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The links between optimal control of dynamical systems and neural networks have proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited these links to investigate the stability of…
Quantum critical (QC) phase transitions generally lead to the absence of quasiparticles. The resulting correlated quantum fluid, when thermally excited, displays rich universal dynamics. We establish non-perturbative constraints on the…
The nonequilibrium thermodynamics of interacting quantum many-body systems is investigated within the framework of thermal time-dependent density functional theory using a generalized linear-response formulation for the full quantum work…
Motivated by the widespread use of temporal-difference (TD-) and Q-learning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation (SA) procedures under a mild "ergodic-like" assumption on the…
We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of the entropy functional with prescribed energy correspond…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
Although electrostatics can be incorporated into machine-learned interatomic potentials, existing approaches are computationally very demanding, limiting large-scale, long-time simulations of electrostatics-driven phenomena such as…
Neural circuits exhibit structured connectivity, including an overrepresentation of reciprocal connections between neuron pairs. Despite important advances, a full understanding of how such partial symmetry in connectivity shapes neural…
We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of four-fold coordinated sites connected via variable length one-dimensional chains.…
We present a novel variant of fictitious play dynamics combining classical fictitious play with Q-learning for stochastic games and analyze its convergence properties in two-player zero-sum stochastic games. Our dynamics involves players…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
In "Large Associative Memory Problem in Neurobiology and Machine Learning," Dmitry Krotov and John Hopfield introduced a general technique for the systematic construction of neural ordinary differential equations with non-increasing energy…
Dynamic decision-making under distributional shifts is of fundamental interest in theory and applications of reinforcement learning: The distribution of the environment in which the data is collected can differ from that of the environment…
We consider the cyber-physical security of parallel server systems, which is relevant for a variety of engineering applications such as networking, manufacturing, and transportation. These systems rely on feedback control and may thus be…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
This paper gives sufficient conditions for having complete synchronization of oscillators in connected undirected networks. The considered oscillators are not necessarily identical and the synchronization terms can be nonlinear. An…
An asymmetric generalization of the zero-temperature q-state Potts model on a one dimensional lattice, with and without boundaries, has been studied. The dynamics of the particle number, and specially the large time behavior of the system…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
After having developed a method that measures real time evolution of quantum systems at a finite temperature, we present here the simplest field theory where this scheme can be applied to, namely the 1+1 Ising model. We will compute the…
The equilibrium properties of allocation algorithms for networks with a large number of nodes with finite capacity are investigated. Every node is receiving a flow of requests and when a request arrives at a saturated node, i.e. a node…