Related papers: Multiplicative combinatorial properties of return …

This dissertation investigates the geometric combinatorics of convex polytopes and connections to the behavior of the simplex method for linear programming. We focus our attention on transportation polytopes, which are sets of all tables of…

Let $\Delta=\Delta_1\times\ldots\times \Delta_d\subseteq\mathbb{R}^n$, where $\mathbb{R}^n=\mathbb{R}^{n_1}\times\cdots\times\mathbb{R}^{n_d}$ with each $\Delta_i\subseteq\mathbb{R}^{n_i}$ a non-degenerate simplex of $n_i$ points. We prove…

Given a family of subspaces we investigate existence, quantity and quality of common complements in Hilbert spaces and Banach spaces. In particular we are interested in complements for countable families of closed subspaces of finite…

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…

We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…

We present a simple physical model that recapitulates several features of biological evolution, while being based only on thermally-driven attachment and detachment of elementary building blocks. Through its dynamics, this model samples a…

Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When the dynamical system is subjected to small parameter…

This paper discusses the thermodynamic properties for certain time-dependent dynamical systems. In particular, we are interested in time-dependent dynamical systems with the specification property. We show that each time-dependent dynamical…

The famous Michael selection theorem deals with the characterisation of paracompact spaces by continuous selections of lower semi-continuous mappings in Banach spaces. In this paper, we will discuss several equivalent forms of this theorem,…

Let $(X, T)$ be a weakly mixing minimal system, $p_1, \cdots, p_d$ be integer-valued generalized polynomials and $(p_1,p_2,\cdots,p_d)$ be non-degenerate. Then there exists a residual subset $X_0$ of $X$ such that for all $x\in X_0$ $$\{…

We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.

We investigate differences between upper and lower porosity. In finite dimensional Banach spaces every upper porous set is directionally upper porous. We show the situation is very different for lower porous sets; there exists a lower…

We consider random dynamical systems on manifolds modeled by a skew product which have certain geometric properties and whose measures satisfy quenched decay of correlations at a sufficient rate. We prove that the limiting distribution for…

This article studies regularity properties of multiplicative stochastic processes on infinite-dimensional Lie groups. We investigate conditions under which these processes admit c\`adl\`ag modifications and derive bounds on their local…

We study the posterior contraction behavior of the latent population structure that arises in admixture models as the amount of data increases. We adopt the geometric view of admixture models - alternatively known as topic models - as a…

Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…

This paper's major purpose is to continue the work of Zhu and Ma[1]. To begin, the $\mathbf{g}$-almost product property, more general irregular and regular sets, and some new notions of the Banach upper density recurrent points and…

We prove the existence of Rado sets in the Banach space of continuous functions on [0,1]. A countable dense set S is Rado if with probability 1, the infinite geometric random graph on S, formed by probabilistically making adjacent elements…

In this paper, we show that the subadditive dual of a feasible conic mixed-integer program (MIP) is a strong dual whenever it is feasible. Moreover, we show that this dual feasibility condition is equivalent to feasibility of the conic dual…

In our paper we study multiplicative properties of difference sets $A-A$ for large sets $A \subseteq \mathbb{Z}/q\mathbb{Z}$ in the case of composite $q$. We obtain a quantitative version of a result of A. Fish about the structure of the…