Related papers: A Note on Operator Semigroups Associated to Chaoti…
Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and associated with the transition to a new time level on the basis of the…
A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce…
We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…
In this article, we present a novel inference framework for estimating the parameters of Continuous-State Branching Processes (CSBPs). We do so by leveraging their subordinator representation. Our method reformulates the estimation problem…
The psychological state of flow has been linked to optimizing human performance. A key condition of flow emergence is a match between the human abilities and complexity of the task. We propose a simple computational model of flow for…
Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator…
We consider a linearized dynamical system modelling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model…
We show how to use operators in the description of {\em exchanging processes} often taking place in (complex) classical systems. In particular, we propose a set of rules giving rise to an {\em hamiltonian} operator for such a system $\Sc$,…
We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and…
We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of characteristic polynomials, density of states, spectral correlation…
We investigate the dynamics of large heterogeneous network dynamical systems composed of nonlocally coupled chaotic maps. We show that the mean-field limit of such systems is governed by a suitably defined Self-Consistent Transfer Operator…
We consider a simple modification of the 1D-Laplacian where non-mixed interface conditions occur at the boundaries of a finite interval. It has recently been shown that Schr\"odinger operators having this form allow a new approach to the…
In this paper we consider the operator mapping problem for in-network stream processing applications. In-network stream processing consists in applying a tree of operators in steady-state to multiple data objects that are continually…
Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification…
The chaotic phenomenon of intermittency is modeled by a simple map of the unit interval, the Farey map. The long term dynamical behaviour of a point under iteration of the map is translated into a spin system via symbolic dynamics. Methods…
The transitional regime of plane channel flow is investigated {above} the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal…
Microscopic flows are almost universally linear, laminar and stationary because Reynolds number, $Re$, is usually very small. That impedes mixing in micro-fluidic devices, which sometimes limits their performance. Here we show that truly…
We consider the non-local operator of variable order as follows $$Lf(x)= \int_{\R^d\setminus\{0\}}\big(f(x+z)-f(x)-\<\nabla f(x),z\> \I_{\{|z|\le 1\}}\big)\frac{n(x,z)}{|z|^{d+\alpha(x)}}\,dz.$$ Under mild conditions on $\alpha(x)$ and…
The dynamic Laplace operator arises from extending problems of isoperimetry from fixed manifolds to manifolds evolved by general nonlinear dynamics. Eigenfunctions of this operator are used to identify and track finite-time coherent sets,…
We propose a mechanism by which the efficiency of mixing in chaotic flows can be enhanced. Our mechanism consists of introducing small changes in the system parameters in regions of phase space where the local Lyapunov exponent falls…