Affirm Lord Rayleigh's conjecture on curved spaces for clamped plates.
problem Lord Rayleigh's conjecture for vibrating clamped plates on curved spaces.
method Nodal-decomposition argument, Lévy-Gromov isoperimetric inequality, Gaussian hypergeometric functions, sharp spectral gap estimates.
result Positive curvature enhances genuine differences between low- and high-dimensional settings.
Fast sampling method for Determinantal Point Processes.
problem Sampling from strongly Rayleigh measures.
method Fast mixing Markov Chain sampler.
result Fast sampling for Determinantal Point Processes.
The paper analyzes the excess risk of PCA and provides a precise characterization.
problem Understanding the excess risk of principal component analysis (PCA).
method Established a central limit theorem for PCA error and derived the excess risk distribution.
result Obtained a non-asymptotic upper bound on the excess risk of PCA.
The world GDP distribution is described using thermodynamics principles.
problem Understanding the distribution of GDP among countries.
method Applied Rayleigh-Jeans thermalization to GDP data.
result Emergence of low GDP states similar to condensation in optics.
In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to zero, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler …
We develop polynomial time algorithms for dual volume sampling.
problem Lack of polynomial time algorithms for dual volume sampling.
method Developed exact and derandomized polynomial time sampling algorithms.
result Dual volume sampling satisfies the Strong Rayleigh property, enabling fast mixing Markov chains.
The study applies wealth thermalization hypothesis to social networks and explains inequality.
problem Explains inequality in human society through wealth thermalization hypothesis.
method Uses Random Matrix Theory and social networks with nonlinear perturbation.
result Shows that wealth distribution follows Rayleigh-Jeans distribution, leading to inequality.
The paper proves instability of translating λ-solitons and provides bounds on their length.
problem Stability of translating λ-solitons in cylindrical geometry.
method Analytical proof of instability and explicit length bounds.
result Explicit bounds on the length of unstable translating λ-solitons.
The paper derives the QGS equations using stochastic central extensions.
problem Deriving the viscous quasi-geostrophic equations on the torus.
method Central extensions of Lie groups and Lie algebras, stochastic Lagrangian formulation, and Euler-Poincaré reduction.
result Stochastic perturbations to the central extension lead to solutions of the QGS equations.
The paper develops efficient algorithms for sampling from random spanning trees and determinantal point processes.
problem Sampling from strongly Rayleigh distributions efficiently.
method Optimal sublinear sampling algorithms for random spanning trees and determinantal point processes.
result Achieves optimal sublinear sampling for strongly Rayleigh distributions.
Paper develops IFTRR to solve sparse generalized eigenvalue problems efficiently.
problem Finding the leading eigenvector with at most k nonzero entries in sparse generalized eigenvalue problems.
method Inverse-free truncated Rayleigh-Ritz method (IFTRR) with a new truncation strategy.
result IFTRR efficiently finds the support set of the leading eigenvector for large scale problems.
This note proves a Gaussian version of a Pólya-Szegö conjecture using rearrangement techniques.
problem Finding the domain with the minimum Gaussian principal frequency when the Gaussian torsional rigidity is fixed.
method Adapted Kohler-Jobin rearrangement technique to the Gauss space, considering a modified torsional rigidity and rearranging layers to half-spaces.
result The Gaussian principal frequency is minimized for the half-space when the Gaussian torsional rigidity is fixed.
Develops fast Markov chain samplers for constrained probability measures.
problem Sampling from constrained probability measures efficiently.
method Fast Markov chain samplers for Strongly Rayleigh (SR) measures and probabilistic models with hard constraints.
result Sharp polynomial bounds on the mixing time for SR measures, leading to fast MCMC samplers for DPPs.
New MIMO constellation design for noncoherent communications reduces hardware complexity.
problem Designing efficient MIMO constellations for noncoherent communications over fading channels.
method Geodesic curves of the Grassmann manifold for structured constellation design.
result Achieves comparable error performance to unstructured designs with reduced hardware complexity.
New criterion for cylinder stability in curved spaces.
problem Stability of cylinders in curved spaces.
method Extending Plateau-Rayleigh criterion to curved spaces and proving existence of instability threshold.
result Existence of a positive number L0 for cylinder instability in E(κ,τ) spaces. New method estimates sparse canonical vectors efficiently.
problem Sparse canonical vectors estimation in CCA.
method Quasi-Bayesian estimation via Rayleigh quotient function.
result Achieves minimax rate with low computational cost.
The techniques and analysis presented in this paper provide new methods to solve optimization problems posed on Riemannian manifolds. A new point of view is offered for the solution of constrained optimization problems. Some classical optimization techniques on Euclidean space are generalized to Riemannian manifolds. S…
Physics-informed neural networks improve surrogate modeling of turbulent Rayleigh-Bénard convection.
problem Modeling turbulent Rayleigh-Bénard convection with high accuracy and efficiency.
method Physics-informed neural networks (PINNs) with novel padding and regularization techniques.
result Significantly improved predictive accuracy of surrogate models at high Rayleigh numbers Ra = 2 × 10^9.
Proposes Rifle method for solving sparse GEP with optimal rates.
problem Sparse generalized eigenvalue problem in high-dimensional models.
method Two-stage approach: convex relaxation followed by truncated Rayleigh flow.
result Truncated Rayleigh flow converges linearly to optimal solution.
Improved lower bound for first eigenvalue of minimal hypersurfaces in spheres.
problem Finding a tighter bound for the first eigenvalue of minimal hypersurfaces in spheres.
method Rayleigh quotient estimate for a harmonic extension of an eigenfunction.
result Proved a new lower bound for the first eigenvalue of minimal hypersurfaces in spheres.
Physics-informed model reduces RBC simulation costs.
problem Computational infeasibility of direct numerical simulations for turbulent systems.
method Combines CNN and recurrent architecture, penalized with PDEs, uses conformal prediction.
result Significant reduction in computational cost for long-term simulations.
Study on GEPs with generative priors, showing optimal statistical rates and proposing an iterative algorithm.
problem Generalized eigenvalue problems with generative priors.
method Assumption of Lipschitz continuous generative model, Projected Rayleigh Flow Method (PRFM).
result PRFM converges linearly to an estimated vector achieving the optimal statistical rate.
Proposes a framework to extract ordered eigenfunctions from contextual kernels.
problem Lack of exact spectral decomposition in existing methods.
method Modular building blocks for compatibility with contextual kernels and scalability.
result Extracted eigenfunctions provide effective importance scores for feature selection.
We consider a column of a rotating stationary surface in Euclidean space. We obtain a value l0>0 in such way that if the length l of column satisfies l>l0, then the surface is instable. This extends, in some sense, previous results due to Plateau and Rayleigh for columns of surfaces with constant mean curvature…
Generalized R2R handles non-Gaussian noise for deep network training.
problem Training deep networks from noisy data alone.
method Extending R2R to handle various noise distributions.
result GR2R loss is an unbiased estimator of supervised loss.
Study stability and bifurcation of liquid interfaces in cylindrical supports.
problem Stability and bifurcation of liquid interfaces in cylindrical support surfaces.
method Analysis of eigenvalues of the Jacobi operator, Plateau-Rayleigh instability, bifurcation theory.
result Conditions for the emergence of new morphologies and bifurcations from circular cylinders.
Improved GAN for chaotic systems reduces training time and captures statistics.
problem Training GANs for chaotic dynamical systems is challenging and often fails to capture true statistics.
method Statistical constraints enforced in GANs to improve model fidelity and reduce training time.
result Statistical regularization leads to better performance in capturing physical properties and significantly reduced training time.
New SLC distributions enable easier control over diversity.
problem Lack of easy control over diversity in existing models.
method Developed strongly log-concave distributions and two tools for sampling and mode finding.
result Established weak log-submodularity for SLC functions and optimization guarantees for mode finding.
Study fundamental tones of clamped plates on curved spaces.
problem Prove fundamental tone bounds and isoperimetric inequalities on curved spaces.
method Prove spectral gap estimates and isoperimetric inequalities.
result Fundamental tone bounds and isoperimetric inequalities for clamped plates on nonpositively curved spaces.
For a bounded domain Ω with a piecewise smooth boundary in a complete Riemannian manifold M, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. By making use of a fact that eigenfunctions form an orthonormal basis of L2(Ω) in place of the Rayleigh-Ritz formula, we obtain inequalities for …
The paper extends a spectral evolution model for link prediction in evolving networks.
problem Link prediction in evolving networks.
method Approximated eigenvalue trajectories using Rayleigh quotient and extrapolation.
result Learning algorithms based on approximated trajectories outperform traditional methods.
Sharp inequalities in nonnegative Ricci curvature spaces using mass transport.
problem Proving sharp isoperimetric and Sobolev inequalities in nonnegative Ricci curvature spaces.
method Optimal mass transport theory, symmetrization techniques, and volume non-collapsing properties.
result Sharp isoperimetric and Sobolev inequalities established in Riemannian manifolds with nonnegative Ricci curvature.
Enhanced VMC methods improve neural wavefunction training.
problem Efficiently training neural wavefunctions in VMC to converge to energy minimum.
method Rayleigh-Gauss-Newton (RGN) optimization and parallel tempering sampling.
result RGN method achieves superlinear convergence with reduced computational cost.
Paper introduces REED for noncoherent OTA-FL, reducing latency without phase alignment.
problem Noncoherent OTA-FL requires signed model updates without phase alignment.
method Introduces REED for continuous signed aggregation using resource-element energy difference.
result Exact variance laws for REED and chip-diverse extension in Rayleigh fading.
Sharp-SSL uses random projections to identify important variables for semi-supervised learning.
problem High-dimensional semi-supervised learning problems.
method Careful aggregation of low-dimensional results from many axis-aligned random projections.
result Sharp-SSL algorithm can recover signal coordinates with high probability.
We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' vers…
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic fo…
We consider the SO(3) Witten-Reshetikhin-Turaev quantum invariants of random 3-manifolds. When the level r is prime, we show that the asymptotic distribution of the absolute value of these invariants is given by the standard Rayleigh distribution and independent of the choice of level. Hence the probability that the qu…
Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
problem Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
method Reformulating Stein discrepancy construction as an explicit SNR^2 maximisation problem
result Avoiding exponential SNR^2 collapse and achieving stable SNR^2
In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a bounded domain (with smooth boundary) in a given complete (not compact a priori) Riemannian manifold with Ricci bounded below . For this, we use test functions for the Rayleigh quotient subordinated to a family of open se…
We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB) problems. A machine learning paradigm popular within Cognitive Network related topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the rewards are exponentially distributed, which is common when dealing with Rayleigh fading c…
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the aperture. This allows us to use results about the invertibility of the kernel mean m…
Adversaries can fool deep learning modulator classifiers over wireless channels.
problem Vulnerability of deep learning modulator classifiers to adversarial attacks over wireless channels.
method Presented various adversarial attacks considering channel effects, including targeted and non-targeted attacks, and a universal adversarial perturbation attack.
result Modulation classification is vulnerable to adversarial attacks over wireless channels with realistic channel effects.
This work provides guaranteed bounds on the total variation distance for univariate mixtures.
problem Lack of closed-form expressions for total variation distance between mixtures.
method Two methods: information monotonicity for lower bounds and geometric envelopes for upper bounds.
result Demonstrated tightness of bounds on Gaussian, Gamma, and Rayleigh mixtures.
New algorithm learns communications systems without channel models.
problem Need for a differentiable channel model in end-to-end learning.
method Iterative training between receiver and transmitter using reinforcement learning.
result Works as well as fully supervised methods on AWGN and RBF channels.
New algorithm approximates maximum of certain distributions on subsets.
problem Finding maximum of distributions on subsets.
method Connection between sampling and optimization via exchange inequalities and local random walks.
result Simple nearly-optimal approximation algorithm for MAP inference.
We develop fast bounds for mixture model divergences.
problem Bounding the Kullback-Leibler divergence of mixtures.
method Piecewise log-sum-exp inequalities for closed-form bounds.
result Fast and generic method for entropy, cross-entropy, and KL divergence bounds.
A thermodynamic theory explains EU election vote distributions.
problem Describing EU election vote distributions.
method Tracing parallels between system energies of coupled nonlinear oscillators and party vote fractions.
result The Rayleigh-Jeans (RJ) theory well depicts EU vote results and candidate vote dispersion.