Related papers: Beyond Diagonal Noise: A Better Predator-Prey Mode…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
We analyze predator-prey dynamics in one dimension in which a Brownian predator adopts a chasing strategy that consists in stochastically resetting its current position to locations previously visited by a diffusive prey. We study three…
This paper addresses an open inverse problem at the interface of mathematical analysis and spatial ecology: the unique identification of unknown spatial anomalies -- interpreted as zones of habitat degradation -- and their associated…
We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…
Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…
Since its introduction, some sixty years ago, the Montroll-Weiss continuous time random walk has found numerous applications due its ease of use and ability to describe both regular and anomalous diffusion. Yet, despite its broad…
We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…
Failing to account for ecological processes such as dispersal and connectivity when modeling distributions can lead to biased inference about environmental drivers and reduced predictive performance. Spatial dynamic occupancy models are…
Several theoretical frameworks have been proposed to explain observed biodiversity patterns, ranging from the classical niche-based theories, mainly employing a continuous formalism, to neutral theories, based on statistical mechanics of…
Many physical systems characterized by nonlinear multiscale interactions can be effectively modeled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative…
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance…
This work derives sufficient conditions for the permanence and ergodicity of a stochastic predator-prey model with Beddington-DeAngelis functional response. The conditions obtained in fact are very close to the necessary conditions. Both…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…
Previously, we developed a population model incorporating the Allee effect and periodic environmental fluctuations, in which organisms alternate between nomadic and colonial behaviours. This switching strategy is regulated by biological…
In computational system biology, the mesoscopic model of reaction-diffusion kinetics is described by a continuous time, discrete space Markov process. To simulate diffusion stochastically, the jump coefficients are obtained by a…
Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…
In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…
We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as,…