We discuss a new notion of distance on the space of finite and nonnegative measures on Ω ⊂ Rd, which we call Hellinger–Kantorovich distance. It can be seen as an infconvolution of the well-known Kantorovich–Wasserstein distance and the HellingerKakutani distance. The new distance is based on a dynamical formulation given by an Onsager operator that is the sum of a Wasserstein diffusion part and...

By considering the Langevin dynamics of the SK spin glass with a spherical constraint we calculate the asymptotic distance between two real replicas that evolve with the same thermal noise from different initial conditions. Despite the simplicity of the model its dynamics is known to be non trivial and presents aging phenomena. We found that the asympotic distance between two replicas is maxima...

introduction: in this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. epilepsy is considered as a dynamical change in nonlinear and complex brain system. the ability of the proposed measure for characterizing the normal and epileptic eeg signals when the signal is short or is...

in this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. it is shown that it generates the kolmogorov entropy as a special case. if $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

‎in this text we prove that in generalized shift dynamical system $(x^gamma,sigma_varphi)$‎ ‎for finite discrete $x$ with at least two elements‎, ‎infinite countable set $gamma$ and‎ ‎arbitrary map $varphi:gammatogamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(x^gamma,sigma_varphi)$ is‎ li-yorke chaotic;‎ - the dynamical system $(x^gamma,sigma_varphi)$ has‎ an scr...

Dynamical mass measurements to date have allowed determinations of the mass M and the distance D of a number of nearby supermassive black holes. In the case of Sgr A*, these measurements are limited by a strong correlation between the mass and distance scaling roughly as M ∼ D2. Future very long baseline interferometric (VLBI) observations will image a bright and narrow ring surrounding the sha...

The stability radius of an n×n matrix A (or distance to instability) is a well-known measure of robustness of stability of the linear stable dynamical system ẋ = Ax. Such a distance is commonly measured either in the 2-norm or in the Frobenius norm. Even if the matrix A is real, the distance to instability is most often considered with respect to complex valued matrices (in such case the two no...

The Paulsen problem is a basic open problem in operator theory: Given vectors u1, . . . , un ∈ R d that are ǫ-nearly satisfying the Parseval’s condition and the equal norm condition, is it close to a set of vectors v1, . . . , vn ∈ R that exactly satisfy the Parseval’s condition and the equal norm condition? Given u1, . . . , un, the squared distance (to the set of exact solutions) is defined a...

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

We study the ability of discrete dynamical systems to transform/generate randomness in cellular spaces. Thus, we endow the space of bi-infinite sequences by a metric inspired by information distance (defined in the context of Kolmogorov complexity or algorithmic information theory). We prove structural properties of this space (non-separability, completeness, perfectness and infinite topologica...