Population kinetic models for social dynamics: Dependence on structural parameters

A kinetic equation of the Boltzmann kind is adopted to approach the analysis of a population of individuals subject to social interactions. The state variable, referred to a dominant social feature such as the individual wealth, is defined on the whole real axis. Different kinds of interactions are allowed, both on a stochastic and a deterministic basis. Structural parameters are varied, and the related system sensitivity analysed. © 2002 Elsevier Science Ltd. All rights reserved

The modelling of political dynamics by generalized kinetic (Boltzmann) models

This paper deals with the development of mathematical structures suitable to include a variety of Boltzmann type models for social competition. The first part is devoted to derive the framework suitable to design general models. The second part deals with some applications and simulations in the field of social dynamics, and specifically about-the free choice of each individual about one among several families which partition the whole population. Finally, a critical analysis towards research perspectives is proposed. (C) 2003 Elsevier Science Ltd. All rights reserved

Abelian versus non-Abelian Baecklund Charts: some remarks

Connections via Baecklund transformations among different non-linear evolution equations are investigated aiming to compare corresponding Abelian and non Abelian results. Specifically, links, via Baecklund transformations, connecting Burgers and KdV-type hierarchies of nonlinear evolution equations are studied. Crucial differences as well as notable similarities between Baecklund charts in the case of the Burgers - heat equation, on one side and KdV -type equations are considered. The Baecklund charts constructed in [16] and [17], respectively, to connect Burgers and KdV-type hierarchies of operator nonlinear evolution equations show that the structures, in the non-commutative cases, are richer than the corresponding commutative ones.Comment: 18 page

A novel noncommutative KdV-type equation, its recursion operator, and solitons

A noncommutative KdV-type equation is introduced extending the Baecklund chart in [S. Carillo, M. Lo Schiavo, and C. Schiebold, SIGMA 12 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in [P.J. Olver and V.V. Sokolov Commun. Math. Phys. 193 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies and an explicit solution class are derived

An artificial neural network approach for modelling the ward atmosphere in a medical unit

Artificial neural networks (ANNs) have been developed, implemented and tested on the basis of a four-year-long experimental data set, with the aim of analyzing the performance and clinical outcome of an existing medical ward, and predicting the effects that possible readjustments and/or interventions on the structure may produce on it. Advantages of the ANN technique over more traditional mathematical models are twofold: on one hand, this approach deals quite naturally with a large number of parameters/variables, and also allows to identify those variables which do not play a crucial role in the system dynamics; on the other hand, the implemented ANN can be more easily used by a staff of non-mathematicians in the unit, as an on-site predictive tool. As such, the ANN model is particularly suitable for the case study. The predictions from the ANN technique are then compared and contrasted with those obtained from a generalized kinetic approach previously proposed and tested by the authors. The comparison on the two case periods shows the ANN predictions to be somewhat closer to the experimental values. However, the mean deviations and the analysis of the statistical coefficients over a span of multiple years suggest the kinetic model to be more reliable in the long run, i.e., its predictions can be considered as acceptable even on periods that are quite far away from the two case periods over which the many parameters of the model had been optimized. The approach under study, referring to paradigms and methods of physical and mathematical models integrated with psychosocial sciences, has good chances of gaining the attention of the scientific community in both areas, and hence of eventually obtaining wider diffusion and generalization.

A threefold ill-posed problem

Da un insieme di 135 reperti archeologici di bronzo, pesati mediante un sistema decimale e unita' di misura in grammi, e' stata cercata una possibile comune unita' di misura ponderale che potesse giustificare la loro grandezza e il fatto che, a suo tempo, questi furono prescelti ad altri e conservati nei ripostigli nei quali sono stati oggi trovati. Metodi statistici ben noti sono stati usati, ed alcuni proposti, per tentare la soluzione di un problema evidentemente mal posto. Serie: Biblioteca di Antichita` Cipriote vol.

Un tentativo di modello per un problema esplicito di dinamica sociale

intervento in incontro scientifico Dipartimento di Matematica Politecnico Torin

Kinetic Modelling and Electoral Competition

The structure of generalized kinetic models is developed to enquire how effectively theycan be used in the fields of human reactions and of the social sciences. In particular, a specific model is designed to describe the dynamics of a composite, structured society such as that of a competing bipartisan political system. The model structure contains terms with localized interactions and mean field terms. The first part of the paper deals with the mathematical framework. In the second part, a comprehensive model is proposed. Finally, some results of a set of simulations are mentioned and a critical analysis towards research perspectives is formulated