Kinetic Models of Collective Phenomena and Data Science

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 15 November 2024 | Viewed by 694

Special Issue Editors


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Guest Editor
Department of Mathematics, University of Campania “Luigi Vanvitelli”, 81100 Caserta, Italy
Interests: analysis of the mathematical structure of the kinetic theory and its applications to many kinds of many-particle systems, with particular reference to psychological, social and economic systems, and to the problem of diffusion of infectious diseases

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Guest Editor
Department of Mathematics, Univesity of Naples “Federico II”, 80131 Naples, Italy
Interests: mathematical physics; kinetic theory; complex systems; PDEs; integro-differential equations; probability theory
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Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to offer to scientists who work in the field of mathematical physical models of natural phenomena, about many-particle systems. We are particularly concerned with successful schemes based on the recent extensions of Boltzmann’s Kinetic Theory and its different types of applications, ranging from biology to psychology, from social sciences to the economy, and from the theory of evolution to the mechanical behaviors of swarms and crowds, and, very recently, the interactions between the random variables describing correlated experiments, thus entering the domain of data science. We address expert scientists and young researchers interested in the study of collective phenomena.

We are pleased to invite you to contribute a paper to this Special Issue of Mathematics on Kinetic Models of Collective Phenomena and Data Science, aiming to offer help with mathematical formulations of their problems and information about the current research on many-particle systems, with a particular concern for models and applications related to biology, the social sciences, and data management, including suitable reinterpretations and formal modifications of kinetic models.

In this Special Issue, original research articles and reviews are welcome. The research areas may include (but are not limited to) the following:

  • Kinetic models for biology;
  • Kinetic models for social sciences and economics;
  • The role of random variables and stochastic processes in the formulation of kinetic models;
  • The possible formulation of kinetic models for systems of random variables.

We look forward to receiving your contributions.

Prof. Dr. Bruno Carbonaro
Dr. Marco Menale
Guest Editors

Manuscript Submission Information

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Keywords

  • mathematical models
  • stochastic models
  • kinetic theory
  • probability
  • random variables

Published Papers (1 paper)

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Research

14 pages, 297 KiB  
Article
Markov Chains and Kinetic Theory: A Possible Application to Socio-Economic Problems
by Bruno Carbonaro and Marco Menale
Mathematics 2024, 12(10), 1571; https://doi.org/10.3390/math12101571 - 17 May 2024
Viewed by 434
Abstract
A very important class of models widely used nowadays to describe and predict, at least in stochastic terms, the behavior of many-particle systems (where the word “particle” is not meant in the purely mechanical sense: particles can be cells of a living tissue, [...] Read more.
A very important class of models widely used nowadays to describe and predict, at least in stochastic terms, the behavior of many-particle systems (where the word “particle” is not meant in the purely mechanical sense: particles can be cells of a living tissue, or cars in a traffic flow, or even members of an animal or human population) is the Kinetic Theory for Active Particles, i.e., a scheme of possible generalizations and re-interpretations of the Boltzmann equation. Now, though in the literature on the subject this point is systematically disregarded, this scheme is based on Markov Chains, which are special stochastic processes with important properties they share with many natural processes. This circumstance is here carefully discussed not only to suggest the different ways in which Markov Chains can intervene in equations describing the stochastic behavior of any many-particle system, but also, as a preliminary methodological step, to point out the way in which the notion of a Markov Chain can be suitably generalized to this aim. As a final result of the discussion, we find how to develop new very plausible and likely ways to take into account possible effects of the external world on a non-isolated many-particle system, with particular attention paid to socio-economic problems. Full article
(This article belongs to the Special Issue Kinetic Models of Collective Phenomena and Data Science)
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