Related papers: The Becker-D\"oring process: pathwise convergence …
Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein.…
The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like…
We present a stochastic dynamics model of coupled evolution for the binary states of nodes and links in a complex network. In the context of opinion formation node states represent two possible opinions and link states a positive or…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
Homogenization of a stochastic nonlinear reaction-diffusion equation with a large non- linear term is considered. Under a general Besicovitch almost periodicity assumption on the coefficients of the equation we prove that the sequence of…
The Keller--Segel PDE is a model for chemotaxis known to exhibit possible finite-time blow-up. Following a seminal work by Tello and Winkler, a logistic damping term is added in this PDE and local well-posedness of mild solutions is proven.…
The asymptotic behavior of a class of stochastic reaction-diffusion-advection equations in the plane is studied. We show that as the divergence-free advection term becomes larger and larger, the solutions of such equations converge to the…
In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…
We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a non-diffusive…
Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…
We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…
Adaptive control is a classical control method for complex cyber-physical systems, including transportation networks. In this work, we analyze the convergence properties of such methods on exemplar graphs, both theoretically and…
We study the qualitative behavior of a model to represent local regulation in a metabolic network. The model is based on the end-product control structure introduced in [A. Goelzer, F. Bekkal Brikci, I. Martin-Verstraete et al., BMC Syst…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
We construct by using B-spline functions a class of copulas that includes the Bernstein copulas arising in Baker's distributions. The range of correlation of the B-spline copulas is examined, and the Frechet--Hoeffding upper bound is proved…
The molecular evolution in a gene regulatory network is classically modeled by Markov jump processes. However, the direct simulation of such models is extremely time consuming. Indeed, even the simplest Markovian model, such as the…
In this paper I show that, for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state…
We characterize the identified sets of a wide range of stochastic choice models, including random utility, various models of boundedly-rational behavior, and dynamic discrete choice. In each of these settings, we show two distributions over…