Related papers: Approximate conjugacy and full groups of Cantor mi…
Let $G$ be a second-countable, locally compact group. In this article we study amenable $G$-actions on Kirchberg algebras that admit an approximately central embedding of a canonical quasi-free action on the Cuntz algebra…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
In this work we study variational properties of approximate solutions of scalar conservation laws. Solutions of this type are described by a kinetic equation which is similar to the kinetic representation of admissible weak solutions due to…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
We develop a generalized hyperdynamics method, which is able to simulate slow dynamics in atomistic general (both energy and entropy-dominated) systems. We show that a few functionals of the pair correlation function, involving two-body…
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version of…
In a recent breakthrough, Gilmer proved the union closed conjecture up to a constant factor. Using Gilmer's method and additional ideas, Chase and Lovett proved an optimal result for almost union-closed set systems. Here that result is…
This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov-Poisson…
The goal of the paper is to lay the foundation for the qualitative analogue of the classical, quantitative sparse graph limit theory. In the first part of the paper we introduce the qualitative analogues of the Benjamini-Schramm and…
Let $G$ be a locally compact second countable group equipped with an admissible non-degenerate Borel probability measure $\mu$. We generalize the notion of $\mu$-stationary systems to $\mu$-stationary $G$-factor maps $\pi: (X,\nu)\to…
We present a new approach to derive the connectivity properties of pairwise interacting n-body systems in thermal equilibrium. We formulate an integral equation that relates the pair connectedness to the distribution of nearest neighbors.…
In this paper, it is shown that if a dynamical system is null and distal, then it is equicontinuous. It turns out that a null system with closed proximal relation is mean equicontinuous. As a direct application, it follows that a null…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
In this paper we study speedups of dynamical systems in the topological category. Specifically, we characterize when one minimal homeomorphism on a Cantor space is the speedup of another. We go on to provide a characterization for strong…
We introduce the dynamic comparison property for minimal dynamical systems which has applications to the study of crossed product C*-algebras. We demonstrate that this property holds for a large class of systems which includes all examples…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
Approximate simulation, an extension of simulation relations from formal methods to continuous systems, is a powerful tool for hierarchical control of complex systems. Finding an approximate simulation relation between the full "concrete"…
In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix…
Starting form a microscopic system-environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the…
We consider several weaker versions of the notion of conjugacy and orbit equivalence of measure preserving actions of countable groups on probability spaces, involving equivalence of the ultrapower actions and asymptotic intertwining…