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Networks can provide a useful model and graphic image useful for the description of a wide variety of web-like structures in the physical and man-made realms, e.g. protein networks, food webs and the Internet. The contributions gathered in the present volume provide both an introduction to, and an overview of, the multifaceted phenomenology of complex networks. Statistical Mechanics of Complex Networks also provides a state-of-the-art picture of current theoretical methods and approaches.
The availability of large data sets have allowed researchers to uncover complex properties such as large scale fluctuations and heterogeneities in many networks which have lead to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. For example, a vast number of everyday systems, from the brain to ecosystems, power grids and the Internet, can be represented as large complex networks. This new and recent account presents a comprehensive explanation of these effects.
This book provides a comprehensive yet short description of the basic concepts of Complex Network theory. In contrast to other books the authors present these concepts through real case studies. The application topics span from Foodwebs, to the Internet, the World Wide Web and the Social Networks, passing through the International Trade Web and Financial time series. The final part is devoted to definition and implementation of the most important network models. The text provides information on the structure of the data and on the quality of available datasets. Furthermore it provides a series of codes to allow immediate implementation of what is theoretically described in the book. Readers already used to the concepts introduced in this book can learn the art of coding in Python by using the online material. To this purpose the authors have set up a dedicated web site where readers can download and test the codes. The whole project is aimed as a learning tool for scientists and practitioners, enabling them to begin working instantly in the field of Complex Networks.
Aimed at graduate students, this book explores some of the core phenomena in non-equilibrium statistical physics. It focuses on the development and application of theoretical methods to help students develop their problem-solving skills. The book begins with microscopic transport processes: diffusion, collision-driven phenomena, and exclusion. It then presents the kinetics of aggregation, fragmentation and adsorption, where the basic phenomenology and solution techniques are emphasized. The following chapters cover kinetic spin systems, both from a discrete and a continuum perspective, the role of disorder in non-equilibrium processes, hysteresis from the non-equilibrium perspective, the kinetics of chemical reactions, and the properties of complex networks. The book contains 200 exercises to test students' understanding of the subject. A link to a website hosted by the authors, containing supplementary material including solutions to some of the exercises, can be found at www.cambridge.org/9780521851039.
This book is the culmination of three years of research effort on a multidisciplinary project in which physicists, mathematicians, computer scientists and social scientists worked together to arrive at a unifying picture of complex networks. The contributed chapters form a reference for the various problems in data analysis visualization and modeling of complex networks.
In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.
This course-tested primer provides graduate students and non-specialists with a basic understanding of the concepts and methods of statistical physics and demonstrates their wide range of applications to interdisciplinary topics in the field of complex system sciences, including selected aspects of theoretical modeling in biology and the social sciences. Generally speaking, the goals of statistical physics may be summarized as follows: on the one hand to study systems composed of a large number of interacting units, and on the other to predict the macroscopic, collective behavior of the system considered from the perspective of the microscopic laws governing the dynamics of the individual entities. These two goals are essentially also shared by what is now called 'complex systems science,' and as such, systems studied in the framework of statistical physics may be considered to be among the simplest examples of complex systems – while also offering a rather well developed mathematical treatment. The second edition has been significantly revised and expanded, featuring in particular three new chapters addressing non-conserved particles, evolutionary population dynamics, networks, properties of both individual and coupled simple dynamical systems, and convergence theorems, as well as short appendices that offer helpful hints on how to perform simple stochastic simulations in practice. Yet, the original spirit of the book – to remain accessible to a broad, non-specialized readership – has been kept throughout: the format is a set of concise, modular and self-contained topical chapters, avoiding technicalities and jargon as much as possible, and complemented by a wealth of worked-out examples, so as to make this work useful as a self-study text or as textbook for short courses. From the reviews of the first edition: “... a good introduction to basic concepts of statistical physics and complex systems for students and researchers with an interest in complex systems in other fields ... .” Georg Hebermehl, Zentralblatt MATH, Vol. 1237, 2012 “... this short text remains very refreshing for the mathematician.” Dimitri Petritis, Mathematical Reviews, Issue 2012k
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
A comprehensive and pedagogical text on nonequilibrium statistical physics, covering topics from random walks to pattern formation.