scholarly journals On the Complex Interaction between Collective Learning and Social Dynamics

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 967 ◽  
Author(s):  
Diletta Burini ◽  
Silvana De Lillo
Keyword(s):  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Social Dynamics ◽  
Nonlinear Problems ◽  
Collective Learning ◽  
Complex Interaction ◽  
General Description ◽  
Cognitive Sciences ◽  
Learning Dynamics ◽  
Asymmetric Learning

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.

scholarly journals On the modeling of collective learning dynamics

2011 ◽  
Vol 24 (11) ◽  
pp. 1861-1866 ◽  
Author(s):  
S. De Lillo ◽  
N. Bellomo
Keyword(s):  
Collective Learning ◽  
Learning Dynamics

Collective learning modeling based on the kinetic theory of active particles

2016 ◽  
Vol 16 ◽  
pp. 123-139 ◽  
Author(s):  
D. Burini ◽  
S. De Lillo ◽  
L. Gibelli
Keyword(s):  
Kinetic Theory ◽  
Collective Learning ◽  
Active Particles

ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES

2012 ◽  
Vol 22 (01) ◽  
pp. 1130001 ◽  
Author(s):  
N. BELLOMO ◽  
A. BELLOUQUID ◽  
J. NIETO ◽  
J. SOLER
Keyword(s):  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Critical Analysis ◽  
Asymptotic Theory ◽  
Blow Up ◽  
Cellular Interactions ◽  
Biological Functions ◽  
Active Particles ◽  
Tissue Models ◽  
Macroscopic Equations

This paper proposes a review and critical analysis of the asymptotic limit methods focused on the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis deals with suitable parabolic, hyperbolic, and mixed limits. The review includes the derivation of the classical Keller–Segel model and flux limited models that prevent non-physical blow up of solutions.

scholarly journals Personality and Reputation: A Complex Relationship in Virtual Environments

2018 ◽  
Vol 10 (12) ◽  
pp. 120 ◽  
Author(s):  
Stefania Collodi ◽  
Sara Panerati ◽  
Enrico Imbimbo ◽  
Federica Stefanelli ◽  
Mirko Duradoni ◽  
...  
Keyword(s):  
Virtual Environments ◽  
Social Factors ◽  
Social Dynamics ◽  
Ultimatum Game ◽  
Complex Interaction ◽  
Psychological Traits ◽  
Mediation Effects ◽  
The Individual ◽  
Online Reputation ◽  
Psychological Dimensions

Online reputational systems are nowadays widely and effectively adopted by several online platforms to support and improve peoples’ interactions and communication. Despite the research approached and modeled social dynamics of reputational systems in different domains, adopting different frameworks, the role played by psycho-social factors, and personality traits, determining the individual susceptibility to online reputation is still elusive. To study such mediation effects, we implemented a modified online version of the Ultimatum Game, in which participants (215 adolescents) played before as proposers, and then as responders, always knowing the reputation of their interactors. Furthermore, after the reception phase, participants could evaluate the received offers, giving positive or negative feedback to their proposers. Despite the participants’ belief they were playing with their schoolmates, the interactors’ role was always fulfilled by bots characterized by standardized behaviors. Our results show how psychological traits influence the participants’ behavior in all the game phases, as well as in the rating dynamics. Reputation seems to have a direct effect only in the allocation behavior, while, in regards the other dynamics of the game (i.e., acceptance and rating), it comes into play in a complex interaction with the psychological dimensions.

ASYMPTOTIC ANALYSIS FOR A PARTICLE TRANSPORT EQUATION WITH INELASTIC SCATTERING IN EXTENDED KINETIC THEORY

1998 ◽  
Vol 08 (05) ◽  
pp. 851-874 ◽  
Author(s):  
JACEK BANASIAK ◽  
GIOVANNI FROSALI ◽  
GIAMPIERO SPIGA
Keyword(s):  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Transport Equation ◽  
Free Path ◽  
Null Space ◽  
Collision Operator ◽  
Mean Free Path ◽  
Molecular Flow ◽  
Asymptotic Equation ◽  
Linear Transport

In this paper we perform the asymptotic analysis for a linear transport equation for test particles in an absorbing and inelastically scattering background, when the excited species can be considered as non-participating. This model is derived in the frame of extended kinetic theory and rescaled with the Knudsen number ∊. After examining the main properties of the collision model and of the scattering operator in the case with an infinite interval of energy as well as the case with a finite interval, the modified (compressed) Chapman–Enskog expansion procedure is applied to find the asymptotic equation for small mean free path. A specific feature of this model is that the collision operator has an infinite-dimensional null-space. The main result is that in the small mean free path approximation on [Formula: see text] level we obtain a free molecular flow for a suitable hydrodynamic quantity, rather than the diffusion which is typical for linear transport problems.

MATHEMATICAL PROPERTIES OF INELASTIC SCATTERING MODELS IN LINEAR KINETIC THEORY

2000 ◽  
Vol 10 (02) ◽  
pp. 163-186 ◽  
Author(s):  
JACEK BANASIAK
Keyword(s):  
Cauchy Problem ◽  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Inelastic Scattering ◽  
Drift Diffusion ◽  
Mathematical Properties ◽  
The Cauchy Problem ◽  
Maxwell Models ◽  
Linear Kinetic ◽  
Linear Kinetic Theory

In this paper we analyse properties of collision operators which occur in linear Boltzmann–Maxwell models with inelastic scattering. In particular, we prove the solvability of the Cauchy problem for such models. These results form a basis for further applications of these models and, in particular, for their asymptotic analysis and the derivation of the drift–diffusion approximation.

ON THE ASYMPTOTIC ANALYSIS OF KINETIC MODELS TOWARDS THE COMPRESSIBLE EULER AND ACOUSTIC EQUATIONS

2004 ◽  
Vol 14 (06) ◽  
pp. 853-882 ◽  
Author(s):  
A. BELLOUQUID
Keyword(s):  
Fluid Dynamics ◽  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Small Parameter ◽  
Existence And Uniqueness ◽  
Compressible Euler Equations ◽  
Time Interval ◽  
Uniqueness Theorems ◽  
Acoustic Equations ◽  
Compressible Euler

This paper deals with the analysis of the asymptotic limit for models of the mathematical kinetic theory to the nonlinearized compressible Euler equations or to the acoustic equations when the Knudsen number ε tends to zero. Existence and uniqueness theorems are proven for analytic initial fluctuations on the time interval independent of the small parameter ε. As ε tends to zero, the solution of kinetics models converges strongly to the Maxwellian whose fluid-dynamics parameters solve the Euler and the acoustic systems. The general results are specifically applied to the analysis of the Boltzmann and BGK equations.

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.

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