Related papers: Distal and non-Distal Behavior in Pairs
We study the statistical distribution of the closest encounter between observations computed along different trajectories of a mixing dynamical system. At the limit of large trajectories, the distribution is of Gumbel type and depends on…
We study non-orthogonality of symmetric, regular types and show that it preserves generic stability and is an equivalence relation on the set of all generically stable, regular types. We will also prove that some of the nice properties from…
We consider the empirical versions of geometric quantile and halfspace depth, and study their extremal behaviour as a function of the sample size. The objective of this study is to establish connection between the rates of convergence and…
The paper studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. We illustrate the use of differential positivity on compact forward invariant sets for the characterization…
A discrete Gelfand-Tsetlin pattern is a configuration of particles in Z^2. The particles are arranged in a finite number of consecutive rows, numbered from the bottom. There is one particle on the first row, two particles on the second row,…
We study isometric actions on Riemannian symmetric spaces of noncompact type which are induced by reductive algebraic subgroups of the isometry group. We show that for such an action there exists a corresponding isometric action on a dual…
The quantum dynamics of two weakly coupled nonlinear oscillators is analytically and numerically investigated in the context of nonlinear dissipation. The latter facilitates the creation and preservation of non-classical steady states.…
In this paper, we introduce a ${\mathcal L}_2$ type test for testing mutual independence and banded dependence structure for high dimensional data. The test is constructed based on the pairwise distance covariance and it accounts for the…
Defects are inevitable during the manufacturing processes of materials. Presence of these defects and their dynamics significantly influence the responses of materials. A thorough understanding of dislocation dynamics of different types of…
We study the spatio-temporal dynamics of a model of polar active fluid in two dimensions. The system exhibits a transition from an isotropic to a polarized state as a function of density. The uniform polarized state is, however, unstable…
This work deals with the problem of designing observers for the estimation of a single function of the states for discrete-time nonlinear systems. Necessary and sufficient conditions for the existence of lower order functional observers…
We investigate the out-of-equilibrium behavior of a dissipative gas of Rydberg atoms that features a dynamical transition between two stationary states characterized by different excitation densities. We determine the structure and…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally…
In this study, we explore how a non-minimal coupling between dark matter and gravity can affect the behavior of dark matter in galaxy clusters. We have considered the case of a disformal coupling, which leads to a modification of the…
The main goals of this paper are: i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
We investigate Keisler measures in arbitrary theories. Our initial focus is on Borel definability. We show that when working over countable parameter sets in countable theories, Borel definable measures are closed under Morley products and…
Non-reciprocity and geometric frustration enable many-body systems to avoid crystalline order and instead exhibit complex, liquid-like behavior. Here we show that their interplay is richer than the sum of its parts, leading to surprising…
For a dimer with a non-degenerate orbital built from atomic wave functions of Gaussian shape we evaluate all the electron-phonon couplings derived from the one-body and two-body electronic interactions, considering both the adiabatic and…