Related papers: Dynamics of multi-sensitive non-autonomous systems…
Non-locality consists in the existence of non-classical correlations between local measurements. So far, it has been investigated mostly in isolated quantum systems. Here we show that non-local correlations are present, can be detected and…
In this paper we solve two open problems concerning distributional chaos in non-autonomous discrete dynamical systems stated in [4] and [17]. In the first problem it is wondered if the limit function of pointwise convergent non-autonomous…
Let $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ be a sequence of continuous self-maps on a compact metric space $X$. The non-autonomous dynamical system $(X,f_{0,\infty})$ induces the set-valued system $(\mathcal{K}(X), \bar{f}_{0,\infty})$ and…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
In this paper, we mainly study the relation between regularity, independence and mean sensitivity for minimal systems. In the first part, we show that if a minimal system is incontractible, or local Bronstein with an invariant Borel…
We show by a constructive proof that in all aperiodic dynamical system, for all sequences $(a_n)_{n\in\N}\subset\R_+$ such that $a_n\nearrow\infty$ and $\frac{a_n}{n}\to 0$ as $n\to\infty$, there exists a set $A\in\A$ having the property…
Regular variation of a multivariate measure with a Lebesgue density implies the regular variation of its density provided the density satisfies some regularity conditions. Unlike the univariate case, the converse also requires regularity…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
It was recently argued that one-dimensional systems of several strongly interacting fermions of different mass undergo critical transitions between different spatial orderings when the external confinement adiabatically changes its shape.…
We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…
This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…
The paper introduces robust independence tests with non-asymptotically guaranteed significance levels for stochastic linear time-invariant systems, assuming that the observed outputs are synchronous, which means that the systems are driven…
In this paper we investigate aspects of rigidity and flexibility for conformal iterated function systems. For the case in which the systems are not essentially affine we show that two such systems are conformal equivalent if and only if in…
We study the probability of arbitrary density profiles in conserving diffusive fields which are driven by the boundaries. We demonstrate the existence of singularities in the large-deviation functional, the direct analog of the free-energy…
Recent advances in machine learning, particularly deep learning, have enabled autonomous systems to perceive and comprehend objects and their environments in a perceptual subsymbolic manner. These systems can now perform object detection,…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…
We consider continuous-time consensus systems whose interactions satisfy a form or reciprocity that is not instantaneous, but happens over time. We show that these systems have certain desirable properties: They always converge…
This article focuses on the optimization of a complex system which is composed of several subsystems. On the one hand, these subsystems are subject to multiple objectives, local constraints as well as local variables, and they are…
Differential sensitivity techniques originally developed to study the robustness of energy landscape controllers are generalized to the important case of closed quantum systems subject to continuously varying controls. Vanishing sensitivity…
A time-varying nonlinear dynamical system is called a totally positive differential system (TPDS) if its Jacobian admits a special sign pattern: it is tri-diagonal with positive entries on the super- and sub-diagonals. If the vector field…