Related papers: Capture of the Lamb: Diffusing Predators Seeking a…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…
Linguistic representation learning in deep neural language models (LMs) has been studied for decades, for both practical and theoretical reasons. However, finding representations in LMs remains an unsolved problem, in part due to a dilemma…
This work studies the problem of learning under both large datasets and large-dimensional feature space scenarios. The feature information is assumed to be spread across agents in a network, where each agent observes some of the features.…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
We calculate the survival probability of an immobile target surrounded by a sea of uncorrelated diffusive or subdiffusive evanescent traps, i.e., traps that disappear in the course of their motion. Our calculation is based on a fractional…
We consider the model of spatially distributed population consisting of two species with "\textsl{predator\,--\,prey}" interaction; each of the species occupies two stations. Transfer of individuals between the stations (migration) is not…
Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We address the question of an averaging principle for a general class of multi-scale hybrid predator-prey models. We consider prey-predator models where the kinetic of the prey population, described by a differential equation, is faster…
We describe here a new concept of one group chasing another, called "group chase and escape", by presenting a simple model. We will show that even a simple model can demonstrate rather rich and complex behavior. In particular, there are…
We study the dynamics of a single diffusing particle (a "man") with diffusivity $D_M$ that is attacked by another diffusing particle (a "mosquito") with fixed diffusivity $D_m$. Each time the mosquito meets and bites the man, the…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
This short paper concerns a diffusive logistic equation with the heterogeneous environment and a free boundary, which is formulated to study the spread of an invasive species, where the free boundary represents the expanding front. A…
This article adopts game theory to build a model for explaining the predation behavior of animals.We assume that both the prey and the preydator have two stratigies in this game,the active one and the passive one.By calculating the outcome…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
This paper studies Distributionally Robust Optimization (DRO), a fundamental framework for enhancing the robustness and generalization of statistical learning and optimization. An effective ambiguity set for DRO must involve distributions…
The ways in which an innovation (e.g., new behaviour, idea, technology, product) diffuses among people can determine its success or failure. In this paper, we address the problem of diffusion of innovations over multiplex social networks…