Related papers: On Dynamical System and Topological Transitivity v…
While there is only one natural dimension concept for separable, metric spaces, the theory of dimension in noncommutative topology ramifies into different important concepts. To accommodate this, we introduce the abstract notion of a…
We elaborate and validate a generalization of the renowned transition-path-sampling algorithm for a paradigmatic model of active particles, namely the Run-and-Tumble particles. Notwithstanding the non-equilibrium character of these…
In this paper, we demonstrate the existence of topological states in a new collective dynamics model. This individual-based model (IBM) describes self-propelled rigid bodies moving with constant speed and adjusting their rigid-body attitude…
We present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. We also give an algorithm for…
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
We introduce a new concept in the Absorbing Ideal Theory in commutative rings, that is, the $\omega$-stable groups. We will provide examples and non-examples of these groups, and establish their relationship with H-congruence. Ultimately,…
To link the Auslander point dynamics property with topological transitivity, in this paper we introduce dynamically compact systems as a new concept of a chaotic dynamical system $(X,T)$ given by a compact metric space $X$ and a continuous…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
We introduce a notion of duality solution for a single or a system of transport equations in spaces of probability measures reminiscent of the viscosity solution notion for nonlinear parabolic equations. Our notion of solution by duality…
Network connectedness is indispensable for the normal operation of transmission networks. However, there still remains a lack of efficient constraints that can be directly added to the problem formulation of optimal transmission switching…
Consider a colloidal suspension of rigid particles in a steady Stokes flow. In a celebrated work, Einstein argued that in the regime of dilute particles the system behaves at leading order like a Stokes fluid with some explicit effective…
Many problems in dynamic data driven modeling deals with distributed rather than lumped observations. In this paper, we show that the Monge-Kantorovich optimal transport theory provides a unifying framework to tackle such problems in the…
It is shown that dynamics of the interface between ideal fluid and light viscous fluid is exactly integrable in the approximation of small surface slopes for two-dimensional flow. Stokes flow of viscous fluid provides a relation between…
The concept of impedance, which characterises the current response to a periodical driving, is introduced in the context of stochastic transport. In particular, we calculate the impedance for an exactly solvable model, namely the stochastic…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
This paper is concerned with some stronger forms of transitivity in non-autonomous discrete systems$(f_{ 1,\infty})$ generated by a uniformly convergent sequence of continuous self maps. Firstly, we present two counterexamples to show that…
In this paper, we propose a concept to design, track, and compare application-specific feature definitions expressed as sets of critical points. Our work has been inspired by the observation that in many applications a large variety of…
We study the uniform ergodicity property for non-invertible topological and measure-preserving dynamical systems. It is shown that for topological dynamical systems uniform ergodicity is equivalent to eventually periodicity and that for…