Related papers: Noncontinous additive entropies of partitions
In this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ram\'irez C., Math. Program. 104 (2005), no. 2-3, Ser. B,…
The Tsallis entropy is shown to be an additive entropy of degree-q that information scientists have been using for almost forty years. Neither is it a unique solution to the nonadditive functional equation from which random entropies are…
The one-body free volume, which determines the entropy of a hard disk system, has extensive (cavity) and intensive (cell) contributions. So far these contributions have not been unified and considered separately. The presented theory…
In analogy to the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study…
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for…
We study the convexity of the entropy functional along particular interpolating curves defined on the space of finitely supported probability measures on a graph.
Noncommutative topological entropy estimates are obtained for polynomial gauge invariant endomorphisms of Cuntz algebras, generalising known results for the canonical shift endomorphisms. Exact values for the entropy are computed for a…
The type $A$ Kostant partition function is an important combinatorial object with various applications: it counts integer flows on the complete directed graph, computes Hilbert series of spaces of diagonal harmonics, and can be used to…
In this paper, we obtain asymptotic formulas for an infinite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.
We propose entropy functions based on fractional calculus. We show that this new entropy has the same properties than the Shannon entropy except additivity, therefore making this entropy non-extensive. We show that this entropy function…
In this article we encode Hadwiger's covering conjecture and Borsuk's partition conjecture into continuous functions defined on the spaces of convex bodies, propose a four-step program to approach them, and obtain some partial results.
We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent $L$, the points of which with…
This is the 13th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. It discusses the relation between the instanton partition functions and the partition function of the topological…
We discuss conditions under which a convex cone $\K\subset \R^{\Omega}$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely…
By using the sequential effect algebra theory, we establish the partitions and refinements of quantum logics and study their entropies.
In this expository paper we summarize the connection between random partitions and 4-dimensional supersymmetric gauge theories discovered in hep-th/0306238. There is also a brief section about how this extends to 3-dimensional partitions…
We consider the computational aspects of lossy data compression problem, where the compression error is determined by a cover of the data space. We propose an algorithm which reduces the number of partitions needed to find the entropy with…
We develop a new closed-form arithmetic and recursive formula for the partition function and a generalization of Andrews' smallest parts (spt) function. Using the inclusion-exclusion principle, we additionally develop a formula for the…