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Let $(\mathfrak{M},\rho,\mu)$ be a metric measure space satisfying a doubling condition, $p_0\in (1,\infty)$, and $T(t):L^{p_0}(\mathfrak{M},\mu)\rightarrow L^{p_0}(\mathfrak{M},\mu)$, $t\geq 0$, a strongly continuous semi-group. We provide…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective…
We consider the non-isothermal flow of a compressible fluid through pipes. Starting from the full set of Euler equations, we propose a variational characterization of solutions that encodes the conservation of mass, energy, and entropy in a…
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…
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…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The…
Recent theoretical developments revived the interest in charged particle multiplicities and their wide-spread parametrization, the negative binomial distribution (NBD). The central observable of the studies is the Shannon entropy of the…
Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…
For any discrete probability distributions with bounded entropy, we can generate exactly a random variate using only a finite expected number of perfect coin flips. A perfect coin flip is the outcome of an unbiased Bernoulli random…
We study restricted permutations of sets which have a geometrical structure. The study of restricted permutations is motivated by their application in coding for flash memories, and their relevance in different applications of networking…
This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis…
In this note, we use entanglement entropy as a tool to explore the universal properties of CFTs dual to extremal BTZ black holes. We demonstrate that the entanglement entropies computed in the CFTs at the boundary of the extremal BTZ and…
Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…
To quantify the complexity of a system, entropy-based methods have received considerable critical attentions in real-world data analysis. Among numerous entropy algorithms, amplitude-based formulas, represented by Sample Entropy, suffer…
Let $E$ be a subset of positive integers such that $E\cap\{1,2\}\ne\emptyset$. A weakly mixing finite measure preserving flow $T=(T_t)_{t\in\Bbb R}$ is constructed such that the set of spectral multiplicities (of the corresponding Koopman…
In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
We consider bounded weak solutions to the Burgers equation for which every entropy dissipation is representable by a measure and we prove that all these measures are concentrated on the graphs of countably many Lipschitz curves. The main…