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The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular,…
We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orbits of a given dynamical system. We develop theory for it…
The cutoff phenomenon was recently shown to systematically follow from non-negative curvature and the product condition, for all Markov diffusions. The proof crucially relied on a classical \emph{chain rule} satisfied by the carr\'e du…
This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models} for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees…
Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this…
Recurrence determinism, one of the fundamental characteristics of recurrence quantification analysis, measures predictability of a trajectory of a dynamical system. It is tightly connected with the conditional probability that, given a…
Conditional Random Field (CRF) and recurrent neural models have achieved success in structured prediction. More recently, there is a marriage of CRF and recurrent neural models, so that we can gain from both non-linear dense features and…
In this paper we provide examples of topological dynamical systems having either finite or countable scrambled sets. In particular we study conditions for the existence of Li-Yorke, asymptotic and distal pairs in constant--length…
This paper studies the counting problem in random dynamical systems. We noticed that the nature of counting in the random setting is completely different than that of the deterministic systems in the sense that non-exponential growth is…
In this work we introduce the notion of an angular spectrum for a linear discrete time nonautonomous dynamical system. The angular spectrum comprises all accumulation points of longtime averages formed by maximal principal angles between…
We study the contraction properties (up to shift) for admissible Rankine-Hugoniot discontinuities of $n\times n$ systems of conservation laws endowed with a convex entropy. We first generalize the criterion developed in [47], using the…
We provide an explicit method to construct dynamical systems which admit an a-priori prescribed attracting set. As application, we provide a method to construct perturbations of conservative dynamical systems, which admit an a-priori…
Recent research in both the experimental and mathematical communities has focused on biochemical interaction systems that satisfy an "absolute concentration robustness" (ACR) property. The ACR property was first discovered experimentally…
This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible…
Living systems maintain stable internal states despite environmental fluctuations. Absolute concentration robustness (ACR) is a striking homeostatic phenomenon in which the steady-state concentration of a species remains invariant despite…
Recurrent networks are a special class of artificial neural systems that use their internal states to perform computing tasks for machine learning. One of its state-of-the-art developments, i.e. reservoir computing (RC), uses the internal…
We address an inverse problem in non-Archimedean dynamics: given a finite discrete dynamical system (equivalently, a functional graph on $N$ states), construct a continuous $p$-adic dynamical system whose residue-level behavior reproduces…
We analyze the ground state localization properties of an array of identical interacting spinless fermionic chains with quasi-random disorder, using non-perturbative Renormalization Group methods. In the single or two chains case…
We prove a generalized contraction principle with control function in complete partial metric spaces. The contractive type condition used allows the appearance of self distance terms. The obtained result generalizes some previously obtained…
Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…