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In this paper, we study ergodic optimization of continuous functions for flows by concentrating on the entropy spectrum of their maximizing measures. Precisely, over a wide family of flows with non-uniformly hyperbolic structure, we obtain…
In this paper we introduce a contact process in an evolving random environment (CPERE) on a connected and transitive graph with bounded degree, where we assume that this environment is described through an ergodic spin systems with finite…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…
We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding technique being a combination of time delay and spatial embedding.…
The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP.…
This paper discusses a more general contractive condition for a class of extended cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same…
Entanglement constitutes one of the key concepts in quantum mechanics and serves as an indispensable tool in the understanding of quantum many-body systems. In this work, we perform extensive numerical investigations of extensive…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…
The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen-Margulis-Sullivan measure. Some immediate applications include an asymptotic…
A model-free measure of coupling between dynamical variables is built from time series embedding principle. The approach described does not require a mathematical form for the dynamics to be assumed. The approach also does not require…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
In this note we re-visit the fundamental question of the strong law of large numbers and central limit theorem for processes in continuous time with conditional stationary and independent increments. For convenience we refer to them as…
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field…
It is known that sectional-hyperbolic attracting sets, for a $C^2$ flow on a finite dimensional compact manifold, have at most finitely many ergodic physical invariant probability measures. We prove an upper bound for the number of distinct…
Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…
We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…
We introduce a systematic expansion tailored to systems with strong local interactions and capable of computing response functions, including finite DC transport, analytically. The expansion is controlled by a small parameter $s^2$ that…