Mathematical Sociology

Current theories from biosocial (e.g.: the role of neurotransmitters in behavioral features), ecological (e.g.: cultural, political, and institutional conditions), and interpersonal (e.g.: attachment) perspectives have grounded interpersonal and romantic relationships in normative social experiences. However, these theories have not been developed to the point of providing a solid theoretical understanding of the dynamics present in interpersonal and romantic relationships, and integrative theories are still lacking. In this paper, mathematical models are use to investigate the dynamics of interpersonal and romantic relationships, which are examined via ordinary and stochastic differential equations, in order to provide insight into the behaviors of love. The analysis starts with a deterministic model and progresses to nonlinear stochastic models capturing the stochastic rates and factors (e.g.: ecological factors, such as historical, cultural and community conditions) that affect proximal experiences and shape the patterns of relationship. Numerical examples are given to illustrate various dynamics of interpersonal and romantic behaviors (with emphasis placed on sustained oscillations, and transitions between locally stable equilibria) that are observable in stochastic models (closely related to real interpersonal dynamics), but absent in deterministic models.

We introduce a conceptual-mathematical model that simulates the spread of information. We represent the states of the actors in the information flow using compartments. The compartment diagram is translated into a system of coupled ordinary differential equations. The diversity of social groups (subpopulations) is incorporated in the model, and the model is applicable for a heterogeneous community. We determine four possible spots that can be influenced to control the information propagation such as (1) controlling the inflow and outflow of people in each subpopulation, (2) regulating the media of communication, (3) influencing the belief system of the actors, and (4) introducing an antithesis to the circulating information.

Herrenhausen International Symposium “Bribery, Fraud, Cheating – How to explain and avoid organizational wrongdoing”, Herrenhausen Palace, October 5-7, 2017 Hannover, Germany organized by Volkswagenstiftung and Ruprecht-Karls-Universität Heidelberg
“Lightning Talk” presentation & poster: Why the fight against corruption is a struggle for the European dimension of the European Union?

In my sociological research, I deal with the political and social structure of the European Union, and I am particularly interested in the geopolitics of the EU, especially in the Eastern Dimension of the European Neighborhood Policy (Eastern Partnership). Fundamental threat to the security of ENP countries is the privatization (corruption) of public systems, especially the judiciary. Every corrupt political system is an uncontrolled and counter-productive system. Such a system is the source of internal and external destabilization and chaos.
The corrupt justice system means that not the legislative power is the right but the low-level service of the judicial and executive system. The law in a corrupt state actually does not exist, although it is established, it does not, in fact, regulate social, economic and political life. Therefore, democracy in a corrupt state is a pure decoration, without real influence on the course of public affairs. Without democracy, there is no EU and its European (axiological) neighborhood. That is why the fight against corruption is a fight for democracy. This is why the fight against corruption is a struggle for the European dimension of the European Union and the profile of European eastern and southern neighbors compatible with European values.

In the postwar USSR, there were a few scattered research groups engaged in research most closely resembling “Western” mainstream economics. Inspired by the new sciences of the artificial, these groups were able to make important contributions to various fields of economic theory. This article focuses on the story of one group created by the control engineer Mark Aizerman at the Institute of Control Sciences in Moscow. It discusses the origins and the outstanding diversity and dynamics of the group’s research agenda, reconstructs the factors that made Aizerman turn from the cybernetics of mechanical or biological systems to the abstract theory of choice and rationality, and demonstrates how the group was related to—and communicated with—the scholars doing work in social choice, mechanism design, and formal political theory. It also speculates on one missed research opportunity of doing experimental economics—something that, given the ideological and intellectual constraints Aizerman was facing, was hardly possible in the Soviet context, but could have been a synthesis of economics and engineering. The article also discusses a research culture Aizerman created and nurtured in his lab by encouraging research collaboration, sharing ideas, and freely moving across various disciplines.

From September 4 to 11, 1992, a first meeting between Ukrainian and German scientists interested in mathematical and computer modeling of social processes was held at Vorzel' near Kiev. The meeting had been planned for nearly three years by Igor V. Chernenko and Mikhail V. Kuz'min, then members of the research group on mathematical modeling in sociology at the Institute of Sociology of the Academy of Science of the Ukrainian Republic, and had to be postponed twice due to the political development in the former Soviet Union, but thanks to the organizers' perseverance (and in spite of a strike of the airport personell at Kiev Borispol Airport on the eve of the conference) the conference could at last be realized.

The main purpose of the conference was to discuss a synergetic interpretation of large-scale destructive social processes as catastrophic phenomena in self-organized systems.

Collaboration between German and Ukrainian scientists in the field of
mathematical simulation of socio-economic processes has a good tradition that gave a set of original nonlinear models of creative self-organization as well as a new catastrophic approach to examine social evolution. The conditional forecasts of social cataclysms obtained in the papers presented at the conference were corroborated by the subsequent events in the former Soviet Republics.

Social catastrophe means that the self-organized driver of  system growth  is transmuted into  a factor  of  system  decay. Nonlinear models  of  such  crucial  metamorphoses  were  the  most exciting subjects of discussions,  because  these  models  provide an opportunity to see into the  contradictory  nature  of  living systems and to study hidden functional links  between  micro and macro levels of self-reproductive systems  and  conditions  of their transformations.

From the beginning of the conference preparations it had been clear that the ``chaotic'' and sometimes ``catastrophic'' processes in state and society of the successors to the Soviet republics should be in the center of interest of the participants. One of the crucial questions was whether mathematical analysis and computer simulation can make a useful contribution to the understanding of the processes of rapid social and economic change in the Community of Independent States, and whether reasonable use can be made of the precise mathematical concepts of ``chaos'' and ``catastrophe'' to describe these processes --- since the everyday meanings of these words are so often used for such a description.

These proceedings try to answer this question, starting from four papers which are intended to give some orientation in the field of modeling complex systems: Kisil gives a somewhat pessimistic view on sociological measurement as a fundamental for sociological modeling and simulation, while Weidlich and Troitzsch present the modeling approaches they have been using for some time to show that even in systems of small complexity processes of self-organization may arise. Shatikhin finishes this first part with a paper concentrating on the macroscopic view of systems.

The second part of these proceedings presents some modeling tools and
algorithms. We start with two papers on the MIMOSE modeling and simulation system which was developed by Möhring's and Troitzsch's working group at Koblenz. Borodyanski's and Burgin's papers open
a new perspective on non-algorithmic procedures. The second part is
finished by Polumiyenko's paper on a very complex game theoretical model of an ecosystem which serves as a means to show the possible contribution of game theory as a tool for understanding complex systems.

The third part contains a number of special models of self-organizing
processes, of catastrophic and of chaotic phenomena. Flache and his coauthors discuss a model of cooperation in a group rewarded team, thus focussing the microscopic perspective. The papers by Tsvetkov, Dubrovskiy, Chernenko, Chernyshenko, Kuzmin, and Platon describe several variations of a model of evolution in a society consisting of several
cooperating and competing subpopulations (a model which is also used to illustrate the facilities of the MIMOSE simulation system in Möhring's and Strotmann's paper). While this model and the variations described in these three papers is macroscopic, Troitzsch's paper investigates the catastrophic jump from a microscopic perspective. Chesnokov and Chernenko in their paper try to reconcile concepts of Eastern mystic and modern mathematics to understand self-organization processes. Niyazov gives a semi-empirical analysis of large cycles in US economy during the last two centuries and proposes a model which could make these cycles understandable.

The proceedings end in a paper presented by Erdmann and discussed for hours by the conference participants, in which he models economic aspects of institutional change in Eastern Europe, proposing some political recommendations how to improve the economical situation in the countries of Eastern Europe.

For at least twenty‐five years, the concept of the clique has had a prominent place in sociometric and other kinds of sociological research. Recently, with the advent of large, fast computers and with the growth of interest in graph‐theoretic social network studies, research on the definition and investigation of the graph theoretic properties of clique‐like structures has grown. In the

Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive classes of graphs - for formalizing and studying evolution of complex networks. Our definition of probabilistic inductive class of graphs (PICG) extends the standard notion of inductive class of graphs (ICG) by imposing a probability space. A PICG is given by: (1) class B of initial graphs, the basis of PICG, (2) class R of generating rules, each with distinguished left element to which the rule is applied to obtain the right element, (3) probability distribution specifying how the initial graph is chosen from class B, (4) probability distribution specifying how the rules from class R are applied, and, finally, (5) probability distribution specifying how the left elements for every rule in class R are chosen. We point out that many of the existing...

Using Coleman's well-known scheme as an anchor, we review key features of explanations of social phenomena that employ micro-macro models. Some antecedents of micro-macro models and of Coleman's scheme as well as some paradigmatic examples of micro-macro links are sketched. We then discuss micro-level assumptions in micro-macro explanations and the robustness of macro-level implications to variations in micro-level assumptions. We conclude with an overview of some recent developments in micro-macro modeling and of the contributions to the special issue.

In a groundbreaking article, Moody and White (2003) introduced the concept of structural cohesion, simultaneously characterizing emergent communities and their internally embedded layers by the number of node-independent paths interconnecting individuals. Like many studies, however, they “corrected” the directionality discovered in some of their data. While often done for important purposes, doing so potentially confounds structural cohesion with unrelated concepts. Some relations, especially those relating to the dynamic aspects of social life, are inherently directed, in whole or in part, and it may prove worthwhile to respect this directionality. In this article, I recast structural cohesion in terms of directed social relations and identify four distinct ways of measuring it. In two example data sets—hiring relations among graduate programs and trust relations among neighborhood residents—I show that only strong embeddedness, a type of structural cohesion emerging from directed relations, proves to be a powerful, robust, independent explanatory factor. I further show that if the directionality in the data in these examples had been “corrected,” the importance of structural cohesion would have been dramatically undervalued.

Studies concerning social patterns that appear as a result of propaganda and rumors generally tend to neglect considerations of the behavior of individuals that constitute these patterns. This places obvious limitations upon the scope of research. We propose a dynamical model for the mechanics of the processes of polarization and formation of echo chambers. This model is based on the Rashevsky neurological scheme of decision-making.

This work proposes a mathematics-based sociological model of social evolution. Proposing a synthesis between Norbert Elias' Civilising Theory and the so-called Analytical Sociology, the paper deals with a causal link between social evolution processes and individuals' communicative abilities. Recurring to the elementary features of Set Theory, the paper proposes a mathematical framework to describe and explicate such link as cultural change. Paper delves into the role of individuals in such change thoroughly and outlines a body of sociological propositions linked to mathematical equations to sketch out explanatory statements of the process, applicable to the evolutionary dynamics in concrete societies.

ABSTRACT This paper studies the influence of individual social capital on the persistence of socioeconomic inequality. The set of social relations constitute a form of capital that provides the individual with a wide range of resources. Social capital interacts with other forms of capital, particularly with human capital, to enhance inequality. The overlapping-generations model proposed here focuses on the long-term investment processes in human and social capital. When these effects are considered, a society may end up divided into two groups. The first comprises people stuck in a trap of low intergenerational mobility resources. The second group includes people with increasing levels of education and social capital. Within the last group, income inequalities persist due to initial differences in social capital.

Page 1. Journal of Mathematical Sociology © 1996 OPA (Overseas Publishers Association) 1996, Vol. 21(1-2), pp. 133-148 Amsterdam BV Published in The Netherlands Reprints available directly from the publisher under license by Gordon and Breach Science ...

Since the advent of formal economics in the late 19th century there has been a latent trade-off between formal and institutional economics. A quarter century ago, Douglass North bridged some of the divide between the two strands. However to grasp the full strength of formal modelling for institutional analysis and institutional design his task has to be completed by stating the definition for institutions in terms of formal game theory. Starting from classical examples, this article defines institutions as sets of stable Nash equilibria arising from humanly devised additional elements in the game structure of human interaction. The article is organized into a brief overview of the relationship between formal and institutional economics, the derivation and a short discussion of the definition, and examples illustrating the productivity of the approach. the students in the respective courses for their feedback and suggestions.

This paper presents a stochastic dynamic mathematical model, in which a Family Policy Index (XFPI) is included to measure and compare two different models of provision of resources to support families with children from 0 to 3 years old. The main variables in this model are the XFPI, fertility, mortality, emigration and immigration rates. This mathematical model was validated in two different countries, Spain and Norway, during the 2007–2015 period. A sensitivity analysis was applied to simulate the future trend (2016–2030), examining the influence of providing public pre-school services (0 to 3 years) on (XISF). The results obtained show that these services may indeed have an influence on fertility rates, as long as they are developed extensively.

This article considers the potential for using agent models to explore theories of residential segregation in urban areas. Results of generative experiments conducted using an agent-based simulation of segregation dynamics document that varying a small number of model parameters representing constructs from urban-ecological theories of segregation can generate a wide range of qualitatively distinct and substantively interesting segregation patterns. The results suggest how complex, macro-level patterns of residential segregation can arise from a small set of simple micro-level social dynamics operating within particular urban-demographic contexts. The promise and current limitations of agent simulation studies are noted and optimism is expressed regarding the potential for such studies to engage and contribute to the broader research literature on residential segregation.[An appendix to this article is featured as an online supplement at the publisher's website.]

ABSTRACT Sociologists use negative feedback loop systems to explain identity processes, interpersonal behavior, crowd behavior, organizational behavior, social relationships, and the behavior of political systems. Control system models help us to understand how actors enact social roles with enough stability to preserve institutional arrangements, while still demonstrating remarkable creativity in unusual circumstances. These theories take us away from an oversocialized view of the actor, without relegating us to exclusive reliance on grounded theory. They provide a foundation for several generative theories of adaptive, goal-seeking behavior on the part of social actors and institutions. This chapter begins by tracing the history of control theorizing in sociology, then describes several contemporary theories that rely on control imagery, reviews the empirical support for these theories, describes some of their significant points of overlap and departure, and examines some of the key tested and untested implications of a control system approach in sociology.

Page 1. Journal of Mathematical Sociology © 1998 OPA (Overseas Publishers Association) NV 1998, Vol. 23(1), pp. 1-27 Published by license under Reprints available directly from the publisher the Gordon and Breach Publishers imprint. Photocopying permitted by license only ...