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Dynamics Of Complex Systems (Studies in Nonlinearity)

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This book is a big disappointment. In a 800- hundred pages volume one would expect to find the main ideas of the hot area of complexity. Most of the recent results obtained over the last 10 years are not there. Not a single word on criticality and scaling, modelling of random networks, the implications of critical phenomena to complexity, or the recent approaches to evolutionary dynamics. Even those problems already presented in other monographs (as pattern formation in biology) do not receive an adequate attention to those interested in complexity issues. Save your money.

This text provides an excellent introduction to the numerous and diverse techniques used in the study of complex systems. The field of complex systems emerged from a union of ideas from many seemingly disparate areas of research. Where many texts on complex systems speak to this union of ideas, Bar-Yam's text focuses on both the ideas and their implementation in the form of techniques and methods used in the study of these systems. These methodologies originate from many fields of research and several texts could be written about any single one; however I feel that the author has done an excellent job in choosing an important set of problems to present and the detail in which they are presented. This book is appropriate for advanced undergraduates and graduate students. I highly recommended it to my students in my course on complex systems, and if your interests coincide with the topics covered in this book, I highly recommend it to you.

This book is designed as a text to introduce graduate students in science to the concepts and methods in the ``science of complexity'' which comprises studies in mathematics, physics, chemistry, biology, computer science, sociology, psychology, economics, anthropology, and philosophy. Written from the perspectives of a physicist, definitions are informal; thus a concise definition of a complex system is not given. The concept of a complex system is introduced through examples, and informally described as having ``a large number of interacting parts'' although ``even a few interacting objects can behave in complex ways.'' More precisely, complexity is defined as ``the amount of information necessary to describe a system.'' Another key concept is the phenomenon of emergence which arises when ``the collective behavior [of a complex system] is not readily understood from the behavior of its parts.''

Dynamics of Complex Systems opens with a long chapter (278 pages) of ``introduction and preliminaries'' which surveys iterative maps; thermodynamics and statistical mechanics; activated processes (glasses); cellular automata; statistical fields; computer simulations; information theory; computation; and fractals, scaling and renormalization. It is suggested that this chapter can serve as the basis for a one-semester course. This introductory chapter is followed by eight chapters devoted two each to four different subjects: neural networks, protein folding, biological evolution, and human civilization. In each of these pairs of chapters, the first is more detailed and the second more general. Thus the first of the two chapters on neural networks describes neural network models (Hopfield's attactor models) whereas the second discusses the phenomenon of sleep and models of mind, with similar divisions of labor in the pairs of chapters on protein folding and on biological evolution. In the final chapter, it is noted that ``human civilization is more complex than we are as individuals.''

Alwyn Scott
http://personal.riverusers.com/~rover/

That physical systems are complex has been acknowledged for centuries, but only in recent decades has the scientific community, especially physicists and biologists, directly confronted complexity. This book discusses complex systems from the dynamical systems perspective, and as such can be read by physicists, mathematicians, and mathematical biologists. Biologists in particular will find the discussion of `emergence' the most important one, especially systems biologists. Physicists and mathematicians who study dynamical systems tend to not be concerned with their origins, whether they are in biology or some other area. But physicists do concern themselves with the experimental relevance of dynamical systems, unlike mathematicians who are sorely concerned with their formal properties, and do not care at all if they can find expression in the real world. But it goes without saying that the theory of complex systems has found application in finance, genetic engineering, cryptography, network engineering, and many other areas. This book gives a good overview of the techniques used to study complex systems, and can be read by anyone with the necessary mathematical preparation, consisting of probability theory and elementary calculus.

Systems that are simple can become complex by only a slight alteration in their configuration. The gravitational three-body system in classical mechanics is a good example of this. The dynamics of two objects interacting gravitationally can be solved explicitly, but the system consisting of three bodies cannot. The complexity in these two cases is measured by the availability of solutions to the dynamics of the system. The author is very aware that more involved measures of complexity are needed and he gives examples of these in the book. Mathematical techniques from probability and statistics are of course used throughout the book to frame these measures more quantitatively. This reflects the author's stated strategy throughout the book, namely to describe the essential characteristics of a class of systems, and employ statistical techniques to find the properties and behaviors of these systems.

The concepts of emergence and complexity are fundamental to a study of complex systems, the author argues and early on in the book he clears up some of the confusions behind the use of these terms in the scientific literature. A `complex system' is one which is constructed from many components and whose behavior cannot be determined from the behavior of these components, i.e. the behavior of the system is `emergent.' The `complexity' of a system, on the other hand, is the amount of information needed to describe the system. This is a somewhat subtle definition, and quite a few proposals have been put forward in the literature for measuring complexity. The author settles on a familiar method, the `entropy' for measuring complexity, but with a warning to the reader that the calculation of the entropy is dependent on the particular length or time scale over which the system is observed. For extremely long time scales (of observation), one can get away with describing systems as always in equilibrium. In this case the entropy would be maximum but the system would not be viewed as being complex. For very short time scales (of observation) , the entropy of the system is very small but due to the ability to observe the microscopic dynamics of the system it would be viewed as highly complex.

These considerations lead the author to introduce the concept of a 'complexity profile' of a system, which he discusses at some length in the last pages of the book. The complexity profile is designed to study the the dependence of complexity on both length and time scales. The concept is dependent on the notion of a sequence of observers that are ordered according to their ability to distinguish microstates. The author calculates the complexity profile of the ideal gas and shows that the complexity of a microstate for this case is simply the entropy, but as the number of microstates with a given region increases, the complexity approaches zero. Other examples of the complexity profile are discussed, one being for observers that only measure the positions of particles and not the momentum. The author also studies the connection between the complexity profile and the predictability or chaotic behavior of the system, where chaotic systems are viewed as being ones where information from a particular scale can be transferred to a larger scale, as contrasted with dissipative systems where information on a large scale is transferred to a smaller scale. The author gives various arguments and calculations that illustrate the difference in complexity profiles between chaotic systems and those of conservative, nonchaotic systems. The discussion is fairly convincing but if the complexity profile is important in complex systems, its defintion and properties should have been included at the beginning of the book, and serve as a central theme behind the discussions throughout the entire book. As it stands the complexity profile comes across as a concept that is purely ancillary to the study of complex systems. It certainly does not appear to be indispensable in discussing irreversibility of physical systems, this problem still being the most pressing one in statistical mechanics and is still hotly debated at the present time.

This is a presentation of the models of complexity in a very clear and thought provoking way. Clearly presented for upper undergraduate/graduate level, rich in examples to deepen in the concepts with amounts and amounts of questions, pronblems and challenges, that are completely answered in the text. It unifiess most complexity issues giving a framework picture of todays frontiers.

This is a beautifully written and thought-provoking work that presents the field of complex systems in a unified manner. The writing is highly engaging and stimulating with a broad range of topics. The material is pitched at just the right level, focusing on the concepts without getting buried in unnecessary details, while avoiding superficiality. I highly recommend this excellent book.

that information is the opposite of entropy which is a measure of disorder or uncertainty. However because this book is about complexity and not information per se, I will only briefly refer to his mistakes with the latter as I have explained them further in other reviews that are specifically on that topic.

Shannon's information rate from communications theory, R, is an entropy like formula but most critically it is a state function difference of the uncertainty reduction to a recognizer after a measurement. Entropy is not a proper measure of disorder or uncertainty; the 2nd law of entropy increase of the universe applied long before there were any observers. It is a measure of the dispersal of energy. Going back in time is not going back to perfect order, but quite the opposite. I have not seen proper definitions in any book but there are PhD level articles available on the internet with proper definitions such as the Principia Cybernetica Web and molecular biologist Dr Thomas Schneider's website. Biologist Richard Dawkins also has an accurate short article on the internet. Most physicists have the definitions wrong unfortunately and believe information evolved before life, which is false. (A recognizer is required, whether a ribosome or mind etc.) Instead a better definition of complexity than the present author offers would indicate that the universe has increased in complexity through gravitational clumping (among other things). By making the mistake then the physicists and present author believe maximum information is randomness or equilibrium. This is the definition of algorithmic complexity.

As the author adapts algorithmic theory to his complexity profile he arrives at formulas that are observer dependant: "the complexity profile [is] the length of the description [of] the error allowed [as] the description increases." This is of little or no practical use. Again the universe has grown in complexity (or at least in pockets or we wouldn't be here) without relying on the degree of focus of any observer. A crystal is highly ordered relative to say a human cell whose complexity is a result of a multitude of interactions of chemical agents and macro molecules. This is where his analysis falls silent, in fact wrong. He says (page 741) "short-range correlations decrease the microstate complexity..." Well that's because he has a flawed method of using statistical mechanics. There is likely no universal complexity algorithm. Consider that a single gene can yield up to thousands of different proteins. One should be wary however of any formula that treats correlations as reduced complexity! Again the crystal vs the cell!

However there are ways of measuring the critical biological requirement of interactions that in fact increase complexity, the opposite of equilibrium statistical mechanics, a flawed tool. For instance in a recent article at lanl.arXiv.org, authors Edwin Wang et. al. apply Pearson's correlation coefficient to show that "genes with higher cis-regulation complexity are more coordinately regulated by transcription factors at the transcriptional level and by micro RNA's at the post-transcriptional level. This is a potentially novel discovery of a mechanism for coordinated regulation of gene expression...We found a positive correlation between these two groups of transcriptional regulators... " Measures of correlations are key in studying biological complexity and are not based on an observer's focus ability.

For a layman's guide to the issue of correlations for life see Irun Cohen's book 'Tending Adam's Garden' (though it has no quantitative aspect).

The book is a tour around the paradigms used by scientists in
Complex Systems. While normal science is about using and re-using the paradigms without much creativity or true aportation to knowledge or understanding, the situation is worse in complex systems, since, as an emerging area it has multiple (competing?) paradigms, to the point that it is not possible to define a "complex system" in a form that encompases all the paradigms. The book certainly does not solve this problem, yet the author acknowledges the difficulty present in saying what a complex system is.
Complex systems is not an area of research but a community of researchers united by their interests.
The book is then a compilation of the "how to" and the believes for each paradigm, several of them carry very little science and have left the idea of "refutation" burried under piles of meaningless papers. Not surprissingly, some authors claim that complex systems is a postmodern scienceComplexity and Postmodernism: Understanding Complex Systems. And truly, the complex systems of Bar-Yam are only possible after we have buried reason and have accepted that science has nothing to do with truth.
Too much for me, not a book I recommend to my students.

This is a simplistic, out of date treatment of a diverse and rapidly changing field. It is a disappoint that Bar Yam failed to capture the depth of the field, instead offering a cursory look at, mostly, classical examples in which Bar Yam did not take part. I would prefer, instead, to see a leader in the field write such a text, such that I could be assured that details that were omitted were less relevant, not simply forgotten.