Cauchy
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution
arXiv:2506.21278v3 Announce Type: replace-cross Abstract: We propose spherical Cauchy (spCauchy) latent variables for variational autoencoders on hyperspherical latent spaces. The spCauchy family has heavy-tailed global behavior and admits an exact differentiable reparameterization by applying a M\"obius transformation to uniform samples on the sphere. We show that, in the high-concentration limit, spCauchy recovers the local tangent-space geometry of the von Mises-Fisher (vMF) distribution...
L2G-Net: Local to Global Spectral Graph Neural Networks via Cauchy Factorizations
arXiv:2602.18837v2 Announce Type: replace Abstract: Despite their theoretical advantages, spectral methods based on the graph Fourier transform (GFT) are seldom used in graph neural networks (GNNs) due to the cost of computing the eigenbasis and the lack of vertex-domain locality in the resulting representations. As a result, most GNNs rely on local approximations such as polynomial Laplacian filters or message passing, which limit their ability to model long-range dependencies. In this...
Strain localization in softening plasticity without modifying standard constitutive models: a deformable Cosserat approach
Announce Type: new Abstract: This paper presents a formulation for strain localization in softening plasticity based on a deformable Cosserat model. The approach enables the direct use of standard elastoplastic constitutive models formulated for a classical Cauchy continuum, without modifying the stress update algorithm or consistent tangent operator. A key feature of the framework is the strict separation of dissipative and energetic mechanisms: all dissipation is confined to the...
The hidden pockets of the universe where the future can cause the past
Inside some very special black holes, there may be a boundary called a Cauchy horizon. Columnist Leah Crane explores the place beyond which physics breaks and anything is possible
Adaptive Reduced-Basis Trust-Region Methods for Defect Identification in Elastic Materials
arXiv:2605.19896v2 Announce Type: replace Abstract: Monitoring the integrity of elastic structures using ultrasonic waves requires the efficient identification of material parameters from measured surface displacements. The displacement field is governed by Cauchy's equation of motion, i.e., an elastic wave equation. Consequently, defect localization leads to a high-dimensional spatial parameter identification problem for a hyperbolic system with given initial and boundary conditions.
3d Summation-by-Parts scheme for Linear Wave Equations on Hyperboloidal Slices
arXiv:2606.02051v1 Announce Type: cross Abstract: We derive a fully 3-dimensional Summation-By-Parts scheme for a class of linear wave equations on hyperboloidal slices that meet future null infinity on a Minkowski background. The scheme is derived in spherical polar coordinates, with a major strength being that it is provably stable and allows having grid points at the origin and on the $z$-axis, despite coordinate singularities, and at infinity, by introducing compactification followed by...
Spectral Anatomy of Quantum Gaussian Process Kernels
Announce Type: new Abstract: Two recent results have reshaped quantum Gaussian processes (QGPs). On the one hand, \citet{lowe2025assessing} rule out the exponential speedups claimed by HHL-based QGP regression in the typical, well-conditioned regime; on the other, an independent line of work shows that highly expressive quantum kernels suffer posterior pathologies that break Bayesian optimization.
inGSEA: An Improved Method for Gene Set Enrichment Analysis Using a Weighted Integral Statistic
Gene Set Enrichment Analysis (GSEA) is one of the most popular methods for transcriptomic analysis, yet its statistical power is limited when the biological pathways exhibit heterogeneous or non-concordant expression patterns. We propose an improved GSEA method, textbf{in}tegral-based GSEA (inGSEA). inGSEA introduces a novel enrichment score based on the Anderson-Darling weighted integral statistic.
Unified Regularization of 2D Singular Integrals for Axisymmetric Galerkin BEM in Eddy-Current Evaluation
arXiv:2601.19542v2 Announce Type: replace Abstract: This paper presents an axisymmetric Galerkin boundary element method (BEM) for modeling eddy-current interactions between excitation coils and conductive objects. The formulation derives boundary integral equations from the Stratton-Chu representation for the azimuthal component of the vector potential in both air and conductive regions. The central contribution is a unified regularization framework for the two-dimensional (2D) singular...
Quaternion Dirac--Coulomb--Breit Integral Transformation for Relativistic Four-Component Correlated Electronic Structure Theory
Announce Type: new Abstract: High-accuracy correlated four-component relativistic electronic structure methods are typically formulated in terms of integrals over molecular orbital (MO). Consequently, an efficient and scalable strategy is required to deal with the complexity of transforming relativistic two-electron integrals from the atomic orbital (AO) to the MO basis. The transformation bottleneck is particularly acute for approaches that include Breit interaction integrals, whose...