Book Description
At a time of unprecedented expansion in the life sciences, evolution is the one theory that transcends all of biology. Any observation of a living system must ultimately be interpreted in the context of its evolution. Evolutionary change is the consequence of mutation and natural selection, which are two concepts that can be described by mathematical equations.Evolutionary Dynamics is concerned with these equations of life. In this book, Martin Nowak draws on the languages of biology and mathematics to outline the mathematical principles according to which life evolves. His work introduces readers to the powerful yet simple laws that govern the evolution of living systems, no matter how complicated they might seem.
Evolution has become a mathematical theory, Nowak suggests, and any idea of an evolutionary process or mechanism should be studied in the context of the mathematical equations of evolutionary dynamics. His book presents a range of analytical tools that can be used to this end: fitness landscapes, mutation matrices, genomic sequence space, random drift, quasispecies, replicators, the Prisoner's Dilemma, games in finite and infinite populations, evolutionary graph theory, games on grids, evolutionary kaleidoscopes, fractals, and spatial chaos. Nowak then shows how evolutionary dynamics applies to critical real-world problems, including the progression of viral diseases such as AIDS, the virulence of infectious agents, the unpredictable mutations that lead to cancer, the evolution of altruism, and even the evolution of human language. His book makes a clear and compelling case for understanding every living system--and everything that arises as a consequence of living systems--in terms of evolutionary dynamics.
Customer Reviews:
An engrossing read - highly recommended.......2007-09-05
This is a wonderful book by a master of the field. Prof. Nowak, who teaches at Harvard, has managed a minor miracle: writing a book on mathematical biology that is mathematically rigorous and extremely readable at the same time.
The book is divided into two broad sections. The first nine chapters explore various abstract models of evolution. Simple models of evolution do not demonstrate cooperation between individuals, while examples of it abound in the real world. This fact quite rightly fascinates the author and informs his presentation. The last four chapters of the book use some of the modeling techniques developed in previous chapters to study real-world systems, such as HIV infection and cancer.
This book is highly recommended for anyone interested in the mathematical aspects of biology. More broadly, it will be of interest to anyone who's interested in mathematical models of complex systems.
Excellent and Approachable Survey.......2007-05-23
This book is an accessible introduction to the mathematics of evolution and results in the field of evolutionary dynamics with a heavy emphasis on applications including the immune system, virulence, AIDS, and even the evolution of language. Many of the ideas are from fairly recent papers and results in mathematical biology, particularly the sections regarding the evolution of universal grammar and in the emerging field of evolutionary graph theory, which adds population structure to the mathematical analysis. (This is a now necessary generalization of evolutionary game theory, which assumes uniform population structure.) As noted above, this is the first book to present many of these ideas outside of scientific and mathematical journals.
Although the mathematical content is significant, Nowak diligently explains the implications of the mathematics in the text of the book, widening the potential audience of the book dramatically. Simply put, this book is filled with delicious evolutionary content, backed up with mathematical rigor for the interested reader, but you need not have a degree in mathematics in order to understand much of the material.
Highly recommended for those truly interested in evolution.
The Marriage of Mathematics and Evolution.......2007-01-10
Excellent book for the mathematically and evolutionarily minded. However, not for general reading unless you are doing graduate work in either mathematics or evolutionary biology. Just excellent survey.
A dazzling book.......2006-11-22
This is, quite simply, a dazzling book. Nowak manages to take very deep mathematical ideas that are on the cutting edge of science and make them fun and pretty rigorous at the same time. The review in Nature said "It should be on the shelf of anyone who has, or thinks they might have, an interest in theoretical biology" and I completely agree. The section on HIV, explaining mathematically why there is a long delay between infection and the disease, and how this proposal in 1990 correctly predicted several biolgical facts which were subseqently discovered (but not mentioning execpt in the notes, that this was his work) is truly exceptional. We are moving beyond the "Just So stories" phase of evolution (such as wooly rhetoric about "Selfish Genes") to real, mathematically rigorous, science.
wonderful life.......2006-10-13
This is a remarkable book, absolutely original, containing a lot of material which has never before appeared in book form. It is written in a very accessible style, and leads almost effortlessly from first principles to state-of-the-art research.
The book takes an eagle's view on evolution, covering an vast range of topics from molecules to man. It emphasises analytical methods and presents a large canvas of superbly elegant mathematical models.
The author has chosen a very personal, highly idiosyncratic sample of subjects of amazing diversity, basically because he feels excited about them: and this excitement shows through, and makes the book very engaging, a positively bracing experience. On all of the topics, the author has contributed substantially, and the feel to get it `straight from the horse's mouth' is one of the great assets of the book. I believe that it will be a splendid hit with students, and regret that I did not have anything like that when I was young.
The style of the book is lucid and vigorous, with short, clear sentences, occasionally in staccato style. The mathematics is reduced to the bare minimum. It is incredible how much mileage the author can get out of it. The illustrations play an important role, and are well devised.
The chapters are short, and they address an amazing array of topics, ranging from molecular evolution to evolutionary games, from HIV to cancer, and from cooperation to language. In spite of their different subjects, they are homogenous: first comes a breezy introduction to the biological (or chemical, or linguistic) facts, then a simple model, then an analysis, without heavy machinery, usually leading up to some remarkable results which could not be obtained without mathematics, then a summary in a few short statements and finally an extensive list of references, including both the classics and the very newest results in the field. The fact that in each case, a few pages suffice to start from scratch and lead to the cutting edge of present-day research is quite remarkable.
The book will certainly have a big impact, and raise a lot of follow-up work. There is hardly a better recipe for young PhDs than to pick one of the chapters and start doing their own research. But in addition, `the whole is more than the sum of its parts'. I usually hate this slogan but here it holds in a spectacular way. By simply putting together the different applications of simple models in so spectacularly diverse fields, Nowak's book promotes a radical `hands-on'-approach to evolution which, I am sure, will have seminal repercussions.
Book Description
This book describes how understanding the structure of reality leads to the Theory of Everything Equation. The equation unifies the forces of nature and enables the merging of relativity with quantum theory. The book explains the big bang theory and everything else.
Customer Reviews:
The Real Deal.......2006-09-25
Although Mr. Wheatley is a little verbose in sections, his documentation of Zen Buddhistic Principles found throughout the disciplines of Mathematics, Physics, Theology, etc. forms a nice reference guide for anyone tuned into that wavelength. In particular, his explanation of how Godel's Theorem and Cantor's "Confusion" shed great light on the difference between GOD's Logic and Man's Logic should be a revelation to any undergraduate level math students who encounter these ideas for the first time. Curiously, Mr. Wheatley makes many misstatements about both Zen Buddhism Principles and the Bible, however. For example, by accepting the false biblical teaching of Original Sin, he misses the point that eating the proverbial apple gave Adam and Eve the ability to make Moral Discernments in fulfillment of GOD'S PERFECT PLAN. As proof, read Genesis 1 which states that Man and Woman were made in GOD's Image. Genesis 4 shows that Adam and Eve weren't the first humans on Earth at all, there were plenty of others by then. The allegorical meaning of the story of Eden, then, isn't that Adam and Eve were the first humans on Earth, but they were the first humans with the ability to make Moral Discernments (in GOD's Image). In fact, Moral Discernment is God's Unique Gift to Man, which is the basis of consciousness, not some Math Formula. But because the wages of the resulting, unavoidable sin are Death, many people foolishly try to return to Eden by: (1) living a sinless Life (2) by removing choice altogether by passing and enforcing strict Laws (3) by attempting to do away with Moral Discernment and the resulting consequences for our actions altogether by trying to remove Shame from Shameful actions. GOD is not some ethereal Man-In-Space, but is simply the Totality of all Real Things, The Set of All Real Sets. GOD's Love manifests itself from the amazing sub-atomic relationships that underly this magic Life all the way to the grandest of Macroscopic Scales, the Interconnected Totality itself. The Zen Buddhism connection can be found by simply superimposing the 0 symbol and the symbol for infinity (8 on its side) in Mr. Wheatley's supposedly "new" formulation that 1 = 0 x infinity. Superimposing them gives you the yin-yang symbol. A potential disadvantage of artificially separating the infinity from the zero, however, is that Mr. Wheatley is able to equate the entire expression to be equal to 1. This potentially might obscure the fact that the deepest meaning of the yin-yang symbol is that it is both 2 and 1 AT THE SAME TIME. His overall equation does preserve that important meaning by utilizing a single element on one side of the equation and two elements on the other side of his final TOE equation. This may be hard to see for some at first, however, which could potentially obscure the richest meaning of this beautiful symbol/equation. A much more GODLY TOE, in my opinion, comes from Euler, who discovered that e ^ (i * pi) - 1 = 0. When someone can explain that relationship, then they can say they know GOD.
A life changing experience??.......2005-06-13
This book is an easy read and does succeed in being somewhat thought-provoking. However, I am a little surprised at the awesome, "life changing" experience it apparently was for many of the readers. Wheatley's conclusions were interesting but nothing really new. All of his material should have passed through the mind of any thinking person without the aid of this book.
The reason I gave this book three stars is because he uses unneccessarily wordy ways of describing simple things. Also, the author and many other reviewers insist that Wheatley makes only one assumption. Wrong-his whole theory is one big assumption.
Overall though it was a very interesting and worthy book.
Should be Required Reading for everyone.......2004-06-26
This book will change your life. You will never think the same way you did before reading it.
I have a degree in chemistry and I think this book should be read by everyone in the sciences. Without a doubt, the best book I've ever read. Why and what are two of our best friends
A Very Important Book.......2004-01-26
I must preface my review by stating that I have never been so excited and moved by a book that I have wanted to contact the author. That is what I found myself doing upon reading this book. This book is just what its title says. The author does not "miss a beat" describing in great detail using practically every aspect of scientific knowledge from atomic structure through logic to quantum theory---we are even given a valuable explanation of Love. This text may be challenging to read for those unfamiliar with scientific terminology. And it can also be difficult for those with a science background, such as myself. However, for me it is well worth the work necessary to strive to understand the unfamiliar terminology. (I am continually learning from this book. I am presently on my third reread).
One of the author's main messages is "not" to believe anything without first verifying it with reality, as we know it. He calls it the "Personal Explanation Principle". He indicates that religions are just such belief systems that we as people "fall" victims of; because we do not verify the beliefs with the facts, as we know them, of reality. He gives a very detailed explanation of how the New Testament can be explored using his methodology.
The author methodically and meticulously walks us through his thought processes, which took 30 years to assimilate, of delineating the structure of reality and the nature of consciousness. Included in the "walk" are many of reality's phenomena made revelatory. An example of that, for me, would be the dual nature of light. It's particle/wave duality, which is explained as "functions". Also, when the author took me on the mental journey of "Setness" an exhilaration of the magnificence of life swelled up in me.
To me this is a very important book that should be read by all that are seekers of truth. It is for all those wanting to gain an understanding of the purpose for their existence, wanting to know where life is headed towards, and wanting to know who God is.
This book will enlighten and develop one's mind substantially. You will discover that this is our objective.
And yes, I contacted the author and he responded openly.
Illuminating!!!.......2002-12-30
This is a really great book. It combines philosophy and science in order to tackle a multitude of existential problems. The author's style of writing is fresh and alive, I recommend ths book to anyone interested in expanding the fronteirs of their understanding. Books I also liked are a Universe in an Nutshell by Steven Hawkings and Descent into Illusions by Paul Omeziri.
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Disease Evolution: Models, Concepts, and Data Analyses (Dimacs Series in Discrete Mathematics and Theoretical Computer Science)
Manufacturer: American Mathematical Society
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Book Description
Infectious diseases are continuing to threaten humankind. While some diseases have been controlled, new diseases are constantly appearing. Others are now reappearing in forms that are resistant to drug treatments. A capacity for continual re-adaptation furnishes pathogens with the power to escape our control efforts through evolution. This makes it imperative to understand the complex selection pressures that are shaping and reshaping diseases. Modern models of evolutionary epidemiology provide powerful tools for creating, expressing, and testing such understanding.
Bringing together international leaders in the field, this volume offers a panoramic tour of topical developments in understanding the mechanisms of disease evolution. The volume's first part elucidates the general concepts underlying models of disease evolution. Methodological challenges addressed include those posed by spatial structure, stochastic dynamics, disease phases and classes, single- and multi-drug resistance, the heterogeneity of host populations and tissues, and the intricate coupling of disease evolution with between-host and within-host dynamics. The book's second part shows how these methods are utilized for investigating the dynamics and evolution of specific diseases, including HIV/AIDS, tuberculosis, SARS, malaria, and human rhinovirus infections.
This volume is particularly suited for introducing young scientists and established researchers with backgrounds in mathematics, computer science, or biology to the current techniques and challenges of mathematical evolutionary epidemiology.
Copublished with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were copublished with the Association for Computer Machinery (ACM).
Book Description
In a world supposedly governed by ruthless survival of the fittest, why do we see acts of goodness in both animals and humans? This problem plagued Charles Darwin in the 1850s as he developed his theory of evolution through natural selection. Indeed, Darwin worried that the goodness he observed in nature could be the Achilles heel of his theory. Ever since then, scientists and other thinkers have engaged in a fierce debate about the origins of goodness that has dragged politics, philosophy, and religion into what remains a major question for evolutionary biology.
The Altruism Equation traces the history of this debate from Darwin to the present through an extraordinary cast of characters-from the Russian prince Petr Kropotkin, who wanted to base society on altruism, to the brilliant biologist George Price, who fell into poverty and succumbed to suicide as he obsessed over the problem. In a final surprising turn, William Hamilton, the scientist who came up with the equation that reduced altruism to the cold language of natural selection, desperately hoped that his theory did not apply to humans.
Hamilton's Rule, which states that relatives are worth helping in direct proportion to their blood relatedness, is as fundamental to evolutionary biology as Newton's laws of motion are to physics. But even today, decades after its formulation, Hamilton's Rule is still hotly debated among those who cannot accept that goodness can be explained by a simple mathematical formula. For the first time, Lee Alan Dugatkin brings to life the people, the issues, and the passions that have surrounded the altruism debate. Readers will be swept along by this fast-paced tale of history, biography, and scientific discovery.
Customer Reviews:
I am the Author - some clips from reviews.......2007-06-12
I am the author of "The Altruism Equation," and thought some recent reviews of the book might help potential readers. Incidentally, I did not wish to rate my own book (in terms of stars), but Amazon required it.
Clips from recent reviews:
"Dugatkin has done for social behavior what James Watson did for the history of the discovery of the structure of DNA with the book 'The Double Helix." Stephen Pruett-Jones, BioScience
"interested readers... will learn a great deal from The Altruism Equation" Matthew Cobb, London Times Supplement
"The Altruism Equation is very well written and extremely informative. Dugatkin's immense enthusiasm shines through every page. . . . Because the scientific concepts are explained so clearly, concisely and engagingly, newcomers to sociobiology will find The Altruism Equation an enlightening read. At the same time, it will be of interest to connoisseurs of the literature who wish to gain a panoramic view of the altruism debate. . . . The Altruism Equation is a splendid book."--David Livingstone Smith, Evolutionary Psychology
"Exhilerating. . . . [This] is an engaging book with devoted enthusiasm for the ideas of the main protagonist, William Hamilton. . . . Dugatkin's . . . account offers much to think about."--Caroline Ash, Science
" This superb tale of scientific discovery is required reading for everyone interested in the nature of human morality."--Publishers Weekly
"Dugatkin tells the story . . . with clear prose and poise. In doing so he celebrates the internal consistencies of science and the beauty of clear thinking. Written for a general audience, this book provides vignettes featuring the lives of key thinkers, which foster an understanding of how the social context of the times influences the advance of scientific understanding."--Choice
Little or no equation.......2007-06-09
An interesting collection of short related stories, but scarcely a mention of the actual equation, which is really trivial, or its development. Pity - a lost opportunity.
A future edition could usefully include a few math appendices so the average scientist can see what all the fuss is about.
An enlightening read.......2006-10-03
I enjoyed this delightfully written book of "science history". "The Altruism Equation" tells the story of the seven scientists - from Darwin, Huxley and Kropotkin up through WD Hamilton - and their quest to understand the evolution of altruism. In addition to being very well-written, this book demonstrates the power of natural selection to shape the world we live in. It should help quiet the ID crowd (although it is hard to quiet people that aren't listening to anything that they don't want to hear).
A Special difficulty that does prove fatal.......2006-10-03
This is a useful and interesting account of the kin selection problem in biology from the time of Darwin onward. It is interesting how Darwinists tend to avoid public discussion of this question because it shows the agenda of Darwinists and the plain fact that the phenomenon of altruism falsifies the generalizations about natural selection. If people were more generally aware of this side of the question a reaction as common sense might help to put the evolution debate in perspective. At first sight the progression of trick arguments designed to save Darwinism, from Darwin himself to Hamilton, seem to come to the rescue, at least to positivistic scientists, but in fact these arguments are a front for the great void in Darwin's theory. Part of the problem is that not enough people can handle the math for the equations produced by Hamilton and that makes the snowjob of the experts fairly easy to bring off. But the problem remains and is direct, a point sensed immediately by Kropotkin, who is discussed in the book. The problem is that you must explain altruism! And not explain it away. To explain altruism you must explain the evolution of consciousness, and an ethical consciousness, primitive to complex,able to make branching decisions based on issues of values. Darwinism is totally unable to even define this kind of explanation and sticks its head in the sand, content to brandish this ridiculous line of argument where selfishness is made to explain its opposite. Armed with this deuce Darwinists wish to take on the entire spiritual tradition of mankind. Small wonder they become a bit timid. Don't be intimidated by this superficial appearance of scientific rigor. The whole argument is speculative and completely unverified in the evolution of man. In fact, we see the ideology of classical liberalism at work here in direct and naked clarity.
The human psychological apparatus is a complex and subtle instrument with many dimensions of consciousness. Don't let Darwinists get away with this kind of simplistic reductionism that refuses to even attempt a real understanding of evolution.
The rating given represents a challenge to this kind of thinking while the book itself as such is a useful, if perverse, addition to the literature and the debate (and a long time coming).
A History of Altruism Glowing with the Author's Enthusiasm.......2006-09-11
The altruism equation relates to a very simple equation explaining altruism among kin in terms of costs, benefits, and the degree of relatedness. The equation does not have the generality of Newton's Third Law or Einstein's mass-energy equation, but it may well be the most important quantitative relationship in biology.
But, this book is more about people than about equations. It consists of a beautiful set of cameos of some the the greatest biologists who have worked on the issue of altruism, including Darwin, Huxley, Kropotkin, Hamilton, Dawkins, and Price. It is an easy read and very elegant and exciting. There is some mention of results beyond 1970, but they are very, very sparse. Perhaps an historical narrative is warranted only when all the principals are dead. At any rate, for a discussion of the modern theory human altruism, together with spandrels, sociobiology, a scientific approach to morality and the social emotions, you will have to look elsewhere.
Book Description
Every form of behavior is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realized how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centered not on the concept of rational players but on the population dynamics of behavioral programs. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions that can alter the basis of their success, i.e., to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions that punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.
Customer Reviews:
The Best There Is On Evolutionary Dynamics.......2000-07-14
When I was writing the chapter on evolutionary dynamics for my book Game Theory Evolving (Princeton, 2000), I looked at all the books available and found nothing. Then Hofbauer and Sigmund's new book (a totally revised version of their earlier Theory of Evolution and Dynamical Systems) came out, and I knew I had a masterpiece in hand.
The book does not assume the reader knows basic differential equation theory--it presents all the theory necessary. Indeed, it is a wonderful way to learn differential equation theory, since one immediately is faced with meaningful problems to solve. It does assume the reader is familiar with multivariate calculus. The book should be accessible to biologists and game theorists with a minimum understanding of each other's disciplines.
There are four parts. First, HS deal with Lotka-Volterra equations of the type prevalent in predator-prey models, which they extend to ecological models and several populations. Like the rest of the book, there are lots of problems and the presentation is elegant and succinct.
The second part deals with game theory dynamics and replicator equations, including sections on evolutionary games and asymmetric games. This too is extremely nicely presented, and the links to the Lotka-Volterra models are made clear.
Part three is on dynamical systems especially of relevance to biochemistry--catalytic hypercycles--as well as higher dimensional phase space dynamics of ecological models.
Part four deal with population genetic models using a differential equation approach. This section is also excellent, though for serious readers it should be complemented by Karlin and Taylor's Second Course in Stochastic Processes (which is much more mathematically demanding).
The physical production of the book is also first rate--a pleasure to read and use.
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Lectures on Nonlinear Evolution Equations: Initial Value Problems (Aspects of Mathematics Ser)
Reinhard Racke
Manufacturer: Ballen Booksellers Intl
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Structural Equation Modeling: Applications in Ecological and Evolutionary Biology
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Cause and Correlation in Biology: A User's Guide to Path Analysis, Structural Equations and Causal Inference
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A Primer Of Ecological Statistics
ASIN: 0521781337 |
Book Description
This book presents an introduction to the methodology of structural equation modeling, illustrates its use, and goes on to argue that it has revolutionary implications for the study of natural systems. A major theme of this book is that we have, up to this point, attempted to study systems primarily using methods (such as the univariate model) that were designed only for considering individual processes. Understanding systems requires the capacity to examine simultaneous influences and responses. Structural equation modeling (SEM) has such capabilities. It also possesses many other traits that add strength to its utility as a means of making scientific progress. In light of the capabilities of SEM, it can be argued that much of ecological theory is currently locked in an immature state that impairs its relevance. It is further argued that the principles of SEM are capable of leading to the development and evaluation of multivariate theories of the sort vitally needed for the conservation of natural systems. Supplementary information can be found at the authors website,http://www.jamesbgrace.com/. • Details why multivariate analyses should be used to study ecological systems • Exposes unappreciated weakness in many current popular analyses • Emphasises the future methodological developments needed to advance our understanding of ecological systems
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Semi-Linear Hyperbolic Problems in Bounded Domains (Mathematical Reports, Vol 3, Pt 1)
A. Haraux
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- A Good Presentation For the More Advanced Student
- Good but requires that you keep paper and pencil at hand.
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Elementary Stability and Bifurcation Theory (Undergraduate Texts in Mathematics)
Gerard Iooss , and
Daniel D. Joseph
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ASIN: 0387970681 |
Book Description
This second edition has been substantially revised. Its purpose is to teach the theory of bifurcation of asymptotic solutions of evolution problems governed by nonlinear differential equations. It is written not only for mathematicians, but for the broadest audience of potentially interested learners, including engineers, biologists, chemists, physicists and economists. For this reason, it uses only well-known methods of classical analysis at a foundation level. Applications and examples are stressed throughout, and these were chosen to be as varied as possible.
Customer Reviews:
A Good Presentation For the More Advanced Student.......2003-12-10
I have used Iooss and Joseph for over 20 years now, starting with the first edition back in the early 80s.
The book is for the more advanced student, one who has a bacic working knowledge of real and functional analysis. Unfortunately, these days, few engineering and physical science students have such a background. Hence, the book would be better if it contained some supporting basic material on mathematical analysis.
The first edition contained numerous "typos". While much improved, the second edition still contains too many "typo" errors.
Overall, the book is a good source of information that should be consulted by anyone interested in bifurcation theory. The book contains material (like the bifurcation of forced T-periodic solutions) not normally included in an elementary treatment of bifurcations.
John Stensby, Professor
Electrical and Computer Engineering
University of Alabama in Huntsville
Huntsville, AL
Good but requires that you keep paper and pencil at hand........1999-09-08
This is an exellent book on stability and bifurcation theory, from an applied math perspective. A reader could just skim and pick up a broad outline but would be better off working though at least some of the messy details to make sure that (s)he is really following the thread of the argument.
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Feynman-Kac Formulae
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ASIN: 0387202684 |
Book Description
This book contains a systematic and self-contained treatment of Feynman-Kac path measures, their genealogical and interacting particle interpretations, and their applications to a variety of problems arising in statistical physics, biology, and advanced engineering sciences. Topics include spectral analysis of Feynman-Kac-Schrödinger operators, Dirichlet problems with boundary conditions, finance, molecular analysis, rare events and directed polymers simulation, genetic algorithms, Metropolis-Hastings type models, as well as filtering problems and hidden Markov chains.
This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviations principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods and worked out illustrations of the key aspect of the theory.
With practical and easy to use references as well as deeper and modern mathematics studies, the book will be of use to engineers and researchers in pure and applied mathematics, statistics, physics, biology, and operation research who have a background in probability and Markov chain theory.
From the reviews:
"I also recommend this book as informal reading for anyone intersted in the subject, preferably with a strong background in Markov processes; in particular, for someone also familiar with one of the many fields to which the book applies Feynman-Kac models. The book is entertaining and informative."
Journal of the American Statistical Association, December 2005
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