchers as they perform literature reviews.  \nParticipants were 4 Computer Science PhD students (3 female, 1 male; avg. 2.75 yrs. into PhD program) who had prior experience conducting literature reviews in the field of visualization.\nSessions lasted approximately 45 minutes. \nParticipation was voluntary with no compensation. \n\nWe presented the first two participants with an initial version of the literature review tool. \nAfter incorporating feedback in the next iteration of the system, we worked with the next two participants using the updated system.\nFinally, we incorporated feedback from all formative study participants in {\\rmfamily \\scshape vitaLITy}{}, presented in the next section.\n\n\n\\subsection{Current Workflow}\n\\label{sec:workflow}\n\nAfter obtaining informed consent, we asked participants to describe their typical workflow for conducting literature reviews via a semi-structured interview.\nParticipants expressed some haphazard nature to the beginning of their processes, e.g., \\textit{``someone tells [them] about a paper, and [they] look up the citations and branch out from there''} (P1) or \\textit{``use a starting point from an advisor''} (P2).\nFrom there, there are some commonalities in processes.\n\nParticipants all utilized keyword searches on Google Scholar (P1-4).\nAs a fairly comprehensive database, participants did not worry whether a venue or paper would be present, and they appreciated the ``cited by'' feature to identify more recent relevant papers.\nHowever, participants also expressed that keyword searches on Google Scholar result in many irrelevant papers that require a lot of manual filtering for relevance.\nFor instance, P4 viewed Google Scholar as a last resort, expressing they really only use it \\textit{``if [they] don't have a better starting point seed paper.''} \nEchoing some of the motivation for this work, P1 indicated, \\textit{``if a keyword is used differently in different fields, [they] have to read a lot of abstracts to determine whether it's relevant or not.''}\n\nWhile Google Scholar seems to be the default search tool, there are others that participants integrate in various parts of their workflow when conducting literature reviews. \nFor instance, P4 indicated regular use of bibliography management tools like Mendeley and Zotero.\nAmong our relatively small sample in this formative study, participants did not mention some other elements in their workflow that we anticipated, e.g., DBLP, manual scripting \/ web scraping, etc. \n\n\n\n\n\\subsection{Preliminary Feedback}\n\\label{sec:prelim_feedback}\n\nNext, participants used a preliminary version of our literature review tool. \nThe preliminary tool included \\texttt{17,926} papers from the following venues over the past \\texttt{39} years (1982-2020): \\{\\emph{CGA, CGF, EuroVis, Graphics Interface, Information Visualization, Interact, Journal of Visualization, PacificVis, SciVis, TVCG, VAST, VIS}\\} and supported two main mechanisms for searching the corpus: keyword search and similarity search (described in greater detail in the next section).\nAfter using the tool, we asked participants for additional feedback about the current implementation, possible improvements, and any new capabilities that they could envision to better support their literature review process. \n \nParticipants appreciated the ability to start their search with a seed paper or papers (P1 said they got \\textit{``pages and pages of results which is what [they] would get on Google Scholar, but these are actually more relevant''}). \nP2 searched based on the seminal paper on hypothetical outcome plots (HOPs)~\\cite{hullman2015hypothetical} and observed \\textit{``it pulled up lots of uncertainty vis papers, which were not in the title -- cool!''}\nbut expressed that there was still a lot of noise when searching by keywords.\n\n\nParticipants \\revised{suggested several} new features: being able to visualize connections between papers (e.g., by citations, co-authors, etc. - P1), adding critical information on citation count as a mechanism for determining importance of a paper (P1), making the overview interactive (with brushing and linking, summarizing dynamic regions, etc. - P2), and being able to type in a custom abstract or paper idea as the basis of the similarity search (e.g., to identify relevant literature for a paper idea that hasn't been fully fleshed out yet - P2). \nParticipants also steered away from one of the features in the tool: the word cloud. \nP4 indicated \\textit{``it wasn't clear how it was related to what [they] had selected.''}\n\nOverall, participants indicated that a tool like this in their workflow could supplement tools like Google Scholar for serendipitous exploration. \nP4 suggested it would be beneficial in the early ``discovery'' phases of literature review, with the caveat that the data on included venues needed to be sufficiently comprehensive. \nAs a result of this feedback, we updated the system to address these ideas, including scraping data from additional venues, adding citation counts, adding brushing and linking between views, and searching by a custom abstract. \nWe did not add features based on citation networks in our system\\revised{; instead, we focused on leveraging transformer models to serve as a complementary literature search technique to existing tools that address these needs}. \\removed{due to space and complexity constraints in the tool.}\n\n\n\\subsection{Design Goals}\n\\label{sec:design_goals}\n\nCollectively, these interviews led us to the following set of four design goals for our literature review system.\n\n\\smallskip\n\\noindent\\textbf{DG 1. Serendipity:} Enable serendipitous identification of semantically related articles that do not necessarily have shared keywords through visual exploration.\n\n\\smallskip\n\\noindent\\textbf{DG 2. Familiarity:} Facilitate a familiar search functionality to what users are currently accustomed to, such as keyword and author search.\n\n\\smallskip\n\\noindent\\textbf{DG 3. Novelty:} Afford users to find semantically related articles by searching based on the author's own ideas in the form of unpublished sentences \/ abstract.\n\n\\smallskip\n\\noindent\\textbf{DG 4. Overview:} Enable users to interact with a visual overview of a group of papers.\n\n\n\\section{Related Work} \n\\label{sec:related_work}\n\n\\subsection{Literature Review Methodologies}\nLiterature reviews and surveys are an essential part of scientific disciplines. \nThey are broadly defined as systematic ways of collecting and synthesizing research on a specific topic \\cite{baumeister1997writing,snyder2019literature}. \nThere are a variety of different guidelines and methodologies, such as systematic reviews \\cite{moher2009preferred}, narrative reviews \\cite{baumeister1997writing}, and integrative reviews \\cite{torraco2005writing}. \nThese guidelines and methods mostly vary in how they organize, synthesize, and analyze a set of selected articles through a combination of quantitative and qualitative methods \\cite{snyder2019literature}. \nThese methodologies often include multiple stages, the first of which is related to identifying a strategy for searching and selecting a set of related literature. \nFor example, Hannah Snyder states that \\textit{``a search strategy for identifying relevant literature must be developed. \nThis includes selecting search terms and appropriate databases and deciding on inclusion and exclusion criteria. \nHere, a number of important decisions must be made that are crucial and will eventually determine the quality and rigor of the review''}\\cite{snyder2019literature}. \n\nSimilarly, within the visualization community, defining search strategies and keywords are described as the primary step for conducting literature reviews \\cite{mcnabb2019write}.\nMany visualization survey papers include explicit excerpts about their selection criteria that describe keywords, databases, and the search process of each survey paper \\cite{tong2018storytelling,fuchs2016systematic,roberts2018visualising}. \nFor example, in their survey of glyph visualization techniques, Fusch et al. employ a ``snow ball'' sampling technique in which they start by searching the keyword ``glyph'' within various libraries, select all the findings, filter based on their exclusion criteria, and then look at the related work of the selected papers to find more papers \\cite{fuchs2016systematic}. \n\nAlthough keyword search is the most prevalent method for searching literature, it comes with some limitations:\n\\begin{itemize}[nosep]\n    \\item Often it won't yield papers that do not include a specific keyword but might be very related to the topic at hand.\n    \\item Within different communities, different keywords are used to represent a common concept.\n   \n\\end{itemize}\n\nAs a result, selecting sufficiently broad yet relevant keywords can be a challenge.\n{\\rmfamily \\scshape vitaLITy}{} offers a visual system that complements traditional keyword search-based methods to enhance literature searches\n{\\rmfamily \\scshape vitaLITy}{} implements a state-of-the-art transformer-based document similarity search that can find semantically similar documents that may not always share the same set of keywords.\n\n\n\n\n\n\n\\subsection{Visualization of Academic Articles}\nVisual analytics research has been effective in incorporating many machine learning and natural language processing models (e.g., topic modeling or word embeddings) into vis systems for exploratory analysis of large corpora of text documents \\cite{Endert2012,liu2018bridging,dou2013hierarchicaltopics,el2017progressive}. A common task is identifying similar documents \\cite{endert2017state}. Early visualization papers on document similarities used representations of a corpus' similarity matrix through dot plots \\cite{church1993dotplot} or histograms \\cite{freire2008visualizing}. More recent vis systems have considered more author assigned keyword-based approaches like constructive text similarity \\cite{abdul2017constructive} and GlassViz \\cite{benito2020glassviz}.\nAlternative approaches have considered word embeddings including for iterative lexicon construction \\cite{park2017conceptvector} that provide related ability to query documents. \n\nOne key application area for incorporating visual techniques to help users find similar and relevant documents is in searches for academic articles. Several prominent article databases have implemented such systems to find relevant articles. Text Analyzer by JSTOR extracts the most important topics and keywords from entered papers and recommends other relevant documents to users (\\url{https:\/\/www.jstor.org\/analyze\/}). Pubmed uses a word-based technique to help users retrieve the most similar papers ( \\url{https:\/\/pubmed.ncbi.nlm.nih.gov\/help\/#pubmedhelp.Computation_of_Weighted_Relev}). Open Knowledge graph uses similarity scores provided by Pubmed and develops a circle packing visualization to help users understand groups of related research relevant to their search terms (\\url{https:\/\/openknowledgemaps.org\/}).\n\nWithin the visualization community, several works highlight the importance of understanding and visualizing academic literature. \nFelix et al., introduce a design space and highlight how different keyword summarization techniques might impact users' understanding of related literature \\cite{felix2017taking}. \nUsing the open source vis literature dataset (VisPubData), Isenberg et al. introduce KeyVis and analyze keywords utilized in the visualization community~\\cite{isenberg2016visualization,Isenberg:2017:VMC}. \nOthers introduce relevant systems for supporting dissemination of curated survey results~\\cite{beck2015visual}, \\revised{visualization of lead-lag analysis of text corpora~\\cite{liu2014exploring}}, analysis of the contextual \\emph{reasons} for citations~\\cite{yoon2020conference}, and an emergent design space for considering visualizations of literature collections~\\cite{hinrichs2015speculative}.\nIn general, within visualization systems on academic literature we can observe three themes: (1) visualization systems that focus on citation networks (e.g.,~\\cite{wilkins2015evolutionworks,heimerl2015citerivers,chou2011papervis,dattolo2018visualbib}), systems that focus on clustering or similarity (typically by matching keywords, e.g.,~\\cite{wang2019vispubcompas}, or using topic modeling, e.g.,~\\cite{alexander2014serendip,isenberg2016visualization}), and (3) systems that focus on both citation networks and similarity measures (e.g.,~\\cite{nakazawa2018analytics,chen2006citespace}).\n\\revised{In the latter category, CiteSpace II introduces a technique to computationally define \\emph{co-citation clusters}.}\n\nInspired by these works, our paper introduces (1) a more comprehensive public dataset of visualization literature, and (2) utilizes state-of-the-art document embedding techniques using transformers to enable serendipitous discovery of articles.\n\n\n\n\n\n\n\n\\subsection{Word Embeddings and Transformers}\nDocument similarity is a classic problem in natural language processing and information retrieval \\cite{Jurafsky2021}. \nWord embeddings provide an approach in which words (or documents) that have similar meanings have similar (vector) representations.\n\\revised{Recent advances in word embeddings have yielded significant improvements in standard similarity benchmarks like STS or SentEval \\cite{arora2017simple,reimers-gurevych-2019-sentence,cohan2020specter}.} \nBeginning with word2vec \\cite{mikolov2013efficient}, many extensions of learned dense representations of word vectors have followed including GloVe \\cite{pennington2014glove}, fasttext \\cite{bojanowski2017enriching}, skipthought \\cite{kiros2015skip}, ELMo \\cite{peters2018deep}, and BERT \\cite{devlin2018bert}. \\revised{More recently, specialized transformer models like SPECTER \\cite{cohan2020specter} have been developed to specialize in domains like academic literature. SPECTER combines self-supervised pre-training on transformer architectures (e.g., BERT-like) on academic abstracts and is ``citation-informed'' to enhance performance for tasks like academic literature recommendation and topic classification.}\n\n\\revised{SPECTER provides four advantages over past word embedding  approaches for {\\rmfamily \\scshape vitaLITy}{}'s task. First, it incorporates contextual embeddings (via BERT\/transformer architecture) that enable different vector representations depending on the context (e.g., ``bias'' in different contexts). Second, the model was pre-trained on academic titles and abstracts (sciBERT \\cite{beltagy2019scibert}). This enables the model to have transfer learning gains from pre-training with a BERT-like \\cite{devlin2018bert} transformer architecture but with specialization for academic literature recommendation. Third, it incorporates a triplet-loss pre-training objective that enables it to use citations as an inter-document incidental supervision signal for fine-tuning. By incorporating both text pre-training with citation fine-tuning, the model achieved state-of-the-art performance for academic literature recommendations as well as six additional tasks like citation prediction, user activity (view or read), and topic classification. Tasks like citation prediction or user activity were out of scope of {\\rmfamily \\scshape vitaLITy}{}'s design due to data limitations, but future work could easily incorporate such tasks with additional citation or activity data. Fourth, the model is available out-of-the-box without fine-tuning as well as in model deployment through a publicly released API. This API enables fast and efficient real time scoring in {\\rmfamily \\scshape vitaLITy}{}.} \n\n\n\n\n\\section{Introduction}\n\nVisualization research is inherently interdisciplinary, borne out of fields such as Computer Graphics and Human-Computer Interaction, with heavy influence from fields outside of computing such as Perceptual Psychology and Cognitive Science. \nFurthermore, visualization is applied to explore data and support data-driven decision making problems in domains ranging from enterprise analytics to medicine. \nAs a result of the multi-faceted nature of the field, there may be parallel research efforts that can be difficult to become aware of, even with a comprehensive methodology for conducting literature reviews. \n\nOne challenge of interdisciplinary research is when different fields use similar terminology to study different problems. \nFor instance, \\emph{transformer} in electronics refers to a device that transfers energy between circuits~\\cite{kulkarni2017transformer}; while in computing, \\emph{transformer} refers to a type of neural network based on attention mechanisms, commonly applied to unstructured text data~\\cite{vaswani2017attention}.\nAs a result, keyword searches often yield irrelevant work. \nFurther, sifting through all hits from a keyword search may still miss critical work.\nFor instance, the recent wave of work on \\emph{bias} in visualization (e.g.,~\\cite{dimara2017attraction,dimara2019mitigating,WallBias,wall2018four,cho2017,valdez2018priming,LRG,Lumos}) seldom mentions \\emph{uncertainty} (e.g.,~\\cite{hullman2015hypothetical,hullman2019authors}).\nYet, as the seminal work on bias in Cognitive Science points out, bias emerges when people make decisions under uncertainty~\\cite{Tversky1974}; hence, there is a critical need to examine uncertainty literature that may fundamentally address similar problems using different terminology.\nAs a result, conducting a simple keyword search for ``bias'' (i.e., matching tokens in a paper title or abstract) \nto identify relevant work may neglect pockets of influential research.\nHowever, these challenges are not unique to data visualization research or even computing. \nThey extend to virtually all interdisciplinary research.\n\nCurrent prevalent practices for conducting literature reviews tend to utilize two common search strategies: (1) keyword search and (2) examination of back-references from a snowballing set of seed papers, usually through searching Google Scholar or DBLP. \nThese approaches can successfully identify a large number of relevant citations, but can suffer from at least two key limitations: thoroughness and efficiency. \nThat is, they may fail to unearth related papers that use different terminology, and they require significant manual effort to gauge relevancy of potentially thousands of hits. \nIn other words, a prominent challenge, then, in conducting literature reviews or surveys is to effectively identify research of significance to a given topic based on similarity of topics, irrespective of matching exact keywords.\n\nTo address these challenges, we introduce {\\rmfamily \\scshape vitaLITy}{}, an open-source visualization system designed to support a flexible exploration of research articles. \nInspired by work on \\emph{insight} in visualization (i.e., ``eureka'' or ``aha'' moments~\\cite{chang2009defining}), we similarly aim to support \\emph{serendipity} with {\\rmfamily \\scshape vitaLITy}, \\revised{operationally intended to describe the goal that users may ``stumble upon'' relevant literature, when other search approaches might otherwise fail}. \n\\revised{{\\rmfamily \\scshape vitaLITy}{} incorporates SPECTER \\cite{cohan2020specter}, a state-of-the-art document-level contextual embedding model for scientific document recommendation.\nUnlike many pre-trained language models that use a general corpus like Wikipedia or the Common Crawl \\cite{mikolov2013efficient,pennington2014glove,devlin2018bert}, SPECTER was pre-trained on academic literature (sciBERT \\cite{beltagy2019scibert}) and fine-tuned with citations which provides out-of-the-box state-of-the-art performance for academic literature recommendations and topic classification.\n\n\n\nIn summary, this work presents the following contributions: \n\\begin{enumerate}[nosep]\n    \\item results of a formative interview study in which visualization researchers identified key challenges in current literature review practices (Section~\\ref{sec:formative}),\n    \\item a dataset of scraped metadata from \\texttt{59,232} academic articles (\\textbf{\\url{https:\/\/figshare.com\/articles\/dataset\/VitaLITy_A_Dataset_of_Academic_Articles\/14329151}}~\\cite{Narechania2021}, CC0 License), including paper titles, keywords, and abstracts from \\texttt{38} popular venues for visualization research (Section~\\ref{sec:data}),\n    \\item an open-source tool, {\\rmfamily \\scshape vitaLITy}{} (\\textbf{\\url{http:\/\/vitality-vis.github.io}}, MIT License), for supporting discovery of relevant articles while conducting literature reviews (Section~\\ref{sec:system_overview}),\n    \\item usage scenarios describing potential workflows in which {\\rmfamily \\scshape vitaLITy}{} might be used in different ways to support serendipitous discovery of relevant academic literature\n   \n   \n   \n  \n   \n    (Section~\\ref{sec:case_study}), and \n    \\item results of a summative evaluation of {\\rmfamily \\scshape vitaLITy}{} (Section~\\ref{sec:evaluation}).\n\\end{enumerate}\n\n\n\n\n\n\n\\begin{comment}\nThe remainder of this paper is organized as follows. \nIn Section~\\ref{sec:related_work}, we describe existing literature review methodologies and word embedding techniques. \nWe next describe a formative interview study that led to a set of design goals for the system in Sections~\\ref{sec:design_considerations}-\\ref{sec:system}.\nWe present results of a benchmarking evaluation in Section~\\ref{sec:evaluation} and a case study application of our system in the domain of bias in visualization in Section~\\ref{sec:case_study}.\nWe discuss challenges, limitations, and future work and conclude with final remarks in Sections~\\ref{sec:discussion}-\\ref{sec:conclusion}.\n\\end{comment}\n\n\n\n\n\n\n\n\n\n\n\n\n\\input{sections\/related_work}\n\\input{sections\/formative}\n\\input{sections\/system}\n\\input{sections\/bias}\n\\input{sections\/evaluation}\n\\input{sections\/discussion}\n\\input{sections\/conclusion}\n\n\n\n\\bibliographystyle{abbrv-doi}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{Introduction}\n\\label{Section_I_Introduction}\n\n\nRealizing the promises of quantum computing requires the ability to manipulate and measure complex states of quantum devices with high fidelity. An outstanding challenge towards reaching this goal is the realization of fast and high-fidelity entangling gates with large on-off ratio. An approach to turn on and off entangling interactions is to frequency tune pairs of qubits in and out of resonance. However, noise in the control parameter allowing to tune the qubit frequency introduces an additional source of dephasing, which can be mitigated by operating the qubits at sweet spots where they are first-order insensitive to this noise channel \\citep{vionManipulatingQuantumState2002}.\n\nIn superconducting qubits such as the transmon \\cite{kochChargeinsensitiveQubitDesign2007a}, tuning the qubit frequency is most commonly accomplished by threading a loop with magnetic flux. While for static dc flux bias there are a few sweet spots per single flux period $\\Phi_0$, it was recently shown that tailored ac modulation of the flux or direct voltage drive on the qubits extends these few static sweet spots to a larger class of dynamical sweet spots \\citep{huangEngineeringDynamicalSweet2020,didierFluxControlSuperconducting2019,guoDephasinginsensitiveQuantumInformation2018,didierACFluxSweet2019,valeryDynamicalSweetSpot2021}. This gives more flexibility in choosing the operating points to both maximize dephasing times and facilitate two-qubit gates. \n\nIn the presence of a continuous ac drive, the static computational basis of the qubits is replaced by a set of eigenstates of the periodic Floquet Hamiltonian, also known as Floquet states. Protocols for initialization, readout, single-qubit operations and entangling gates on these Floquet qubits have been theoretically proposed \\citep{huangEngineeringDynamicalSweet2020} and experimentally investigated \\citep{mundadaFloquetengineeredEnhancementCoherence2020} showing improvements in the dephasing time of the qubits. Floquet qubits can be frequency-tuned in large frequency range by changing the parameters of the drive. This tunability can be used, for example, to implement single-qubit phase gates, but also to bring together pairs of Floquet qubits to activate SWAP-type interactions \\citep{huangEngineeringDynamicalSweet2020}. On the other hand, for X-type single-qubit gates,  or for two-qubit gates such as the cross-resonance \\citep{rigettiFullyMicroTunable2010}, a second drive is introduced to induce transitions between the Floquet-qubit states \\cite{huangEngineeringDynamicalSweet2020}. \nMoreover, as shown in Refs.~\\cite{huangEngineeringDynamicalSweet2020,mundadaFloquetengineeredEnhancementCoherence2020}, the readout of the Floquet qubit can be performed in a two-step process: the Floquet qubit is first mapped to the laboratory-frame qubit by adiabatically turning off the drive. At that point, a usual dispersive readout is performed by driving a cavity coupled to the qubit \\citep{Blais2021}.\n\nIn this work, we exploit the Many-Mode Floquet theory (MMFT) introduced in Refs.~\\citep{hoFloquetLiouvilleSupermatrixApproach1986, shirleySolutionSchrodingerEquation1965a, shillSEMICLASSICALMANYMODEFLOQUET1983} to provide an analytical description of the dynamics of the Floquet qubit during such gates, which involve more than one drive frequency. Generalized spectra describing the system during the operation of the gate can be used to optimize gate parameters, as well as to understand the dynamics of higher-energy states.\n\nUsing this approach, which allows for multiple simultaneous drives, we also show how it is possible to use a driven coupler to engineer a longitudinal interaction between the Floquet qubit and a readout cavity. Thanks to both the longitudinal nature of this interaction -- which is known to lead to fast qubit measurements \\citep{didierFastQuantumNondemolition2015} -- and to the fact that there is no need to map the Floquet qubit back to the undriven qubit states before the readout, we find from numerical simulations that this approach can lead to fast and high-fidelity Floquet qubit readout. A superconducting circuit design for this longitudinal Floquet readout is proposed.\n\n\nThe paper is structured as follows. In \\cref{Section_II_Floquet_Framework}, we review the Floquet and MMFT frameworks. In \\cref{Section_III_Single_qubit_operations} we show how X-type gates can be implemented on Floquet states by adding a second drive to the qubit and we apply MMFT to the driven Floquet qubits during the gate.\nWe then demonstrate the feasibility of dynamical longitudinal readout of Floquet states with an additional drive in \\cref{Section_IV_Readout_of_floquet_states}, and compare our analytical results to full numerics. Finally, in \\cref{Section_V_Initialization_of_arbitrary_states} we explore the  timescales necessary for the initialization of a Floquet qubit.\n\n\n\\section{Floquet Framework} \n\\label{Section_II_Floquet_Framework}\n\n\n\\subsection{Floquet qubits}\n\\label{Section_II_Subsection_I_Floquet_Qubits}\n\nDriven quantum systems are part of a larger class of systems evolving under a time-periodic Hamiltonian with period $T=2\\pi\/\\omega_{d}$ and which are efficiently described by the Floquet formalism \\citep{grifoniDrivenQuantumTunneling1998b,chuFloquetTheoremGeneralized2004b}, where a system Hamiltonian $H_{\\text{s}}$ with Hilbert-space dimension $d$ is replaced with the time-dependent Floquet Hamiltonian (with $\\hbar = 1$): \n\\begin{equation}\n\\label{General_Floquet_Hamiltonian}\n    H_F(t) = H_{\\text{s}}+V(t)-i\\frac{\\partial}{\\partial t},  \n\\end{equation}\nwith $V(t)=V(t+T)$ the periodic drive on the system. Based on the symmetry of the Hamiltonian $H_F$ under time translation $t\\rightarrow t+T$, the Floquet theorem states the existence of a full set of solutions to the time-dependent Schrodinger equation so that $\\forall t,~ H_F(t)\\ket{\\psi_n(t)} = 0, (n=1,2,...,d)$. To complete the analogy with the static Hamiltonian, these solutions are related to the eigenvalue problem for the Floquet Hamiltonian $\\forall t,~ H_F(t)\\ket{\\phi_n(t)} = \\epsilon_{n}\\ket{\\phi_n(t)}, (n=1,2,...,d)$ with: \n\\begin{equation}\n\\label{General_Floquet_Modes}\n  \\forall t,\\forall n\\leq d, ~\\ket{\\psi_{n}(t)} = e^{-i\\epsilon_nt}\\ket{\\phi_{n}(t)},\n\\end{equation}\nwhere the \\textit{Floquet modes} $\\ket{\\phi_{n}(t)}$ are $T$-periodic in time, and the \\textit{quasienergies} $\\epsilon_{n}$ are real-valued coefficients which are invariant under translation by multiples $k$ of the drive frequency $\\omega_{d}$. The term \\textit{quasienergies} thus refers to representatives of equivalence classes, often chosen in the first Brillouin zone $[-\\omega_{d}\/2, \\omega_{d}\/2]$. With appropriately designed driving protocols, one can convert an undriven Hamiltonian $H_{s}$ into the dressed $H_F(t)$ and continuously map the energies to the quasienergies and the eigenstates to the corresponding Floquet states, hence the name \\textit{Floquet qubit} when the time-dependent dressed states are used to define the two-level system.\\\\\n\n\nIn this context, dynamical protection consists of operating the Floquet qubit at extrema of the quasienergy difference with respect to the drive parameters subject to noise \\citep{didierACFluxSweet2019, didierFluxControlSuperconducting2019, huangEngineeringDynamicalSweet2020}. As shown by \\textcite{huangEngineeringDynamicalSweet2020}, dynamical sweet spots represent manifolds in parameter space, in contrast with the few isolated static sweet spots that are found in the absence of a drive. This allows for an increased freedom in the parameter choice that can be used to operate the Floquet qubit while being protected from low-frequency noise, which translates to high coherence times. This property is compatible with single and two-qubit gate operations, which justifies the promising role Floquet qubits could play in quantum information processing.\\\\\n\n\n\\subsection{Many-Mode Floquet Theory}\n\\label{Section_II_Subsection_II_Many_Mode_Floquet_Theory}\n\nFloquet qubits describe a subgroup of driven systems evolving under the dynamics of a $T$-periodic Hamiltonian as introduced in \\cref{General_Floquet_Hamiltonian}. Here, the Hamiltonian often includes the effect of only one drive on a static system or else multiple drives at different harmonics of one characteristic frequency. In some cases such as certain gates on Floquet qubits, one can face Hamiltonians with two distinct time-dependent terms:\n\\begin{equation}\n\\label{General_Floquet_Hamiltonian_Two_Tones}\n    H_F(t) = H_{\\text{s}}+V_1(t)+V_2(t)-i\\frac{\\partial}{\\partial t},\n\\end{equation}\nwith $V_1,V_2$ respectively $2\\pi\/\\omega_1$ and $2\\pi\/\\omega_2$ periodic in time. The Floquet qubit is generated by the first driving term and the system Hamiltonian, while the second term is typically only switched on during the gate without any \\emph{a priori} link between the frequencies $\\omega_1$ and $\\omega_2$. We will limit ourselves to two distinct frequencies and their harmonics, even if the scheme used in studies of Hamiltonians with multiple drives is more general \\citep{fainshteinNONLINEARSUSCEPTIBILITIESLIGHT1992, dorrMultiphotonProcessesIntense1991a, crowleyTopologicalClassificationQuasiperiodically2019, boyersExploring2DSynthetic2020, longNonadiabaticTopologicalEnergy2020}.\n\nIn the rotating-wave approximation (RWA), the two distinct frequencies typically result in a single effective frequency on the system at the difference $(\\omega_1 - \\omega_2)$, but Floquet analysis aims at describing the dynamics of driven systems without such simplification.\nWe first notice that the extension of Floquet theory to commensurate frequencies is straightforward using the greatest common divisor $\\omega_{\\mathrm{GCD}}=\\mathrm{GCD}(\\omega_1, \\omega_2)$ as the new frequency of a single-tone Floquet system for the duration of the gate \\citep{poertnerBichromaticDressingRydberg2020}. This result translates into the definition of Floquet states and quasienergies for \\cref{General_Floquet_Hamiltonian_Two_Tones} which create the continuous connection between Floquet states before and after the gate. These intermediary states can be numerically evaluated, but complexity arises as the new period of the system can be orders of magnitude greater than the distinct timescales $2\\pi\/\\omega_1$ and $2\\pi\/\\omega_2$. In practice, this leads to long simulation times.\n\nA generalization of these ideas for multiple incommensurate frequencies exists under the name of Many-Mode Floquet Theory\n\\citep{chuFloquetTheoremGeneralized2004b, hoSemiclassicalManymodeFloquet1985a,hoSemiclassicalManymodeFloquet1983}. The main idea here \nis to look for a generalization of the $N$ Floquet states and quasienergies by considering a Fourier basis with two dimensions rather than only one:\n\\begin{align}\n\\label{General_Fourier_Basis_Two_Tones}\n    \\forall n\\leq N,~\\ket{\\phi_n(t)} &= \\sum_{k_1, k_2}e^{i(k_1\\omega_1+k_2\\omega_2)t}\\ket{\\phi_{n,k_1,k_2}}\\\\\n    \\forall n\\leq N,~\\epsilon_{n, k_1, k_2} &= \\epsilon_{n, 0, 0} + k_1\\omega_1 + k_2\\omega_2.\n\\end{align}\nMMFT has been implemented into a numerical solver using truncated Fourier bases \\citep{poertnerValidityManymodeFloquet2020a}, which we do not make use of in this work. However, the generalization of quasienergies and Floquet Modes provides an analytical approach to understand the dynamics of driven systems with additional drives such as naturally occurs in Floquet qubits.\n\n\n\n\\section{Single-qubit operations} \n\\label{Section_III_Single_qubit_operations}\n\nApproaches to realize $X$, $\\sqrt{X}$ and single-qubit phase gates on Floquet qubits were proposed in Ref.~\\citep{huangEngineeringDynamicalSweet2020} with fidelities obtained from numerical simulations exceeding $99.99\\%$ and gate durations on the order of tens of nanoseconds. Our focus here is on the $X$ and $\\sqrt{X}$ gates based on adding a secondary drive to the Floquet qubit to induce Rabi oscillations between the Floquet states. \n\nWe extend the principle of the Floquet spectrum to driven Floquet qubits, widely used in static systems with a single drive frequency. This approach has recently been  used by \\textcite{Petrescu2021} to extract gate parameters maximizing the gate rate while minimizing higher order $ZZ$-terms. The generalized Floquet spectrum is defined with respect to the second drive frequency acting on the periodic Floquet System, typically the drive inducing a X-Gate on a Floquet qubit. We characterize the generalized avoided crossings appearing at resonances in the spectrum of the Floquet qubit.\n\n\\subsection{X-Gate in the RWA}\n\\label{Section_III_Subsection_I_XGate_in_the_RWA}\n \nWe use as logical states the eigenstates of a two-level system (TLS) and, without loss of generality, we will set a transition frequency $\\omega_0\/2\\pi = 5.02~\\text{GHz}$ and a near-resonant Rabi drive with amplitude $\\varepsilon_{d1}\/2\\pi = 0.21$ GHz and with a detuning $\\Delta = \\omega_{0}-\\omega_{d1}$:\n\\begin{equation}\n\\label{TLS_Floquet_Hamiltonian}\n  H(t) = \\frac{\\omega_0}{2}\\sigma_z + \\varepsilon_{d1}\\cos(\\omega_{d1}t)\\sigma_x.\n\\end{equation}\nGoing to a frame rotating at $\\omega_{d1}$ and applying the RWA by assuming $\\varepsilon_{d1}\\ll~\\omega_{d1}$, the Floquet states and quasi-energies of the Hamiltonian of \\cref{TLS_Floquet_Hamiltonian} take the form:\n\\begin{equation}\n\\begin{split}\n\\label{TLS_Floquet_Modes}\n    \\epsilon_{0,1} &= \\pm\\sqrt{\\left(\\frac{\\Delta}{2}\\right)^2+\\varepsilon_{d1}^2}, \\\\\n    \\ket{\\phi_{0,1}(t)} &= \\frac{e^{+i\\omega_{d1}t\/2}}{\\sqrt{\\varepsilon_{d1}^2+(\\epsilon_{0,1}-\\frac{\\Delta}{2})^2}}\\begin{pmatrix} |\\varepsilon_{d1}|e^{-i\\omega_{d1}t} \\\\ \\epsilon_{0,1}-\\frac{\\Delta}{2}\\end{pmatrix}.\n\\end{split}\n\\end{equation}\nFurther imposing $|\\Delta|\\ll\\varepsilon_{d1}$, the Floquet states $\\ket{\\phi_{0,1}}$ are located near the equatorial plane of the Bloch sphere. Following \\textcite{huangEngineeringDynamicalSweet2020}, the addition of a second drive along the $Z$-axis in the laboratory frame with a frequency $\\omega_{d2}$ chosen close to the quasienergy difference induces Rabi oscillations of the Floquet qubit. With this addition the  Hamiltonian now reads:\n\\begin{equation}\n\\label{TLS_FLoquet_with_Drive}\n  H(t)= \\frac{\\omega_0}{2}\\sigma_z+\\varepsilon_{d1}\\cos\\left(\\omega_{d1} t\\right)\\sigma_x+\\varepsilon_{d2}\\cos\\left(\\omega_{d2} t\\right)\\sigma_z,\\\\\n\\end{equation}\nwhere $\\varepsilon_{d2}$ is the amplitude of the second drive. As an example, for a transmon qubit, a drive along the $Z$ axis is realized by flux pumping the qubit's SQUID loop \\cite{kochChargeinsensitiveQubitDesign2007a}.\n\nIn \\cref{Figure_XGate_Floquet_Qubits}(a) we plot results from an integration of the Schr\\\"odinger equation showing a full population transfer between the states $\\ket{\\phi_0(t)}, \\ket{\\phi_1(t)}$ with fidelity 99.99\\% and ramp times of the order of $20~\\text{ns}$, corresponding to the pulses represented in \\cref{Figure_XGate_Floquet_Qubits}(b). There, the green curve corresponds to the amplitude $\\varepsilon_{d1}$ of the first drive and is used to establish the Floquet logical states. A second, flux, tone (blue curve) is switched on for the duration of the gate and its frequency $\\omega_{d2}$ is close to twice the amplitude $\\varepsilon_{d1}$ of the Floquet qubit drive.\n\nThe analysis in this section relies on the RWA and is therefore only valid in the limit  $|\\Delta|\\ll\\varepsilon_{d1}$. An analogous application of the RWA would be further necessary when treating the second drive, for example in order to express the gate rate of the Floquet-qubit X-gate. Corrections beyond the RWA, applicable also in the more general case of off-resonant drives can be derived \\cite{mirrahimi2015dynamics}. Instead, in the following subsection we rely on the exact Floquet two-tone numerical method to obtain the gate rate.\n\n\n\\begin{figure}[t]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/Final_Fig\/Fig1_quasiphase_0810.pdf}\n    \\caption{a) Population of the Floquet modes $\\ket{\\phi_0(t)}$ and $\\ket{\\phi_1(t)}$ as a function of time under the Hamiltonian \\cref{TLS_FLoquet_with_Drive}. \n    b) Typical drive amplitude as a function of time. The first drive $\\varepsilon_{d1}$ (green line) is used to generate the Floquet qubit states while the second drive $\\varepsilon_{d2}$ (blue line) drives Rabi oscillations between these levels.\n    c) Four quasiphase spectra for different numerators $p=1, 2, 3, 4$ in the ratio $\\omega_{d2}\/\\omega_{d1}=p\/q$. The colored dots are obtained from diagonalization of the propagator associated with \\cref{TLS_FLoquet_with_Drive} after a common period $2\\pi\/\\omega_{\\mathrm{GCD}}$ and by sweeping the values of $q$. Because of the folded space, several crossings are observed. However, a unique anticrossing corresponding to the resonance of the second drive with the Floquet qubit is observed (vertical line).}\n    \\label{Figure_XGate_Floquet_Qubits}\n\\end{figure}\n\n\\subsection{Two-tone Floquet analysis}\n\\label{Section_III_Subsection_II_Two_tone_floquet_analysis}\n\nHere, we propose an alternative approach to analyze a gate on the Floquet states based on a two-tone Floquet analysis. A Floquet spectrum is obtained from the Hamiltonian of \\cref{TLS_FLoquet_with_Drive} with respect to the second drive frequency $\\omega_{d2}$ without requiring any of the previous RWAs. To do so, we regroup the time-dependent terms into a single quasi-periodic drive $V(t)$.\nIf the frequencies $\\omega_{d1}$ and $\\omega_{d2}$ are commensurate, then the periodicity of $V(t)$ is given by the greatest common divisor $\\omega_{\\mathrm{GCD}} = \\mathrm{GCD}(\\omega_{d1}, \\omega_{d2})$. \n\nIn the presence of two tones, the quasienergy spectrum is probed by sweeping one of the drive frequencies.\nHowever, because the quasienergies are only defined modulo $\\omega_{\\mathrm{GCD}}$ and because this quantity will strongly depend on the chosen $\\omega_{d2}$, it is not possible to define a continuous quasienergy spectrum. \n\nAs explained in \\cref{Section_II_Floquet_Framework}, when the drive frequencies can be written as an irreducible fraction $\\omega_{d1}\/\\omega_{d2} = p\/q$, the frequency $\\omega_{\\mathrm{GCD}}$ can be expressed as $\\omega_{\\mathrm{GCD}} = \\omega_{d1}\/p = \\omega_{d2}\/q$. Here, $\\omega_{d1}$ is taken as a fixed parameter such that \neach numerator $p$ corresponds to a distinct first Brillouin zone. For each numerator $p$, we can introduce a discrete quasienergy spectrum satisfying $\\omega_{d2}=\\omega_{d1}\\times q\/p$ for $q\\in\\mathbb{N}$. To compare quasienergy spectra corresponding to different numerators $p$, we normalize the Floquet quasienergy spectrum $\\epsilon_{1\/2}(\\omega_{d2})$ defined over the range $[-\\omega_{\\mathrm{GCD}}\/2,\\omega_{\\mathrm{GCD}}\/2]$ to obtain the Floquet quasiphase spectrum defined as $\\phi^F_{1\/2}(\\omega_{d2}) = \\epsilon_{1\/2}(\\omega_{d2})\\times 2\\pi\/\\omega_{\\mathrm{GCD}}$ over $[-\\pi, \\pi]$.\\\\\n\n\nIn \\cref{Figure_XGate_Floquet_Qubits}(c), we plot the quasiphase spectra associated with the Hamiltonian \\cref{TLS_FLoquet_with_Drive} for commensurate ratios $\\omega_{d2}\/\\omega_{d1}$ with small numerators. The different subplots illustrate the discrete quasiphase spectra for different values of the numerator $q$. The difference between the two quasiphases $\\phi^F_{1}$ and $\\phi^F_{2}$ exhibits a local minimum over all the subplots around $\\omega_{d2}\/\\omega_{d1}\\approx 0.04$ which is linked to an avoided crossing characterizing the resonance of the second drive with the Floquet qubit and thus yields the gate rate.\nThe analytical approximation obtained in the previous subsection shows good agreement when the parameter choice satisfies the RWA conditions. A precise numerical estimate of the size of this anticrossing, valid without any RWA, is obtained by increasing the maximum allowed numerator at the cost of longer simulations. \nA detailed procedure for extracting the local minimum corresponding to the avoided crossing can be found in \\cref{Appendix_I_Numerical_approach}. \nNotably, we mitigate the need for intensive numerical simulations by taking advantage of Dysolve \\citep{shillitoFastDifferentiableSimulation2020a}, a recent semi-analytic solver capturing the effects of oscillatory terms in the system Hamiltonian and whose performances are discussed in \\cref{Appendix_I_Numerical_approach}.\n\nThe validity of the approach presented here goes beyond the two-level approximation used in this work and can easily be extented to, for example, the higher energy levels of Floquet qubits.\n\n\n\\section{Longitudinal Floquet qubit readout}\n\\label{Section_IV_Readout_of_floquet_states}\n\nWe now turn to the readout of the Floquet qubit. In Refs.~\\cite{huangEngineeringDynamicalSweet2020,mundadaFloquetengineeredEnhancementCoherence2020,Deng2015}, this is realized by adiabatically mapping the Floquet logical states back to the original undriven qubit states, followed by a usual dispersive qubit readout \\cite{Blais2021}. This two-step process, adiabatic mapping following by readout, leads to a longer measurement time than strictly necessary. Here, we introduce an approach to directly measure the Floquet qubit without the additional step of an adiabatic mapping. Moreover, we show how it is possible to engineer a longitudinal coupling between the Floquet qubit and a readout mode by using a modulated transversal coupling. Because of its longitudinal nature, this readout can reach a large signal-to-noise ratio (SNR) in a measurement time that is small compared to the usual dispersive readout of circuit QED \\cite{didierFastQuantumNondemolition2015}. This approach bears similarities with the stroboscopic measurements of Ref.~\\citep{eddinsStroboscopicQubitMeasurement2018} and the Kerr-cat qubit readout of Ref.~\\citep{grimmKerrCatQubitStabilization2020}. \n\n\n\\subsection{Engineered longitudinal coupling}\n\\label{Section_IV_Subsection_I_Derivation_of_the_readout}\n\nOur approach is based on the usual capacitive, or transversal, coupling between a laboratory-frame qubit and a readout cavity. In the laboratory frame, the Hamiltonian reads\n\\begin{equation}\n    \\label{TLS_Readout_Theorical_Hamiltonian}\n    H_\\mathrm{lab}(t) = \\frac{\\omega_0}{2}\\sigma_z+\\varepsilon_{d1}\\cos(\\omega_1t)\\sigma_x+\\omega_r\\hat{a}^\\dag\\hat{a}+g(t)(\\hat{a}+\\hat{a}^\\dag)\\sigma_x,\n\\end{equation}\nwhere we have added to the driven qubit (first two terms) a cavity of frequency $\\omega_r$ and annihilation operator $\\hat a$ coupled to the qubit with a strength $g(t)$ which we allow to be time-dependent. In the regime where the detuning between the drive and the qubit $\\Delta$ is small compared to the drive amplitude $\\varepsilon_{d1}$, the laboratory frame $\\sigma_x$ acts as $\\sigma_z$ on the Floquet qubit corresponding to a longitudinal coupling to the cavity mode.\n\nTo make this more apparent, we move to the interaction frame defined by the transformation\n\\begin{equation}\n\\label{TLS_Readout_Propagator}\n   U(t;0) = e^{-i\\omega_r t \\hat{a}^\\dag\\hat{a} }\n   \\sum_{j\\in\\{0,1\\}} \\ket{\\phi_j(t)}\\bra{\\phi_j(0)}e^{-i\\epsilon_j t},\n\\end{equation}\n\\noindent where, in the limit $\\Delta\/\\varepsilon_{d1} \\ll 1$, the interaction-picture Hamiltonian takes the form\n\\begin{equation}\n    \\label{TLS_Readout_Interaction_Picture}\n        H_\\mathrm{int}(t) \\approx g(t)\\cos(\\omega_{0}t)(\\hat{a}e^{i\\omega_rt}+\\hat{a}^\\dag e^{-i\\omega_rt})\\sigma_z^{F}(0).\n\\end{equation}\nHere, we have introduced the interaction-picture Pauli matrices $\\sigma_k^{F}(t)$ with $k=x,y,z$ acting on the basis of the Floquet modes $\\left\\{\\ket{\\phi_0(t)},\\ket{\\phi_1(t)}\\right\\}$. Choosing the time-dependent coupling to be of the form $g(t) = \\tilde g \\cos(\\omega_m t)$ with a modulation frequency $\\omega_m = \\omega_r-\\omega_0$ (and\/or $\\omega_r+\\omega_0$) yields the longitudinal coupling Hamiltonian \\cite{didierFastQuantumNondemolition2015}\n\\begin{equation}\n\\label{TLS_Readout_Interaction_Picture_Modulated}\n    H_\\mathrm{int}(t) \\approx \\frac{\\tilde{g}}{2} (\\hat{a}+\\hat{a}^\\dag)\\sigma_z^{F}(0).\n\\end{equation}\nAs discussed in Ref.~\\cite{didierFastQuantumNondemolition2015}, evolution under this Hamiltonian leads to an optimal separation of the cavity pointer states where the initial cavity vacuum state is displaced 180 degrees out of phase depending on the state of the qubit.\n\n\\begin{figure}[t!]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/Final_Fig\/Fig2_0825.pdf}\n    \\caption{a) Pointer-state separation $D(t)$ as a function of time for longitudinal Floquet readout (full blue line), dispersive readout without state mapping (full green line), dispersive readout with the necessary state mapping with a ramp time of $T_\\mathrm{map}=30~\\text{ns}$ (dashed green line). b) Pointer state separation $D(t)$ over the steady-state separation $D(\\infty) = \\tilde g \/\\kappa$ as obtained from numerical integration under \\cref{TLS_Readout_Theorical_Hamiltonian} as a function of time and for different tilt angles $\\Delta\/\\varepsilon_{d1}$. As expected, for small $\\Delta\/\\varepsilon_{d1}$ the pointer states follow the ideal longitudinal dynamics expected from \\cref{TLS_Readout_Interaction_Picture_Modulated}. c) Pointer state separation $D(t)$ over the steady-state separation $D(\\infty)$ as found from numerical simulation of the system dynamics under the Hamiltonian of \\cref{Eq:3KNO}. Here, $D(\\infty)$ is numerically evaluated at long times and at small $\\Delta\/\\varepsilon_{d1}$, corresponding to the average value of the bottom-right corner in panel (c). As in panel (b), the pointer state dynamics follow the expected behavior for small with $\\Delta\/\\varepsilon_{d1}$. The parameters used in panel (c) are $\\{ \\bm{\\omega}_a, \\bm{\\omega}_b, \\bm{\\omega}_c\\}\/2\\pi = \\{8.2,  5.2,7.78\\}~\\text{GHz}$, $\\{\\bm{\\alpha}_b\/2,\\bm{\\alpha}_c\/2\\}\/2\\pi =\\{-0.17,0.4\\}~\\text{GHz}$, $\\{g_a,g_b\\}\/2\\pi = \\{0.2,0.2\\}~\\text{GHz}$, $\\tilde{\\epsilon}_{d1}\/2\\pi = 0.7~\\text{GHz}$ and $\\kappa\/2\\pi = 0.05~\\text{GHz}$.\n    }\n    \\label{Figure_Pointer_state_separation}\n\\end{figure}\n\nTo compare this Floquet longitudinal readout to the approach based on an adiabatic map followed by a dispersive readout of Refs.~\\cite{huangEngineeringDynamicalSweet2020,mundadaFloquetengineeredEnhancementCoherence2020,Deng2015}, we show in \\cref{Figure_Pointer_state_separation}(a) the measurement pointer state separation \\cite{Blais2021} $D(t)=\\left|\\langle \\hat{a}\\rangle_0(t) -\\langle \\hat{a}\\rangle_1(t)\\right|$. This quantity is an helpful proxy for the signal-to-noise ratio (SNR) assuming a unit measurement-chain efficiency, as obtained from the expression \\citep{bultinkGeneralMethodExtracting2018}\n\\begin{equation}\n    \\label{General_SNR_optimal}\n         \\text{SNR}(T) = \\sqrt{2\\kappa\\int_0^TD(t)^2 dt }.\n\\end{equation}\nIn this expression, $T$ is the measurement time, $\\kappa$ the decay rate of the cavity. For longitudinal coupling, this separation takes the simple form \\cite{didierFastQuantumNondemolition2015}\n\\begin{equation}\n    \\label{TLS_readout_Pointer_state_displacement}\n    D(t) = \\frac{\\tilde{g}}{\\kappa} \\left( 1 - e^{-\\kappa t\/2}\\right).\n\\end{equation}\n\nThe full blue lines in \\cref{Figure_Pointer_state_separation} correspond to longitudinal readout while the green lines to dispersive readout for which an expression equivalent to \\cref{TLS_readout_Pointer_state_displacement} can be obtained \\cite{didierFastQuantumNondemolition2015}. Comparing the full blue and full green lines, we see that longitudinal readout leads to much faster separation of the pointer states than dispersive readout even when ignoring the adiabatic mapping stage. When taking into account the required mapping stage (dashed green line), the advantage of the longitudinal approach over dispersive becomes even clearer. Here, we have used a mapping time of $T_\\mathrm{map}=30~\\text{ns}$ as in Ref.~\\cite{huangEngineeringDynamicalSweet2020}. Finally, as a reference, the dashed blue line corresponds to a situation where the mapping stage is followed by a longitudinal readout. Although this would lead to a faster separation of the pointer state at short times as compared to the standard dispersive readout, we see that the main gain in the longitudinal Floquet readout introduced here comes from the fact that mapping to the laboratory frame qubit is no longer required.\n\nAs a further verification, \\cref{Figure_Pointer_state_separation}(b) shows the pointer state separation $D(t)$ as obtained from numerical integration of the system dynamics under the laboratory-frame Hamiltonian in \\cref{TLS_Readout_Theorical_Hamiltonian} as a function of time and for different ratios $\\Delta\/\\varepsilon_{d1}$. In the laboratory frame, we take the modulated coupling to be of the form $g(t) = \\tilde{g} [\\cos(\\omega_r t-\\omega_0 t)+\\cos(\\omega_r t + \\omega_0 t)]$. In each simulation, the initial state of the cavity is chosen to be vacuum and the Floquet qubit state $\\ket{\\phi_0(0)}$ or $\\ket{\\phi_1(0)}$. For ratios $\\Delta\/\\varepsilon_{d1}<0.01$ (horizontal green dashed line), we find the expected exponential increase up to the steady-states $D(\\infty)$ in agreement with the analytical result of \\cref{TLS_readout_Pointer_state_displacement} shown in panel (a). On the other hand and as expected from the discussion below \\cref{TLS_Readout_Theorical_Hamiltonian}, when the Floquet qubit is too far away from resonance $\\Delta\/\\varepsilon_{d1}>0.1$ (horizontal red dashed line), the separation between the pointer states does not follow the trajectory predicted by \\cref{TLS_readout_Pointer_state_displacement} and the readout is suboptimal.\n\n\n\\subsection{Superconducting circuit implementation}\n\\label{Section_IV_Subsection_III_Circuit_implementation}\n\nA possible realization of this longitudinal Floquet readout with superconducting quantum circuits is illustrated in \\cref{Figure_Appendix_B_CQED}. Here, a transmon qubit ($\\hat b$) is interaction with a readout cavity ($\\hat a$) via a flux-tunable coupler ($\\hat c$). This system can be modeled as a triplet of coupled Kerr oscillators \\cite{Petrescu2021}\n\\begin{align}\n    H = H_a + H_b + H_c(t) + H_g + H_d(t), \\label{Eq:3KNO}\n\\end{align}\nwhere $H_a = \\bm{\\omega}_a \\hat{\\bm{a}}^\\dagger \\hat{\\bm{a}}$ corresponds to the linear readout resonator, and $H_b = \\bm{\\omega}_b \\hat{\\bm{b}}^\\dagger \\hat{\\bm{b}} + (\\bm{\\alpha}_b\/2) \\hat{\\bm{b}}^{\\dagger 2} \\hat{\\bm{b}}^2$ to the transmon-like qubit with negative anharmonicity $\\bm{\\alpha}_b$. The coupler Hamiltonian takes the same form $H_c = \\bm{\\omega}_c(t) \\hat{\\bm{c}}^\\dagger \\hat{\\bm{c}} + (\\bm{\\alpha}_c\/2) \\hat{\\bm{c}}^{\\dagger 2} \\hat{\\bm{c}}^2$, except that it is parametrically modulated with $\\bm{\\omega}_c(t)=\\bm{\\omega}_c + \\delta \\bm{\\omega}_c (t)$ using a time-dependent flux. The capacitive interactions are modeled by a linear off-diagonal Hamiltonian coupling the bare modes $H_g = \\sum_{\\alpha < \\beta} g_{\\alpha \\beta} \\hat{\\bm{\\alpha}}^\\dagger \\hat{\\bm{\\beta}} + \\text{H.c.}$, where the summation runs over the mode indices $a,b,c$. As shown in \\cref{Appendix_II_Coupler_mediated_interaction}, switching to a normal-mode representation, we can eliminate these bilinear terms to obtain the desired modulated coupling $g(t)$ of \\cref{TLS_Readout_Theorical_Hamiltonian} between the normal modes corresponding to the qubit and the readout resonator. This is achieved by modulating the coupler frequency at one or both of the sidebands $\\omega_a \\pm \\omega_b$. Finally, the drive on the qubit takes the usual form $H_d(t) = -i \\varepsilon_{d1}(t) (\\hat{\\bm{b}}- \\hat{\\bm{b}}^\\dagger)$.\n\nThe coupling strength $\\tilde{g}$ depends on the three capacitive couplings, on the placement of the coupler frequency and on the amplitude of the modulation. Here, we choose this frequency to satisfy the constraint $\\bm{\\omega}_a < \\bm{\\omega}_c < \\bm{\\omega}_b$ to avoid excessive asymmetry. \\Cref{Figure_Pointer_state_separation}(c) shows the pointer state separation under the evolution generated by \\cref{Eq:3KNO} and with similar conditions and parameters to those used in panel (b). At $\\Delta\/\\varepsilon_{d1}$ small, we verify that the cavity pointer state displacement induced in the cavity by the readout of the Floquet States in the simulation of the full system \\cref{Eq:3KNO} matches that of Hamiltonian \\cref{TLS_Readout_Theorical_Hamiltonian}. Importantly, the fast separation of the pointer states at short time is clearly observed.\n\n\n\\begin{figure}[t!]\n    \\centering\n    \\includegraphics[width=0.8\\columnwidth]{Figures\/Final_Fig\/Fig3_cqed_0708.pdf}\n    \\caption{Possible realization of the longitudinal Floquet readout. A driven transmon qubit (green) is coupled to a readout cavity (blue) via a flux modulated coupler (gray).}\n    \\label{Figure_Appendix_B_CQED}\n\\end{figure}\n\n\\section{Initialization of arbitrary Floquet states}\n\\label{Section_V_Initialization_of_arbitrary_states}\n\nIn this section, we consider the timescale needed to initialize a Floquet qubit state with high fidelity. In particular, we point out that the adiabatic state transfer protocols of Refs.~\\citep{mundadaFloquetengineeredEnhancementCoherence2020, desbuquoisControllingFloquetState2017a} are not optimal in the regime advantageous for longitudinal Floquet readout, \\emph{i.e.},\\  small $\\Delta\/\\varepsilon_{d1}$. Instead, we introduce an instantaneous ramping protocol which leads to high preparation fidelity in that regime.\n\n\\subsection{Adiabatic Regime}\n\\label{Section_V_Subsection_I_Adiabatic_regime}\n\nWe first consider the timescale needed to initialize a Floquet qubit with a given fidelity in the adiabatic regime. More precisely, we consider an initial laboratory frame state $\\alpha\\ket{0} + \\beta\\ket{1}$ and evaluate the fidelity of the Floquet-state preparation protocol by projecting on the expected resulting Floquet state $\\ket{\\psi(T_\\mathrm{ramp})} = \\alpha\\ket{\\phi_0(t)} + \\beta\\ket{\\phi_1(t)}$ after some ramp-up time $T_\\mathrm{ramp}$ of the drive amplitude. Without loss of generality, we take $\\alpha=1$ and $\\beta=0$, and compute the preparation fidelity $\\mathcal{F} = |\\braket{\\psi(T_\\text{ramp})}{\\phi_0(T_\\text{ramp})}|^2$ as a function of the ramp time $T_\\text{ramp}$ and for various ratios $\\Delta\/\\varepsilon_{d1}$ for the drive profile illustrated in \\cref{Figure_Initialization_Floquet_Qubits}(a).\n\nUsing a binary search in the range $\\left[1~\\text{ns},3000~\\text{ns}\\right]$, we extract in \\cref{Figure_Initialization_Floquet_Qubits}(c) the minimal value for $T_\\text{ramp}$ corresponding to a fidelity $\\mathcal{F}$ larger than 99\\% (plain green), 99.9\\% (hatched green) and 99.99\\% (dotted green) for each ratio $\\Delta\/\\varepsilon_{d1}$. We characterize the boundary of these empirical regions (dashed lines in log-log scale) by fitting an empirical law\n\\begin{equation}\n\\label{Initialization_Empirical_Law}\nT_\\text{ramp} \\times \\left|\\frac{\\Delta}{\\varepsilon_{d}}\\right|\\geq C_1,\n\\end{equation}\nwhere we find $C_1=18.9~\\text{ns}$ for a 99\\% fidelity, $C_1=28.4~\\text{ns}$ for 99.9\\%, and $C_1=36.4~\\text{ns}$ for 99.99\\%, respectively. Extrapolating this proportionality relation closer to resonance $\\Delta=0$, we obtain the divergence of the adiabatic ramping time already observed in the context of driven two-body quantum systems~\\citep{desbuquoisControllingFloquetState2017a}. In particular, for the small $\\Delta\/\\varepsilon_{d1}$ used in the longitudinal readout of the previous section, we find that the initialization is limited by the adiabatic lower bound $T_\\text{ramp} = C_1\/0.01 = 1.9~\\text{ms}$ for a 99\\% fidelity and $2.8~\\text{ms}$ for a 99.9\\% fidelity.\n\n\\begin{figure}[b!]\n    \\centering\n    \\includegraphics[width=\\columnwidth]{Figures\/Final_Fig\/Fig4_initialization_0810.pdf}\n    \\caption{\n        Ramp profile for a) adiabatic and b) instantaneous preparation pulses, as well as illustrative paths on the Bloch sphere. The grey area can be used to compare the timescales involved in the two subplots. c) Initialization fidelity versus title angle $\\Delta\/\\varepsilon_{d1}$ and ramp time $T_\\mathrm{ramp}$. The different highlighted areas correspond to sectors where an initialization fidelity higher than 99\\% (plain), 99.9\\% (hatched) and 99.99\\% (dotted) can be obtained in the adiabatic limit (green) and the instantaneous (blue) regimes.\n        }\n    \\label{Figure_Initialization_Floquet_Qubits}\n\\end{figure}\n\n\\subsection{Instantaneous regime}\n\\label{Section_V_Subsection_II_Instantaneous_regime}\n\nBecause of the long preparation time required with small $\\Delta\/\\varepsilon_{d1}$ which is optimal for the longitudinal readout of \\cref{Section_IV_Readout_of_floquet_states}, we now consider an alternative in the form of an instantaneous ramping protocol. Here, the main idea consists in preparing an initial superposition of the laboratory states $\\alpha\\ket{0} + \\beta\\ket{1}$ that matches the instantaneous eigenstate $\\ket{\\phi_0(0)}$ of the desired time-dependent Hamiltonian. An abrupt increase of the drive amplitude $\\varepsilon_{d1}(t)$, as illustrated in \\cref{Figure_Initialization_Floquet_Qubits}(b), then connects the eigenstates $\\ket{\\phi_0(0)}$ of the instantaneous Hamiltonian $H(t_0)$ and the Floquet states $\\ket{\\phi_0(t)}$ of the time-dependent Hamiltonian $H(t)$. The same idea can, in principle, be also used for the reverse mapping.\n\nComputing again the fidelity of the protocol as a function of the ramp time and ratio $\\Delta\/\\varepsilon_{d1}$, we find in \\cref{Figure_Initialization_Floquet_Qubits}(c) that the high-fidelity region (plain blue) is now delimited in parameter space by an upper bound in log-log scale rather than by a lower bound as was the case for the adiabatic protocol:\n\\begin{equation}\n\\label{Initialization_Empirical_Law_Instantaneous}\nT_\\text{ramp}\\times \\frac{\\Delta}{\\varepsilon_{d1}}\\leq C_2,\n\\end{equation}\nwhere $C_2=0.18~\\text{ns}$ for a 99\\% fidelity, $C_2=0.06~\\text{ns}$ for 99.9\\%, and $C_2=0.03~\\text{ns}$ for 99.99\\%, respectively. For the desired ratio $\\Delta\/\\varepsilon_{d1}=0.01$ which led to a fast longitudinal readout, this corresponds to a ramp time of up to $18~\\text{ns}$ (resp.~$6~\\text{ns}$) to reach 99\\% (resp.~99.9\\%) fidelity. For larger ratios $\\Delta\/\\varepsilon_{d1}>0.3$, we were unable to reach convergence of the simulations, which indicates that the timescales involved are less than $1~\\text{ns}$.\n\n\n\\section{Summary}\n\nWith the objective of identifying optimal gate parameters for Floquet qubits, we have shown how to define the quasiphase spectra of a static system with two distinct drives and how to extract gate parameters from such spectra. To compensate for the computational cost of this approach, we use the semi-analytic Dysolve method for the integration of the unitary dynamics in our system \\cite{shillitoFastDifferentiableSimulation2020a}. In this way, we find a tenfold improvement in simulation time as compared to the QuTiP solver \\cite{johanssonQuTiPPythonFramework2013}, opening up a path toward precise quasiphase spectra of complex quantum systems with two drives and a larger Hilbert space. Additionally, we introduce longitudinal Floquet readout which, in contrast with previous methods, does not require mapping the Floquet qubit to the laboratory-frame qubit before the measurement. This approach for readout of Floquet qubits completes the existing procedures for initialization, single-qubit gates and two-qubit gates, showing that quantum information processing on Floquet qubits is possible without having to come back to the underlying static undriven system. These results open new possibilities to further optimize gates and operations on Floquet qubits using the analytical understanding of the extended Floquet theory when only a few uncorrelated driving frequencies are involved. In future work, we will apply this framework to two-Floquet qubit gates with the objective of identifying optimal gate parameters with an approach that is free of approximations.\n\n\\section*{Acknowledgments}\nWe thank Marie Lu, Jean-Loup Ville, and Joachim Cohen for a collaboration on a related topic and Ziwen Huang, Jens Koch for stimulating discussions. This work was undertaken thanks to funding from NSERC, the Canada First Research Excellence Fund and the U.S. Army Research Office Grant No.~W911NF-18-1-0411. This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}
+{"text":"\\section{The PKS 1830-211 gravitationally lensed quasar}\\label{sec:introduction}\nPKS 1830-211 is a high redshift (z=2.5 \\citep{1999ApJ...514L..57L}) Flat Spectrum Radio Quasar (FSRQ) which has been detected in all wavelengths from radio to high-energy gamma-rays. It is a known gravitationally lensed  object with two compact images of the quasar nucleus visible in the radio  \\citep{1991Natur.352..132J} and optical \\citep{2005A&A...438L..37M} passbands. The Einstein ring, well visible\nat radio frequencies, comes from the imaging of the quasar jet \\citep{1992ApJ...401..461K}.   \nThe quasar source is lensed by a foreground galaxy at  z=0.89 \\citep{1996Natur.379..139W}. The angular size of the \nEinstein ring and separation of compact images is roughly 1 arcsecond so that it cannot be resolved with high-energy instruments such as H.E.S.S. (50 GeV-50 TeV range) or {\\it Fermi-LAT} (100 MeV-100 GeV range). PKS 1830-211 is seen as a bright, high-energy source by the {\\em Fermi-LAT} instrument and had several flaring periods during the decade of {\\em Fermi-LAT} observations.  \nPKS 1830-211 is listed in the 1FHL \\citep{2013ApJS..209...34A} and the 3FHL \\citep{2017ApJS..232...18A}  catalogues with a \nphoton index above 10 GeV of $3.55 \\pm  0.34$ which corresponds to the average \"low-state\" spectrum. \nNo significant curvature in the spectrum was detected. Photons up to 35 GeV, potentially detectable by H.E.S.S. have been observed by {\\em Fermi-LAT} \\citep{2017ApJS..232...18A}. \nObservations of these very high energy photons and the measurement of the very high energy tail of the spectrum would give useful constraints on EBL at redshift z=2.5.\n\nSince the components of the lens cannot be resolved at high or very high energy, the evidence for lensing was searched indirectly on the observed light curve. Due to the different travel paths, the \nlight curves of the two compact components of the lens have a relative time delay, measured in the radio \\citep{1998ApJ...508L..51L} and  microwave \\citep{2001ASPC..237..155W} pass-bands, of  $26\\pm5$ days. \n\\cite{2011A&A...528L...3B} have studied the first three years of the {\\em Fermi-LAT} light curve with cepstral and autocorrelation methods. \nEvidence for a delay of  $27.5\\pm1.3$ days was found with a 3 $\\sigma$ significance. The time delay between the compact images of PKS 1830-211 was also studied by the {\\em Fermi-LAT} collaboration \\citep{2015ApJ...799..143A}. They selected  several flaring periods and calculated the autocorrelation function of the light curve. No significant peak was found. A possible peak of  \n$\\sim 20$ days was found with a 1-day binning of the data, which could be attributed to the $\\sim 20$ days separation between two flaring events and perhaps to gravitational lensing. \n\\citet{2015ApJ...809..100B} have argued that the time delay measured by high-energy instruments could be very different than the value measured by radio telescopes. The delay measured by \n\\cite{1998ApJ...508L..51L} is obtained from the emission of the compact images. \nSince the jet of the PKS 1830-211 source is imaged close to the Einstein ring, the time difference\nbetween the intial burst and its lensed image can be much smaller if the source of high-energy emission is located inside the jet.\n\nPKS 1830-211 is monitored by {\\em Fermi-LAT} and its light curve is posted on the internet\n\\footnote{\\tiny https:\/\/fermi.gsfc.nasa.gov\/ssc\/data\/access\/lat\/msl\\_lc\/source\/PKS\\_1830-211}\non a daily basis. \nH.E.S.S. observations of PKS 1830-211 were triggered by an alert posted by the {\\em Fermi-LAT} team on August 2, 2014 \\citep{2014ATel.6361....1K}. The flare seen by the {\\em Fermi-LAT} instrument started on July 27 and lasted $\\sim$4 days.  The H.E.S.S. observations are described in Section \\ref{sec:observations} and data analysis in Section \\ref{sec:analyses}. The H.E.S.S. limits are compared to the \n{\\em Fermi-LAT} signal in Section \\ref{sec:limits} and discussed in Section \\ref{sec:conclusion}. \n\\begin{figure}\n\\centering\n\\includegraphics[height=6cm]{fig1-2.pdf}\n\\caption{$\\theta^2$ plot of PKS 1830-211 obtained with the {\\em Mono} reconstruction. The background, shown by crosses, is estimated with the ring background method.\n}\n\\label{fig:hess-obs1}\n\\end{figure} \n\n \n\n\\section{H.E.S.S. observations}\\label{sec:observations}\nThe very-high-energy (50 GeV-50 TeV range) gamma-ray observatory of the H.E.S.S. collaboration consists of\nfive  Imaging Atmospheric Cherenkov Telescopes (IACTs) located in the Khomas Highland \nof Namibia ($23 ^{\\circ}$ 16' 18'' S, $16 ^{\\circ}$ 30' 1'' E), 1800 m above sea level. \nFrom January 2004 to October 2012, the array was a four-telescope instrument, with telescopes labeled CT1-4. \n Each of the telescopes, located at the corners of a square with a side length of 120 m has an effective mirror \nsurface area of 107~m$^{2}$, and is able to detect cosmic gamma-rays in the energy \nrange 0.1 -- 50 TeV .\nIn October 2012, a fifth telescope CT5, with an effective mirror surface area of 600~m$^{2}$ and an improved camera \\citep{2014NIMPA.761...46B} was installed at the center of the original square, giving access to energies below 100 GeV \\citep{2017A&A...600A..89H}. \n\nPKS 1830-211 was observed by the five telescopes of the H.E.S.S. IACT array between August 12 2014 and August 26 2014, to allow for the detection of delayed flares with time delays ranging from 20 to 27 days. \nThe observations were taken at an average zenith angle of 12 degrees. \n\n\\section{Data analyses}\\label{sec:analyses}\n This paper is based on a sample of 12.4 hours of high quality data. Data selection cuts have been described in\n \\citep{2017A&A...600A..89H}.\n  Data were next analyzed with the Model analysis \\citep{2009APh....32..231D} and cross-checked with the ImPACT analysis \\citep{2014APh....56...26P}, the two methods giving compatible results.  The two analyses use different calibration chains. \n With both reconstruction chains, data of CT5 were analyzed either alone ({\\em Mono} reconstruction) or combined with the CT1-4 data ({\\em Combined} reconstruction).   The {\\em Mono} reconstruction has an energy threshold of 67 GeV. \nThe {\\em Combined} reconstruction has a higher threshold of 144 GeV,\n but a larger effective area. \n\nA point source is searched at the location of PKS 1830-211.  \nFig. \\ref{fig:hess-obs1} shows the distribution of the squared angular distance $\\theta^2$ of candidate photons from the target position. This distribution, obtained in the {\\em Mono} analysis, is compared to \nthe background from hadrons mis-identified as photons. The background is calculated with the {\\em ring background} method \\citep{2007A&A...466.1219B}, other methods giving similar results. \n\nTable \\ref{tab:results} summarizes the number of candidate photons in the signal region, the expected background and the significance of the excess,  calculated with Li and Ma formula 17 \\citep{1983ApJ...272..317L}. \n\\begin{table}\n\\caption{Analysis results of observations of PKS 1830-211 by H.E.S.S.}\n\\label{tab:results}\n\\centering\n\\begin{tabular}{c c c c}\n\\hline \\hline\nReconstruction& $N_\\mathrm{ON}$ & $N_\\mathrm{background}$ & significance ($\\sigma$) \\\\\n\\hline\n{\\em Mono} & 1641 & 1649.2 & -0.2 \\\\\n{\\em Combined} & 935 & 954.4 & -0.6 \\\\\n\\hline\n\\end{tabular}\n\\end{table}\nNo significant excess of photons over background is seen by H.E.S.S. at the position of PKS 1830-211.  A similar search using the {\\em Combined} analysis also gives a negative result.\n\nBecause of the very soft spectrum measured by {\\em Fermi LAT} in the low state, PKS~1830-211 has a chance of being detectable by H.E.S.S. only during flares. \nThe delayed flare lasts only less than about 4 days, however, due to the uncertainties on the date of the flare, it could have happened at any time \nbetween August 17 = MJD 56886  (time delay of 20 days) and August 24  = MJD 56893 (radio time delay of 27 days) as explained in Section \\ref{sec:introduction}. \nFig. \\ref{fig:hess-obs2b} shows the evolution over time of significance, binned by 28-minute runs.\nNo significant daily photon excess was detected during the H.E.S.S. observation period. \n\n\\begin{figure}\n\\centering\n\\includegraphics[height=4.5cm]{fig2-2.pdf}\n\\caption{\nSignificance of the H.E.S.S. signal versus date, obtained with the {\\em Mono} analysis. The red arrow shows the expected date of the delayed flare for a lensing time delay \nof 27 days. \n}\n\\label{fig:hess-obs2b}\n\\end{figure} \n\n\n\n\\section{Flux upper limits and comparison to the {\\em Fermi-LAT} spectra}\\label{sec:limits}\nThe non-detection by H.E.S.S. \ntranslates into 99\\% confidence level (C.L.) upper limits  on the average very-high-energy flux of PKS 1830-211 during H.E.S.S. observations. These upper limits are shown in Fig. \\ref{fig:hess-ul}. Red (resp. blue) arrows \nshow the limits obtained from the {\\em Mono} (resp. {\\em Combined}) analysis and the corresponding solid lines show the effect of deabsorption using the Extragalactic Background Light (EBL) model of  \\citet{2012MNRAS.422.3189G}. \n\\begin{figure}\n\\centering\n\\includegraphics[width=9cm]{fig3-1.pdf}\n\\caption{99\\% C.L. upper limits  (arrows) on the PKS 1830-211 flux between 67 GeV and 1 TeV for the August 2014 H.E.S.S. observations.  A constant photon index of -3 was assumed. The solid lines show the effect of EBL deabsorption, assuming the EBL model of \\citet{2012MNRAS.422.3189G}.  \n}\n\\label{fig:hess-ul}\n\\end{figure} \n\nH.E.S.S. upper limits are compared to {\\em Fermi-LAT} GeV spectra on Fig \\ref{fig:hess-fermi-comp}. \nThe {\\em Fermi-LAT} observations have been analyzed with Fermi Science Tools v10-r0p5\nand Pass8 data, in the Enrico framework \\citep{2013arXiv1307.4534S}. The spectral data from 26-30 July 2014 (flare) are well \ndescribed by a power-law spectrum with an index of $n_{flare}= -2.36 \\pm 0.17$ for photon energies $> 1$ GeV. The relatively high low-energy cut was used to avoid contamination from the Galactic plane. \n The flare spectrum is much harder than the spectrum measured in the low state of PKS 1830-211, but $n_{flare}$ is compatible with the photon indices of previous flare spectra, as measured by {\\em Fermi-LAT}  \\citep{2015ApJ...799..143A}. The \nspectrum of PKS 1830-211 obtained from the {\\em Fermi-LAT} observations within the H.E.S.S. observation window is well described by a power-law with an index of $n_{low}=-2.97 \\pm 0.44$ above 1 GeV.  The value of $n_{low}$ is compatible with the value published in the 3FHL catalogue.\n\\begin{figure}\n\\centering\n\\includegraphics[width=9cm]{fig4-2-mod2.pdf}\n\\caption{Comparison of H.E.S.S. flux 99 \\%C.L. upper limits (red solid line: {\\em Mono} analysis, long dashed line: {\\em Combined} analysis) to the measured\nspectra in the GeV region obtained with the {\\em Fermi-LAT} data. The horizontal lines show the spectral resolution of the analyses. The lower blue butterfly is the GeV spectrum of PKS 1830-211 during H.E.S.S. observations. The upper blue butterfly is the \ncorresponding spectrum during the July 2014 flare.  The absorption of the July flare spectrum by EBL is calculated with models by \\citet{2012MNRAS.422.3189G} (black dash-dotted line),\\citet{2010ApJ...712..238F} (dotted line) and \\citet{2008A&A...487..837F} (black solid line).  \n}\n\\label{fig:hess-fermi-comp}\n\\end{figure} \n\n\nA proper comparison between H.E.S.S. upper limits and the Fermi signal has to take into account the effect of the absorption of the flux of PKS 1830-211 by the \n EBL and the difference between the flare duration and H.E.S.S. exposure. Since no significant curvature of the spectrum was measured bt the Fermi-LAT collaboration, the unabsorbed spectrum was modeled by a powerlaw.\n  The effect of light absorption by EBL from PKS 1830-211 has been estimated with the models of  \n \\citet{2012MNRAS.422.3189G} (black dash-dotted line), \\citet{2010ApJ...712..238F} (dotted line) and \\citet{2008A&A...487..837F} (black solid line).  Fig. \\ref{fig:hess-fermi-comp} shows that there \n is a substantial difference between the predictions of these models for a source at redshift 2.5 such as PKS 1830-211. \n Note that EBL absorption could also be affected by the lens environment.\n Light from lensed AGN is expected to be more absorbed than average, due to the presence of galaxies along the line of sight. Indeed, absorption from the intervening galaxy has been detected by \\cite{2005A&A...438..121D} in the X-ray spectrum of PKS 1830-211. However \\cite{2014ApJ...790..147B} and \\cite{2016A&A...595A..14B}  have argued that gravitational lensing \n could  help gamma-rays from a distant source avoiding excess absorption. \n The {\\em Fermi-LAT} flare spectrum from Fig \\ref{fig:hess-fermi-comp} is a 4-night average while the H.E.S.S. exposure amounts to 10 nights of data taking. The steady source upper limits from Fig \\ref{fig:hess-ul} are thus  a factor $\\sim\\sqrt{10\/4}$ too constraining, which is corrected for in Fig   \\ref{fig:hess-fermi-comp}. \n \n \n\\section{Conclusion}\\label{sec:conclusion} \n \nNo significant delayed flare from PKS 1830-211 was detected by either H.E.S.S. or {\\em Fermi-LAT}. The flare did not repeat or was too faint to be detected.\nFig \\ref{fig:hess-fermi-comp} shows however that the detection of a strong flare would have been possible \nclose to the {\\em Mono} analysis energy threshold if the level of EBL absorption was at or below the absorption predicted\nby the model of  \\citet{2008A&A...487..837F}.\nDue to its lensed nature, observation of flaring event of PKS 1830-211 in the TeV passband could be useful to constrain EBL models at redshift as large as  2.5. \nThe detection of the lensing time delay in future very high energy observations\n\n would help pinpoint the spatial origin of the high-energy emission \\citep{2015ApJ...809..100B}.\n It would also permit more exotic applications such as constraining photon mass \\citep{2017ApJ...850..102G} or testing Lorentz Invariance Violation \\citep{2009MNRAS.396..946B}.\n\n\n\n\\section*{Acknowledgments}\n{\\small\nThe support of the Namibian authorities and of the University of Namibia in facilitating the construction\n and operation of  H.E.S.S. is    gratefully acknowledged, as is the support by the German Ministry for Education and Research (BMBF), \n the Max Planck Society, the German Research Foundation (DFG), the Helmholtz Association, the Alexander von Humboldt Foundation,\nthe French Ministry of Higher Education, Research and Innovation, the Centre National de la Recherche Scientifique (CNRS\/IN2P3 and CNRS\/INSU), \nthe Commissariat  \\`a    l' Energie Atomique et aux Energies Alternatives (CEA), \nthe  U.K. Science and Technology Facilities Council (STFC), the Knut and Alice Wallenberg Foundation, the National Science Centre, \n Poland grant no. 2016\/22\/M\/ST9\/00382, the South African Department of Science and Technology and National \nResearch Foundation, the University of Namibia, the National Commission on Research, Science \\&  Technology of  Namibia (NCRST), the Austrian Federal Ministry of Education, Science and Research \nand the Austrian Science Fund (FWF), the Australian Research Council (ARC), the Japan Society for the Promotion of Science and by the University of Amsterdam. \nWe appreciate the excellent work of the technical\n support staff in Berlin, Zeuthen, Heidelberg, Palaiseau, Paris, Saclay, T\\\"uebingen and in Namibia in the construction and operation of the equipment. This work benefited from services provided by the\nH.E.S.S. Virtual Organisation, supported by the national resource providers of the EGI Federation\n}\n\n\n\\bibpunct{(}{)}{;}{a}{}{,}\n\\bibliographystyle{mnras}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}