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Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
Many human social phenomena, such as cooperation, the growth of settlements, traffic dynamics and pedestrian movement, appear to be accessible to mathematical descriptions that invoke self-organization. Here we develop a model of pedestrian…
In dealing with thermal transport in composite systems, high contrast materials pose a special problem for numerical simulation: the time scale or step size in the high conductivity material must be much smaller than in the low conductivity…
In this work, we employ autoregressive models developed in financial engineering for modeling of forest dynamics. Autoregressive models have some theoretical advantage over currently employed forest modeling approaches such as Markov chains…
The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement…
A correlated Gaussian random walk(CGRW) model is proposed as a simple model of animal dispersal. The general features of CGRW is described. We will discuss how from this single model a number of different kinds of correlated random walk can…
The elephant random walk (ERW) is a microscopic, one-dimensional, discrete-time, non-Markovian random walk, which can lead to anomalous diffusion due to memory effects. In this study, I propose a multi-dimensional generalization in which…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
This paper studies the problem of detection and tracking of general objects with long-term dynamics, observed by a mobile robot moving in a large environment. A key problem is that due to the environment scale, it can only observe a subset…
Advances in satellite-based data collection techniques have served as a catalyst for new statistical methodology to analyze these data. In wildlife ecological studies, satellite-based data and methodology have provided a wealth of…
In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it…
Animals within groups need to coordinate their reactions to perceived environmental features and to each other in order to safely move from one point to another. This paper extends our previously published work on the flight patterns of…
Random walks and related spatial stochastic models have been used in a range of application areas including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing, and oncology. Classical random walk…
Modeling how human moves in the space is useful for policy-making in transportation, public safety, and public health. Human movements can be viewed as a dynamic process that human transits between states (\eg, locations) over time. In the…
We propose a general statistical mechanics framework for the collective motion of animals. The framework considers the principle of maximum entropy, the interaction, boundary, and desire effects, as well as the time-delay effect. These…
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to…
We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks in the quarter plane are characterized by the fact that the one-step transition probabilities…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
Active walker models have recently proved their great value for describing the formation of clusters, periodic patterns, and spiral waves as well as the development of rivers, dielectric breakdown patterns, and many other structures. It is…