Related papers: Introduction to Queueing Theory and Stochastic Tel…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…
The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis…
In studying randomized search heuristics, a frequent quantity of interest is the first time a (real-valued) stochastic process obtains (or passes) a certain value. The processes under investigation commonly show a bias towards this goal,…
These are lecture notes for a mini-course on stochastic sewing, taught at the University of Edinburgh and Beijing Institute of Technology in Spring/Summer 2025. The aim is to introduce the reader to stochastic sewing techniques and to show…
The present paper proposes a stochastic model of the traffic flow. This model has a discrete set of states and the continuous time. The model is a generalization of the discrete stochastis model that has been considered in a previous paper…
Traffic prediction plays an essential role in intelligent transportation system. Accurate traffic prediction can assist route planing, guide vehicle dispatching, and mitigate traffic congestion. This problem is challenging due to the…
To understand large, connected systems, we cannot only zoom into the details. We also need to see the large-scale features from afar. One way to take a step back and get the whole picture is to model the systems as a network. However, many…
Analysis and prediction of network traffic has applications in wide comprehensive set of areas and has newly attracted significant number of studies. Different kinds of experiments are conducted and summarized to identify various problems…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
We present in this article an algebraic approach to model and simulate road traffic networks. By defining a set of road traffic systems and adequate concatenating operators in that set, we show that large regular road networks can be easily…
Time series modeling and forecasting has fundamental importance to various practical domains. Thus a lot of active research works is going on in this subject during several years. Many important models have been proposed in literature for…
Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the…
We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
Traffic prediction is pivotal for rational transportation supply scheduling and allocation. Existing researches into short-term traffic prediction, however, face challenges in adequately addressing exceptional circumstances and integrating…