Related papers: Analysis of a splitting-differentiation population…

This paper is concerned with two frequency-dependent SIS epidemic reaction-diffusion models in heterogeneous environment, with a cross-diffusion term modeling the effect that susceptible individuals tend to move away from higher…

State estimation remains a fundamental challenge across numerous domains, from autonomous driving, aircraft tracking to quantum system control. Although Bayesian filtering has been the cornerstone solution, its classical model-based…

While originally designed for image generation, diffusion models have recently shown to provide excellent pretrained feature representations for semantic segmentation. Intrigued by this result, we set out to explore how well…

We study optimal control problems for interacting branching diffusion processes, a class of measure-valued dynamics capturing both spatial motion and branching mechanisms. From the perspective of the dynamic programming principle, we…

The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…

In segmentation problems, inference on change-point position and model selection are two difficult issues due to the discrete nature of change-points. In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable formulae…

We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the…

This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting…

Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a…

In a recent work, Dantas and Stilck studied a model that generalizes the contact process model with diffusion. Our approach, based on the supercritical expansion, showed that for a weak diffusion regime the crossover exponent between the…

Diffusion processes arise in many fields, and so simulating the path of a diffusion is an important problem. It is usually necessary to make some sort of approximation via model-discretization, but a recently introduced class of algorithms,…

Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in predictive learning. However, unlike typical generation tasks that encourage sample…

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…

Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…

We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…

We introduce a novel discretization technique for both elliptic and parabolic fractional diffusion problems based on double exponential quadrature formulas and the Riesz-Dunford functional calculus. Compared to related schemes, the new…

The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…

We study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. We show first exponential stabilization and then finite-time stabilization in arbitrary small-time of the linearized system around uniform…

Modelling diffusion processes on dynamic contact networks is an important research area for epidemiology, marketing, cybersecurity, and ecology. However, current diffusion models cannot capture transmissions occurring for indirect…