English
Related papers

Related papers: Using Relative Entropy to Find Optimal Approximati…

200 papers

We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…

Statistical Mechanics · Physics 2007-05-23 Jayanth Banavar , Amos Maritan

One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used…

Numerical Analysis · Mathematics 2019-05-23 Gideon Simpson , Daniel Watkins

We derive the special and general relativistic hydrodynamic equations of motion for ideal fluids from a variational principle. Our approach allows to find approximate solutions, whenever physically motivated trial functions can be used.…

High Energy Physics - Phenomenology · Physics 2007-05-23 H. -Th. Elze , T. Kodama , Y. Hama , M. Makler , J. Rafelski

We give near-optimal algorithms for computing an ellipsoidal rounding of a convex polytope whose vertices are given in a stream. The approximation factor is linear in the dimension (as in John's theorem) and only loses an excess logarithmic…

Data Structures and Algorithms · Computer Science 2023-11-17 Yury Makarychev , Naren Sarayu Manoj , Max Ovsiankin

In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…

Mathematical Physics · Physics 2018-02-22 Hans Wilhelm Alt

Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…

Artificial Intelligence · Computer Science 2013-03-08 William B. Poland , Ross D. Shachter

We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…

Metric Geometry · Mathematics 2020-12-17 Tom Leinster , Emily Roff

We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary…

Soft Condensed Matter · Physics 2021-03-09 Benaoumeur Bakhti , Gerhard Müller

The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…

Information Theory · Computer Science 2024-03-12 Jiefeng Zhou , Zhen Li , Kang Hao Cheong , Yong Deng

A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…

Statistical Mechanics · Physics 2021-12-20 Ahmad Yousefi

We investigate the problem of density estimation on the unit circle and the unit sphere from a computational perspective. Our primary goal is to develop new density estimators that are both rate-optimal and computationally efficient for…

Statistics Theory · Mathematics 2026-05-08 Athanasios G. Georgiadis , Andrew P. Percival

We present new method for studying the equilibrium properties of interacting fluids in an arbitrary external filed. The method is valid in any dimension and it yields an exact results in one dimension. Using this approach, we derive a…

Soft Condensed Matter · Physics 2017-02-17 Benaoumeur Bakhti

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

Information Theory · Computer Science 2021-09-22 Gilad Gour , Marco Tomamichel

We present a maximum entropy approach to analyze the internal dynamics of a small system in contact with a large bath e.g. a solute-solvent system. For the small solute, the fluctuations around the mean values of observables are not…

Statistical Mechanics · Physics 2015-06-11 Purushottam D. Dixit

We propose a novel method for parameterizations of triangle meshes by finding an optimal quasiconformal map that minimizes an energy consisting of a relative entropy term and a quasiconformal term. By prescribing a prior probability measure…

Numerical Analysis · Mathematics 2025-11-03 Zhipeng Zhu , Lok Ming Lui

We introduce an approximation for the pair distribution function of the inhomogeneous hard sphere fluid. Our approximation makes use of our recently published averaged pair distribution function at contact which has been shown to accurately…

Soft Condensed Matter · Physics 2015-06-19 Paho Lurie-Gregg , Jeff B. Schulte , David Roundy

The most efficient way to pack equally sized spheres isotropically in 3D is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution…

Soft Condensed Matter · Physics 2010-01-05 Robert S. Farr , Robert D. Groot

Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…

Quantum Physics · Physics 2026-02-03 Ma-Cheng Yang , Cong-Feng Qiao

The Principle of Maximum Entropy is a rigorous technique for estimating an unknown distribution given partial information while simultaneously minimizing bias. However, an important requirement for applying the principle is that the…

Information Theory · Computer Science 2026-02-03 Kenneth Bogert , Matthew Kothe

Recently, we introduced Relative Resolution as a hybrid formalism for fluid mixtures [1]. The essence of this approach is that it switches molecular resolution in terms or relative separation: While nearest neighbors are characterized by a…

Statistical Mechanics · Physics 2019-10-09 Aviel Chaimovich , Kurt Kremer , Christine Peter