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Fractals and Disordered Systems
Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In ten chapters written by leading experts in the field, the reader is introduced to basic concepts and techniques in disordered systems and is led to the forefront of current research. This second edition has been substantially revised and updates the literature in this important field.
Fractals in Science
A deeply detailed discussion of fractals in biology, heterogeneous chemistry, polymers, and the earth sciences. Beginning with a general introduction to fractal geometry it continues with eight chapters on self-organized criticality, rough surfaces and interfaces, random walks, chemical reactions, and fractals in chemisty, biology, and medicine. A special chapter entitled "Computer Exploration of Fractals, Chaos, and Cooperativity" presents computer demonstrations of fractal models: 14 programs are included on a 3 1/2" MS-DOS diskette which run on any PC with at least 1 MB RAM and a EGA or VGA graphics card, 16 colors.
Complex Networks
Examining important results and analytical techniques, this graduate-level textbook is a step-by-step presentation of the structure and function of complex networks. Using a range of examples, from the stability of the internet to efficient methods of immunizing populations, and from epidemic spreading to how one might efficiently search for individuals, this textbook explains the theoretical methods that can be used, and the experimental and analytical results obtained in the study and research of complex networks. Giving detailed derivations of many results in complex networks theory, this is an ideal text to be used by graduate students entering the field. End-of-chapter review questions help students monitor their own understanding of the materials presented.
Mathematics of Complexity and Dynamical Systems
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Diffusion and Reactions in Fractals and Disordered Systems
This book describes diffusion and transport in disordered media such as fractals and random resistor networks.
Fractals, Scaling and Growth Far from Equilibrium
A comprehensive, 1998 account of the practical aspects and pitfalls of the applications of fractal modelling in the physical sciences.
Dynamic Social Network Modeling and Analysis
In the summer of 2002, the Office of Naval Research asked the Committee on Human Factors to hold a workshop on dynamic social network and analysis. The primary purpose of the workshop was to bring together scientists who represent a diversity of views and approaches to share their insights, commentary, and critiques on the developing body of social network analysis research and application. The secondary purpose was to provide sound models and applications for current problems of national importance, with a particular focus on national security. This workshop is one of several activities undertaken by the National Research Council that bears on the contributions of various scientific disciplines to understanding and defending against terrorism. The presentations were grouped in four sessions â€" Social Network Theory Perspectives, Dynamic Social Networks, Metrics and Models, and Networked Worlds â€" each of which concluded with a discussant-led roundtable discussion among the presenters and workshop attendees on the themes and issues raised in the session.
Spatial Networks
This book provides a complete introduction into spatial networks. It offers the mathematical tools needed to characterize these structures and how they evolve in time and presents the most important models of spatial networks. The book puts a special emphasis on analyzing complex systems which are organized under the form of networks where nodes and edges are embedded in space. In these networks, space is relevant, and topology alone does not contain all the information. Characterizing and understanding the structure and the evolution of spatial networks is thus crucial for many different fields, ranging from urbanism to epidemiology. This subject is therefore at the crossroad of many fields and is of potential interest to a broad audience comprising physicists, mathematicians, engineers, geographers or urbanists. In this book, the author has expanded his previous book ("Morphogenesis of Spatial Networks") to serve as a textbook and reference on this topic for a wide range of students and professional researchers.
Morphogenesis of Spatial Networks
This book develops a morphodynamical approach of spatial networks with a particular emphasis on infrastructure networks such as streets, roads and transportation networks (subway, train). The author presents the mathematical tools needed to characterize these structures and how they evolve in time. The book discusses the most important empirical results and stylized facts, and will present the most important models of spatial networks. The target audience primarily comprises research scientists interested in this rapidly evolving and highly interdisciplinary field, but the book may also be beneficial for graduate students interested in large networks.
Biological Network Analysis
Biological Network Analysis: Trends, Approaches, Graph Theory, and Algorithms considers three major biological networks, including Gene Regulatory Networks (GRN), Protein-Protein Interaction Networks (PPIN), and Human Brain Connectomes. The book's authors discuss various graph theoretic and data analytics approaches used to analyze these networks with respect to available tools, technologies, standards, algorithms and databases for generating, representing and analyzing graphical data. As a wide variety of algorithms have been developed to analyze and compare networks, this book is a timely resource.
