scholarly journals Modeling Complex Living Systems: A Kinetic Theory and Stochastic Game Approach

2013 ◽  
Vol 64 (12) ◽  
pp. 1866-1866
Author(s):  
Janet Smart
Keyword(s):  
Kinetic Theory ◽  
Stochastic Game ◽  
Living Systems

scholarly journals A Kinetic Theory Model of the Dynamics of Liquidity Profiles on Interbank Networks

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 363
Author(s):  
Marina Dolfin ◽  
Leone Leonida ◽  
Eleonora Muzzupappa
Keyword(s):  
Kinetic Theory ◽  
Network Formation ◽  
Transition Probabilities ◽  
Stochastic Game ◽  
Theory Model ◽  
Point Of View ◽  
Network Efficiency ◽  
Modelling Framework ◽  
Wide Range ◽  
Complex Adaptive

This paper adopts the Kinetic Theory for Active Particles (KTAP) approach to model the dynamics of liquidity profiles on a complex adaptive network system that mimic a stylized financial market. Individual incentives of investors to form or delete a link is driven, in our modelling framework, by stochastic game-type interactions modelling the phenomenology related to policy rules implemented under Basel III, and it is exogeneously and dynamically influenced by a measure of overnight interest rate. The strategic network formation dynamics that emerges from the introduced transition probabilities modelling individual incentives of investors to form or delete links, provides a wide range of measures using which networks might be considered “best” from the point of view of the overall welfare of the system. We use the time evolution of the aggregate degree of connectivity to measure the time evolving network efficiency in two different scenarios, suggesting a first analysis of the stability of the arising and evolving network structures.

Forecasting environmental health risks based on the kinetic theory of aging of living systems

2015 ◽  
Vol 5 (3) ◽  
pp. 141-146 ◽  
Author(s):  
A. A. Viktorov ◽  
V. D. Gladkikh ◽  
A. I. Ksenofontov ◽  
E. E. Morozova
Keyword(s):  
Kinetic Theory ◽  
Environmental Health ◽  
Health Risks ◽  
Living Systems ◽  
Environmental Health Risks ◽  
Theory Of Aging

scholarly journals Analysis and Forecast Based on the Kinetic Equation for Changing the Numerical Composition of Living Systems

2020 ◽  
Vol 2 (2) ◽  
pp. 8-18
Author(s):  
Alexander Alexandrovich Victorov ◽  
Viacheslav Alexandrovich Kholodnov
Keyword(s):  
Kinetic Equation ◽  
Kinetic Theory ◽  
Population Growth ◽  
Biological Object ◽  
Human Life ◽  
Developed Countries ◽  
Living Systems ◽  
Subsequent Decrease ◽  
Final Population ◽  
Theory Of Aging

The possibility of applying the kinetic theory of aging of biological species published earlier by the authors of this work to assess and predict changes in the number of specific populations is evaluated. The populations of the USA, China and Russia, as well as the population of mice observed in the experiment "mouse paradise" of the American scientist John Calhoun are considered. To this end, a historically consistent analysis of the main previously proposed multi-scenario mathematical models describing demographic data and predicting the dynamics of the population was performed. The results of these models show a decrease in the population growth rate, a tendency toward a limit with an increase in historical time, the achievement of such a limit in some developed countries with a relatively high level of social security, a subsequent decrease in the number and further uncertainty of the final population outlook in the distant future. In addition, these models made it possible to establish that the observed population growth in developed countries is unambiguously accompanied by its aging - a relative predominant increase in the number of elderly people compared to the number of the younger generation (people are aging, the population of countries is aging). In this work, the assumption was made and confirmed that the dynamics of the aging of the population of the countries of the World corresponds to the dynamics of aging of a person of one generation and is mathematically described by the differential equation of the kinetic theory of aging of living systems of the same type with close values of the parameters. The biophysical meaning of the parameters of the kinetic equation reflects G. Selye's concept of the determining role of stress in human life and populations. An analysis of the changes in the numbers of the considered populations of humans and mice at various stages of their development is qualitatively commented on from the standpoint of comparative tension according to G. Selye. To assess the degree of aging of a biological object of one population in kinetic theory, the probability of death during life is selected as an indicator of aging. In this work, the probability of reaching the maximum population size was chosen as an indicator of the aging of a biological object of various populations. The published literature predicts various options for changing the population after reaching a maximum - maintaining the reached maximum level and decreasing to a certain limit, less than the maximum achieved. In this paper, based on an analysis of its results and an analogy with the complete degeneration of mice in the “mouse paradise” experiment, a conclusion is drawn about a hypothetically possible third variant of the limiting decrease in the population - its complete degeneration.

scholarly journals A Model of Population Change Based on The Kinetic Theory of Aging of Living Systems.

2020 ◽  
pp. 1-9
Keyword(s):  
Kinetic Theory ◽  
Population Growth ◽  
Biological Object ◽  
Population Change ◽  
Human Life ◽  
Developed Countries ◽  
Living Systems ◽  
Subsequent Decrease ◽  
Final Population ◽  
Theory Of Aging

Abstract The possibility of applying the kinetic theory of aging of biological species published earlier by the authors of this work to assess and predict changes in the number of specific populations is evaluated. The populations of the USA, China and Russia, as well as the population of mice observed in the experiment "mouse paradise" of the American scientist John Calhoun are considered. To this end, a historically consistent analysis of the main previously proposed multi-scenario mathematical models describing demographic data and predicting the dynamics of the population was performed. The results of these models show a decrease in the population growth rate, a tendency toward a limit with an increase in historical time, the achievement of such a limit in some developed countries with a relatively high level of social security, a subsequent decrease in the number and further uncertainty of the final population outlook in the distant future. In addition, these models made it possible to establish that the observed population growth in developed countries is unambiguously accompanied by its aging - a relative predominant increase in the number of elderly people compared to the number of the younger generation (people are aging, the population of countries is aging). In this work, the assumption was made and confirmed that the dynamics of the aging of the population of the countries of the World corresponds to the dynamics of aging of a person of one generation and is mathematically described by the differential equation of the kinetic theory of aging of living systems of the same type with close values of the parameters. The biophysical meaning of the parameters of the kinetic equation reflects G. Selye's concept of the determining role of stress in human life and populations. An analysis of the changes in the numbers of the considered populations of humans and mice at various stages of their development is qualitatively commented on from the standpoint of comparative tension according to G. Selye. To assess the degree of aging of a biological object of one population in kinetic theory, the probability of death during life is selected as an indicator of aging. In this work, the probability of reaching the maximum population size was chosen as an indicator of the aging of a biological object of various populations. The published literature predicts various options for changing the population after reaching a maximum - maintaining the reached maximum level and decreasing to a certain limit, less than the maximum achieved. In this paper, based on an analysis of its results and an analogy with the complete degeneration of mice in the “mouse paradise” experiment, a conclusion is drawn about a hypothetically possible third variant of the limiting decrease in the population - its complete degeneration.

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.

Prediction of Life Expectancy in Prostate Cancer Patients Based on the Kinetic Theory of the Aging of Living Systems

2017 ◽  
Vol 7 (4) ◽  
pp. 290-295 ◽  
Author(s):  
A. A. Viktorov ◽  
G. M. Zharinov ◽  
N. Yu. Neklasova ◽  
E. E. Morozova
Keyword(s):  
Prostate Cancer ◽  
Life Expectancy ◽  
Kinetic Theory ◽  
Cancer Patients ◽  
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.

Kinetic theory for aging of living systems

2013 ◽  
Vol 3 (4) ◽  
pp. 261-267 ◽  
Author(s):  
A. A. Viktorov ◽  
V. A. Kholodnov
Keyword(s):  
Kinetic Theory ◽  
Living Systems

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.

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