Related papers: Using Relative Entropy to Find Optimal Approximati…
In pump-probe spectroscopy, one often needs to analyse the transmission or reflection of electromagnetic waves through optically pumped media. Here, it is common practice to approximate the analysis in order to extract non-equilibrium…
Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}$), arise as redundancies under…
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…
The paper analyzes the entropy of a system composed by non-interacting and indistinguishable particles whose quantum state numbers are modelled as independent and identically distributed classical random variables. The crucial observation…
Approximating distributions from their samples is a canonical statistical-learning problem. One of its most powerful and successful modalities approximates every distribution to an $\ell_1$ distance essentially at most a constant times…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
We give efficient deterministic one-pass streaming algorithms for finding an ellipsoidal approximation of a symmetric convex polytope. The algorithms are near-optimal in that their approximation factors differ from that of the optimal…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the…
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of…
The Ornstein-Zernike integral equation method has been employed for a single-component hard sphere fluid in terms of the Percus-Yevick (PY) and Martynov-Sarkisov (MS) approximations. Virial equation of state has been computed in both…
Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric…
In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the notion of measure-valued entropy solutions. Further we survey…
A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of $L^2$ divergence-free velocity fields, is maximized relative to…
Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such comparisons for relative entropies between comparable densities, including the relative entropy of a density with respect to…
This paper explores Tadmor's minimum entropy principle for the relativistic hydrodynamics (RHD) equations and incorporates this principle into the design of robust high-order discontinuous Galerkin (DG) and finite volume schemes for RHD on…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and non-local diffusion and isentropic pressure. The local viscosity is allowed to degenerate as the density…
It is known that the Maximum relative Entropy (MrE) method can be used to both update and approximate probability distributions functions in statistical inference problems. In this manuscript, we apply the MrE method to infer magnetic…