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the coherent exchange of optical near fields between two neighboring dipoles plays an essential role for the optical properties, quantum dynamics and thus for the function of many naturally occurring and artificial nanosystems. these interactions are inherently short - ranged, extending over a few nanometers only, and depend sensitively on relative orientation, detuning and dephasing, i. e., on the vectorial properties of the coupled dipolar near fields. this makes it challenging to analyze them experimentally. here, we introduce plasmonic nanofocusing spectroscopy to record coherent light scattering spectra with 5 - nm spatial resolution from a small dipole antenna, excited solely by evanescent fields and coupled to plasmon resonances in a single gold nanorod. we resolve mode couplings, resonance energy shifts and purcell effects as a function of dipole distance and relative orientation, and show how they arise from different vectorial components of the interacting optical near - fields. our results pave the way for using dipolar alignment to control the optical properties and function of nanoscale systems.
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arxiv:1801.10426
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we have analysed all the x - ray images centred on gamma ray bursts generated by swift over the last 15 years using automatic tools that do not require any expertise in x - ray astronomy, producing results in excellent agreement with previous findings. this work, besides presenting the largest medium - deep survey of the x - ray sky and a complete sample of blazars, wishes to be a step in the direction of achieving the ultimate goal of the open universe initiative, that is to enable non expert people to fully benefit of space science data, possibly extending the potential for scientific discovery, currently confined within a small number of highly specialised teams, to a much larger population. we have used the swift _ deepsky docker container encapsulated pipeline to build the largest existing flux - limited and unbiased sample of serendipitous x - ray sources. swift _ deepsky runs on any laptop or desktop computer with a modern operating system. the tool automatically downloads the data and the calibration files from the archives, runs the official swift analysis software and produces a number of results including images, the list of detected sources, x - ray fluxes, sed data, and spectral slope estimations. we used our source list to build the logn - logs of extra - galactic sources, which perfectly matches that estimated by other satellites. combining our survey with multi - frequency data we selected a complete radio flux - density limited sample of high energy peaked ( hbl ) blazars.
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arxiv:2003.05153
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quantum mechanics together with general relativity leads to the k \ ' arolyh \ ' azy relation and a corresponding energy density of quantum fluctuations of space - time. based on the energy density we propose a dark energy model, in which the age of the universe is introduced as the length measure. this dark energy is consistent with astronomical data if the unique numerical parameter in the dark energy model is taken to be a number of order one. the dark energy behaves like a cosmological constant at early time and drives the universe to an eternally accelerated expansion with power - law form at late time. in addition, we point out a subtlety in this kind of dark energy model.
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arxiv:0707.4049
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we establish an effective markov theory for the rotational brownian motion of hot nanobeads and nanorods. compact analytical expressions for the effective temperature and friction are derived from the fluctuating hydrodynamic equations of motion. they are verified by comparison with recent measurements and with gpu powered parallel molecular dynamics simulations over a wide temperature range. this provides unique insights into the physics of hot brownian motion and an excellent starting point for further experimental tests and applications involving laser - heated nanobeads, nanorods and janus particles.
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arxiv:1203.3221
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precise masses of red - giant stars enable a robust inference of their ages, but there are cases where these age estimates are highly precise yet very inaccurate. examples are core - helium - burning ( cheb ) stars that have lost more mass than predicted by standard single - star evolutionary models. members of star clusters in the $ { \ it kepler } $ database represent a unique opportunity to identify such stars, because they combine exquisite asteroseismic constraints with independent age information. in this work we focus on the single, metal - rich, li - rich, low - mass, cheb star kic4937011, which is a member of the open cluster ngc 6819 ( turn - off mass of $ \ approx 1. 6 \, m _ \ odot $, i. e. age of $ \ approx 2. 4 $ gyr ). this star has $ \ approx 1 \, m _ \ odot $ less mass than expected for its age and metallicity, which could be explained by binary interactions or mass - loss along the red - giant branch ( rgb ). to infer formation scenarios for this object, we perform a bayesian analysis by combining the binary stellar evolutionary framework $ \ texttt { binary _ c v2. 2. 3 } $ with the dynamic nested sampling approach contained in the $ \ texttt { dynesty v2. 1. 1 } $ package. we find that this star is likely the result of a common - envelope evolution ( cee ) phase during the rgb stage of the primary star in which the low - mass ( $ < 0. 71 \, m _ \ odot $ ) main sequence companion does not survive. during the cee phase $ \ approx 1 \, m _ \ odot $ of material is ejected from the system, and the final star reaches the cheb stage after helium flashes as if it were a single star of mass $ \ approx 0. 7 \, m _ \ odot $, which is what we observe today. although the proposed scenario is consistent with photometric and spectroscopic observations, a quantitative comparison with detailed stellar evolution calculations is needed to quantify the systematic skewness of radius, luminosity, and effective temperature distributions towards higher values than observations.
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arxiv:2408.11095
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we present a single domain galerkin - collocation method to calculate puncture initial data sets for single and binary, either in the trumpet or wormhole geometries. the combination of aspects belonging to the galerkin and the collocation methods together with the adoption of spherical coordinates in all cases show to be very effective. we have proposed a unified expression for the conformal factor to describe trumpet and spinning black holes. in particular, for the spinning trumpet black holes, we have exhibited the deformation of the limit surface due to the spin from a sphere to an oblate spheroid. we have also revisited the energy content in the trumpet and wormhole puncture data sets. the algorithm can be extended to describe binary black holes.
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arxiv:1703.09131
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the eigenmode spectrum is a fundamental starting point for the analysis of plasma stability and the onset of turbulence, but the characterization of the spectrum even for the simplest plasma model, ideal magnetohydrodynamics ( mhd ), is not fully understood. this is especially true in configurations with no continuous geometric symmetry, such as a real tokamak when the discrete nature of the external magnetic field coils is taken into account, or the alternative fusion concept, the stellarator, where axisymmetry is deliberately broken to provide a nonzero winding number ( rotational transform ) on each invariant torus of the magnetic field line dynamics ( assumed for present purposes to be an integrable hamiltonian system ). quantum ( wave ) chaos theory provides tools for characterizing the spectrum statistically, from the regular spectrum of the separable case ( integrable semiclassical dynamics ) to that where the semiclassical ray dynamics is so chaotic that no simple classification of the individual eigenvalues is possible ( quantum chaos ). the mhd spectrum exhibits certain nongeneric properties, which we show, using a toy model, to be understable from the number - theoretic properties of the asymptotic spectrum in the limit of large toroidal and poloidal mode ( quantum ) numbers when only a single radial mode number is retained. much more realistically, using the ideal mhd code cas3d, we have constructed a data set of several hundred growth - rate eigenvalues for an interchange - unstable three - dimensional stellarator equilibrium with a rather flat, nonmonotonic rotational transform profile. statistical analysis of eigenvalue spacings shows evidence of generic quantum chaos, which we attribute to the mixing effect of having a large number of radial mode numbers.
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arxiv:physics/0608304
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sequential recommendation aims to infer user preferences from historical interaction sequences and predict the next item that users may be interested in the future. the current mainstream design approach is to represent items as fixed vectors, capturing the underlying relationships between items and user preferences based on the order of interactions. however, relying on a single fixed - item embedding may weaken the modeling capability of the system, and the global dynamics and local saliency exhibited by user preferences need to be distinguished. to address these issues, this paper proposes a novel diffusion recommendation algorithm based on multi - scale cnn and residual lstm ( areal ). we introduce diffusion models into the recommend system, representing items as probability distributions instead of fixed vectors. this approach enables adaptive reflection of multiple aspects of the items and generates item distributions in a denoising manner. we use multi - scale cnn and residual lstm methods to extract the local and global dependency features of user history interactions, and use attention mechanism to distinguish weights as the guide features of reverse diffusion recovery. the effectiveness of the proposed method is validated through experiments conducted on two real - world datasets. specifically, areal obtains improvements over the best baselines by 2. 63 % and 4. 25 % in terms of hr @ 20 and 5. 05 % and 3. 94 % in terms of ndcg @ 20 on all datasets.
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arxiv:2312.10885
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we describe two new generation mechanisms for dark matter composed of sterile neutrinos with $ { \ cal o } ( 1 ) $ kev mass. the model contains a light scalar field which coherently oscillates in the early universe and modulates the majorana mass of the sterile neutrino. in a region of model parameter space, the oscillations between active and sterile neutrinos are resonantly enhanced. this mechanism allows us to produce sterile neutrino dm with small mixing angle with active neutrinos, thus evading the x - ray constraints. at the same time the spectrum of produced dm is much cooler, than in the case of ordinary oscillations in plasma, opening a window of lower mass dm, which is otherwise forbidden by structure formation considerations. in other regions of the model parameter space, where the resonance does not appear, another mechanism can operate : large field suppresses the active - sterile oscillations, but instead sterile neutrinos are produced by the oscillating scalar field when the effective fermion mass crosses zero. in this case dm component is cold, and even 1 kev neutrino is consistent with the cosmic structure formation.
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arxiv:1809.09123
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the pure rotational spectrum of yboh has been recorded and analyzed to produce fine and magnetic hyperfine parameters for the $ \ tilde { x } ^ 2 \ sigma ^ + $ ( 0, 0, 0 ) state. these parameters are compared with those determined from the optical study [ melville and coxon, j. chem. phys. 115, 6974 - 6978 ( 2001 ) ] and with the values for ybf [ dickinson et al. 115, 6979 - 6989 ( 2001 ) ]. the results support the existence of an unobserved perturbing state near the $ \ tilde { a } ^ 2 \ pi _ { 1 / 2 } $ state, similar to that previously found in ybf. the precisely determined parameters lay the foundation for laser cooling yboh, which will aid in the search for new physics beyond the standard model.
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arxiv:1810.02791
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in this technical note, we introduce and analyze awnn : an adaptively weighted nearest neighbor method for performing matrix completion. nearest neighbor ( nn ) methods are widely used in missing data problems across multiple disciplines such as in recommender systems and for performing counterfactual inference in panel data settings. prior works have shown that in addition to being very intuitive and easy to implement, nn methods enjoy nice theoretical guarantees. however, the performance of majority of the nn methods rely on the appropriate choice of the radii and the weights assigned to each member in the nearest neighbor set and despite several works on nearest neighbor methods in the past two decades, there does not exist a systematic approach of choosing the radii and the weights without relying on methods like cross - validation. awnn addresses this challenge by judiciously balancing the bias variance trade off inherent in weighted nearest - neighbor regression. we provide theoretical guarantees for the proposed method under minimal assumptions and support the theory via synthetic experiments.
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arxiv:2505.09612
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a smart ponzi scheme is a new form of economic crime that uses ethereum smart contract account and cryptocurrency to implement ponzi scheme. the smart ponzi scheme has harmed the interests of many investors, but researches on smart ponzi scheme detection is still very limited. the existing smart ponzi scheme detection methods have the problems of requiring many human resources in feature engineering and poor model portability. to solve these problems, we propose a data - driven smart ponzi scheme detection system in this paper. the system uses dynamic graph embedding technology to automatically learn the representation of an account based on multi - source and multi - modal data related to account transactions. compared with traditional methods, the proposed system requires very limited human - computer interaction. to the best of our knowledge, this is the first work to implement smart ponzi scheme detection through dynamic graph embedding. experimental results show that this method is significantly better than the existing smart ponzi scheme detection methods.
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arxiv:2108.09305
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we present the techniques used to determine redshifts and to characterize the spectra of objects in the caltech faint galaxy redshift survey in terms of spectral classes and redshift quality classes. these are then applied to spectra from an investigation of a complete sample of objects with $ k _ s < 20 $ mag in a 2 by 7. 3 arcmin ^ 2 field at j005325 + 1234. redshifts were successfully obtained for 163 of the 195 objects in the sample ; these redshifts lie in the range [ 0. 173, 1. 44 ] and have a median of 0. 58 ( excluding 24 galactic stars ). the sample includes two broad lined agns and one qso.
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arxiv:astro-ph/9809066
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∂ t, ∂ ∂ x, ∂ ∂ y, ∂ ∂ z ) { \ displaystyle \ textstyle \ left ( { \ frac { \ partial } { \ partial t } }, { \ frac { \ partial } { \ partial x } }, { \ frac { \ partial } { \ partial y } }, { \ frac { \ partial } { \ partial z } } \ right ) }. { \ displaystyle \ box } or 2 { \ displaystyle { \ box } ^ { 2 } } ( here an actual box, not a placeholder ) denotes the d ' alembertian or squared four - gradient, which is a generalization of the laplacian to four - dimensional spacetime. in flat spacetime with euclidean coordinates, this may mean either − ∂ 2 ∂ t 2 + ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 + ∂ 2 ∂ z 2 { \ displaystyle ~ \ textstyle - { \ frac { \ partial ^ { 2 } } { \ partial t ^ { 2 } } } + { \ frac { \ partial ^ { 2 } } { \ partial x ^ { 2 } } } + { \ frac { \ partial ^ { 2 } } { \ partial y ^ { 2 } } } + { \ frac { \ partial ^ { 2 } } { \ partial z ^ { 2 } } } ~ \ ; } or + ∂ 2 ∂ t 2 − ∂ 2 ∂ x 2 − ∂ 2 ∂ y 2 − ∂ 2 ∂ z 2 { \ displaystyle \ ; ~ \ textstyle + { \ frac { \ partial ^ { 2 } } { \ partial t ^ { 2 } } } - { \ frac { \ partial ^ { 2 } } { \ partial x ^ { 2 } } } - { \ frac { \ partial ^ { 2 } } { \ partial y ^ { 2 } } } - { \ frac { \ partial ^ { 2 } } { \ partial z ^ { 2 } } } ~ \ ; } ; the sign convention must be specified. in curved spacetime ( or flat spacetime with non - euclidean coordinates ), the definition is more complicated. also called box or quabla. = = linear and multilinear algebra = = ( capital - sigma notation ) 1. denotes the sum of a finite number of terms, which are determined by subscripts and superscripts ( which can also be placed below and above
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https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols
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in the wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. instead, the compatibility of hamilton ' s equations and the heisenberg equations are the starting point, and no further assumptions are made about how the position and momentum operators commute. wigner quantization leads to new classes of solutions, and representations of lie superalgebras are needed to describe them. for the n - dimensional wigner harmonic oscillator, solutions are known in terms of the lie superalgebras osp ( 1 | 2n ) and gl ( 1 | n ). for n = 3n, the question arises as to how the angular momentum decomposition of representations of these lie superalgebras is computed. we construct generating functions for the angular momentum decomposition of specific series of representations of osp ( 1 | 6n ) and gl ( 1 | 3n ), with n = 1 and n = 2. this problem can be completely solved for n = 1. however, for n = 2 only some classes of representations allow executable computations
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arxiv:1111.0757
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ground - plane cloak designs are presented, which minimize scattering of electromagnetic radiation from metallic objects in the visible spectrum. it is showed that simplified ground - plane cloaks made from only a few blocks of all - dielectric isotropic materials, either embedded in a background medium or in free space, can provide considerable cloaking performance while maintaining their broadband nature. a design which operates isolated in free space that cloaks radiation originating from a specified direction is also analyzed. these schemes should be much easier to be demonstrated experimentally compared to full designs.
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arxiv:0902.1692
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the terms ' human - level artificial intelligence ' and ' artificial general intelligence ' are widely used to refer to the possibility of advanced artificial intelligence ( ai ) with potentially extreme impacts on society. these terms are poorly defined and do not necessarily indicate what is most important with respect to future societal impacts. we suggest that the term ' transformative ai ' is a helpful alternative, reflecting the possibility that advanced ai systems could have very large impacts on society without reaching human - level cognitive abilities. to be most useful, however, more analysis of what it means for ai to be ' transformative ' is needed. in this paper, we propose three different levels on which ai might be said to be transformative, associated with different levels of societal change. we suggest that these distinctions would improve conversations between policy makers and decision makers concerning the mid - to long - term impacts of advances in ai. further, we feel this would have a positive effect on strategic foresight efforts involving advanced ai, which we expect to illuminate paths to alternative futures. we conclude with a discussion of the benefits of our new framework and by highlighting directions for future work in this area.
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arxiv:1912.00747
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with the increasing demand for internet of things ( iot ) applications, especially for location - based services, how to locate passive mobile targets ( mts ) with minimal beam control has become a challenge. resonant beam systems are considered promising iot technologies with advantages such as beam self - alignment and energy concentration. to establish a resonant system in the radio frequency ( rf ) band and achieve multi - target localization, this paper designs a multi - target resonant system architecture, allowing a single base station ( bs ) to independently connect with multiple mts. by employing a retro - directive array, a multi - channel cyclic model is established to realize one - to - many electromagnetic wave propagation and mt direction - of - arrival ( doa ) estimation through echo resonance. simulation results show that the proposed system supports resonant establishment between the bs and multiple mts. this helps the bs to still have high doa estimation accuracy in the face of multiple passive mts, and can ensure that the doa error is less than 1 degree within a range of 6 meters at a 50degree field of view, with higher accuracy than active beamforming localization systems.
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arxiv:2412.15597
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the transport of heat mediated by thermal photons in hyperbolic multilayer metamaterials is studied using the fluctuational electrodynamics theory. we demonstrate that in comparison to bulk materials the flux inside layered hyperbolic materials can be transported at much longer distances, making these media very promising for thermal management and for near - field energy harvesting.
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arxiv:1403.2664
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formation of fourth - sound shock waves in narrow channels filled with superfluid helium is studied. physical and mathematical conditions at the surface of discontinuity are established. these conditions differ somewhat from those in case of first - and second - sound waves. the velocity of discontinuity coincides with that of fourth sound. the jumps of temperature and the superfluid velocity are shown to be of the first order as to the pressure jumps.
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arxiv:1511.04755
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multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. in order to extend this technique to elliptic hypergeometric series, we present three new multidimensional matrix inversions. as applications, we obtain a new $ a _ r $ elliptic jackson summation, as well as several quadratic, cubic and quartic summation formulas.
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arxiv:2005.02203
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understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. unexpected behaviour of dynamic systems or even system failure is sometimes difficult to comprehend. such a data - mismatch can be caused by endogenous model errors including misspecified interactions and inaccurate parameter values. these are often difficult to distinguish from unmodelled process influencing the real system like unknown inputs or faults. localizing the root cause of these errors or faults and reconstructing their dynamics is only possible if the measured outputs of the system are sufficiently informative. here, we present criteria for the measurements required to localize the position of error sources in large dynamic networks. we assume that faults or errors occur at a limited number of positions in the network. this invariable sparsity differs from previous sparsity definitions for inputs to dynamic systems. we provide an exact criterion for the recovery of invariable sparse inputs to nonlinear systems and formulate an optimization criterion for invariable sparse input reconstruction. for linear systems we can provide exact error bounds for this reconstruction method.
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arxiv:2105.04304
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robust topologically trivial low - energy andreev bound states ( abss ) induced by position - dependent effective potentials have recently come under renewed focus, in light of a remarkable set of experiments observing robust quantized zero - bias conductance plateaus in semiconductor - superconductor heterostructures. we show that ( 1 ) the partial spatial separation of the wave functions of the component majorana bound states ( mbss ) is crucial for the creation and stability of topologically trivial near - zero - energy andreev bound states, ( 2 ) the signs of the spin polarizations of the component mbss can be either the same or opposite, depending on the profile of the inducing potential, and ( 3 ) the spin polarizations do not play a fundamental role in generating vastly different coupling strengths to local probes and / or ensuring the robustness of the near - zero - energy abs. consequently, in contrast to recent theoretical claims ( vuik et al., arxiv : 1806. 02801 ), we find that a robust, quantized zero - bias conductance plateau of height 2e ^ 2 / h measured in the topologically trivial regime necessarily requires partially separated abss ( ps - abss ), independent of the relative signs of the spin - polarizations. in addition, we show that ( 4 ) well - defined energy splitting oscillations involve mbss characterized by exponential tails pointing toward each other, and ( 5 ) ps - abss generated by the tunnel barrier itself produce zero - bias conductance peaks with a characteristic width that increases strongly with the applied magnetic field. finally, we propose ( 6 ) a quantitative scheme for analyzing the stability of majorana modes based on probability distributions of splitting susceptibilities and show that a ps - abs mode can be remarkably robust when judged based on its signature in a charge tunneling experiment, but, in essence, is topologically unprotected.
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arxiv:1811.02557
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in this paper the linearly damped oscillator equation is considered with the damping term generalized to a caputo fractional derivative. the order of the derivative being considered is 0 less than or equal to nu which is less than or equal to 1. at the lower end, nu = 0, the equation represents an un - damped oscillator and at the upper end, nu = 1, the ordinary linearly damped oscillator equation is recovered. a solution is found analytically and a comparison with the ordinary linearly damped oscillator is made. it is found that there are nine distinct cases as opposed to the usual three for the ordinary equation ( damped, over - damped, and critically damped ). for three of these cases it is shown that the frequency of oscillation actually increases with increasing damping order before eventually falling to the limiting value given by the ordinary damped oscillator equation. for the other six cases the behavior is as expected, the frequency of oscillation decreases with increasing order of the derivative ( damping term ).
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arxiv:0908.1683
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the aim of this paper it to establish sufficient conditions for consistency of moving block bootstrap for non - stationary time series with periodic and almost periodic structure. the parameter of the study is the mean value of the expectation function. consistency holds in quite general situations : if all joint distributions of the series are periodic, then it suffices to assume the central limit theorem and strong mixing property, together with summability of the autocovariance function. in the case where the mean function is almost periodic, we additionally need uniform boundedness of the fourth moments of the root statistics. it is shown that these theoretical results can be applied in statistical inference concerning the fourier coefficients of periodically ( pc ) and almost periodically ( apc ) correlated time series. a simulation example shows how to use a graphical diagnostic test for significant frequencies and stationarity within these classes of time series.
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arxiv:0711.4493
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we design magnetic traps for atoms based on the average magnetic field of vortices induced in a type - ii superconducting thin film. this magnetic field is the critical ingredient of the demonstrated vortex - based atom traps, which operate without transport current. we use bean ' s critical - state method to model the vortex field through mesoscopic supercurrents induced in the thin strip. the resulting inhomogeneous magnetic fields are studied in detail and compared to those generated by multiple normally - conducting wires with transport currents. various vortex patterns can be obtained by programming different loading - field and transport current sequences. these variable magnetic fields are employed to make versatile trapping potentials.
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arxiv:1004.0064
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this paper examines two aspects of the isolated sign language recognition ( islr ) task. first, despite the availability of a number of datasets, the amount of data for most individual sign languages is limited. it poses the challenge of cross - language islr model training, including transfer learning. second, similar signs can have different semantic meanings. it leads to ambiguity in dataset labeling and raises the question of the best policy for annotating such signs. to address these issues, this study presents logos, a novel russian sign language ( rsl ) dataset, the most extensive islr dataset by the number of signers and one of the largest available datasets while also the largest rsl dataset in size and vocabulary. it is shown that a model, pre - trained on the logos dataset can be used as a universal encoder for other language slr tasks, including few - shot learning. we explore cross - language transfer learning approaches and find that joint training using multiple classification heads benefits accuracy for the target lowresource datasets the most. the key feature of the logos dataset is explicitly annotated visually similar sign groups. we show that explicitly labeling visually similar signs improves trained model quality as a visual encoder for downstream tasks. based on the proposed contributions, we outperform current state - of - the - art results for the wlasl dataset and get competitive results for the autsl dataset, with a single stream model processing solely rgb video. the source code, dataset, and pre - trained models are publicly available.
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arxiv:2505.10481
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we report the demonstration of a low - power pixelated readout system designed for three - dimensional ionization charge detection and digital readout of liquid argon time projection chambers ( lartpcs ). unambiguous 3d charge readout was achieved using a custom - designed system - on - a - chip asic ( larpix ) to uniquely instrument each pad in a pixelated array of charge - collection pads. the larpix asic, manufactured in 180 nm bulk cmos, provides 32 channels of charge - sensitive amplification with self - triggered digitization and multiplexed readout at temperatures from 80 k to 300 k. using an 832 - channel larpix - based readout system with 3 mm spacing between pads, we demonstrated low - noise ( $ < $ 500 e $ ^ - $ rms equivalent noise charge ) and very low - power ( $ < $ 100 $ \ mu $ w / channel ) ionization signal detection and readout. the readout was used to successfully measure the three - dimensional ionization distributions of cosmic rays passing through a lartpc, free from the ambiguities of existing projective techniques. the system design relies on standard printed circuit board manufacturing techniques, enabling scalable and low - cost production of large - area readout systems using common commercial facilities. this demonstration overcomes a critical technical obstacle for operation of lartpcs in high - occupancy environments, such as the near detector site of the deep underground neutrino experiment ( dune ).
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arxiv:1808.02969
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in the 80 ' s m. cornalba and j. harris discovered a relation among the hodge class and the boundary classes in the picard group with rational coefficients of the moduli space of stable, hyperelliptic curves. they proved the relation by computing degrees of the classes involved for suitable one - parameter families. in the present article we show that their relation can be obtained as the class of an appropriate, geometrically meaningful empty set, thus conforming with c. faber ' s general philosophy to finding relations among tautological classes in the chow ring of the moduli space of curves. the empty set we consider is the closure of the locus of smooth, hyperelliptic curves having a special ramification point.
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arxiv:math/0008176
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text - to - image generation models have achieved remarkable advancements in recent years, aiming to produce realistic images from textual descriptions. however, these models often struggle with generating anatomically accurate representations of human hands. the resulting images frequently exhibit issues such as incorrect numbers of fingers, unnatural twisting or interlacing of fingers, or blurred and indistinct hands. these issues stem from the inherent complexity of hand structures and the difficulty in aligning textual descriptions with precise visual depictions of hands. to address these challenges, we propose a novel approach named hand1000 that enables the generation of realistic hand images with target gesture using only 1, 000 training samples. the training of hand1000 is divided into three stages with the first stage aiming to enhance the model ' s understanding of hand anatomy by using a pre - trained hand gesture recognition model to extract gesture representation. the second stage further optimizes text embedding by incorporating the extracted hand gesture representation, to improve alignment between the textual descriptions and the generated hand images. the third stage utilizes the optimized embedding to fine - tune the stable diffusion model to generate realistic hand images. in addition, we construct the first publicly available dataset specifically designed for text - to - hand image generation. based on the existing hand gesture recognition dataset, we adopt advanced image captioning models and llama3 to generate high - quality textual descriptions enriched with detailed gesture information. extensive experiments demonstrate that hand1000 significantly outperforms existing models in producing anatomically correct hand images while faithfully representing other details in the text, such as faces, clothing, and colors.
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arxiv:2408.15461
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legal expert systems routinely rely on date computations to determine the eligibility of a citizen to social benefits or whether an application has been filed on time. unfortunately, date arithmetic exhibits many corner cases, which are handled differently from one library to the other, making faithfully transcribing the law into code error - prone, and possibly leading to heavy financial and legal consequences for users. in this work, we aim to provide a solid foundation for date arithmetic working on days, months and years. we first present a novel, formal semantics for date computations, and formally establish several semantic properties through a mechanization in the f * proof assistant. building upon this semantics, we then propose a static analysis by abstract interpretation to automatically detect ambiguities in date computations. we finally integrate our approach in the catala language, a recent domain - specific language for formalizing computational law, and use it to analyze the catala implementation of the french housing benefits, leading to the discovery of several date - related ambiguities.
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arxiv:2403.08935
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recently, vision - language models have made remarkable progress, demonstrating outstanding capabilities in various tasks such as image captioning and video understanding. we introduce valley2, a novel multimodal large language model designed to enhance performance across all domains and extend the boundaries of practical applications in e - commerce and short video scenarios. notably, valley2 achieves state - of - the - art ( sota ) performance on e - commerce benchmarks, surpassing open - source models of similar size by a large margin ( 79. 66 vs. 72. 76 ). additionally, valley2 ranks second on the opencompass leaderboard among models with fewer than 10b parameters, with an impressive average score of 67. 4. the code and model weights are open - sourced at https : / / github. com / bytedance / valley.
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arxiv:2501.05901
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the gibbs partition function is an important quantity in describing statistical properties of a system in thermodynamic equilibrium. there are several proposals to calculate the partition functions on near - team quantum computers. however, the existing schemes require many copies of the gibbs states to perform an extrapolation for the calculation of the partition function, and these could be costly performed on the near - term quantum computers. here, we propose an efficient scheme to calculate the gibbs function with the imaginary time evolution. to calculate the gibbs function of $ n $ qubits, only $ 2n $ qubits are required in our scheme. after preparing gibbs states with different temperatures by using the imaginary time evolution, we measure the overlap between them on a quantum circuit, and this allows us to calculate the gibbs partition function.
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arxiv:2109.14880
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recent gravitational - wave transient catalogs have used \ pastro { }, the probability that a gravitational - wave candidate is astrophysical, to select interesting candidates for further analysis. unlike false alarm rates, which exclusively capture the statistics of the instrumental noise triggers, \ pastro { } incorporates the rate at which triggers are generated by both astrophysical signals and instrumental noise in estimating the probability that a candidate is astrophysical. multiple search pipelines can independently calculate \ pastro { }, each employing a specific data reduction. while the range of \ pastro { } results can help indicate the range of uncertainties in its calculation, it complicates interpretation and subsequent analyses. we develop a statistical formalism to calculate a \ emph { unified } \ pastro { } for gravitational - wave candidates, consistently accounting for triggers from all pipelines, thereby incorporating extra information about a signal that is not available with any one single pipeline. we demonstrate the properties of this method using a toy model and by application to the publicly available list of gravitational - wave candidates from the first half of the third ligo - virgo - kagra observing run. adopting a unified \ pastro { } for future catalogs would provide a simple and easy - to - interpret selection criterion that incorporates a more complete understanding of the strengths of the different search pipelines
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arxiv:2305.00071
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we compute the bare step - scaling function $ s _ b $ for su ( 3 ) lattice gauge theory with $ n _ f = 12 $ massless fundamental fermions, using the non - perturbative wilson - flow - optimized monte carlo renormalization group two - lattice matching technique. we use a short wilson flow to approach the renormalized trajectory before beginning rg blocking steps. by optimizing the length of the wilson flow, we are able to determine an $ s _ b $ corresponding to a unique discrete $ \ beta $ function, after a few blocking steps. we carry out this study using new ensembles of 12 - flavor gauge configurations generated with exactly massless fermions, using volumes up to $ 32 ^ 4 $. the results are consistent with the existence of an infrared fixed point ( irfp ) for all investigated lattice volumes and number of blocking steps. we also compare different renormalization schemes, each of which indicates an irfp at a slightly different value of the bare coupling, as expected for an ir - conformal theory.
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arxiv:1311.2679
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quasi - elliptic cohomology is conjectured by sati and schreiber as a particularly suitable approximation to equivariant 4 - th cohomotopy, which classifies the charges carried by m - branes in m - theory in a way that is analogous to the traditional idea that complex k - theory classifies the charges of d - branes in string theory. in this paper we compute quasi - elliptic cohomology of 4 - spheres under the action by some finite subgroups that are the most interesting isotropy groups where the m5 - branes may sit.
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arxiv:2408.02278
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we study the h \ " olderian regularity of gaussian wavelets series and show that they display, almost surely, three types of points : slow, ordinary and rapid. in particular, this fact holds for the fractional brownian motion. we also show that this property is satisfied for a multifractal extension of gaussian wavelet series. finally, we remark that the existence of slow points is specific to these functions.
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arxiv:2203.05472
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we say that a digraph is a $ ( t, \ lambda ) $ - liking digraph if every $ t $ vertices have exactly $ \ lambda $ common out - neighbors. in 1975, plesn \ ' { i } k [ graphs with a homogeneity, 1975. { \ it glasnik mathematicki } 10 : 9 - 23 ] proved that any $ ( t, 1 ) $ - liking digraph is the complete digraph on $ t + 1 $ vertices for each $ t \ geq 3 $. choi { \ it et al }. [ a digraph version of the friendship theorem, 2023. arxiv preprint arxiv : 2305. 04058 ] ( to appear in { \ it discrete mathematics } ) showed that a $ ( 2, 1 ) $ - liking digraph is a fancy wheel digraph or a $ k $ - diregular digraph for some positive integer $ k $. in this paper, we extend these results by completely characterizing the $ ( t, \ lambda ) $ - liking digraphs with $ t \ geq \ lambda + 2 $ and giving some equivalent conditions for a $ ( t, \ lambda ) $ - liking digraph being a complete digraph on $ t + \ lambda $ vertices.
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arxiv:2405.02662
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it is well - known that conformal embeddings can be used to construct non - diagonal modular invariants for affine lie algebras. this idea can be extended to construct infinite series of non - diagonal modular invariants for coset cfts. in this paper, we systematically approach the problem of identifying higher - spin bulk duals for these kind of non - diagonal invariants. in particular, for a special value of the ' t hooft coupling, there exist a class of partition functions that have enhanced supersymmetry, which should be reflected in a bulk dual. as a illustration of this, we show that a partition function of a orthogonal group coset cft has a $ \ mathcal n = 1 $ supersymmetric higher - spin bulk dual, in the ' t hooft limit. we also propose that two of the series of cft partition functions, obtained from conformal embeddings, are equal, generalising the well - known dual interpretation of the 3 - state potts model as a $ \ frac { su ( 2 ) _ 3 \ otimes su ( 2 ) _ 1 } { su ( 2 ) _ 4 } $ and also as a $ \ frac { su ( 3 ) _ 1 \ otimes su ( 3 ) _ 1 } { su ( 3 ) _ 2 } $ coset model.
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arxiv:1606.00791
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let $ g $ be an algebraic real reductive group and $ z $ a real spherical $ g $ - variety, that is, it admits an open orbit for a minimal parabolic subgroup $ p $. we prove a local structure theorem for $ z $. in the simplest case where $ z $ is homogeneous, the theorem provides an isomorphism of the open $ p $ - orbit with a bundle $ q \ times _ l s $. here $ q $ is a parabolic subgroup with levi decomposition $ lu $, and $ s $ is a homogeneous space for a quotient $ d = l / l _ n $ of $ l $, where $ l _ n $ is normal in $ l $, such that $ d $ is compact modulo center.
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arxiv:1310.6390
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the micro - continuum method is a novel approach to simulate flow and transport in multiscale porous materials. for such materials, the domain can be divided into three sub - domains depending on the local porosity { \ epsilon } : fully resolved solid phase, for which { \ epsilon } = 0, fully resolved pores, for which { \ epsilon } = 1. 0, and unresolved pores, for which 0 < { \ epsilon } < 1. 0. for such domains, the flow can be solved using the darcy - brinkman - stokes ( dbs ) equation, which offers a seamless transition between unresolved pores, where flow is described by darcy ' s law, and resolved pores, where flow is described by the navier - stokes equations. species transport can then be modelled using a volume - averaged equation. in this work, we present a derivation of the closure problem for the micro - continuum approach. effective dispersivity tensors can then be calculated through a multi - stage process. first, high resolution images are chosen for characterizing the structure of the unresolved pores. porosity, permeability and effective dispersivity for the unresolved part are calculated by solving a closure problem based on direct numerical simulation ( dns ) in the high - resolution images. the effective dispersivity is then expressed as a function of the p \ ' eclet number, which describes the ratio of advective to diffusive transport. this relationship, along with porosity and permeability, is then integrated into the multiscale domain and the effective dispersivity tensor for the full image is calculated. our novel method is validated by comparison with the numerical solution obtained for a fully - resolved simulation in a multiscale 2d micromodel. it is then applied to obtain an effective dispersivity model in digital twins for two multiscale materials : hierarchical ceramic foams and microporous carbonate rocks.
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arxiv:2405.06155
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robots which interact with the physical world will benefit from a fine - grained tactile understanding of objects and surfaces. additionally, for certain tasks, robots may need to know the haptic properties of an object before touching it. to enable better tactile understanding for robots, we propose a method of classifying surfaces with haptic adjectives ( e. g., compressible or smooth ) from both visual and physical interaction data. humans typically combine visual predictions and feedback from physical interactions to accurately predict haptic properties and interact with the world. inspired by this cognitive pattern, we propose and explore a purely visual haptic prediction model. purely visual models enable a robot to " feel " without physical interaction. furthermore, we demonstrate that using both visual and physical interaction signals together yields more accurate haptic classification. our models take advantage of recent advances in deep neural networks by employing a unified approach to learning features for physical interaction and visual observations. even though we employ little domain specific knowledge, our model still achieves better results than methods based on hand - designed features.
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arxiv:1511.06065
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we introduce a factorization for the map between moduli spaces of stable maps which forgets one marked point. this leads to a study of universal relations in the cohomology of stable map spaces in genus zero.
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arxiv:math/0607431
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the guesswork of a quantum ensemble quantifies the minimum number of guesses needed in average to correctly guess the state of the ensemble, when only one state can be queried at a time. here, we derive analytical solutions of the guesswork problem subject to a finite set of conditions, including the analytical solution for any qubit ensemble with uniform probability distribution. as explicit examples, we compute the guesswork for any qubit regular polygonal and polyhedral ensemble.
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arxiv:2012.09350
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reinforcement learning provides a framework for learning to control which actions to take towards completing a task through trial - and - error. in many applications observing interactions is costly, necessitating sample - efficient learning. in model - based reinforcement learning efficiency is improved by learning to simulate the world dynamics. the challenge is that model inaccuracies rapidly accumulate over planned trajectories. we introduce deep gaussian processes where the depth of the compositions introduces model complexity while incorporating prior knowledge on the dynamics brings smoothness and structure. our approach is able to sample a bayesian posterior over trajectories. we demonstrate highly improved early sample - efficiency over competing methods. this is shown across a number of continuous control tasks, including the half - cheetah whose contact dynamics have previously posed an insurmountable problem for earlier sample - efficient gaussian process based models.
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arxiv:2011.01226
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the monoidal category of soergel bimodules categorifies the hecke algebra of a finite weyl group. in the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. we define a quotient category, also given in terms of planar graphs, which categorifies the temperley - lieb algebra. certain ideals appearing in this quotient are related both to the 1 - skeleton of the coxeter complex and to the topology of 2d cobordisms. we demonstrate how further subquotients of this category will categorify the cell modules of the temperley - lieb algebra.
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arxiv:1003.3416
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we presented a general classification scheme for the tripartite $ l \ times n \ times n $ entangled system under stochastic local operation and classical communication. the whole classification procedure consists of two correlated parts : the simultaneous similarity transformation of a commuting matrix pair into a canonical form and the study of internal symmetry of parameters in the canonical form. based on this scheme, a concrete example of entanglement classification for a $ 3 \ times n \ times n $ system is given.
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arxiv:1108.5636
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modern astronomical potentials modeling galaxies or stellar systems can be rather involved, and deriving their first derivatives ( accelerations ) and second derivatives ( variational equations ) in order to compute orbits and their chaoticity may be a formidable task. we present here a fully automated routine, dubbed smart, with which the accelerations and the variational equations of an arbitrary potential that has been written in the fortran 77 language can be computed. almost any fortran 77 statement is admitted in the potential, and the output are standard fortran 77 routines ready to use. we validate our algorithm with a set of potentials including time - dependent, velocity - dependent and very complex potentials that even involve auxiliary routines. we also describe with some detail a realistic seven - component galactic potential, milkywayhydra, which yields very involved derivatives, thus being a good test bed for smart.
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arxiv:2205.15980
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we show that $ h $ - deformation can be obtained, by a singular limit of a similarity transformation, from $ q $ - deformation ; to be specefic, we obtain $ \ gl _ h ( 2 ) $, its differential structure, its inhomogenous extension, and $ \ uh { \ sl ( 2 ) } $ from their $ q $ - deformed counterparts.
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arxiv:hep-th/9410135
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we study a model of quantum mechanical fermions with matrix - like index structure ( with indices $ n $ and $ l $ ) and quartic interactions, recently introduced by anninos and silva. we compute the partition function exactly with $ q $ - deformed orthogonal polynomials ( stieltjes - wigert polynomials ), for different values of $ l $ and arbitrary $ n $. from the explicit evaluation of the thermal partition function, the energy levels and degeneracies are determined. for a given $ l $, the number of states of different energy is quadratic in $ n $, which implies an exponential degeneracy of the energy levels. we also show that at high - temperature we have a gaussian matrix model, which implies a symmetry that swaps $ n $ and $ l $, together with a wick rotation of the spectral parameter. in this limit, we also write the partition function, for generic $ l $ and $ n, $ in terms of a single generalized hermite polynomial.
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arxiv:1703.02454
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we introduce completion moment detection for actions - the problem of locating the moment of completion, when the action ' s goal is confidently considered achieved. the paper proposes a joint classification - regression recurrent model that predicts completion from a given frame, and then integrates frame - level contributions to detect sequence - level completion moment. we introduce a recurrent voting node that predicts the frame ' s relative position of the completion moment by either classification or regression. the method is also capable of detecting incompletion. for example, the method is capable of detecting a missed ball - catch, as well as the moment at which the ball is safely caught. we test the method on 16 actions from three public datasets, covering sports as well as daily actions. results show that when combining contributions from frames prior to the completion moment as well as frames post completion, the completion moment is detected within one second in 89 % of all tested sequences.
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arxiv:1805.06749
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recent advances in condensed matter theory have revealed that new and exotic phases of matter can exist in spin models ( or more precisely, local bosonic models ) via a simple physical mechanism, known as " string - net condensation. " these new phases of matter have the unusual property that their collective excitations are gauge bosons and fermions. in some cases, the collective excitations can behave just like the photons, electrons, gluons, and quarks in our vacuum. this suggests that photons, electrons, and other elementary particles may have a unified origin - - string - net condensation in our vacuum. in addition, the string - net picture indicates how to make artificial photons, artificial electrons, and artificial quarks and gluons in condensed matter systems.
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arxiv:cond-mat/0407140
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celestial holography proposes a duality between the gravitational $ \ mathcal { s } $ - matrix and correlators in a conformal field theory living on the celestial sphere. in this white paper, solicited for the 2022 snowmass process, we review the motivation from asymptotic symmetries, fundamentals of the proposed holographic dictionary, potential applications to experiment and theory, and some important open questions.
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arxiv:2111.11392
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while large language models ( llms ) equipped with techniques like chain - of - thought prompting have demonstrated impressive capabilities, they still fall short in their ability to reason robustly in complex settings. however, evaluating llm reasoning is challenging because system capabilities continue to grow while benchmark datasets for tasks like logical deduction have remained static. we introduce musr, a dataset for evaluating language models on multistep soft reasoning tasks specified in a natural language narrative. this dataset has two crucial features. first, it is created through a novel neurosymbolic synthetic - to - natural generation algorithm, enabling the construction of complex reasoning instances that challenge gpt - 4 ( e. g., murder mysteries roughly 1000 words in length ) and which can be scaled further as more capable llms are released. second, our dataset instances are free text narratives corresponding to real - world domains of reasoning ; this makes it simultaneously much more challenging than other synthetically - crafted benchmarks while remaining realistic and tractable for human annotators to solve with high accuracy. we evaluate a range of llms and prompting techniques on this dataset and characterize the gaps that remain for techniques like chain - of - thought to perform robust reasoning.
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arxiv:2310.16049
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the second born corrections to the electrical and thermal conductivities are calculated for the dense matter in the liquid metal phase for various elemental compositions of astrophysical importance. inclusion up to the second born corrections is sufficiently accurate for the coulomb scattering of the electrons by the atomic nuclei with z < 26. our approach is semi - analytical, and is in contrast to that of the previous authors who have used fully numerical values of the cross section for the coulomb scattering of the electron by the atomic nucleus. the merit of the present semi - analytical approach is that this approach affords us to obtain the results with reliable z - dependence and \ rho - dependence. the previous fully numerical approach has made use of the numerical values of the cross section for the scattering of the electron off the atomic nucleus for a limited number of z - values, z = 6, 13, 29, 50, 82, and 92, and for a limited number of electron energies, 0. 05mev, 0. 1mev, 0. 2mev, 0. 4mev, 0. 7mev, 1mev, 2mev, 4mev, and 10mev. our study, however, has confirmed that the previous results are sufficiently accurate. they are recovered, if the terms higher than the second born terms are taken into account. we make a detailed comparison of the present results with those of the previous authors. the numerical results are parameterized in a form of analytic formulae that would facilitate practical uses of the results. we also extend our calculations to the case of mixtures of nuclear species. the corresponding subroutine can be retrieved from http : / / www. ph. sophia. ac. jp / ~ itoh - ken / subroutine / subroutine. htm
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arxiv:0708.2967
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we propose an algorithm to find a lower bound for the number of cyclic codes over any finite field with any given exponent. besides, we give a formula to find the exponent of bch codes.
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arxiv:2208.14287
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we develop the concept of trajectories in anyon spectra, i. e., the continuous dependence of energy levels on the kinetic angular momentum. it provides a more economical and unified description, since each trajectory contains an infinite number of points corresponding to the same statistics. for a system of non - interacting anyons in a harmonic potential, each trajectory consists of two infinite straight line segments, in general connected by a nonlinear piece. we give the systematics of the three - anyon trajectories. the trajectories in general cross each other at the bosonic / fermionic points. we use the ( semi - empirical ) rule that all such crossings are true crossings, i. e. \ the order of the trajectories with respect to energy is opposite to the left and to the right of a crossing.
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arxiv:hep-th/9507034
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we consider a situation where an $ n $ - level system ( nls ) is coupled to a heat bath without being necessarily thermalized. for this situation we derive general jarzinski - type equations and conclude that heat and entropy is flowing from the hot bath to the cold nls and, vice versa, from the hot nls to the cold bath. the clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities which have already been considered in the literature. our approach is illustrated by an analytical example.
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arxiv:2104.05350
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the main result is that the group $ \ textrm { homeo } ( k ) $ of homeomorphisms of the universal knaster continuum contains an open subgroup with a comeager conjugacy class. actually, this open subgroup is the very natural subgroup consisting of degree - one homeomorphisms. we give a general fact about finding comeager orbits in polish group actions which are approximated densely by direct limits of actions with comeager orbits. the main theorem comes as a result of this fact and some finer analysis of the conjugacy action of the group $ \ textrm { homeo } _ + [ 0, 1 ] $.
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arxiv:2308.13023
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this work is concerned with the issue of applications of the semi - definite programming ( sdp ) in the field of quantum information science. our results of the analysis of certain quantum information protocols using this optimization technique are presented, and an implementation of a relevant numerical tool is introduced. the key method used is npa discovered by navascues et al. [ phys. rev. lett. 98, 010401 ( 2007 ) ]. in chapter 1 a brief overview of mathematical methods used in this work is presented. in chapter 2 an introduction to quantum information science is given. chapter 3 concerns the device - independent ( di ) and semi - device - independent ( sdi ) approaches in quantum cryptography. in chapter 4 our results regarding quantum information protocols which we developed using sdp are described. the results include a new type of quantum key distribution protocol based on hardy ' s paradox ; several protocols for quantum random number expansion ; a method of formulation of sdp relaxations of sdi protocols ; and a di santha - vazirani source of randomness amplification protocol. in chapter 5 an introduction to interior point methods is given. in chapter 6 the implementation of our numerical tool dedicated to problems occurring in chapter 4 are discussed and compared with other solutions.
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arxiv:1810.05145
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engineering. below is a list of recognized branches of engineering. there are additional sub - disciplines as well. = = interdisciplinary engineering = = interdisciplinary engineering draws from more than one of the principle branches of the practice. historically, naval engineering and mining engineering were major branches. other engineering fields are manufacturing engineering, acoustical engineering, corrosion engineering, instrumentation and control, automotive, information engineering, petroleum, systems, audio, software, architectural, biosystems, and textile engineering. these and other branches of engineering are represented in the 36 licensed member institutions of the uk engineering council. new specialties sometimes combine with the traditional fields and form new branches – for example, earth systems engineering and management involves a wide range of subject areas including engineering studies, environmental science, engineering ethics and philosophy of engineering. = = practice = = one who practices engineering is called an engineer, and those licensed to do so may have more formal designations such as professional engineer, chartered engineer, incorporated engineer, ingenieur, european engineer, or designated engineering representative. = = methodology = = in the engineering design process, engineers apply mathematics and sciences such as physics to find novel solutions to problems or to improve existing solutions. engineers need proficient knowledge of relevant sciences for their design projects. as a result, many engineers continue to learn new material throughout their careers. if multiple solutions exist, engineers weigh each design choice based on their merit and choose the solution that best matches the requirements. the task of the engineer is to identify, understand, and interpret the constraints on a design in order to yield a successful result. it is generally insufficient to build a technically successful product, rather, it must also meet further requirements. constraints may include available resources, physical, imaginative or technical limitations, flexibility for future modifications and additions, and other factors, such as requirements for cost, safety, marketability, productivity, and serviceability. by understanding the constraints, engineers derive specifications for the limits within which a viable object or system may be produced and operated. = = = problem solving = = = engineers use their knowledge of science, mathematics, logic, economics, and appropriate experience or tacit knowledge to find suitable solutions to a particular problem. creating an appropriate mathematical model of a problem often allows them to analyze it ( sometimes definitively ), and to test potential solutions. more than one solution to a design problem usually exists so the different design choices have to be evaluated on their merits before the one judged most suitable is chosen. genrich altshuller, after gathering statistics on a large number of patents, suggested that compromises are
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https://en.wikipedia.org/wiki/Engineering
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this lecture addresses the concept of form factor in magnetic scattering of thermal neutrons, analyzing its meaning, discussing its measurement by polarized neutrons and detailing its computation for the ions by the spherical tensor operator formalism.
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arxiv:0706.0335
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we study theoretically how local measurements perfomed on critical quantum ground states affect long - distance correlations. these states are highly entangled and feature algebraic correlations between local observables. as a consequence, local measurements can have highly nonlocal effects. our focus is on tomonaga - luttinger liquid ( tll ) ground states, a continuous family of critical states in one dimension whose structure is parameterized by a luttinger parameter $ k $. we show that arbitrarily weak local measurements, performed over extended regions of space, can conspire to drive transitions in long - distance correlations. conditioning first on a particular measurement outcome we show that there is a transition in the character of the post - measurement quantum state for $ k < 1 $, and highlight a formal analogy with the effect of a static impurity on transport through a tll. to investigate the full ensemble of measurement outcomes we consider averages of physical quantities which are necessarily nonlinear in the system density matrix. we show how their behavior can be understood within a replica field theory, and for the measurements that we consider we find that the symmetry of the theory under exchange of replicas is broken for $ k < 1 / 2 $. a well - known barrier to experimentally observing the collective effects of multiple measurements has been the need to post - select on random outcomes. here we resolve this problem by introducing cross - correlations between experimental measurement results and classical simulations, which act as resource - efficient probes of the transition. the phenomena we discuss are, moreover, robust to local decoherence.
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arxiv:2207.09476
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in this short mostly expository note, we sketch a program for gauging fully extended topological field theories in 3 dimensions. one begins with the spherical fusion category with which one wants to do levin - wen or turaev - viro. one then computes a homotopic space with certain $ \ pi _ \ bullet $ given by autoequivalences, invertible objects and the ground ( algebraic ) field. then for each desired symmetry group $ g $ one looks at mapping $ bg $ into that. this classifies equivalence classes of g - extended fusion categories. this is an equivalence at a fully extended level so will allow many defects rather than only evaluating partition functions on closed manifolds. we can now use these categories to build a new fully extended 3d topological field theory, but now possibly with extra data. this is the result of permeating defect walls and saying how that affects the assignment to the point strata.
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arxiv:1605.08398
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in this paper, we construct quantum synchronizable codes ( qscs ) based on the sum and intersection of cyclic codes. further, infinite families of qscs are obtained from bch and duadic codes. moreover, we show that the work of fujiwara ~ \ cite { fujiwara1 } can be generalized to repeated root cyclic codes ( rrccs ) such that qscs are always obtained, which is not the case with simple root cyclic codes. the usefulness of this extension is illustrated via examples of infinite families of qscs from repeated root duadic codes. finally, qscs are constructed from the product of cyclic codes.
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arxiv:1508.05977
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we propose a novel conditional quantile prediction method based on complete subset averaging ( csa ) for quantile regressions. all models under consideration are potentially misspecified and the dimension of regressors goes to infinity as the sample size increases. since we average over the complete subsets, the number of models is much larger than the usual model averaging method which adopts sophisticated weighting schemes. we propose to use an equal weight but select the proper size of the complete subset based on the leave - one - out cross - validation method. building upon the theory of lu and su ( 2015 ), we investigate the large sample properties of csa and show the asymptotic optimality in the sense of li ( 1987 ). we check the finite sample performance via monte carlo simulations and empirical applications.
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arxiv:2003.03299
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the advent of machine learning models that surpass human decision - making ability in complex domains has initiated a movement towards building ai systems that interact with humans. many building blocks are essential for this activity, with a central one being the algorithmic characterization of human behavior. while much of the existing work focuses on aggregate human behavior, an important long - range goal is to develop behavioral models that specialize to individual people and can differentiate among them. to formalize this process, we study the problem of behavioral stylometry, in which the task is to identify a decision - maker from their decisions alone. we present a transformer - based approach to behavioral stylometry in the context of chess, where one attempts to identify the player who played a set of games. our method operates in a few - shot classification framework, and can correctly identify a player from among thousands of candidate players with 98 % accuracy given only 100 labeled games. even when trained on amateur play, our method generalises to out - of - distribution samples of grandmaster players, despite the dramatic differences between amateur and world - class players. finally, we consider more broadly what our resulting embeddings reveal about human style in chess, as well as the potential ethical implications of powerful methods for identifying individuals from behavioral data.
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arxiv:2208.01366
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in many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. for example, in hypertext classification, the labels of linked pages are highly correlated. a standard approach is to classify each entity independently, ignoring the correlations between them. recently, probabilistic relational models, a relational version of bayesian networks, were used to define a joint probabilistic model for a collection of related entities. in this paper, we present an alternative framework that builds on ( conditional ) markov networks and addresses two limitations of the previous approach. first, undirected models do not impose the acyclicity constraint that hinders representation of many important relational dependencies in directed models. second, undirected models are well suited for discriminative training, where we optimize the conditional likelihood of the labels given the features, which generally improves classification accuracy. we show how to train these models effectively, and how to use approximate probabilistic inference over the learned model for collective classification of multiple related entities. we provide experimental results on a webpage classification task, showing that accuracy can be significantly improved by modeling relational dependencies.
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arxiv:1301.0604
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i review some aspects of antenna subtraction at next - to - next - to - leading order ( nnlo ) in qcd and provide motivation for its extension to n $ ^ 3 $ lo. next, i introduce the antenna functions required for the construction of infrared counterterms for final - state radiation at this order. lastly, i describe the evaluation of the antenna functions and their phase - space integration, first presented in [ 1 - 3 ], and i elaborate on their application to precision observables in jet production at lepton colliders.
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arxiv:2407.14597
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in this paper, we consider networks with multiple unicast sessions. generally, non - linear network coding is needed to achieve the whole rate region of network coding. yet, there exist networks for which routing is sufficient to achieve the whole rate region, and we refer to them as routing - optimal networks. we identify a class of routing - optimal networks, which we refer to as information - distributive networks, defined by three topological features. due to these features, for each rate vector achieved by network coding, there is always a routing scheme such that it achieves the same rate vector, and the traffic transmitted through the network is exactly the information transmitted over the cut - sets between the sources and the sinks in the corresponding network coding scheme. we present more examples of information - distributive networks, including some examples from index coding and single unicast with hard deadline constraint.
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arxiv:1401.8244
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we investigate the double - layer electron system in a parabolic quantum well at filling factor $ \ nu = 2 $ in a tilted magnetic field using capacitance spectroscopy. the competition between two ground states is found at the zeeman splitting appreciably smaller than the symmetric - antisymmetric splitting. although at the transition point the system breaks up into domains of the two competing states, the activation energy turns out to be finite, signaling the occurrence of a new insulator - insulator quantum phase transition. we interpret the obtained results in terms of a predicted canted antiferromagnetic phase.
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arxiv:cond-mat/9903396
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let $ g = gl _ n ( k ) $ be the general linear group defined over an infinite field $ k $ of positive characteristic $ p $ and let $ \ delta ( \ lambda ) $ be the weyl module of $ g $ which corresponds to a partition $ \ lambda $. in this paper we classify all homomorphisms $ \ delta ( \ lambda ) \ to \ delta ( \ mu ) $ when $ \ lambda = ( a, b, 1 ^ d ) $ and $ \ mu = ( a + d, b ) $, $ d > 1 $. in particular, we show that $ hom _ g ( \ delta ( \ lambda ), \ delta ( \ mu ) ) $ is nonzero if and only if $ p = 2 $ and $ a $ is even. in this case, we show that the dimension of the homomorphism space is equal to 1 and we provide an explicit generator whose description depends on binary expansions of various integers. we also show that these generators in general are not compositions of carter - payne homomorphisms.
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arxiv:2411.08208
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in instances of online kernel learning where little prior information is available and centralized learning is unfeasible, past research has shown that distributed and online multi - kernel learning provides sub - linear regret as long as every pair of nodes in the network can communicate ( i. e., the communications network is a complete graph ). in addition, to manage the communication load, which is often a performance bottleneck, communications between nodes can be quantized. this letter expands on these results to non - fully connected graphs, which is often the case in wireless sensor networks. to address this challenge, we propose a gossip algorithm and provide a proof that it achieves sub - linear regret. experiments with real datasets confirm our findings.
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arxiv:2301.09848
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we report the measurement of the two - neutrino double - beta ( $ 2 \ nu \ beta \ beta $ ) decay of $ ^ { 100 } $ mo to the ground state of $ ^ { 100 } $ ru using lithium molybdate ( \ crystal ) scintillating bolometers. the detectors were developed for the cupid - mo program and operated at the edelweiss - iii low background facility in the modane underground laboratory. from a total exposure of $ 42. 235 $ kg $ \ times $ d, the half - life of $ ^ { 100 } $ mo is determined to be $ t _ { 1 / 2 } ^ { 2 \ nu } = [ 7. 12 ^ { + 0. 18 } _ { - 0. 14 } \, \ mathrm { ( stat. ) } \ pm0. 10 \, \ mathrm { ( syst. ) } ] \ times10 ^ { 18 } $ years. this is the most accurate determination of the $ 2 \ nu \ beta \ beta $ half - life of $ ^ { 100 } $ mo to date. we also confirm, with the statistical significance of $ > 3 \ sigma $, that the single - state dominance model of the $ 2 \ nu \ beta \ beta $ decay of $ ^ { 100 } $ mo is favored over the high - state dominance model.
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arxiv:1912.07272
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we study the dynamics of a supersonically expanding ring - shaped bose - einstein condensate both experimentally and theoretically. the expansion redshifts long - wavelength excitations, as in an expanding universe. after expansion, energy in the radial mode leads to the production of bulk topological excitations - - solitons and vortices - - driving the production of a large number of azimuthal phonons and, at late times, causing stochastic persistent currents. these complex nonlinear dynamics, fueled by the energy stored coherently in one mode, are reminiscent of a type of " preheating " that may have taken place at the end of inflation.
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arxiv:1710.05800
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steering a car through traffic is a complex task that is difficult to cast into algorithms. therefore, researchers turn to training artificial neural networks from front - facing camera data stream along with the associated steering angles. nevertheless, most existing solutions consider only the visual camera frames as input, thus ignoring the temporal relationship between frames. in this work, we propose a convolutional long short - term memory recurrent neural network ( c - lstm ), that is end - to - end trainable, to learn both visual and dynamic temporal dependencies of driving. additionally, we introduce posing the steering angle regression problem as classification while imposing a spatial relationship between the output layer neurons. such method is based on learning a sinusoidal function that encodes steering angles. to train and validate our proposed methods, we used the publicly available comma. ai dataset. our solution improved steering root mean square error by 35 % over recent methods, and led to a more stable steering by 87 %.
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arxiv:1710.03804
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) \ right \ vert \ leq \ \ frac { 1 } { n ^ { \ varepsilon _ 2 } }. $ $ finally if $ x ^ n $ and $ y ^ { m _ n } $ are independent and $ m _ n = o ( n ^ { 1 / 3 } ) $, then almost surely, the norm of any polynomial in $ ( x ^ n \ otimes i _ { m _ n }, i _ n \ otimes y ^ { m _ n } ) $ converges almost surely towards its free limit. this result is an improvement of a theorem of pisier, who was himself using estimates from haagerup and thorbj \ o rnsen, where $ m _ n $ had size $ o ( n ^ { 1 / 4 } ) $.
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arxiv:1912.04588
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dark matter is postulated to be a neutral dirac fermion, charged under a dark $ u ( 1 ) _ d $ gauge symmetry. scalar partners of the quarks and leptons are also charged under $ u ( 1 ) _ d $. the dark gauge boson $ z _ d $ and the dark higgs boson $ h _ d $ enable either freeze - out or freeze - in mechanisms to account for the correct dark matter relic abundance. dark number $ d $ is connected to baryon number $ b $ and lepton number $ l $ through $ d = 3b + l - ( 2j ) _ { [ mod ~ 2 ] } $ where $ j $ is the intrinsic spin of the particle.
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arxiv:2203.12034
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we consider the most general solutions of eleven - dimensional supergravity preserving $ n = 2 $ supersymmetry whose metrics are warped products of three - dimensional anti - de sitter space with an eight - dimensional manifold, focusing on those realising ( 2, 0 ) superconformal symmetry. we give a set of necessary and sufficient conditions for a solution to be supersymmetric, which can be phrased, in the general case, in terms of a local su ( 2 ) structure and its intrinsic torsion. we show that these supergravity backgrounds always admit a nowhere - vanishing killing vector field that preserves the solution and encodes the u ( 1 ) r - symmetry of the dual field theory. we illustrate our results with examples which have appeared in the literature, including those with su ( 4 ), g $ _ 2 $ and su ( 3 ) structures, and discuss new classes of minkowski solutions.
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arxiv:2209.10680
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we study the online decision making problem ( odmp ) as a natural generalization of online linear programming. in odmp, a single decision maker undertakes a sequence of decisions over $ t $ time steps. at each time step, the decision maker makes a locally feasible decision based on information available up to that point. the objective is to maximize the accumulated reward while satisfying some convex global constraints called goal constraints. the decision made at each step results in an $ m $ - dimensional vector that represents the contribution of this local decision to the goal constraints. in the online setting, these goal constraints are soft constraints that can be violated moderately. to handle potential nonconvexity and nonlinearity in odmp, we propose a fenchel dual - based online algorithm. at each time step, the algorithm requires solving a potentially nonconvex optimization problem over the local feasible set and a convex optimization problem over the goal set. under certain stochastic input models, we show that the algorithm achieves $ o ( \ sqrt { mt } ) $ goal constraint violation deterministically, and $ \ tilde { o } ( \ sqrt { mt } ) $ regret in expected reward. numerical experiments on an online knapsack problem and an assortment optimization problem are conducted to demonstrate the potential of our proposed online algorithm.
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arxiv:2211.03997
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in this work we are going to show weak convergence of a probability measure corresponding to the solution of the following nonlinear stochastic heat equation $ \ frac { \ partial } { \ partial t } u _ { t } ( x ) = \ frac { \ kappa } { 2 } \ delta u _ { t } ( x ) + \ sigma ( u _ { t } ( x ) ) \ eta _ \ alpha $ with colored noise $ \ eta _ \ alpha $ to the measure corresponding to the solution of the same equation but with white noise $ \ eta $ as $ \ alpha \ uparrow 1 $ on the space of continuous functions with compact support. the noise $ \ eta _ \ alpha $ is assumed to be colored in space and its covariance is given by $ \ operatorname { e } \ left [ \ eta _ \ alpha ( t, x ) \ eta _ \ alpha ( s, y ) \ right ] = \ delta ( t - s ) f _ \ alpha ( x - y ) $ where $ f _ \ alpha $ is the riesz kernel $ f _ \ alpha ( x ) \ propto 1 / \ left | x \ right | ^ \ alpha $. we will also state a result about continuity of measure in $ \ alpha $, for $ \ alpha \ in ( 0, 1 ) $. we will work with the classical notion of weak convergence of measures.
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arxiv:1507.05385
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amongst the class of supergravity solutions found by lin, lunin and maldacena, we consider pure and mixed state configurations generated by phase space densities in the dual fermionic picture. a one - to - one map is constructed between the phase space densities and piecewise monotonic curves, which generalize the young diagrams corresponding to pure states. within the fermionic phase space picture, a microscopic formula for the entropy of mixed states is proposed. considering thermal ensembles, agreement is found between the thermodynamic and the proposed microscopic entropies. furthermore, we study fluctuations in thermodynamic ensembles for the superstar and compare the entropy of these ensembles with the area of stretched horizons predicted by the mean fluctuation size.
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arxiv:hep-th/0703223
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to reduce the danger of powerful super - intelligent ais, we might make the first such ais oracles that can only send and receive messages. this paper proposes a possibly practical means of using machine learning to create two classes of narrow ai oracles that would provide chess advice : those aligned with the player ' s interest, and those that want the player to lose and give deceptively bad advice. the player would be uncertain which type of oracle it was interacting with. as the oracles would be vastly more intelligent than the player in the domain of chess, experience with these oracles might help us prepare for future artificial general intelligence oracles.
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arxiv:2010.02911
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the modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. such dynamics is initiated from the injection of side - bands, which translate into an amplitude modulation of the wave field. the nonlinear stage of unstable wave evolution can be described by exact solutions of the nonlinear schr \ " odinger equation ( nlse ). in that case, the amplitude modulation of such coherent extreme wave structures is connected to a particular phase - shift seed in the carrier wave. in this letter, we show that phase - shifts localization applied to the background, excluding any amplitude modulation excitation, can indeed trigger extreme events. such rogue waves can be for instance generated by considering the parametrization of fundamental breathers and thus, by seeding only the local phase - shift information to the regular carrier wave. our wave tank experiments show an excellent agreement with the expected nlse hydrodynamics and confirm that even though delayed in their evolution, breather - type extreme waves can be generated from a purely regular wave train. such novel focusing mechanism awaits experimental confirmation in other nonlinear media, such optics, plasma, and bose - einstein condensates.
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arxiv:2206.09067
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recently, deep learning has been successfully applied to the single - image super - resolution ( sisr ) with remarkable performance. however, most existing methods focus on building a more complex network with a large number of layers, which can entail heavy computational costs and memory storage. to address this problem, we present a lightweight self - calibrated efficient transformer ( scet ) network to solve this problem. the architecture of scet mainly consists of the self - calibrated module and efficient transformer block, where the self - calibrated module adopts the pixel attention mechanism to extract image features effectively. to further exploit the contextual information from features, we employ an efficient transformer to help the network obtain similar features over long distances and thus recover sufficient texture details. we provide comprehensive results on different settings of the overall network. our proposed method achieves more remarkable performance than baseline methods. the source code and pre - trained models are available at https : / / github. com / alexzou14 / scet.
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arxiv:2204.08913
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ultrafast laser measurements probe the non - equilibrium dynamics of excited electrons in metals with increasing temporal resolution. electronic structure calculations can provide a detailed microscopic understanding of hot electron dynamics, but a parameter - free description of pump - probe measurements has not yet been possible, despite intensive research, because of the phenomenological treatment of electron - phonon interactions. we present ab initio predictions of the electron - temperature dependent heat capacities and electron - phonon coupling coefficients of plasmonic metals. we find substantial differences from free - electron and semi - empirical estimates, especially in noble metals above transient electron temperatures of 2000 k, because of the previously - neglected strong dependence of electron - phonon matrix elements on electron energy. we also present first - principles calculations of the electron - temperature dependent dielectric response of hot electrons in plasmonic metals, including direct interband and phonon - assisted intraband transitions, facilitating complete theoretical predictions of the time - resolved optical probe signatures in ultrafast laser experiments.
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arxiv:1602.00625
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we investigate the effectiveness of fine - tuning large language models ( llms ) on small medical datasets for text classification and named entity recognition tasks. using a german cardiology report dataset and the i2b2 smoking challenge dataset, we demonstrate that fine - tuning small llms locally on limited training data can improve performance achieving comparable results to larger models. our experiments show that fine - tuning improves performance on both tasks, with notable gains observed with as few as 200 - 300 training examples. overall, the study highlights the potential of task - specific fine - tuning of llms for automating clinical workflows and efficiently extracting structured data from unstructured medical text.
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arxiv:2503.21349
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ly - alpha emitting galaxies and giant ly - alpha blobs ( labs ) have been extensively observed to study the formation history of galaxies. however, the origin of their extended ly - alpha emission, especially of labs, remains controversial. polarization signals from some labs have been discovered, and this is commonly interpreted as strong evidence supporting that the extended ly - alpha emission originates from the resonance scattering. the monte carlo ly - alpha radiative transfer code lart is updated to investigate the polarization of ly - alpha using the stokes vector formalism. we apply lart to a few models to explore the fundamental polarization properties of ly - alpha. interestingly, individual ly - alpha photon packets are found to be almost completely polarized by a sufficient number of scatterings ( n _ scatt > 10 ^ 4 - 10 ^ 5 in a static medium ) or doppler shifts induced by gas motion, even starting from unpolarized light. it is also found that the polarization pattern can exhibit a non - monotonically increasing pattern in some cases, besides the commonly - known trend that the polarization monotonically increases with radius. the polarization properties are primarily determined by the degree of polarization of individual photon packets and the anisotropy of the ly - alpha radiation field, which are eventually controlled by the medium ' s optical depth and velocity field. if once ly - alpha photon packets achieve ~ 100 % polarization, the radial profile of polarization appears to correlate with the surface brightness profile. a steep surface brightness profile tends to yield a rapid increase of the linear polarization near the ly - alpha source location. in contrast, a shallow surface brightness profile gives rise to a slowly increasing polarization pattern.
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arxiv:2105.15062
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this paper uses noncommutative resolutions of non - gorenstein singularities to construct classical deformation spaces, by recovering the artin component of the deformation space of a cyclic surface singularity using only the quiver of the corresponding reconstruction algebra. the relations of the reconstruction algebra are then deformed, and the deformed relations together with variation of the git quotient achieve the simultaneous resolution. this extends work of brieskorn, kronheimer, grothendieck, cassens - slodowy and crawley - boevey - holland into the setting of singularities $ \ mathbb { c } ^ 2 / h $ with $ h \ leq \ mathrm { gl } ( 2, \ mathbb { c } ) $, and furthermore gives a prediction for what is true more generally.
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arxiv:2208.11966
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the problem of increased queueing delays in the internet motivates the study of currently implemented transport protocols and active queue management ( aqm ) policies. we study compound tcp ( default protocol in windows ) with random early detection ( red ). red uses an exponentially weighted moving average of the queue size to make packet - dropping decisions, aiming to control the queue size. one must study red with current protocols in order to explore its viability in the context of increased queueing delays. we derive a non - linear time - delayed model for compound tcp - red. we derive a sufficient condition for local stability of this model, and examine the impact of ( i ) round - trip time ( rtt ) of the tcp flows, ( ii ) queue averaging parameter and ( iii ) packet - dropping thresholds. further, we establish that the system undergoes a hopf bifurcation as any of the above parameters is varied. this suggests the emergence of limit cycles in the queue size, which may lead to synchronisation of tcp flows and loss of link utilisation. next, we study a regime where queue size averaging is not performed, and packet - dropping decisions are based on instantaneous queue size. in this regime, we derive the necessary and sufficient condition for local stability. a comparison of the stability results for compound tcp - red in the two regimes - - with and without queue size averaging - - reveals that averaging may not be beneficial to system stability. packet - level simulations show that the queue size indeed exhibits limit cycle oscillations as system parameters are varied. we then outline a simple threshold - based queue policy, that could ensure stable low - latency operation. we show that the threshold policy outperforms red in terms of queueing delay, flow completion time and packet loss. we highlight that the threshold - based policy could mitigate the issue of increased queueing delays in the internet.
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arxiv:1907.06302
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we report on a frequency ratio measurement of a $ { } ^ { 199 } $ hg - based optical lattice clock referencing a $ { } ^ { 87 } $ sr - based clock. evaluations of lattice light shift, including atomic - motion - dependent shift, enable us to achieve a total systematic uncertainty of $ 7. 2 \ times 10 ^ { - 17 } $ for the hg clock. the frequency ratio is measured to be $ \ nu _ { \ rm hg } / \ nu _ { \ rm sr } = 2. 629 \, 314 \, 209 \, 898 \, 909 \, 60 ( 22 ) $ with a fractional uncertainty of $ 8. 4 \ times 10 ^ { - 17 } $, which is smaller than the uncertainty of the realization of the si second, i. e., the si limit.
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arxiv:1503.07941
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we present a novel control policy, called predictive network control ( pnc ) to control wireless communication networks ( on packet level ), based on paradigms of model predictive control ( mpc ). in contrast to common myopic policies, who use one step ahead prediction, pnc predicts the future behavior of the system for an extended horizon, thus facilitating performance gains. we define an advanced system model in which we use a markov chain in combination with a bernoulli trial to model the stochastic components of the network. furthermore we introduce the algorithm and present two detailed simulation examples, which show general improved performance and a gain in stability region compared to the standard policy.
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arxiv:1804.00481
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to obtain a light mode in two - dimensional staggered fermions, we introduce four new local operators keeping the rotational invariance for a staggered dirac operator. to split masses of tastes, three cases are considered. the mass matrix and the propagator for free theories are analyzed. we find that one of three cases is a good candidate for taking a single mode by the mass splitting. in the case, it is possible that a heavy mode obtains infinite mass on even sites or odd sites.
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arxiv:hep-lat/0609025
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given a one dimensional perturbed schroedinger operator h = - ( d / dx ) ^ 2 + v ( x ) we consider the associated wave operators w _ +, w _ - defined as the strong l ^ 2 limits as s - > \ pm \ infty of the operators e ^ { ish } e ^ { - ish _ 0 } we prove that the wave operators are bounded operators on l ^ p for all 1 < p < \ infty, provided ( 1 + | x | ) ^ 2 v ( x ) is integrable, or else ( 1 + | x | ) v ( x ) is integrable and 0 is not a resonance. for p = \ infty we obtain an estimate in terms of the hilbert transform. some applications to dispersive estimates for equations with variable rough coefficients are given.
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arxiv:math-ph/0509059
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we present and discuss a list of some interesting points that are currently open in nonextensive statistical mechanics. their analytical, numerical, experimental or observational advancement would naturally be very welcome.
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arxiv:1102.2408
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let g _ r be a lie group acting on an oriented manifold m, and let $ \ omega $ be an equivariantly closed form on m. if both g _ r and m are compact, then the integral $ \ int _ m \ omega $ is given by the fixed point integral localization formula ( theorem 7. 11 in [ bgv ] ). unfortunately, this formula fails when the acting lie group g _ r is not compact : there simply may not be enough fixed points present. a proposed remedy is to modify the action of g _ r in such a way that all fixed points are accounted for. let g _ r be a real semisimple lie group, possibly noncompact. one of the most important examples of equivariantly closed forms is the symplectic volume form $ d \ beta $ of a coadjoint orbit $ \ omega $. even if $ \ omega $ is not compact, the integral $ \ int _ { \ omega } d \ beta $ exists as a distribution on the lie algebra g _ r. this distribution is called the fourier transform of the coadjoint orbit. in this article we will apply the localization results described in [ l1 ] and [ l2 ] to get a geometric derivation of harish - chandra ' s formula ( 9 ) for the fourier transforms of regular semisimple coadjoint orbits. then we will make an explicit computation for the coadjoint orbits of elements of g _ r * which are dual to regular semisimple elements lying in a maximally split cartan subalgebra of g _ r.
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arxiv:math/0302352
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adaptively monitoring the states of nodes in a large complex network is of interest in domains such as national security, public health, and energy grid management. here, we present an information theoretic adaptive tracking and sampling framework that recursively selects measurements using the feedback from performing inference on a dynamic bayesian network. we also present conditions for the existence of a network specific, observation dependent, phase transition in the updated posterior of hidden node states resulting from actively monitoring the network. since traditional epidemic thresholds are derived using observation independent markov chains, the threshold of the posterior should more accurately model the true phase transition of a network. the adaptive tracking framework and epidemic threshold should provide insight into modeling the dynamic response of the updated posterior to active intervention and control policies while monitoring modern complex networks.
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arxiv:1307.3125
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educational data mining ( edm ) is a promising field, where data mining is widely used for predicting students performance. one of the most prevalent and recent challenge that higher education faces today is making students skillfully employable. institutions possess large volume of data ; still they are unable to reveal knowledge and guide their students. data in education is generally very large, multidimensional and unbalanced in nature. process of extracting knowledge from such data has its own set of problems and is a very complicated task. in this paper, engineering and mca ( masters in computer applications ) students data is collected from various universities and institutes pan india. the dataset is large, unbalanced and multidimensional in nature. a cluster based model is presented in this paper, which, when applied at preprocessing stage helps in parsimonious selection of variables and improves the performance of predictive algorithms. hence, facilitate in better prediction of students employability.
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arxiv:2407.16884
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the three condensate wavefunctions of a spinor bec on a spherical shell can map the real space to the order - parameter space that also has a spherical geometry, giving rise to topological excitations called lump solitons. the homotopy of the mapping endows the lump solitons with quantized winding numbers counting the wrapping between the two spaces. we present several lump - soliton solutions to the nonlinear coupled equations minimizing the energy functional. the energies of the lump solitons with different winding numbers indicate coexistence of lumps with different winding numbers and a lack of advantage to break a higher - winding lump soliton into multiple lower - winding ones. possible implications are discussed since the predictions are testable in cold - atom experiments.
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arxiv:2301.06556
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we address the problem of evaluating neutron - transfer induced breakup cross sections caused by the borromean nucleus $ ^ { 9 } $ be, using the reaction $ ^ { 197 } $ au ( $ ^ { 9 } $ be, $ ^ { 8 } $ be ) $ ^ { 198 } $ au as a test case. this reaction was recently measured over a wide range of incident energies around the coulomb barrier. to deal with the high density of $ ^ { 198 } $ au states that can be potentially populated in this reaction, we employ the ichimura, austern, vicent model, in which the spectrum of physical states for this system is replaced by the solutions of a complex n + $ ^ { 197 } $ au potential, accounting effectively for the fragmentation of single - particle states into physical states. furthermore, to account for the unbound nature of the emitted $ ^ { 8 } $ be system, we employ a three - body model of $ ^ { 9 } $ be. the calculated stripping cross sections are found to be in good agreement with existing data over a wide range of incident energies. the importance of taking into account the energy spread of the single - particle strength of the outgoing $ ^ { 8 } $ be and the target - like residual nucleus is discussed.
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arxiv:2502.01165
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