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Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems

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Theoretical Neuroscience: Computational and MathematicalModeling of Neural SystemsPeter Dayan and L. F. AbbottMIT Press, Cambridge, $50.00ISBN: 0-262-04199-5460 pagesEvery field of science relies on having its trusted sourcesof knowledge, the books that unite investigators with acommon language and provide them wit h the basictoolbox for approaching problems. Physics, for instance,has its ‘‘Landau and Lifschitz’’; electrical engineers rou-tinely turn to ‘‘Horowitz and Hill’’; and many a neuro-scientist was brought up on ‘‘Kandel and Schwartz.’’Now, at last, the field of computational neuroscience hasone of its own with the recent publication of Dayan andAbbott’s Theoretical Neuroscience: Computational andMathematical Modeling of Neural Systems.The emergence of th is book represents more than theusual feat of textbook publication. It is a significantdevelopment for the field as a whole, because up tonow there has been no single book that unites the basicmethods and models of computational neuroscience inone place. Those who teach courses on computationalmodels have mostly hobbled along by copying papersand chapters from assorted journals and books, or bywriting their own elaborate lecture notes. While thereexist several excellent texts on neural networks—such asIntro duc tio n to the Theory of Neural Computatio n(Hertz, Krogh, & Palmer), Neural Networks for PatternRecognition (Bishop), and Neu ral N etwor ks: A Compre-hensive Foundation (Haykin)—they are mostly writtenfrom the perspective of engineering, math, or p hys ics,and so they do not make serious connections to neuro-science. Others that do address brain function are eithertilted more towards cognitive science, emphasizing high-er-lev el aspects of brain function—such as ParallelDistributed Processing (Mclelland & Rumelhart),An Inroduction to Neural Networks (Anderson ), andAn Introduction to Natural Computation (Ballard)—or else towards lower-level cellular models—as in TheBiophysi cs of Computation: Information Processingin Single Neurons (Koch), and Spikes: Explorin g theNeural Code (Rieke et al.).What sets Day an an d Abbott’s book apart is that itland s right smack in the center of computationalneuroscience, spanning the entire range from modelsat the cellular level, such as ion channel kinetics, tothose at the cogn iti ve level, such as reinforcementlearning. It also does a beautiful job explaining state-of-the-art techn iques in neural coding, as well as recentadvances in unsupervised learning models. And it doesall of these with a level of depth and thoroughness thatis impressive.There tend to be two camps in the field o f compu ta-tional neuroscience, and they are probably best exem-plified by how they use the term ‘‘computation.’’ In one,mat hematical models are constructed primarily todescribe or characterize existing data, and computationis used mainly as a means to simulate or anal yze thedata, in rather the same way as computational ch emist ryor computational fluid dynamics. In the other camp,computation is applied in a more theoretical manner,as a metaphor for what the brain is actually doing.The first six chapters of the book fall m ore in the firstcategor y, by using mathematical and computat io naltechniqu es to characterize neural function . Some ofthese methods attempt to describe neural function incomputational terms, but they are still primarily descri p-tive in nature. These include methods for characterizingspike statistics, reverse correlation techniq ues for meas-uring receptive field properties, meth ods for decodinginformation contained in neural spike trains, and infor-mation theoretic techniques for measuring informationcapacity of neurons and coding efficiency. There are alsotwo chapters covering detailed electrical models ofneurons, including channel kinetics, synapses, and cableproperties. All of these techniques are covered with thekind of nuts-and-bolts detail that will allow readers tobegin implementing and experimenting with them incomputer simulations.The last four chapters of the book fall into the secondcamp of computational neuroscience, presenting moreabstract models that extrapolate beyond the availabledata. Experimentalists often recoil at the idea of enter-taining such models, but they are every bit as essential asthe descriptive models because they provide a theoret-ical framewo rk for inter pr eti ng da ta and motivatingfuture experiments. These chapt ers discuss recurrentnetwor k models with attractor dynamics , models oflearning and adaptation, and theories of representationbased on probabilistic models. Many of these topics arealso covered in the more traditional books on neuralnetworks, but the advantage of the presentation here isthat it makes more direct contact with n euroscienti ficdata. Also, by using terminology and mathematical nota-tion th at is consistent th rough out the book, the authors© 2003 Massachusetts Institute of Technology Journal of Cognitive Neuroscienc e 15:1, pp. 154– 155help to bring the two camps of computational neuro-science under one roof.Of course, many will ask, ‘‘will I need to know a lot ofmath to understand this book ?’’ Indeed, some pagesare rife with equations and formulas, but this is un-avoidable since mathematics provides the most com-pact and precise language for discussing the w orki ngsof a complex system such as the brain. At the sametime, though, the authors have gone out of their way tomake the book accessible to a wide audience, and thereis very little here that requires more than first-yearcalculus or simple linear algebra to understand. Ad mir-ably, the t ext does not use the equations as a crutch,but rath er strives to explain in words what i s meant orimplied by them without sacrificing mathematical rigor.The appendices also provide excellent tutorials andfurther background on topics such as linear algebra,statistics, and optimization.In short, this is a book where students and grownscientists alike can turn to learn the main methods andideas of computational neuroscience. It is a suitable textfor graduate students in neuroscience and psychology,and it could probably be used for teaching advancedundergraduates as well. I have just finish ed using it for agraduate-level computational neuroscience course, andit went over quite well with students com in g fromdiverse backgrounds . I predict th at it will become themainstay for courses on computational neuroscience

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