Related papers: Ellipsoid Methods for Metric Entropy Computation
A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
We prove Macdonald-type deformations of a number of well-known classical branching rules by employing identities for elliptic hypergeometric integrals and series. We also propose some conjectural branching rules and allied conjectures…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
A new sequential approach to investigations of structure of metric spaces at infinity is proposed. Criteria for finiteness and boundedness of metric spaces at infinity are found.
Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…
We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…
Non-uniform grids and mesh adaptation have been a growing part of numerical simulation over the past years. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of…
For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…
We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particle-in-cell (PIC) simulations and use it to interpret plasma physics processes in heliospheric, planetary, and astrophysical systems. First, we…
We introduce MESSY estimation, a Maximum-Entropy based Stochastic and Symbolic densitY estimation method. The proposed approach recovers probability density functions symbolically from samples using moments of a Gradient flow in which the…
We study homeomorphisms of compact metric spaces whose restriction to the nonwandering set has the pseudo-orbit tracing property. We prove that if there are positively expansive measures, then the topological entropy is positive. Some short…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
This article deals with quantitative error analysis resulting from ellipsometric data obtained from measurement on curved surfaces including the influence of non-collimated beams. Numerical model based on the combination of geometrical and…
This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow…
The main purpose of the present paper is to study from a numerical analysis point of view some robust methods designed to cope with stiff (highly anisotropic) elliptic problems. The so-called asymptotic-preserving schemes studied in this…
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational…
In order to study as a whole a wide part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the $h$-derivative, which generalizes the conventional Newton--Leibniz calculus. This new entropy,…
The entropies of molecules in solution are routinely calculated using gas phase formulae. It is assumed that, because implicit solvation models are fitted to reproduce free energies, this is sufficient for modeling reactions in solution.…