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The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…
The use of non parametric hidden Markov models with finite state space is flourishing in practice while few theoretical guarantees are known in this framework. Here, we study asymptotic guarantees for these models in the Bayesian framework.…
The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In finite population, the Moran process may be degenerate in finite time, thus we will study its limiting process in…
The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the…
Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
This work establishes a quenched (trajectory-wise) linear response formula for random intermittent dynamical systems, consisting of Liverani-Saussol-Vaienti maps with varying parameters. This result complements recent annealed (averaged)…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
How biological networks achieve robust control despite relying on imperfect, local information remains an important open question. Here, we identify thermodynamic constraints that can curtail non-equilibrium steady-state responses so…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
Robust data-driven controllers typically rely on datasets from previous experiments, which embed information on the variability of the system parameters across past operational conditions. Complementarily, data collected online can…
We propose a notion of conditioned stochastic stability of invariant measures on repellers: we consider whether quasi-ergodic measures of absorbing Markov processes, generated by random perturbations of the deterministic dynamics and…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…
Robustness is established for the predictor feedback for linear time-invariant systems with respect to possibly time-varying perturbations of the input delay, with a constant nominal delay. Prior results have addressed qualitatively…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
In this paper, we consider N-level quantum angular momentum systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose unawareness of the initial state and physical parameters, entailing the…
We study $N$ run-and-tumble particles (RTPs) in one dimension interacting via a double-well potential $W(r)=-k_0 \, r^2/2+g \, r^4/4$, which is repulsive at short interparticle distance $r$ and attractive at large distance. At large time,…