Related papers: Convolution Preserves Partial Synchronicity of Log…

We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.

We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…

In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of…

We prove new, general versions of Bernstein-von Mises theorem for both well-specified and misspecified models when the log-likelihood is concave in the parameter and the prior distribution is log-concave. Unlike classical versions of…

We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of log-concave measures on the half-line in terms of log-concavity of the…

Stability version of the Prekopa-Leindler inequality for log-concave functions on the n-dimensional Euclidean space is established.

The goal of this paper is to prove coherence results with respect to relational graphs for monoidal endofunctors, i.e. endofunctors of a monoidal category that preserve the monoidal structure up to a natural transformation that need not be…

In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…

We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously…

We survey some of the mechanisms used to prove that naturally defined sequences in combinatorics are log-concave. Among these mechanisms are Alexandrov's inequality for mixed discriminants, the Alexandrov Fenchel inequality for mixed…

We prove that in a large collection of naturally defined sets of permutations of fixed length, the numbers of permutations at Ulam distance k from the identity form a log-concave sequence in k.

This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…

The current paper is devoted to the investigation of the influence of nested invariant cone structure on the dynamics, in the context of non-autonomous (time almost periodic)cases. We first prove that the nested invariant cone structure can…

We call a function $f: X\to Y$ $P$-preserving if, for every subspace $A \subset X$ with property $P$, its image $f(A)$ also has property $P$. Of course, all continuous maps are both compactness- and connectedness-preserving and the natural…

While supporting the execution of business processes, information systems record event logs. Conformance checking relies on these logs to analyze whether the recorded behavior of a process conforms to the behavior of a normative…

A concentration property of the functional ${-}\log f(X)$ is demonstrated, when a random vector X has a log-concave density f on $\mathbb{R}^n$. This concentration property implies in particular an extension of the Shannon-McMillan-Breiman…

Convolutions of independent random variables often arise in a natural way in many applied problems. In this article, we compare convolutions of two sets of gamma (negative binomial) random variables in the convolution order and the usual…

This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which is a recent research field showing significant momentum during the past two decades. For…

We show that Stieltjes moment sequences are infinitely log-convex, which parallels a famous result that (finite) P\'olya frequency sequences are infinitely log-concave. We introduce the concept of $q$-Stieltjes moment sequences of…

In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence…