Related papers: Spatio-Temporal Patterns for a Generalized Innovat…
Recent work has framed decision-making as a sequence modeling problem using generative models such as diffusion models. Although promising, these approaches often overlook latent factors that exhibit evolving dynamics, elements that are…
Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with…
Diffusion models have attracted a lot of attention in recent years. These models view speech generation as a continuous-time process. For efficient training, this process is typically restricted to additive Gaussian noising, which is…
This article is a short exposition of the space-time resonances method. It was introduced by Masmoudi, Shatah, and the author, in order to understand global existence for nonlinear dispersive equations, set in the whole space, and with…
This paper is based on the premise that economic growth is driven by an interplay between innovation and imitation in an economy composed of interacting firms operating in a stochastic environment. A novel approach to modeling imitation is…
Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…
In this study, we introduce a novel method for generating new synthetic samples that are independent and identically distributed (i.i.d.) from high-dimensional real-valued probability distributions, as defined implicitly by a set of Ground…
Axelrod's model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e., individuals become more similar when they interact) and homophily (i.e.,…
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…
Inference of fields defined in space and time from observational data is a core discipline in many scientific areas. This work approaches the problem in a Bayesian framework. The proposed method is based on statistically homogeneous random…
Spatio-temporal hierarchical modeling is an extremely attractive way to model the spread of crime or terrorism data over a given region, especially when the observations are counts and must be modeled discretely. The spatio-temporal…
A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
The advent and proliferation of social media have led to the development of mathematical models describing the evolution of beliefs/opinions in an ecosystem composed of socially interacting users. The goal is to gain insights into…
We propose a latent self-exciting point process model that describes geographically distributed interactions between pairs of entities. In contrast to most existing approaches that assume fully observable interactions, here we consider a…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
Diffusion models have emerged as powerful generative models in the text-to-image domain. This paper studies their application as observation-to-action models for imitating human behaviour in sequential environments. Human behaviour is…
Diffusion of innovation can be interpreted as a social spreading phenomena governed by the impact of media and social interactions. Although these mechanisms have been identified by quantitative theories, their role and relative importance…
The surprisingly mercurial Covid-19 pandemic has highlighted the need to not only accelerate research on infectious disease, but to also study them using novel techniques and perspectives. A major contributor to the difficulty of containing…
Natural disasters may have considerable impact on society as well as on (re)insurance industry. Max-stable processes are ideally suited for the modeling of the spatial extent of such extreme events, but it is often assumed that there is no…