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A Vehicular Ad-hoc Network (VANET) is a collection of wireless vehicle nodes forming a temporary network without using any centralized Road Side Unit (RSU). VANET protocols have to face high challenges due to dynamically changing topologies…

We study a fundamental instability mechanism in nonlinear, nonlocal dynamical systems arising from the interaction of long-range memory and stochastic regime switching. The dynamics are governed by network-coupled, operator-valued Volterra…

Mobile Ad Hoc Network (MANET) is a collection of two or more devices or nodes or terminals with wireless communications and networking capability that communicate with each other without the aid of any centralized administrator also the…

This paper introduces a framework for capturing stochasticity of choice probabilities in neural networks, derived from and fully consistent with the Random Utility Maximization (RUM) theory, referred to as RUM-NN. Neural network models show…

We consider a Mobile Ad-hoc NETwork (MANET) formed by n agents that move at speed V according to the Manhattan Random-Way Point model over a square region of side length L. The resulting stationary (agent) spatial probability distribution…

Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…

We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the…

Predicting surrounding vehicle behaviors are critical to autonomous vehicles when negotiating in multi-vehicle interaction scenarios. Most existing approaches require tedious training process with large amounts of data and may fail to…

Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…

Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…

Autonomous vehicles use a variety of sensors and machine-learned models to predict the behavior of surrounding road users. Most of the machine-learned models in the literature focus on quantitative error metrics like the root mean square…

Momentum methods have been shown to accelerate the convergence of the standard gradient descent algorithm in practice and theory. In particular, the minibatch-based gradient descent methods with momentum (MGDM) are widely used to solve…

We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as…

Predicting future behavior of the surrounding vehicles is crucial for self-driving platforms to safely navigate through other traffic. This is critical when making decisions like crossing an unsignalized intersection. We address the problem…

There is an increase in interest to model driving maneuver patterns via the automatic unsupervised clustering of naturalistic sequential kinematic driving data. The patterns learned are often used in transportation research areas such as…

Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model…

A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and…

We consider stochastic mean field games for which the state space is a network. In the ergodic case, they are described by a system coupling a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation, whose unknowns are the invariant…

This paper describes a general framework called Hybrid Dynamic Mixed Networks (HDMNs) which are Hybrid Dynamic Bayesian Networks that allow representation of discrete deterministic information in the form of constraints. We propose…

Ergodic properties and asymptotic stationarity are investigated in this paper for the pseudo-covariance matrix (PCM) of a recursive state estimator which is robust against parametric uncertainties and is based on plant output measurements…