scholarly journals Special Issue “Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems”—Editorial and Research Perspectives

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 456
Author(s):  
Nicola Bellomo ◽  
Damián A. Knopoff ◽  
Pietro Terna
Keyword(s):  
Kinetic Theory ◽  
Complex Systems ◽  
Collective Learning ◽  
Living Systems ◽  
Theory Approach ◽  
Vehicular Traffic ◽  
Modeling And Simulations ◽  
Special Issue ◽  
Research Perspectives

This editorial paper presents a special issue devoted to the development of mathematical tools from kinetic and swarms theory to the modeling and simulations of the dynamics of living systems constituted by very many interacting living entities. Applications refer to several fields: collective learning, behavioral economy, multicellular systems, vehicular traffic, and human crowds. A forward look to research perspectives is focused on the conceptual links between swarms methods and the kinetic theory approach.

Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems

2021 ◽  
pp. 1-7
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
M. A. J. Chaplain
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Mathematical Models ◽  
Modeling And Simulation ◽  
Critical Analysis ◽  
Living Systems ◽  
Special Issue ◽  
Research Perspectives ◽  
Heterogeneous Features

This editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous features of the complex system under consideration. Subsequently, the contents of the papers in this issue are presented referring to the aforementioned complexity features. Finally, a critical analysis of the overall contents of the issue is proposed, with the aim of providing a forward look to research perspectives.

scholarly journals What is life? A perspective of the mathematical kinetic theory of active particles

2021 ◽  
pp. 1-46
Author(s):  
Nicola Bellomo ◽  
Diletta Burini ◽  
Giovanni Dosi ◽  
Livio Gibelli ◽  
Damian Knopoff ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Case Studies ◽  
General Framework ◽  
Living Systems ◽  
Mathematical Approach ◽  
Collective Behaviors ◽  
Research Perspectives ◽  
Active Particles ◽  
Look Ahead

The modeling of living systems composed of many interacting entities is treated in this paper with the aim of describing their collective behaviors. The mathematical approach is developed within the general framework of the kinetic theory of active particles. The presentation is in three parts. First, we derive the mathematical tools, subsequently, we show how the method can be applied to a number of case studies related to well defined living systems, and finally, we look ahead to research perspectives.

ON THE DIFFICULT INTERPLAY BETWEEN LIFE, "COMPLEXITY", AND MATHEMATICAL SCIENCES

2013 ◽  
Vol 23 (10) ◽  
pp. 1861-1913 ◽  
Author(s):  
N. BELLOMO ◽  
D. KNOPOFF ◽  
J. SOLER
Keyword(s):  
Kinetic Theory ◽  
Complex Systems ◽  
Case Studies ◽  
Mathematical Theory ◽  
Stochastic Games ◽  
Mathematical Structure ◽  
Living Systems ◽  
Active Particles ◽  
Suitable Generalization ◽  
Mathematical Sciences

This paper presents a revisiting, with developments, of the so-called kinetic theory for active particles, with the main focus on the modeling of nonlinearly additive interactions. The approach is based on a suitable generalization of methods of kinetic theory, where interactions are depicted by stochastic games. The basic idea consists in looking for a general mathematical structure suitable to capture the main features of living, hence complex, systems. Hopefully, this structure is a candidate towards the challenging objective of designing a mathematical theory of living systems. These topics are treated in the first part of the paper, while the second one applies it to specific case studies, namely to the modeling of crowd dynamics and of the immune competition.

COMPLEX SYSTEMS: NEW CHALLENGES WITH MODELING HEADACHES

2013 ◽  
Vol 24 (02) ◽  
pp. 213-219 ◽  
Author(s):  
N. BELLOMO ◽  
F. BREZZI
Keyword(s):  
Complex Systems ◽  
Mathematical Theory ◽  
Life Sciences ◽  
Living Systems ◽  
Future Research ◽  
Special Issue ◽  
New Challenges

This brief note is an introduction to the papers published in this special issue devoted to complex systems in life sciences. Out of this presentation some perspective ideas on conceivable future research objectives are extracted and brought to the reader's attention. The final (ambitious) aim is to develop a mathematical theory for complex living systems.

scholarly journals From particles to firms: on the kinetic theory of climbing up evolutionary landscapes

2020 ◽  
Vol 30 (07) ◽  
pp. 1441-1460 ◽  
Author(s):  
Nicola Bellomo ◽  
Giovanni Dosi ◽  
Damián A. Knopoff ◽  
Maria Enrica Virgillito
Keyword(s):  
Kinetic Theory ◽  
Mathematical Theory ◽  
Predictive Ability ◽  
Complex Interaction ◽  
Living Systems ◽  
Mathematical Representation ◽  
Future Research ◽  
Industrial Dynamics ◽  
Modeling And Simulations ◽  
Active Particles

This paper constitutes the first attempt to bridge the evolutionary theory in economics and the theory of active particles in mathematics. It seeks to present a kinetic model for an evolutionary formalization of economic dynamics. The new derived mathematical representation intends to formalize the processes of learning and selection as the two fundamental drivers of evolutionary environments [G. Dosi, M.-C. Pereira and M.-E. Virgillito, The footprint of evolutionary processes of learning and selection upon the statistical properties of industrial dynamics, Ind. Corp. Change, 26 (2017) 187–210]. To coherently represent the aforementioned properties, the kinetic theory of active particles [N. Bellomo, A. Bellouquid, L. Gibelli and N. Outada, A Quest Towards a Mathematical Theory of Living Systems (Birkhäuser-Springer, 2017)] is here further developed, including the complex interaction of two hierarchical functional subsystems. Modeling and simulations enlighten the predictive ability of the approach. Finally, we outline the potential avenues for future research.

scholarly journals Modeling Complex Systems with Particles Refuge by Thermostatted Kinetic Theory Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Carlo Bianca
Keyword(s):  
Mathematical Modeling ◽  
Kinetic Theory ◽  
Complex Systems ◽  
Future Research ◽  
Research Perspectives

This paper is concerned with the mathematical modeling of complex systems characterized by particles refuge. Specifically the paper focuses on the derivation and moments analysis of thermostatted kinetic frameworks with conservative and nonconservative interactions for closed and open complex systems at nonequilibrium. Applications and future research perspectives are discussed in the last section of the paper.

scholarly journals Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives

2019 ◽  
Vol 29 (10) ◽  
pp. 1901-2005 ◽  
Author(s):  
G. Albi ◽  
N. Bellomo ◽  
L. Fermo ◽  
S.-Y. Ha ◽  
J. Kim ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Critical Analysis ◽  
Multiscale Methods ◽  
Vehicular Traffic ◽  
Macroscopic Models ◽  
Mesoscopic Models ◽  
Research Perspectives ◽  
Challenging Research ◽  
Intermediate Role

This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It contains a survey of the kinetic models developed in the last 10 years on the aforementioned topics so that overlapping with previous reviews can be avoided. Although the main focus of this paper lies on the mesoscopic models for collective dynamics, we provide a brief overview on the corresponding micro and macroscopic models, and discuss intermediate role of mesoscopic model between them. Moreover, we provide a number of selected challenging research perspectives for readers’ attention.

LOOKING FOR NEW PARADIGMS TOWARDS A BIOLOGICAL-MATHEMATICAL THEORY OF COMPLEX MULTICELLULAR SYSTEMS

2006 ◽  
Vol 16 (07) ◽  
pp. 1001-1029 ◽  
Author(s):  
NICOLA BELLOMO ◽  
GUIDO FORNI
Keyword(s):  
Kinetic Theory ◽  
Complex Systems ◽  
Critical Analysis ◽  
Mathematical Theory ◽  
Classical Mechanics ◽  
Biological Functions ◽  
Living Matter ◽  
Research Perspectives ◽  
Active Particles ◽  
Large Systems

This paper deals with the development of new paradigms based on the methods of the mathematical kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by a few biological functions which are able to modify the above laws. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The last part of the paper deals with a critical analysis and with the indication of research perspectives concerning the challenging target of developing a biological-mathematical theory for the living matter.

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