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With the advance of experimental techniques such as time-lapse fluorescence microscopy, the availability of single-cell trajectory data has vastly increased, and so has the demand for computational methods suitable for parameter inference…

In this article an anisotropic interaction model avoiding collisions is proposed. Starting point is a general isotropic interacting particle system, as used for swarming or follower-leader dynamics. An anisotropy is induced by rotation of…

There is a growing proportion of people with several disease conditions ("multimorbidity"), placing increasing demands on healthcare systems. One hypothesis is that clusters of diseases may arise from shared underlying disease processes…

This paper considers the classical SIR epidemic model driven by a multidimensional L\'evy jump process. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. Our method differs from…

This paper investigates a special variant of a pursuit-evasion game called lions and contamination. In a graph where all vertices are initially contaminated, a set of lions traverses the graph, clearing the contamination from every vertex…

A new Bayesian state and parameter learning algorithm for multiple target tracking (MTT) models with image observations is proposed. Specifically, a Markov chain Monte Carlo algorithm is designed to sample from the posterior distribution of…

Given a two-dimensional polygonal space, the multi-robot visibility-based pursuit-evasion problem tasks several pursuer robots with the goal of establishing visibility with an arbitrarily fast evader. The best known complete algorithm for…

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…

Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…

Classically, ML models trained with stochastic gradient descent (SGD) are designed to minimize the average loss per example and use a distribution of training examples that remains {\em static} in the course of training. Research in recent…

The purpose of time series analysis via mechanistic models is to reconcile the known or hypothesized structure of a dynamical system with observations collected over time. We develop a framework for constructing nonlinear mechanistic models…

Complex multi-step attacks have caused significant damage to numerous critical infrastructures. To detect such attacks, graph neural network based methods have shown promising results by modeling the system's events as a graph. However,…

We combine a pedestrian dynamics model with a contact tracing method to simulate the initial spreading of a highly infectious airborne disease in a confined environment. We focus on a medium size population (up to 1000 people) with a small…

We consider a nearly-elastic model system with one degree of freedom. In each collision with the "wall", the system can either lose or gain a small amount of energy due to stochastic perturbation. The weak limit of the corresponding slow…

Sparsity is a common issue in many trajectory datasets, including human mobility data. This issue frequently brings more difficulty to relevant learning tasks, such as trajectory imputation and prediction. Nowadays, little existing work…

We consider the partially asymmetric simple exclusion process (PASEP) when its steady-state probability distribution function can be written in terms of a linear superposition of product measures with a finite number of shocks. In this case…

We study the trajectory optimization problem under chance constraints for continuous-time stochastic systems. To address chance constraints imposed on the entire stochastic trajectory, we propose a framework based on the set erosion…

Understanding disease progression at the molecular pathway level usually requires capturing both structural dependencies between pathways and the temporal dynamics of disease evolution. In this work, we solve the former challenge by…