Related papers: When do trajectories matter? Identifiability analy…
Predicting transportation modes from GPS (Global Positioning System) records is a hot topic in the trajectory mining domain. Each GPS record is called a trajectory point and a trajectory is a sequence of these points. Trajectory mining has…
Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of…
Trajectory prediction is a cornerstone in autonomous driving (AD), playing a critical role in enabling vehicles to navigate safely and efficiently in dynamic environments. To address this task, this paper presents a novel trajectory…
Precise trajectory prediction in complex driving scenarios is essential for autonomous vehicles. In practice, different driving scenarios present varying levels of difficulty for trajectory prediction models. However, most existing research…
The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronise populations of interacting species, stabilise them, and diversify gene pools [1-3].…
We study, on a $d$ dimensional hypercubic lattice, a random walk which is homogeneous except for one site. Instead of visiting this site, the walker hops over it with arbitrary rates. The probability distribution of this walk and the…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…
The problem of unicity and reidentifiability of records in large-scale databases has been studied in different contexts and approaches, with focus on preserving privacy or matching records from different data sources. With an increasing…
Mobile phone data has enabled the timely and fine-grained study human mobility. Call Detail Records, generated at call events, allow building descriptions of mobility at different resolutions and with different spatial, temporal and social…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
Recent advances in sensor and mobile devices have enabled an unprecedented increase in the availability and collection of urban trajectory data, thus increasing the demand for more efficient ways to manage and analyze the data being…
Sharing trajectories is beneficial for many real-world applications, such as managing disease spread through contact tracing and tailoring public services to a population's travel patterns. However, public concern over privacy and data…
Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals can lead to emergent dynamics on the macroscopic scale, for instance a…
We present a model for variations in atmospheric temperature from time scales of one day to one million years based on a stochastic diffusion (random walk) model of the turbulent transport of heat energy vertically in a coupled…
The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination…
This paper comprehensively surveys the development of trajectory clustering. Considering the critical role of trajectory data mining in modern intelligent systems for surveillance security, abnormal behavior detection, crowd behavior…