Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
Felix Otto,Cédric Villani +1 more
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In this paper, it was shown that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6, 587-600) for the Gaussian measure, are implied by logarithmic Sobolev inequalities.About:
This article is published in Journal of Functional Analysis.The article was published on 2000-06-01 and is currently open access. It has received 1080 citations till now. The article focuses on the topics: Sobolev inequality & Interpolation inequality.read more
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Fast approximations of the Jeffreys divergence between univariate Gaussian mixture models via exponential polynomial densities.
TL;DR: In this paper, the authors propose a simple yet fast heuristic to approximate the Jeffreys divergence between two univariate GMMs of arbitrary number of components, which relies on converting GMMs into pairs of dually parameterized probability densities belonging to exponential families, and design a goodness-of-fit criterion to measure the dissimilarity between a GMM and a EPD.
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The Adaptive Biasing Force algorithm with non-conservative forces and related topics
TL;DR: In this article, the Adaptive Biasing Force method's robustness under generic (possibly non-conservative) forces is studied. And the authors prove the exponential convergence of both biasing force and law as time goes to infinity, using classical entropy techniques.
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Coupled Gradient Flows for Strategic Non-Local Distribution Shift
TL;DR: In this paper , a coupled partial differential equation model is proposed to capture fine-grained changes in the distribution over time by accounting for complex dynamics that arise due to strategic responses to algorithmic decision-making, non-local endogenous population interactions, and other exogenous sources of distribution shift.
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Stability of the Gaussian Stationary Point in the Han-Kobayashi Region for Z-Interference Channels
TL;DR: In this paper , a simple construction without Hermite polynomial perturbation is proposed, where distributions far from Gaussian are analytically shown to be better than the Gaussian stationary point.
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Provable Particle-based Primal-Dual Algorithm for Mixed Nash Equilibrium
TL;DR: In this article , a particle-based primal dual algorithm (PPDA) was proposed for continuous min-max optimization over continuous variables, which employs the stochastic movements of particles to represent the updates of random strategies for the mixed Nash equilibrium.
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Measure theory and fine properties of functions
TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
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Polar Factorization and Monotone Rearrangement of Vector-Valued Functions
TL;DR: In this paper, it was shown that for every vector-valued function u Lp(X, p; Rd) there is a unique polar factorization u = V$.s, where $ is a convex function defined on R and s is a measure-preserving mapping from (x, p) into (Q, I. I), provided that u is nondegenerate.
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The geometry of dissipative evolution equations: the porous medium equation
TL;DR: In this paper, the authors show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural, and they use the intuition and the calculus of Riemannian geometry to quantify this asymptotic behavior.
Book
Topological methods in hydrodynamics
Vladimir I. Arnold,Boris Khesin +1 more
TL;DR: A group theoretical approach to hydrodynamics is proposed in this article, where the authors consider the hydrodynamic geometry of diffeomorphism groups and the principle of least action implies that the motion of a fluid is described by geodesics on the group in the right-invariant Riemannian metric given by the kinetic energy.
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The variational formulation of the Fokker-Planck equation
TL;DR: The Fokker-Planck equation as mentioned in this paper describes the evolution of the probability density for a stochastic process associated with an Ito Stochastic Differential Equation.