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We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore,…
This paper provides closed-form formulas for a multidimensional two-sided matching problem with transferable utility and heterogeneity in tastes. When the matching surplus is quadratic, the marginal distributions of the characteristics are…
Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…
This letter presents a fast distributed algorithm for aggregating a large number of households with mixed-integer variables and intricate couplings between devices. The proposed fast distributed gradient algorithm is applied to the double…
Infinite mixture models are commonly used for clustering. One can sample from the posterior of mixture assignments by Monte Carlo methods or find its maximum a posteriori solution by optimization. However, in some problems the posterior is…
A fundamental problem in collaborative sensing lies in providing an accurate prediction of critical events (e.g., hazardous environmental condition, urban abnormalities, economic trends). However, due to the resource constraints,…
These are lecture notes from a course in arithmetic dynamics given in Grenoble in June 2017. The main purpose of this text is to explain how arithmetic equidistribution theory can be used in the dynamics of rational maps on P^1. We first…
We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of…
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
In this article, basing upon probabilistic methods, we discuss periodic homogenization of a class of weakly coupled systems of linear elliptic and parabolic partial differential equations. Under the assumption that the systems have rapidly…
Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization of polynomial jump-diffusions on the unit…
In this paper we study a simple cascading process in a structured heterogeneous population, namely, a network composed of two loosely coupled communities. We demonstrate that under certain conditions the cascading dynamics in such a network…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system…
We study equidistribution of certain subsets of periodic orbits for subshifts of finite type. Our results solely rely on the growth of these subsets. As a consequence, effective equidistribution results are obtained for both hyperbolic…
We consider high-dimensional distribution estimation through autoregressive networks. By combining the concepts of sparsity, mixtures and parameter sharing we obtain a simple model which is fast to train and which achieves state-of-the-art…
In our articles of recent years, the technique of gluing two subharmonic functions turned out to be very useful in studying the distribution of the roots or masses of holomorphic or subharmonic functions, respectively. Here we develop and…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of…
We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected…