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We perform an asymptotic analysis of general particle systems arising in collective behavior in the limit of large self-propulsion and friction forces. These asymptotics impose a fixed speed in the limit, and thus a reduction of the…
This paper concerns discrete-time infinite-horizon stochastic control systems with Borel state and action spaces and universally measurable policies. We study optimization problems on strategic measures induced by the policies in these…
The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the…
Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. This notion is new and…
For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of dissipative measure-valued solution and show that such a solution agrees with a classical solution with the same…
In the first part of the paper, we consider a discrete-time stochastic control system. We show that, under certain conditions, the set of random occupational measures generated by the state-control trajectories of the system as well as the…
We study the long-term behavior of the distribution of the solution process to the non-autonomous McKean-Vlasov stochastic delay lattice system defined on the integer set $\mathbb{Z}$. Specifically, we first establish the well-posedness of…
We introduce the Discrete Inverse Continuity Equation (DICE) method, a generative modeling approach that learns the evolution of a stochastic process from given sample populations at a finite number of time points. Models learned with DICE…
In this paper we study a class of \emph{self-consistent dynamical systems}, self-consistent in the sense that the discrete time dynamics is different in each step depending on current statistics. The general framework admits popular…
Competition is the main driver of population dynamics, which shapes the genetic composition of populations and the assembly of ecological communities. Neutral models assume that all the individuals are equivalent and that the dynamics is…
We analyse a non-local parabolic integro-differential equation modelling the evolutionary dynamics of a phenotypically-structured population in a changing environment. Such models arise in a variety of contexts from climate change to…
We consider the problem of simultaneous variable selection and constant coefficient identification in high-dimensional varying coefficient models based on B-spline basis expansion. Both objectives can be considered as some type of model…
In recent years, kinetic equations have been used to model many social phenomena. A key feature of these models is that transition rate kernels involve Dirac delta functions, which capture sudden, discontinuous state changes. Here, we study…
Theoretical analyses of evolution strategies are indispensable for gaining a deep understanding of their inner workings. For constrained problems, rather simple problems are of interest in the current research. This work presents a…
Analysing learning in Multi-Agent Reinforcement Learning (MARL) environments is challenging, in particular with respect to \textit{individual} decision-making. Practitioners frequently struggle to compare training runs due to the inherent…
In this article we study some statistical aspects of surface diffeomorphisms. We first show that for a $C^1$ generic diffeomorphism, a Dirac invariant measure whose \emph{statistical basin of attraction} is dense in some open set and has…
Two mechanisms have recently been proposed that can significantly speed up finding distant improving solutions via mutation, namely using a random mutation rate drawn from a heavy-tailed distribution ("fast mutation", Doerr et al. (2017))…
Conventional wisdom holds that large-batch training is fundamentally incompatible with Reinforcement Learning (RL) - beyond a modest threshold, increasing batch sizes typically yields diminishing returns or performance degradation due to…
Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…
In this paper, we consider a resource-consumer model taking into account a mutation effect between species (with constant mutation rate). The corresponding mutation operator is a discretization of the Laplacian in such a way that the…