Related papers: Minimization Problems Based on Relative $\alpha$-E…
The coupled entropy is proven to correct a flaw in the derivation of the Tsallis entropy and thereby solidify the theoretical foundations for analyzing the uncertainty of complex systems. The Tsallis entropy originated from considering…
In this paper, we study the Tsallis entropic regularized optimal transport in the continuous setting and establish fundamental results such as the $\Gamma$-convergence of the Tsallis regularized optimal transport to the Monge--Kantorovich…
The relative entropy and chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these…
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…
Projection Pursuit methodology permits to solve the difficult problem of finding an estimate of a density defined on a set of very large dimension. In his seminal article, Huber (see "Projection pursuit", Annals of Statistics, 1985)…
Define a forward problem as $\rho_y = G_\#\rho_x$, where the probability distribution $\rho_x$ is mapped to another distribution $\rho_y$ using the forward operator $G$. In this work, we investigate the corresponding inverse problem: Given…
We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory…
Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…
Traditionally, the Method of (Shannon-Kullback's) Relative Entropy Maximization (REM) is considered with linear moment constraints. In this work, the method is studied under frequency moment constraints which are non-linear in…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
Over the past few years, a family of interesting new inequalities for the entropies of sums and differences of random variables has been developed by Ruzsa, Tao and others, motivated by analogous results in additive combinatorics. The…
We initiate the study of relative operator entropies and Tsallis relative operator entropies in the setting of JB-algebras. We establish their basic properties and extend the operator inequalities on relative operator entropies and Tsallis…
We propose a one-parameter family \ $\mathbb{R}_q$ \ of deformations of the reals, which is motivated by the generalized additivity of the Tsallis entropy. We introduce a generalized multiplication which is distributive with respect to the…
The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…
Lokshtanov et al.~[STOC 2017] introduced \emph{lossy kernelization} as a mathematical framework for quantifying the effectiveness of preprocessing algorithms in preserving approximation ratios. \emph{$\alpha$-approximate reduction rules}…
We study the constrained minimum energy problem with an external field relative to the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$ of order $\alpha\in(0,n)$ for a generalized condenser $\mathbf A=(A_i)_{i\in I}$ in $\mathbb R^n$, $n\geqslant…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
In this paper we provide an approximation \`a la Ambrosio-Tortorelli of some classical minimization problems involving the length of an unknown one-dimensional set, with an additional connectedness constraint, in dimension two. We introduce…
The primal problem of multinomial likelihood maximization restricted to a convex closed subset of the probability simplex is studied. Contrary to widely held belief, a solution of this problem may assign a positive mass to an outcome with…