*the science of self-organized criticality*

Author: Per Bak

Publisher: Springer Science & Business Media

ISBN: 1475754264

Category: Mathematics

Page: 212

View: 1542

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### How Nature Works

Self-organized criticality, the spontaneous development of systems to a critical state, is the first general theory of complex systems with a firm mathematical basis. This theory describes how many seemingly desperate aspects of the world, from stock market crashes to mass extinctions, avalanches to solar flares, all share a set of simple, easily described properties. "...a'must read'...Bak writes with such ease and lucidity, and his ideas are so intriguing...essential reading for those interested in complex systems...it will reward a sufficiently skeptical reader." -NATURE "...presents the theory (self-organized criticality) in a form easily absorbed by the non-mathematically inclined reader." -BOSTON BOOK REVIEW "I picture Bak as a kind of scientific musketeer; flamboyant, touchy, full of swagger and ready to join every fray... His book is written with panache. The style is brisk, the content stimulating. I recommend it as a bracing experience." -NEW SCIENTIST

### How Nature Works

### Self-Organized Criticality

A clear and concise introduction to this new, cross-disciplinary field.

### Self-Organized Criticality in Earth Systems

Self-organized criticality (SOC) has become a magic word in various scientific disciplines; it provides a framework for understanding complexity and scale invariance in systems showing irregular fluctuations. In the first 10 years after Per Bak and his co-workers presented their seminal idea, more than 2000 papers on this topic appeared. Seismology has been a field in earth sciences where the SOC concept has already deepened the understanding, but there seem to be much more examples in earth sciences where applying the SOC concept may be fruitful. After introducing the reader into the basics of fractals, chaos and SOC, the book presents established and new applications of SOC in earth sciences, namely earthquakes, forest fires, landslides and drainage networks.

### Self-Organized Criticality in Astrophysics

Markus Aschwanden introduces the concept of self-organized criticality (SOC) and shows that due to its universality and ubiquity it is a law of nature for which he derives the theoretical framework and specific physical models in this book. He begins by providing an overview of the many diverse phenomena in nature which may be attributed to SOC behaviour. The author then introduces the classic lattice-based SOC models that may be explored using numerical computer simulations. These simulations require an in-depth knowledge of a wide range of mathematical techniques which the author introduces and describes in subsequent chapters. These include the statistics of random processes, time series analysis, time scale distributions, and waiting time distributions. Such mathematical techniques are needed to model and understand the power-law-like occurrence frequency distributions of SOC phenomena. Finally, the author discusses fractal geometry and scaling laws before looking at a range of physical SOC models which may be applicable in various aspects of astrophysics. Problems, solutions and a glossary will enhance the pedagogical usefulness of the book. SOC has been receiving growing attention in the astrophysical and solar physics community. This book will be welcomed by students and researchers studying complex critical phenomena.

### Bak's Sand Pile

Did the terrorist attacks on the United States in 2001, the massive power blackout of 2003, Hurricane Katrina in 2005, and the Gulf oil spill of 2010 'just happen'-or were these shattering events foreseeable? Do such calamities in fact follow a predictable pattern? Can we plan for the unforeseen by thinking about the unthinkable?Ted Lewis explains the pattern of catastrophes and their underlying cause. In a provocative tour of a volatile world, he guides the reader through mega-fires, fragile power grids, mismanaged telecommunication systems, global terrorist movements, migrating viruses, volatile markets and Internet storms. Modern societies want to avert catastrophes, but the drive to make things faster, cheaper, and more efficient leads to self-organized criticality-the condition of systems on the verge of disaster. This is a double-edged sword. Everything from biological evolution to political revolution is driven by some collapse, calamity or crisis. To avoid annihilation but allow for progress, we must change the ways in which we understand the patterns and manage systems. Bak's Sand Pile explains how.

### At Home in the Universe

A major scientific revolution has begun, a new paradigm that rivals Darwin's theory in importance. At its heart is the discovery of the order that lies deep within the most complex of systems, from the origin of life, to the workings of giant corporations, to the rise and fall of great civilizations. And more than anyone else, this revolution is the work of one man, Stuart Kauffman, a MacArthur Fellow and visionary pioneer of the new science of complexity. Now, in At Home in the Universe, Kauffman brilliantly weaves together the excitement of intellectual discovery and a fertile mix of insights to give the general reader a fascinating look at this new science--and at the forces for order that lie at the edge of chaos. We all know of instances of spontaneous order in nature--an oil droplet in water forms a sphere, snowflakes have a six-fold symmetry. What we are only now discovering, Kauffman says, is that the range of spontaneous order is enormously greater than we had supposed. Indeed, self-organization is a great undiscovered principle of nature. But how does this spontaneous order arise? Kauffman contends that complexity itself triggers self-organization, or what he calls "order for free," that if enough different molecules pass a certain threshold of complexity, they begin to self-organize into a new entity--a living cell. Kauffman uses the analogy of a thousand buttons on a rug--join two buttons randomly with thread, then another two, and so on. At first, you have isolated pairs; later, small clusters; but suddenly at around the 500th repetition, a remarkable transformation occurs--much like the phase transition when water abruptly turns to ice--and the buttons link up in one giant network. Likewise, life may have originated when the mix of different molecules in the primordial soup passed a certain level of complexity and self-organized into living entities (if so, then life is not a highly improbable chance event, but almost inevitable). Kauffman uses the basic insight of "order for free" to illuminate a staggering range of phenomena. We see how a single-celled embryo can grow to a highly complex organism with over two hundred different cell types. We learn how the science of complexity extends Darwin's theory of evolution by natural selection: that self-organization, selection, and chance are the engines of the biosphere. And we gain insights into biotechnology, the stunning magic of the new frontier of genetic engineering--generating trillions of novel molecules to find new drugs, vaccines, enzymes, biosensors, and more. Indeed, Kauffman shows that ecosystems, economic systems, and even cultural systems may all evolve according to similar general laws, that tissues and terra cotta evolve in similar ways. And finally, there is a profoundly spiritual element to Kauffman's thought. If, as he argues, life were bound to arise, not as an incalculably improbable accident, but as an expected fulfillment of the natural order, then we truly are at home in the universe. Kauffman's earlier volume, The Origins of Order, written for specialists, received lavish praise. Stephen Jay Gould called it "a landmark and a classic." And Nobel Laureate Philip Anderson wrote that "there are few people in this world who ever ask the right questions of science, and they are the ones who affect its future most profoundly. Stuart Kauffman is one of these." In At Home in the Universe, this visionary thinker takes you along as he explores new insights into the nature of life.

### Self-Organised Criticality

An overview of results and methods, written for graduates and researchers in physics, mathematics, biology, sociology, finance, medicine and engineering.

### Complexity

A look at the rebellious thinkers who are challenging old ideas with their insights into the ways countless elements of complex systems interact to produce spontaneous order out of confusion

### Complexity

Examines the field of complexity science, with sections focusing on how the discipline works within computer simulations, natural ecosystems, and various social systems.

### Dynamic Patterns

foreword by Hermann Haken For the past twenty years Scott Kelso's research has focused on extending the physical concepts of self- organization and the mathematical tools of nonlinear dynamics to understand how human beings (and human brains) perceive, intend, learn, control, and coordinate complex behaviors. In this book Kelso proposes a new, general framework within which to connect brain, mind, and behavior.Kelso's prescription for mental life breaks dramatically with the classical computational approach that is still the operative framework for many newer psychological and neurophysiological studies. His core thesis is that the creation and evolution of patterned behavior at all levels -- from neurons to mind -- is governed by the generic processes of self-organization. Both human brain and behavior are shown to exhibit features of pattern-forming dynamical systems, including multistability, abrupt phase transitions, crises, and intermittency.Dynamic Patterns brings together different aspects of this approach to the study of human behavior, using simple experimental examples and illustrations to convey essential concepts, strategies, and methods, with a minimum of mathematics.Kelso begins with a general account of dynamic pattern formation. He then takes up behavior, focusing initially on identifying pattern-forming instabilities in human sensorimotor coordination. Moving back and forth between theory and experiment, he establishes the notion that the same pattern-forming mechanisms apply regardless of the component parts involved (parts of the body, parts of the nervous system, parts of society) and the medium through which the parts are coupled. Finally, employing the latest techniques to observe spatiotemporal patterns of brain activity, Kelso shows that the human brain is fundamentally a pattern forming dynamical system, poised on the brink of instability. Self-organization thus underlies the cooperative action of neurons that produces human behavior in all its forms.

### Fractals, Chaos, Power Laws

This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author - hailed by Publishers Weekly as a modern Lewis Carroll - conveys memorable insights in the form of puns and puzzles. 1992 edition.

### Deterministic Abelian Sandpile Models and Patterns

The model investigated in this work, a particular cellular automaton with stochastic evolution, was introduced as the simplest case of self-organized-criticality, that is, a dynamical system which shows algebraic long-range correlations without any tuning of parameters. The author derives exact results which are potentially also interesting outside the area of critical phenomena. Exact means also site-by-site and not only ensemble average or coarse graining. Very complex and amazingly beautiful periodic patterns are often generated by the dynamics involved, especially in deterministic protocols in which the sand is added at chosen sites. For example, the author studies the appearance of allometric structures, that is, patterns which grow in the same way in their whole body, and not only near their boundaries, as commonly occurs. The local conservation laws which govern the evolution of these patterns are also presented. This work has already attracted interest, not only in non-equilibrium statistical mechanics, but also in mathematics, both in probability and in combinatorics. There are also interesting connections with number theory. Lastly, it also poses new questions about an old subject. As such, it will be of interest to computer practitioners, demonstrating the simplicity with which charming patterns can be obtained, as well as to researchers working in many other areas.

### Think Complexity

Complexity science uses computation to explore the physical and social sciences. In Think Complexity, you’ll use graphs, cellular automata, and agent-based models to study topics in physics, biology, and economics. Whether you’re an intermediate-level Python programmer or a student of computational modeling, you’ll delve into examples of complex systems through a series of worked examples, exercises, case studies, and easy-to-understand explanations. In this updated second edition, you will: Work with NumPy arrays and SciPy methods, including basic signal processing and Fast Fourier Transform Study abstract models of complex physical systems, including power laws, fractals and pink noise, and Turing machines Get Jupyter notebooks filled with starter code and solutions to help you re-implement and extend original experiments in complexity; and models of computation like Turmites, Turing machines, and cellular automata Explore the philosophy of science, including the nature of scientific laws, theory choice, and realism and instrumentalism Ideal as a text for a course on computational modeling in Python, Think Complexity also helps self-learners gain valuable experience with topics and ideas they might not encounter otherwise.

### System Effects

Based on more than three decades of observation, Robert Jervis concludes in this provocative book that the very foundations of many social science theories--especially those in political science--are faulty. Taking insights from complexity theory as his point of departure, the author observes that we live in a world where things are interconnected, where unintended consequences of our actions are unavoidable and unpredictable, and where the total effect of behavior is not equal to the sum of individual actions. Jervis draws on a wide range of human endeavors to illustrate the nature of these system effects. He shows how increasing airport security might actually cost lives, not save them, and how removing dead trees (ostensibly to give living trees more room) may damage the health of an entire forest. Similarly, he highlights the interconnectedness of the political world as he describes how the Cold War played out and as he narrates the series of events--with their unintended consequences--that escalated into World War I. The ramifications of developing a rigorous understanding of politics are immense, as Jervis demonstrates in his critique of current systemic theories of international politics--especially the influential work done by Kenneth Waltz. Jervis goes on to examine various types of negative and positive feedback, bargaining in different types of relationships, and the polarizing effects of alignments to begin building a foundation for a more realistic, more nuanced, theory of international politics. System Effects concludes by examining what it means to act in a system. It shows how political actors might modify their behavior in anticipation of system effects, and it explores how systemic theories of political behavior might account for the role of anticipation and strategy in political action. This work introduces powerful new concepts that will reward not only international relations theorists, but also all social scientists with interests in comparative politics and political theory.

### A Crude Look at the Whole

Imagine trying to understand a stained glass window by breaking it into pieces and examining it one shard at a time. While you could probably learn a lot about each piece, you would have no idea about what the entire picture looks like. This is reductionism—the idea that to understand the world we only need to study its pieces—and it is how most social scientists approach their work. In A Crude Look at the Whole, social scientist and economist John H. Miller shows why we need to start looking at whole pictures. For one thing, whether we are talking about stock markets, computer networks, or biological organisms, individual parts only make sense when we remember that they are part of larger wholes. And perhaps more importantly, those wholes can take on behaviors that are strikingly different from that of their pieces. Miller, a leading expert in the computational study of complex adaptive systems, reveals astounding global patterns linking the organization of otherwise radically different structures: It might seem crude, but a beehive’s temperature control system can help predict market fluctuations and a mammal’s heartbeat can help us understand the “heartbeat” of a city and adapt urban planning accordingly. From enduring racial segregation to sudden stock market disasters, once we start drawing links between complex systems, we can start solving what otherwise might be totally intractable problems. Thanks to this revolutionary perspective, we can finally transcend the limits of reductionism and discover crucial new ideas. Scientifically founded and beautifully written, A Crude Look at the Whole is a powerful exploration of the challenges that we face as a society. As it reveals, taking the crude look might be the only way to truly see.

### Parallel Problem Solving from Nature-PPSN VI

We are proud to introduce the proceedings of the Sixth International Conference on Parallel Problem Solving from Nature, PPSN VI, held in Paris, Prance, on 18-20 September 2000. PPSN VI was organized in association with the Genetic and Evolutionary Computing Conference (GECCO'2000) and the Congress on Evolutionary Computation (CEC'2000), reflecting the beneficial interaction between the conference activities in Europe and in the USA in the field of natural computation. Starting in 1990 in Dortmund, Germany (Proceedings, LNCS vol. 496, Sprin ger, 1991), this biannual meeting has been held in Brussels, Belgium (Procee dings, Elsevier, 1992), Jerusalem, Israel (Proceedings, LNCS vol. 866, Springer, 1994), Berlin, Germany (Proceedings, LNCS vol. 1141, Springer, 1996), and Amsterdam, The Netherlands (Proceedings, LNCS vol. 1498, Springer, 1998), where it was decided that Paris would be the location of the 2000 conference with Marc Schoenauer as the general chair. The scientific content of the PPSN conference focuses on problem solving pa radigms gleaned from a natural models. Characteristic for Natural Computing is the metaphorical use of concepts, principles and mechanisms underlying natural systems, such as evolutionary processes involving mutation, recombination, and selection in natural evolution, annealing or punctuated equilibrium processes of many-particle systems in physics, growth processes in nature and economics, collective intelligence in biology, DNA-based computing in molecular chemistry, and multi-cellular behavioral processes in neural and immune networks.

### Ubiquity

The author outlines his theory of the "Tipping Point"--that tendency for things to organize themselves into a moment of crisis that results in collapse and an eventual rebuilding process--and applies it to human history. 25,000 first printing.

### Microdosimetry and Its Applications

Microdosimetry and Its Applications is an advanced textbook presenting the fundamental concepts and numerical aspects of the absorption of energy by matter exposed to ionizing radiation. It is the only comprehensive work on the subject that can be considered definitive. It provides a deeper understanding of the initial phase of the interaction of ionizing radiation with matter, especially biological matter, and its consequences.

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Publisher: Springer Science & Business Media

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