Stochastic Interacting Systems In Life And Social Sciences

This volume provides an overview of two of the most important examples of interacting particle systems, the contact process, and the voter model, as well as their many variants introduced in the past 50 years. These stochastic processes are organized by domains of application (epidemiology, population dynamics, ecology, genetics, sociology, econophysics, game theory) along with a flavor of the mathematical techniques developed for their analysis.

This volume provides an overview of two of the most important examples of interacting particle systems, the contact process, and the voter model, as well as their many variants introduced in the past 50 years. These stochastic processes are organized by domains of application (epidemiology, population dynamics, ecology, genetics, sociology, econophysics, game theory) along with a flavor of the mathematical techniques developed for their analysis.

Incorporating chaos theory into psychology and the life sciences, this text includes empirical studies of neural encoding, memory, eye movements, warfare, business cycles and selection of time series analysis algorithms. There are theoretical chapters on emergence and social dynamics, and clinical contributions dealing with: the measurement of quality of life for psychiatric patients; psychosis; the organization of self; and the role of love in family dynamics. Finally ideas from non-linear dynamics are applied to understanding the creative process.

In an ever more complex and interrelated world, a better understanding of social systems and of the dynamics of their behavior is of crucial im portance. Many of the tools holding promise of potentially significant contributions to the analysis of social systems have been, or are being developed outside of the social sciences proper, mostly the loose collec tion of diverse scientific approaches called' systems science' or , systems theory' . The editors - all of whom are involved in social systems analysis - have made an attempt in this volume to pull together several aspects of systems science which appear to them to be of particular relevance to the study of social systems: Control systems, stochastic systems, pattern recog nition, fuzzy analysis, simulation, and behavioral models. 29 authors from the disciplines of sociology, social psychology, political science, management science, history, behavioral science, economics, mathematics, engineering, and systems science have contributed to this truly interdis ciplinary effort. All of them have made the attempt to write in a manner understandable by the non-specialist. It is hoped that this volume will be of particular usefulness to students in the social sciences. Most of the articles are too short to provide much more than an initial stimulation. We trust that the references provided by the authors will allow deeper penetration into particular areas.

Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.

1 2 Jean-Dominique Deuschel and Andreas Greven 1 Fakult ̈ at II - Mathematik und Naturwissenschaften, Institut fur ̈ Mathematik, Technische Universit ̈ at Berlin, Straße des 17. Juni 136, D-10623 Berlin Tel. (0049 30) 314-25193, Fax: (0049 30) 314-21695 deuschel@math. tu-berlin. de 2 1 Mathematisches Institut, Bismarckstr. 1 , D-91054 Erlangen, 2 Tel. (0049 9131) 85-22454, Fax (0049 9131) 85-26214 This volume collects original work and reviews on work in the ?eld of pro- bilitywhichtookplacewithintheframeworkoftheDFG-Schwerpunkt:Int- acting stochastic systems of high complexity. This research network started in May 1997 and was funded till May 2003. In this network between 20–30 (depending on the 2-year periods of grant renewal) groups from probab- ity, statistical physics and mathematical statistics within Germany were - tive. An extensive international collaboration was an essential part of this network and here particularly intense contacts were built up between the DFG-Schwerpunkt and EURANDOM, a European institute for research in stochastics, which was founded in 1997. This partnership reached from joint workshops and colloquia to collaborations on speci?c projects. The key scienti?c idea which was behind the research network was to - plore and develop the connections between research in in?nite dimensional stochastic analysis, statistical physics (Gibbs measures, random media), s- tial population models from mathematical biology, complex models of ?n- cial markets or of stochastic models with interacting components in other sciences as for example in climatology.

Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the gambler’s ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright –Fisher model, Kingman’s coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and MatlabTM.

The New Mechanical Philosophy argues for a new image of nature and of science—one that understands both natural and social phenomena to be the product of mechanisms, and that casts the work of science as an effort to discover and understand those mechanisms. Drawing on an expanding literature on mechanisms in physical, life, and social sciences, Stuart Glennan offers an account of the nature of mechanisms and of the models used to represent them. A key quality of mechanisms is that they are particulars - located at different places and times, with no one just like another. The crux of the scientist's challenge is to balance the complexity and particularity of mechanisms with our need for representations of them that are abstract and general. This volume weaves together metaphysical and methodological questions about mechanisms. Metaphysically, it explores the implications of the mechanistic framework for our understanding of classical philosophical questions about the nature of objects, properties, processes, events, causal relations, natural kinds and laws of nature. Methodologically, the book explores how scientists build models to represent and understand phenomena and the mechanisms responsible for them. Using this account of representation, Glennan offers a scheme for characterizing the enormous diversity of things that scientists call mechanisms, and explores the scope and limits of mechanistic explanation.