Mathematical models have been very successful in the study of the physical world. Galilei and Newton introduced point particles moving without friction under the action of simple forces as the basis for the description of concrete motions like the ones of the planets. This approach was sustained by appro priate mathematical methods, namely infinitesimal calculus, which was being developed at that time. In this way classical analytical mechanics was able to establish some general results, gaining insight through explicit solution of some simple cases and developing various methods of approximation for handling more complicated ones. Special relativity theory can be seen as an extension of this kind of modelling. In the study of electromagnetic phenomena and in general relativity another mathematical model is used, in which the concept of classical field plays the fundamental role. The equations of motion here are partial differential equations, and the methods of study used involve further developments of classical analysis. These models are deterministic in nature. However it was realized already in the second half of last century, through the work of Maxwell, Boltzmann, Gibbs and others, that in the discussion of systems involving a great number of particles, the deterministic description is not by itself of great help, in particu lar a suitable "weighting" of all possible initial conditions should be considered.

Social Dynamics: Models and Methods focuses on sociological methodology and on the practice of sociological research. This book is organized into three parts encompassing 16 chapters that deal with the basic principles of social dynamics. The first part of this book considers the development of models and methods for causal analysis of the actual time paths of change in attributes of individual and social systems. This part also discusses the applications in which the use of dynamic models and methods seems to have enhanced the capacity to formulate and test sociological arguments. These models and methods are useful for answering questions about the detailed structure of social change processes. The second part explores the formulation of the continuous-time models of change in both quantitative and qualitative outcomes and the development of suitable methods for estimating these models from the kinds of data commonly available to sociologists. The third part describes a stochastic framework for analyzing both qualitative and quantitative outcome of social changes. This part also discusses the sociologists' perspective on the empirical study of social change processes. This text will be of great value to sociologists and sociological researchers.

This book is an integrated work published in two volumes. The first volume treats the basic Markov process and its variants; the second, semi-Markov and decision processes. Its intent is to equip readers to formulate, analyze, and evaluate simple and advanced Markov models of systems, ranging from genetics and space engineering to marketing. More than a collection of techniques, it constitutes a guide to the consistent application of the fundamental principles of probability and linear system theory. Author Ronald A. Howard, Professor of Management Science and Engineering at Stanford University, begins with the basic Markov model, proceeding to systems analyses of linear processes and Markov processes, transient Markov processes and Markov process statistics, and statistics and inference. Subsequent chapters explore recurrent events and random walks, Markovian population models, and time-varying Markov processes. Volume I concludes with a pair of helpful indexes.

'Et moi - ... - si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais point aile: human race. It has put common sense back where it belongs. on the topmost shelf next Jules Verne (0 the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

This book introduces and studies a number of stochastic models of subsistence, communication, social evolution and political transition that will allow the reader to grasp the role of uncertainty as a fundamental property of our irreversible world. At the same time, it aims to bring about a more interdisciplinary and quantitative approach across very diverse fields of research in the humanities and social sciences. Through the examples treated in this work – including anthropology, demography, migration, geopolitics, management, and bioecology, among other things – evidence is gathered to show that volatile environments may change the rules of the evolutionary selection and dynamics of any social system, creating a situation of adaptive uncertainty, in particular, whenever the rate of change of the environment exceeds the rate of adaptation. Last but not least, it is hoped that this book will contribute to the understanding that inherent randomness can also be a great opportunity – for social systems and individuals alike – to help face the challenge of “survival under uncertainty”.

Significant, and usually unwelcome, surprises, such as floods, financial crisis, epileptic seizures, or material rupture, are the topics of Extreme Events in Nature and Society. The book, authored by foremost experts in these fields, reveals unifying and distinguishing features of extreme events, including problems of understanding and modelling their origin, spatial and temporal extension, and potential impact. The chapters converge towards the difficult problem of anticipation: forecasting the event and proposing measures to moderate or prevent it. Extreme Events in Nature and Society will interest not only specialists, but also the general reader eager to learn how the multifaceted field of extreme events can be viewed as a coherent whole.