Special Issue "Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 29 February 2020.

Special Issue Editor

Guest Editor
Prof. Nicola Bellomo Website E-Mail
Politecnico of Torino, Torino, Italy

Special Issue Information

Dear Colleagues,

This Special Issue aims at presenting scientific articles devoted to research perspectives focusing on modeling, qualitative analysis, and simulations of large systems of interacting living entities by kinetic theory and swarming approaches.

The key concept pushed forward in the issue is a multiscale vision and interpretation by mathematical models of living systems from the micro-scale to organized networks. The overall content is multidisciplinary, as it aims at focusing on vehicular traffic and crowd dynamics, where human behaviors are taken into account, as well as behavioral economy, biology, and animal swarms. More in general, this issue looks at the interactions between the so-called hard sciences and the new science of living systems.

New concepts of symmetry and asymmetry are planned to be presented, looking ahead to a possible future of the science of living systems by advanced tools of mathematics, physics, and computer science.

Prof. Nicola Bellomo
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (6 papers)

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Research

Open AccessArticle
Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions
Symmetry 2019, 11(9), 1093; https://doi.org/10.3390/sym11091093 - 02 Sep 2019
Abstract
This paper is concerned with the modeling and mathematical analysis of vehicular traffic phenomena. We adopt a kinetic theory point of view, under which the microscopic state of each vehicle is described by: (i) position, (ii) velocity and also (iii) activity, an additional [...] Read more.
This paper is concerned with the modeling and mathematical analysis of vehicular traffic phenomena. We adopt a kinetic theory point of view, under which the microscopic state of each vehicle is described by: (i) position, (ii) velocity and also (iii) activity, an additional varible that we use to describe the quality of the driver-vehicle micro-system. We use methods coming from game theory to describe interactions at the microscopic scale, thus constructing new models within the framework of the Kinetic Theory of Active Particles; the resulting models incorporate some of the symmetries that are commonly found in the mathematical models of the kinetic theory of gases. Short-range interactions and mean field interactions are introduced and modeled to depict velocity changes related to passing phenomena. Our main goal is twofold: (i) to use continuum-velocity variables and (ii) to introduce a non-local acceleration term modeling mean field interactions, related to, for example, the presence of tollgates or traffic highlights. Full article
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Open AccessArticle
Forecasting Efficient Risk/Return Frontier for Equity Risk with a KTAP Approach—A Case Study in Milan Stock Exchange
Symmetry 2019, 11(8), 1055; https://doi.org/10.3390/sym11081055 - 16 Aug 2019
Abstract
We introduce and discuss a dynamics of interaction of risky assets in a portfolio by resorting to methods of statistical mechanics developed to model the evolution of systems whose microscopic state may be augmented by variables which are not mechanical. Statistical methods are [...] Read more.
We introduce and discuss a dynamics of interaction of risky assets in a portfolio by resorting to methods of statistical mechanics developed to model the evolution of systems whose microscopic state may be augmented by variables which are not mechanical. Statistical methods are applied in the present paper in order to forecast the dynamics of risk/return efficient frontier for equity risk. Specifically, we adopt the methodologies of the kinetic theory for active particles (KTAP) with stochastic game-type interactions and apply the proposed model to a case study analyzing a subset of stocks traded in Milan Stock Exchange. In particular, we evaluate the efficient risk/return frontier within the mean/variance portfolio optimization theory for 13 principal components of the Milan Stock Exchange and apply the proposed kinetic model to forecast its short-term evolution (within one year). The model has the aim to pave the way to many different research perspectives and applications discussed eventually in the paper. In particular, the case of efficient frontier obtained by minimizing the Conditional Value-at-Risk (CVaR) is introduced and a preliminary result is proposed. Full article
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Open AccessArticle
Diffusive and Anti-Diffusive Behavior for Kinetic Models of Opinion Dynamics
Symmetry 2019, 11(8), 1024; https://doi.org/10.3390/sym11081024 - 08 Aug 2019
Abstract
In the present paper, we study a class of nonlinear integro-differential equations of a kinetic type describing the dynamics of opinion for two types of societies: conformist ( σ = 1 ) and anti-conformist ( σ = 1 ). The essential role [...] Read more.
In the present paper, we study a class of nonlinear integro-differential equations of a kinetic type describing the dynamics of opinion for two types of societies: conformist ( σ = 1 ) and anti-conformist ( σ = 1 ). The essential role is played by the symmetric nature of interactions. The class may be related to the mesoscopic scale of description. This means that we are going to statistically describe an individual state of an agent of the system. We show that the corresponding equations result at the macroscopic scale in two different pictures: anti-diffusive ( σ = 1 ) and diffusive ( σ = 1 ). We provide a rigorous result on the convergence. The result captures the macroscopic behavior resulting from the mesoscopic one. In numerical examples, we observe both unipolar and bipolar behavior known in political sciences. Full article
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Open AccessArticle
Numerical Simulation of a Multiscale Cell Motility Model Based on the Kinetic Theory of Active Particles
Symmetry 2019, 11(8), 1003; https://doi.org/10.3390/sym11081003 - 03 Aug 2019
Abstract
In this work, we deal with a kinetic model of cell movement that takes into consideration the structure of the extracellular matrix, considering cell membrane reactions, haptotaxis, and chemotaxis, which plays a key role in a number of biological processes such as wound [...] Read more.
In this work, we deal with a kinetic model of cell movement that takes into consideration the structure of the extracellular matrix, considering cell membrane reactions, haptotaxis, and chemotaxis, which plays a key role in a number of biological processes such as wound healing and tumor cell invasion. The modeling is performed at a microscopic scale, and then, a scaling limit is performed to derive the macroscopic model. We run some selected numerical experiments aimed at understanding cell movement and adhesion under certain documented situations, and we measure the alignment of the cells and compare it with the pathways determined by the extracellular matrix by introducing new alignment operators. Full article
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Open AccessArticle
On the Complex Interaction between Collective Learning and Social Dynamics
Symmetry 2019, 11(8), 967; https://doi.org/10.3390/sym11080967 - 01 Aug 2019
Abstract
This paper is motivated by the perspective ideas proposed in our previous studies, where some challenging problems, for instance qualitative analysis of the solution to nonlinear problems and micro-macro asymptotic analysis, where posed. Our work focuses on the study of the interactions between [...] Read more.
This paper is motivated by the perspective ideas proposed in our previous studies, where some challenging problems, for instance qualitative analysis of the solution to nonlinear problems and micro-macro asymptotic analysis, where posed. Our work focuses on the study of the interactions between learning dynamics and other types of dynamics which can be modeled by kinetic theory methods. The contents are presented in three parts. First, a general description of different theories of learning dynamics within the framework of cognitive sciences is critically analyzed with the aim of capturing the main features of the system towards modeling. Subsequently, the class of systems which are the object of the modeling approach is defined by showing how the previous structure can be developed, thanks to new conceptual ideas, including the concept of symmetric and asymmetric learning, towards modeling. Finally, some applications are selected to show how the approach can be methodologically applied. Full article
Open AccessArticle
A Critical Analysis of Behavioural Crowd Dynamics—From a Modelling Strategy to Kinetic Theory Methods
Symmetry 2019, 11(7), 851; https://doi.org/10.3390/sym11070851 - 01 Jul 2019
Abstract
This paper proposes a critical analysis of the literature addressed to modelling and simulations of human crowds with the aim of selecting the most appropriate scale out of the microscopic (individual based), mesoscopic (kinetic), and macroscopic (hydrodynamical) approaches. The selection is made focusing [...] Read more.
This paper proposes a critical analysis of the literature addressed to modelling and simulations of human crowds with the aim of selecting the most appropriate scale out of the microscopic (individual based), mesoscopic (kinetic), and macroscopic (hydrodynamical) approaches. The selection is made focusing on possible applications of the model. In particular, model validation and safety problems, where validation consists of studying the ability of models to depict empirical data and observed emerging behaviors. The contents of the paper look forward to computational applications related to the flow crowds on the Jamarat bridge. Full article

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Numerical simulation of a multiscale cell motility model based on the kinetic theory of active particles
Authors: D. Knopoff1, J. Nieto2, L. Urrutia2
Affiliations: 1. Universidad Nacional de Cordoba and CIEM (CONICET)
2. Facultad de Ciencias - Universidad de Granada
Abstract: In this work, we revisit a kinetic model of cell movement that takes into consideration the structure of the extracellular matrix, considering cell membrane reactions, haptotaxis and chemotaxis. We present a kinetic approach with a proper modeling of microscopic interactions, and then a scaling limit is performed
to derive the macroscopic model. We run di erent numerical simulations based on this system. Also, we measure the alignment of the cells, and compare it with the pathways determined by the extracellular matrix.

 

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