Reviews (1)

Nonlinear Dynamics : A Two-Way Trip from Physics to Math
The best book so far i have read on Nonlinear Dynamics. From the best of the best. ... Read more

Book Description

The papers contributed to this volume bring to light some fundamental advances and innovative techniques and collectively contribute significantly to our understanding of a multiplicity of physical, biological, and economic phenomena. Part I of this book present new ideas and developments in dynamics, dynamical systems, and control. Part II presents novel techniques and their applications to a broad variety of problems ranging from the control of cars and robots to optimal spacecraft trajectories to Mars. The papers of Part III explore the potential of dynamics and control for contributing to our understanding of areas such as drug consumption, economic games, epidemics, and human posture control. ... Read more

Book Description

This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject. ... Read more

Reviews (1)

You Don't Need a Math Degree to Understand this
Chaos is such a visually stunning field of study, since you invariably run into those computer generated figures of Julia sets or random fractal landscapes or cloud formations.

But can we get a rigorous, first principles explanation that is broadly accessible to undergraduates with good, but not advanced math preparation? Well, you might consider this recent book. The authors have gone to some length to explain events without appealing to more than simple calculus.

Nothing flashy. But you can obtain a good understanding of fractal dimensions, self iterating systems (like a Sierpinski gasket) and noise. ... Read more

Book Description

A comprehensive, one-stop reference for new system modeling and identification tools

The field of control-oriented identification has grown immensely over the past decade, spawning numerous results and modeling techniques and promising the potential to influence science and engineering for years to come. In this new work, Jie Chen and Guoxiang Gu, two leading authorities on worst-case identification, share their vision and walk readers through carefully selected topics from the vast literature, offering a much-needed, timely comprehensive introduction to the theory of Hƒ identification and model validation.

Chen and Gu clearly demonstrate the pros and cons of the worst-case approach in comparison to traditional techniques and provide researchers in systems and control theory with ready access to many new and complementary identification tools. Through a rigorous yet logical and easy-to-follow treatment, supported by many deep insights, intuitions, and philosophical thinking, they:

• Survey and assess the current state of control and system identification research
• Develop both two-stage and interpolatory algorithms for system identification
• Show readers how to analyze the properties of linear algorithms
• Offer a unique emphasis on model uncertainty estimation and complexity, two of the central issues
• Develop both time-domain and frequency-domain identification algorithms
• Explain in detail uncertainty model validation concepts and techniques
• Devote a chapter to a review of the requisite mathematics

Provide a concise yet self-contained appendix on several key relevant notions ... Read more

Book Description

This text on the increasingly popular topic of chaos is accessible to a varied undergraduate audience. Gulick is co-author of a successful calculus book and is an excellent expositor. His recent interest in teaching chaotic dynamical systems to undergraduates produced a set of class notes that developed into this text. ... Read more

Reviews (3)

Not too bad
In the field of chaotic dynamics, does there exist _the_ standard textbook for undergrads? I think not. Still, in most colleges, _chaos_ is a subtopic you briefly go through (most of the time just `skipped' through) while studying differential equations, mathematical physics or classical physics. To be competely honest, my impression is that those ``subtopics'' usually don't make a good intro to chaotic dynamics, either. I have read some textbooks targeted at undergraduates and Gulick's was not too bad to skim through what we have in chaotic dynamics. However, Gulick pays too much attention on the basics (analysis and differential equations) and this may seem such a waste of space given the limited number of pages (some two hundreds). Naturally, his explanations are not detailed and gives the impression that things are done rather hastily. But, I must say, this book is superier to some other books that spends time neither on the basics nor the analytic aspects of chaotic dynamics.

Only Okay
I had to use this book for a class I took at Bryn Mawr college called "Chaotic Dynamical Systems". There are some mistakes in the book, although I don't remember specifically what they were, and my instructor had to point some of them out. The book, to my knowledge, only covers discrete dynamical systems, and contrary to what the above reviewer says, there is some real analysis involved: i.e. some proofs and definitions involving epsilon and delta. That's about all I can say because I don't remember the book very well, and we only got through about half of it. I recall that most people in my class didn't like the book very much either.

Fantastic Resource for Undergraduates
Denny Gulick opens here a direct access to the mathematical technics for understanding chaotic phenomena. Any undergraduate with some pre or calculus knowledge, little algebra and very few differential equations (rich introductions to these topics are included in every chapter)can access the basics of this growing "Chaos Theory", that is beeing applied to dynamics in all fields. Professor Gulick makes an outstanding aproach with this book. He makes accesible this field to beginners, self-students or newcomers to mathematics, covering so a huge gap in the literature. It is full of examples, detailed exercises and explained in a very comprehensible and student-friendly way, without losing rigour and technic. It has a companion booklet to order separately that includes "all the solutions to the exercises, done step by step and a true Basic software for Pcs or Macs. ... Read more

Book Description

Technical problems often lead to differential equations with piecewise-smooth right-hand sides. Problems in mechanical engineering, for instance, violate the requirements of smoothness if they involve collisions, finite clearances, or stick–slip phenomena. Systems of this type can display a large variety of complicated bifurcation scenarios that still lack a detailed description.This book presents some of the fascinating new phenomena that one can observe in piecewise-smooth dynamical systems. The practical significance of these phenomena is demonstrated through a series of well-documented and realistic applications to switching power converters, relay systems, and different types of pulse-width modulated control systems. Other examples are derived from mechanical engineering, digital electronics, and economic business-cycle theory.

The topics considered in the book include abrupt transitions associated with modified period-doubling, saddle-node and Hopf bifurcations, the interplay between classical bifurcations and border-collision bifurcations, truncated bifurcation scenarios, period-tripling and -quadrupling bifurcations, multiple-choice bifurcations, new types of direct transitions to chaos, and torus destruction in nonsmooth systems.

In spite of its orientation towards engineering problems, the book addresses theoretical and numerical problems in sufficient detail to be of interest to nonlinear scientists in general. ... Read more

Book Description

Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit "chaotic behavior." The first portion of the book is based on lectures given at the University of London and covers the background to dynamical systems, the fundamental properties of such systems, the local bifurcation theory of flows and diffeomorphisms and the logistic map and area-preserving planar maps.The authors then go on to consider current research in this field such as the perturbation of area-preserving maps of the plane and the cylinder.The text contains many worked examples and exercises, many with hints.It will be a valuable first textbook for senior undergraduate and postgraduate students of mathematics, physics, and engineering. ... Read more

Reviews (2)

Excellent Introduction to the Subject
covers most important areas of the subject with a clear yet rigorous approach. Advanced text better suited for graduate students in applied math. It promises as a must for anyone serious about the subject

Excellent focus on what is important
Dynamical systems is a vast subject to which no single book can provide an adequate introduction, but the authors do an excellent job of focusing on what is important and avoiding the temptation to go off on enticing tangents. Their treatment is clear, and this book is highly recommended for any student seeking a solid foundation for further work. ... Read more

Book Description

Contents

1 Quarks and Leptons.2 Particle Interactions in the Standard Mode.3 Electromagnetism as a Gauge Theory.4 Relativistic Quantum Mechanics.5 Quantum Field Theory I.6 Quantum Field Theory II: Interacting Scalar Fields.7 Quantum Field Theory III: Complex Scalar Fields, Dirac and Maxwell fields; Introduction of Electromagnetism.8 Elementary Processes in Scalara and Spinor Electrodynamics.9 Deep Inelastic Electron-nucleon Scattering and the Quark Parton Model.10 Higher Order Processes and Renormalisation. 11 Appendices.Index

Synopsis

This book provides an accessible, practical and comprehensive introduction to the three gauge theories of the 'standard model' of particle physics: quantum electrodynamics (QED), quantum chromodynamics (QCD) and the electroweak theory. For each of them, the authors provide a thorough discussion of the main conceptual points; a detailed exposition of many practical calculations of physical quantities; and a comparison of these quantitative predictions with experimental results.

For this two-volume third edition, much of the book has been re-written to reflect developments over the last decade, both in the curricula of university courses, and in particle physics research. On the one hand, substantial new material has been introduced which is intended for use in undergraduate physics courses. New introductory chapters provide a precise historical account of the properties of quarks and leptons, and a qualitative overview of the quantum field description of their interactions, at a level appropriate to third year courses. The chapter on relativistic quantum mechanics has been enlarged and is supplemented by additional sections on scattering theory and Green functions, in a form appropriate to fourth year courses. On the other hand, since precision experiments now test the theories beyond lowest order in perturbation theory, an understanding of the data requires a more sophisticated knowledge of quantum field theory, including ideas of renormalisation. The treatment of quantum field theory has therefore been considerably extended so as to provide a uniquely accessible and self-contained introduction to quantum field dynamics, as described by Feynman graphs. The level is suitable for advanced fourth year undergraduates and first year graduates.

These developments are all contained in the first volume, which ends with a discussion of higher order corrections in QED; the second volume is devoted to the non-Abelian gauge theories of QCD and the electroweak theory. As in the first two editions, emphasis is placed throughout on developing realistic calculations from a secure physical and conceptual basis.

Readership

Graduate and senior undergraduate students taking courses on the standard model of particle physics. Postgraduate students and researchers in particle physics. ... Read more

Reviews (2)

If you are having trouble with QFT - BUY THIS BOOK!
This book (2nd edition) has 15 chapters . I have just finished chapter 4 entitled QFT and I am compeled to write this review! After a year of studying of QFT informally I can report that this is the way to introduce yourself to the topic. I've been through Mandl & Shaw, Peskin & Schoeder, Ryder, Weinberg and a few others and this is heads and tails the BEST intro available. In 42 pages, Aitchison & Hey make the transistion from classical to QM and from QM to QFT as gracefully as I can conceive. For example, the transition from the discrete Lagrangian to the field Lagrangian is very explicit. One benfit of this is that the dependence of L on partial of phi wrt x is clearly motivated leading to the manifestly relativistically invariant form of L. They explicitly develop physical intuition at every step of the way - for example, this is the only book that I have found that explicitly asks the question where is QM's wavefunction in the QFT formalism? Answer - The vacuum to one-particle matrix elements of the field operators. The transistion from free fields to interacting fields is far clearer than any other treatment I've seen. I also appreciated that the problems were used to basically fill in details left out of the text. I was able to 'practice' the various kinds of manipulations that are required.

Amazingly clear introduction to the subject
This book is the best book I've seen on the subject. The qualitative description of qunatum field theory in particular are amazingly lucid for the subject. The only possible flaw in the book is that the problems at the end of each chapter are both few in number and for the most part do not challenge the student at all; for the most part they are just rote calculations. ... Read more

Reviews (1)

examples and activities give you a real feel for chaos
As a teacher attempting to introduce chaos theory into high school physics and mathematics classes, the book gave many examples of practical activities. It also gave many examples of how chaos could and would become useful. There are currently so many false methods being used to integrate subject matter in education; chaos theory has great potential to demonstrate clear connections between arts, sciences, and social sciences, and Peak and Frame in a simple manner bring this to light. ... Read more

Book Description

No matter what field you are working in or studying, Advanced Systems Thinking, Engineering, and Management offers you a comprehensive understanding of systems ideas and methods to help you achieve unmatched success with your challenging projects. This unique resource helps you add a systems-scientific grounding to systems engineering enterprises, showing you how to solve intractable problems, design systems to accommodate complex environments, and manage both creative and operational systems. You learn how to conceive, design and manage a systems engineering process for optimal results. ... Read more

Book Description

This book presents the genuine essence of engineering of fuzzy sets. It includes sound theory, a general methodological framework, efficient algorithms, and detailed validation schemes. Fuzzy Sets Engineering offers discussions in a top-down fashion, with general methodology followed by specific domains which rely strongly on the methodological foundations. Based on this methodological framework, the book then provides a careful, in-depth exposure to very diversified areas. Numerous application-driven examples are included.It discusses general modelling methodology of fuzzy sets then describes useful ideas of neurocomputations. Self-contained chapters allow readers to customize their reading by selecting any of these essential design topics: fuzzy controller, fuzzy control, or information processing with recurrent systems such as fuzzy flip-flops or fuzzy Petri nets. Topics can be investigated in a variety of orders. This versatile format makes this an ideal textbook or reference source for both novices and experienced individuals. ... Read more

Reviews (1)

This is a very good book for researchers on fuzzy sets
I liked the book very much specially for the chapters on neurofuzzy computations (chapter 3 and 4).The last chapter on fuzzy Petri nets is also interesting. ... Read more

Book Description

This book is a complete treatise on the theory of nonlinear dynamics of chaotic and stochastic systems. It contains both an exhaustive introduction to the subject as well as a detailed discussion of fundamental problems and research results in a field to which the authors have made important contributions themselves. Despite the unified presentation of the subject, care has been taken to present the material in largely self-contained chapters.The present book can thus be used either as a textbook by graduate students or as a modern monograph by researchers in this field. ... Read more

Book Description

The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology.The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics.The book does not follow the traditional scheme of most of today's literature on chaos.The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems.The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image of the origin of dynamical chaos and randomness.An understanding of the origin of the randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry and engineering. ... Read more

Book Description

A virtual prototype is a major interim step towards the creation of a virtual environment. This book explores the simulation, interaction,concepts and tools of virtual prototypes and environments. Itprovides a mixture of state-of-the-art, advanced research andindustrial papers. ... Read more

Book Description

"Do we see the world as it really is, or is the world of our experience mere illusion?" That question has fascinated reflective people since ancient times. Modern neuroscience has finally provided the definitive answer -- it's both -- and The World According To Homo Sapiens explains how this comes to be so.

Aimed primarily at a sophisticated general readership interested in how the human brain works, Homo Sapiens is written in a good-humored conversational style, using only the occasional well-explained technical term. At the same time, however, it clearly has innovative things to say to specialists in the theory-of-mind.

Homo Sapiens deals with three pivotal issues of the new brain-science, each selected because of its inherent interest to general readers: PART I focuses on our systematic human illusions about 'What Is'; PART II develops a biologically based grounding for human moral choice; and PART III addresses the unresolved enigma of human consciousness -- how we are to account for the presence of this amazing property in the naturalized world of modern science.

Book Description

This text gives a thorough presentation of the foundations of linear time-invariant dynamic systems theory. It goes from classic analysis in the time and frequency domains to the modern state-space techniques, while interweaving both continuous-time analysis and treatment of discrete-time and digital computation methods. ... Read more

Amazon.com

Is the universe perfectly balanced? Physicist Frank Close looks at symmetry and the deep structures of the universe in his luminescent book Lucifer's Legacy. Matter and antimatter, positive and negative charge, even the curious properties of quarks all seem to be arranged in diametrically opposed pairs (or triplets, when you consider zero-state properties like neutral charge). Yet we plainly live in a skewed environment--we can't find antimatter unless we make it, almost all of our proteins are left-handed, and there are 10 Windows machines for every Mac. Is this asymmetry essential for life? Is it, in fact, a necessary consequence of creation? Dr. Close examines these questions and more in intimate but not obsessive detail, showing that life as we know it couldn't exist without a few crucial imbalances.

The question of whether or not we just got lucky with this universe is due to be answered in 2005, when CERN, where Close works, will test theories relating to the Big Bang. The author has a gift for explaining the intricacies of particle physics in terms that lay readers can easily grasp and even come to love. His poetic sensibilities, which frame the book and give it its title (from the statue of Lucifer at the Tuileries gardens in Paris), reflect the human and cosmic mysteries inherent in both the nature of physics and the work of physicists. There's a wee bit of math and geometry herein, but not enough to scare off the numerophobic; in fact, the cogent explanations and illustrations may win Close a few converts to hard science. In the final analysis, Lucifer's Legacy carries a hint of irony: it is such a thoroughly good read that you'll find yourself hunting in vain for flaws.--Rob Lightner ... Read more

Reviews (7)

A wonderful first look at physics
This book is a pleasant, painless introduction to particle physics and the applications of symmetry in the universe.I could see how it might annoy an experienced physicist with entire chapters full of metaphors and analogies intended to solidify the reader's understanding of the concepts, but for a beginner these are quite helpful.It also includes a long and detailed history of the major discoveries in atomic physics, which is a tiny bit too long, but still informative and well written.I am a junior in high school, and I enjoyed this book immensely.

For laymen only
Before I start to criticise "Lucifer's Legacy", I should add that I am a trained physicist, and wanted to brush up a bit about ideas of symmetry/asymmetry, which have become essential to our quest to explain the physics of the universe. Having clarified this, I must say the first part of this book was a real disappointment: it seems to be intended for people who have not heard much about physics since they left high school. There are some nice detours about the history of physics about the turn of the century. But apart from that, the book often is annoyingly trivial. Towards the end it gets more interesting, and some ideas about symmetry and symmetry breaking are nicely presented. But if you look for more than light bedtime reading, look somewhere else.

Great Book - Collector's Item?
The book is extremely well written, fascinating, and easy to read. But the best part is the little errata sheet that comes with the book that may make it a collector's item. There is a drawing in the book of the Tullieries Garden in Paris meant to show the symmetry humans wish to achieve. The drawing has an error that breaks the symmetry, just like the one headless Lucifer statue in the Garden broke the symmetry when the author visited it, giving him a starting point for this book. The errata sheet attempts to restore the symmetry with a new drawing, but the irony has already made its point; human attempts at symmetry are doomed to fail in an asymmetric universe.

Breaking the Balances
The world is full of symmetries, broken and unbroken, according to _Lucifer's Legacy: The Meaning of Asymmetry_ (Oxford University Press) by Frank Close.It may be that disrupted symmetries are essential for our very being, and experiments planned for this decade may give us an answer about this.The world of subatomic particles and basic forces is very weird, and so Close spends much of his book discussing symmetries that are a bit easier to understand.For instance, human bodies are mostly symmetric on the outside, but there are interesting exceptions to this rule.Some molecules come in left and right handed forms, and our own molecules are of the left form, as are most biological molecules.(It makes a difference; the molecule limone comes in right and left forms, too, and we can tell the difference: one smells like lemons and one like oranges.)Close tells us why mirrors reverse right and left but not up and down (they don't, really) and why bathtubs drain in different directions in different hemispheres (they don't, really).

Symmetry can break up for all sorts of reasons.Billions of years ago in the Big Bang, for instance, there was equal matter and antimatter.For some reason, as far as we know, matter prevailed.Why?Are there packets of antimatter galaxies in the universe that are buffered from us by light years of separation?How did the asymmetric increase of matter over antimatter come to be?Why is there more matter, and when it comes down to it, why is there anything?

These are questions that the newest generation of particle accelerators will be trying to tackle in the next decade.Close's book does a good job of examining these confusing issues and trying to make some sort of sense of them for the layman.He has a gift for the felicitous metaphor, and his writing on strange subjects is clear.

Reason for the existence of life to elementary particles
The author beautifully narrates to laypersons how broken symmetry, i.e.,asymmetry born from symmetry is important in the natural world for theexistence of life, molecules, atoms and elementary particles. The riddle ofthe symmetry associated with the last of these items when the universe wascreated is yet to be solved in the near future. At the end of the book, thereader will be surprised to learn that Pasteur anticipated the importanceof asymmetry in 1860. In an early chapter the author writes about themoderately well-known teaser "Why do mirrors reverse left and rightbut not top and bottom?" His answer to this is astonishingly simple.However, he should have been careful to give a more educational answer thatincludes the explanation for the reversal of the left- and right-handednessin mirrors, because he describes about "mirror asymmetric"left-handed and right-handed molecules, right-handedness of DNA andleft-handedness of "the mirror DNA," etc. in a later chapter.[The latest academic articles on the mirror reversal problem can be foundin M. C. Corballis, Psychonomic Bulletin & Review Vol. 7, No. 1, pp.163-169 (2000) and T. Tabata and S. Okuda, ibid. pp. 170-173 (2000).] Thisbook would also be interesting for scientists to learn how they can talkwell about scientific topics to laypersons. It would have been much betterfor the book to include a bibliography for citations and further reading. ... Read more

Reviews (13)

The Physics of History
CERTAIN complex systems, under certain circumstances, have been discovered to behave in mathematically simple, similar ways. In 'critical states', there is no reason to look for specific causes of great events. The smallest force can have gigantic effects and sudden upheavals can strike seemingly out of nowhere. The approximate frequency of such upheavals can be predicted, but not when they will happen or what size they will be.

Mark Buchanan's book reviews the current work on the subject to highlight a deep similarity between the upheavals that affect our lives in both physical and human systems. The book warmly communicates this novel way of thinking without compromising scientific integrity. This is made possible because the author is not only a science writer but also a physicist.

Buchanan starts by discussing the principle of ubiquity which is that one should focus on the simplest mathematical game belonging to a same universal class. Details are not important in deciding the outcome because things in a critical state have no inherent typical scale in either time or space. The important issue which this book highlights is that in a critical state, something known as a 'power law' comes into play to reveal a hidden order and simplicity behind complexity. A power law means that there is no such thing as a normal or typical event, and that there is no qualitative difference between the larger and smaller fluctuations.

Buchanan illustrates this with the following example. If one takes a handful of rice (or sand) and drops the grains one by one on to a table top, a pile of rice is built soon. The pile will not grow taller for ever, though. Eventually the addition of one more grain will cause an avalanche. Such a grain is only special because it happened to fall in the right place at the right time. The addition of a single grain may have no effect, precipitate a small avalanche, or collapse the whole structure. One can predict the likely frequency of the avalanches, but not when they will happen or what size each will be. It may come as no surprise that big avalanches occur less frequently than small ones. What is surprising is that there is a power law: each time the size of an avalanche of rice grains is doubled, it becomes twice as rare.

The book reveals that power laws have been discovered for events ranging from forest fires and earthquakes to mass extinctions and stock market crashes. This is the power law for forest fires: when the area covered by a fire is doubled, it becomes about 2.48 times as rare. If the size of an earthquake is doubled, these quakes become four times less frequent. The bigger the quake, the rarer it is. The distribution is scale invariant, that is, what triggers small and large quakes is precisely the same. A power law for the distribution of extinction sizes (that fits the fossil record well) happens to be identical to that for earthquakes: every time the size of an extinction (as measured by the number of families of species that become extinct) is doubled, it becomes four times as rare. Interestingly for economists, a power law has been discovered in the stock market. Price fluctuations in the Standard & Poor 500 stock index were found to become about sixteen times less likely each time the size is doubled.

Not only that, but other human-influenced events come under the same 'natural' laws. Wars seem to strike with the same statistical pattern as do earthquakes or avalanches in the rice-pile game. What is more, the forest-fire game seems to capture the crucial elements of the way that conflicts spread. A war may begin in a manner similar to the ignition of a forest. Statistics over five centuries have uncovered a power law for wars. Every time the number of deaths is doubled, wars of that size become 2.62 times less common. Such a power law implies that when a war starts out no one knows how big it will become. There seem to be no special conditions to trigger a great conflict. Likewise revolutions are moments that got lucky...

This view of history will make no one feel any safer or happier. After all, wars and revolutions could strike out of nowhere. But it is comforting that the tumultuous course of mankind need not be the outcome of human madness, but of simple mathematics. At the end of the book, one feels excitement about ubiquity. It seems that a profound breakthrough in our understanding of history is coming up. I experienced it. Join me. Read the book.

The real ubiquity is complexity itself
Let's begin with a counter-thesis, namely that the "ubiquity" found in simplistic computer models ("games") which are then related to real world systems such as earthquakes, sandpiles, the stock market, political and social history, etc., may be an artificiality and a whole lot less significant than Buchanan supposes.

The fact that the games are, as Buchanan reports, tinkered with so that they yield a "power law" similar to that found in natural phenomena reveals the artificiality. What this "power law" really amounts to is something like "the frequency of a big change is at least two times and maybe four times (or more) less than the frequency of a small change." The "power" in the "power law" is nothing more than an exponent, as in something-squared, or something-cubed, etc. It's simply a power of a number as a measure of difference. Now, if the differences fell exactly on two times or four times, etc., then perhaps there would be some great significance. But when something is 2.14 times less likely (as it is when the avalanche is doubled in the sandpile game [p. 45, p. 57]) or 1.19 times less likely (as it is for magnets pointing in the same direction in the Onsager and Kaufman experiment [p. 129]) then calling the differences an example of a "power law" at work seems a bit forced and, at any rate, trivial.

Incidentally, the word "history" as used in this book refers to a past that is different than now in a way that cannot be exhaustively unraveled. This idea comes from complexity theory and owes something to information theory. Buchanan attempts to apply it to a wide variety of phenomenon with varying degrees of success.

But what is really being asserted here is the mundane fact that a big change is less likely than a small change in a complex system near the edge of chaos. Such systems: forests, the geological earth, the stock market, the international political arena, etc., are seen as having "self-organized criticality," and it is this sort of complexity that they have in common, and this is what is significant, not some artificially derived "power law."

Another key idea in the book is that the immediate "cause" of a big event in such systems is no different (or so it seems to our discernment) than the cause of a small event. This is an idea from complexity theory, and an exciting one. What it means is that such systems are in principle impossible to predict. In the sandpile game, for example, we don't know when we drop the latest grain whether it will trigger a big avalanche or a small one or none at all. This is similar to the "butterfly effect" in complexity theory in which it is thought possible that the flap of a butterfly's wings in the Sahara Desert, for example, may affect the amount of rain that falls on Cuba.

Where I think Buchanan goes astray here is in making unwarranted connections between systems by using superficial and forced similarities. For example, one of the ideas from the study of earthquakes is that there is no typical size for an earthquake. In his desire to generalize Buchanan tries to find the same sort of phenomena in the interesting study Sidney Redner did on the fate of scientific research papers. Buchanan writes on page 200 that there was "no typical number of citations for a paper, and, by extension, no typical magnitude for the reshaping in the network of ideas that any paper ultimately entails." However on the previous page Buchanan has already reported that there was indeed "a typical size." That size was zero. Of the 783,339 papers published, 368,110 had no citations at all.

Buchanan also asserts on page 169 "...there is no size for a city in the United States or elsewhere, and no reason to see special historical or geographical situations behind the emergence of the very biggest." I agree there is no typical size for a city, but to ignore the effect of rivers, lakes and protected harbors as well as other factors such as nearby mineral and other resources in the growth of cities is silly. Chicago, for example, is a big city not by happenstance but because of its location on a great lake and because of its proximity to the middle of a great, growing country. Similar arguments can be made about other great cities in the US and around the world. The historical and geographical circumstances are special and they really are crucial.

Buchanan further extends the thesis to include social and political revolutions. This makes for lively reading and there is no doubt that there are similarities between the critical state of a nation before a revolution and that of a sandpile before an avalanche or a forest before a fire, but the stresses are of an entirely different sort. He sees the readjustments of governments as a way to prevent the maladjustments that lead to revolutions as similar to the small forest fires that forest managers start to prevent a large forest fire as similar. (p. 209) Whether these similarities are more than conceptional analogies is another matter. Buchanan himself notes, still on page 209, "None of this is meant to be fully convincing." And on page 230, when seeing similarities between the "behaviors of the mass of humanity" and the "wild fluctuations of the magnet poised between its...phases," Buchanan adds, "It goes without saying that nothing I have mentioned in the past few chapters proves this. The message is simply that this is a real possibility." I agree, and I think these statements really could apply to the entire book.

In conclusion, I disagree with the notion that the world is simpler than we think. I believe the opposite is manifestly true, and I found nothing in Buchanan's very interesting arguments to prove otherwise.

Pareto is ubiquitous
In the book Ubiquity by Mark Buchanan, processes as diverse as forest fire size, stacking rice grains, market fluctuation, scientific paper citations, species extinction history, epidemiology, sizes of wars and earthquake severity are said to generate occasional catastrophic behavior following similar statistical behavior. Buchanan presents these arguments in a very readable style at a level that can be grasped by the layman. I found the physical descriptions of the processes fascinating. The phenomena is, indeed, ubiquitous. Repeatedly, we find that, if X measures severity and f is the frequency histogram of occurrence, then numerous processes containing a catastrophic component adhere to a linear log-log plot with negative slope. Although unsaid in the book, probably to allow access to a wider audience, the underlying probability density function of the ubiquitous process is a Pareto random variable with probability density function f(x)=(a/b)*(b/x)^(a+1) for x>b and zero otherwise. The enormously fat tails of this distribution allow the outlier-like catastrophic events described in the book. Taking the log of both sides of the density function gives log[f(x)] = -(a+1)*log(x) + constant which is a line of negative slope on a log-log plot. If U is a uniform random variable on (0,1), then X=b*U^(-1/a) is a Pareto RV. Using this, plots similar to the time series and log-log plots in Ubiquity can be straightforwardly simulated. Googling "Pareto distribution" gives a plurality of interesting web accounts, many mathematically deeper, of this remarkable phenomena made wonderfully accessible by Buchanan.

A new kind of hype?
There is no physical theory that explains history, economics, etc. The wary reader should beware that wishful thinking has won over scientific criticism in this book. To be more specific, sandpile models do not explain earthquakes, turbulence, economics, and so on. Sandpile models are an interesting way of trying something new and stimulating in statistical physics but certainly cannot be elevated to the level of explaining the world. Fluid turbulence is not like dynamically an earthquake, financial markets are not like sandpiles, and Hitler is not explained by any model of statistical physics (need one really say this!?). The historians and biologists need not pack their bags and go home...

(A physics professor)

Can my small comments make a change?
This is not one of my favourite reads. In some ways I found it a labour as it went over the same material again and again, albeit in very diverse areas. I understand the power law that Mr Buchanan describes and its implications, but it seems to be such an after-the-event view that can have little material impact on modern endeavours. It proves futility. It is as if what is ubiquitous is our necessary failure to achieve. But I'm sure we do do better than that.

On the other hand there was one revelation in this book that truly fascinated me. I have always been interested in the dinosaurs and their extinction. Books like 'The Dinosaur Heresies' by Bakker and 'Hot-Blooded Dinosaurs' by Desmond developed a genuine need-to-know-more. But the matter of extinction is so challenging. There are strong suggestions that an impact of an asteroid caused such havoc that the dinosaurs became extinct - all of them, the small ones, the large ones, the carnivores, the herbivores, the pterosaurs (flying dinosaurs) and the plesiosaurs (sea-going dinosaurs). And yet, for all that, other animals - notably mammals - did survive. What allowed them through the window of extinction? In my reading I have encountered this debate many times and most writers do have a preference for one theory or another. But even those who do support the impact theory do not have evidence of an impact associated with each of the great periods of extinction that have occured through time. So, the thesis of 'Ubiquity' does provide an alternative - that sometimes the effect of even a small change will cause monumental alterations to the world according to the ubiquitous power law. What was the small change that extinguished the dinosaur SPECIES but allowed others to survive, and in the absence of the dinosurs, thrive? It seems to me that knowing what this small change was would fundamentally advance our knowledge of what the dinosaurs really were.

The most powerful voice in the campaign for popularising the impact theory of dinosaur extinction is Alvarez who discovered the site of the impact that occured 65 million years ago just about the time the last dinosaur walked on the Earth. What Buchanan points out, that so few other writers do is this ....

'...the bulk of the long 1980 paper by Alvarez and his colleagues was 'confined to the geological and physical evidence for an impact, and the physical results of the impact. The discussion of the biological results of the impact occupies only half a page. (quoted from M. Benton) The reason is simple: no one really has much of a clue about what an impact would really do to life all over the planet.'

This is perhaps the strongest argument I have read against the impact causing the extinction of the dinsoaurs. Not that it couldn't have, but that the opinionated science community is so set on Alvarez' findings that they have taken the most tenuous suggestions from Alvarez' paper to support their theories. ... Read more

Book Description

Electrical Engineering System Identification A Frequency Domain Approach How does one model a linear dynamic system from noisy data? This book presents a general approach to this problem, with both practical examples and theoretical discussions that give the reader a sound understanding of the subject and of the pitfalls that might occur on the road from raw data to validated model. The emphasis is on robust methods that can be used with a minimum of user interaction. Readers in many fields of engineering will gain knowledge about:
* Choice of experimental setup and experiment design
* Automatic characterization of disturbing noise
* Generation of a good plant model
* Detection, qualification, and quantification of nonlinear distortions
* Identification of continuous- and discrete-time models
* Improved model validation tools
and from the theoretical side about:
* System identification
* Interrelations between time- and frequency-domain approaches
* Stochastic properties of the estimators
* Stochastic analysis
System Identification: A Frequency Domain Approach is written for practicing engineers and scientists who do not want to delve into mathematical details of proofs. Also, it is written for researchers who wish to learn more about the theoretical aspects of the proofs. Several of the introductory chapters are suitable for undergraduates. Each chapter begins with an abstract and ends with exercises, and examples are given throughout. ... Read more