Neural Networks Books

For an introduction to the subject, this book is unequivocal in my experience with the literature. Great read that has propelled me forward into combining a bayesian network with a physical model to approach a very complex sediment transport problem.

I am very pleased to have found a book that gives a modern, sound, and self-contained introduction to Bayesian networks. The only prerequisite is basic knowledge of probability. This makes sense because a Bayesian network is essentially a directed graph whose vertex set is a collection of random variables, while an edge from one variable X to another variable Y represents a belief that X has a causative effect on Y. For example, X could be the pregnancy status of a cow, while Y could be a blood test administered to the cow. Vertex Y would contain a contingency table that reflects the conditional probability of Y in terms of X. The author does well in explaining this, as well as adequately treating many of the practical issues surrounding Bayesian networks, such as design issues, network learing and tuning, and some basic algorithms (e.g. bucket elimination and junction trees) that aid in the efficient updating of variable probabilities due to new evidence that may instantiate or change the distribution of one or more variables.
The author also provides a good introduction to decision graphs, a close relative of Bayesian networks.

The aspect of Bayesian networks that I find most attractive is the fact that there is a "rational" way of designing a network, based on hypothesis, informational, and mediating variables, and their "causal" relationships. Unlike neural networks in which one is almost forced to guess the appropriate structure of the network, every node in a Bayesian network correpsonds with a state or quantity that can be measured either directly or indirectly through other variables. Thus, changes in a system model should only induce local changes in a Bayesian network, where as system changes might require the design and training of an entirely new neural network.

Another aspect of Bayesian networks that I find very compelling is the way in which they seem quite amendable to learning and the presentation of new evidence. This is true since knowledge updating is done locally (through variables), while the effects of those changes are witnessed globally through appropriate belief-updating algorithms.

On the downside, it should be noted that the operation of belief-updating is in general NP-hard, thus there exists a valid concern about the computational efficiency of Bayesian networks. Contrast this with the fact that once a nueral network has been trained, it is quite easy to compute. One would hope that these concerns will subside with more research, for the above mentioned benefits of Bayesian networks leads me to believe that these networks will have quite an influence on the future directions of machine learning.

Although this book will not go down in history as the definitive reference for Bayesian networks, it serves as a good conduit for explaining this quite interesting area of learning at a time when such few complete and modern references exist.

Chapter 1 is a nice introduction to probability. Chapter 2 is readable. Chapter 3 is poorly presented, and you feel sad for having wasted so much money on a book with only one intelligible chapter.

Among currently available introduction to Bayesian networks (also known as Bayes Net, Bayesian Belief Nets), this book is probably one of the most accessible. The book is divided into part I and II. Part I is intended for BN users (practitioners) and Part II more towards BN developers and researchers, as it contains algorithmic introduction of BN.

Prerequisites of the book as stated in the preface include Graph Theory and Calculus, both at introductory level. I personally did not have exposure to Graph theory, but I was able to understand most of the material without any help. Necessary probability theory is developed, but basic probability knowledge is also a prerequisite to digest the material to a reader without prior exposure of Probability as it shapes the core of the material in the book.

The strength of this text is in Part I where the author provides several examples to illustrate use of Bayesian Networks, Influence Diagrams and other models. I find it useful Influence Diagram as an extension of Bayesian Networks.

Most answers to Exercises at the end of each chapter are provided at the author's homepage, except answers of the last chapter. Answers that require graphical modeling software are also provided in Hugin format. (Hugin Lite can be downloaded from Hugin site.)

The downsides are that writing of the text is somewhat awkward, obscuring readers from understanding, that model building chapter could have been discussed more thoroughly, that material in Learning is barely present, and that definitions are sometimes not introduced upon the first encounter but they appear later in chapters. More different and complex examples could have been discussed to illustrate the material. Note: the author provides a page for Learning at his homepage.

Although this is an introduction to Bayesian Networks and Influence Diagrams, a reader should be equipped with some level of abstract thinking in order to digest the material.

This book is suitable for self-study. It has motivations for the uninitiated. References are provided at the end of the book and I was able to find some of them online. A notable is "A tutorial on Learning with Bayesian Networks" by Heckerman, to fill in the part of Learning in this book.

Other books at this level from users' perspective are:
Edwards, Introduction to Graphical Modeling (Utilizes software MIM.)
Clemen, et al., Making Hard Decisions (Uses Palisade Decision Tools suite. The book discusses Influence Diagrams but not Bayesian Networks.)

Further studies after completion of this book include:
Cowell, et al., Probabilistic Networks and Expert Systems
Lauritzen, Graphical Models
Pearl, Probabilistic Reasoning in Intelligent Systems
Pearl, Causality

The book covers many topics, but doesn't really cover them well. I would not recommend this book. I have learned litte from it.

Do not buy this book unless you already read it in a library and just like it to be on the shelf. All ideas are very well known and code is almost useless.
I found much better sources for free on the web.

Probably my impression would be better if author setup right expectation for this book. As a mathematically inclined person I was disappointed by fact that author left all explanation of crucial concepts and algorithms behind the scenes just referencing "It is described in other books" - see subjects about Maximum Entropy Methods, details in ARIMA. Reader is left to take some concepts for granted without clear understanding of subject. Meantime author missed some important subjects in Neural Networks and even digital filters like recursive digital filters which proved to be superior to filters described in the book. The rest of theory is quite heuristic and based on unproved concepts and author's "feelings" that is not acceptable at least for me. Sometimes author refers to the program code to explain methods but the quality of code whish to be better. He states about code that "It is wildly extravagant in its memory usage in order to save a small amount of execution time. This reflects modern hardware characteristics". Unfortunately this concept is wrong because modern software design requires simple and clear code rather then weird code with questionable improvement in performance, which is difficult to use and read. Shortly, I would not recommend to buy or use this book because it might be only useful for beginning programmers who does not care about the subject to code.

Not much on neural nets. A good overview of a signals and systems textbook for those who want to learn about filters without all the math. I was disappointed that there wasn't a results section for the NPREDICT tool, just a bunch of flags and parameter garbage to tweak.

I usually don't pay attention to readers's comments or reviews.
Because after all this is a very subjective matter. I bought the book for two reasons neither of which has to do with a reader's review. The first reason was because I have a copy of Timothy's book on Practical Neural Networks in C++, which I found excellent, and the second reason was because I had previewed chapter one before I bought the book and liked it very much for what it had to say and the way it said it. Timothy's books are for a wide audience of intelligent people, not necessarily all rocket scientists, and although a mathematician himself, restricts math as much as possible so people do not get bogged down by the math and loose the forest for the trees. On the other hand there is sufficient amount of bibliography for any one who is interested to pursue most rigorous or more exotic approaches. The code examples are good and the executable file NPREDICT, works without any further processing, for those who don't want to mess with code and compiling. The treatment of Box-Jekins ARMA model,and the multivariate example on temperature and precipitation is very good. The book is highly recomended to any one who has little or no knowledge of the subject, and wants to understand what time series is all about

Prediction methods for time series are a multi-million dollar industry and are of upmost importance in financial engineering, weather prediction, logistics, network modeling, and myriads of other fields. This book gives an overview of various methodologies for time series prediction, and is written for readers with substantial experience in this area. The author emphasizes that time series prediction is more of an art rather than a science, with the practitioner usually employing hybrids of established techniques, only some of which have a rigorous mathematical foundation. In fact, despite the subject matter, this book is very lean on mathematics, and the reader will have to consult other books for a more detailed mathematical treatment. The NPredict package accompanying the book is designed to run on an NT and a DOS platform, and illustrates the main points in the book. Readers who have familiarity with the authors earlier books on neural networks will definitely find this one easier to follow. It is, again, not written for beginning students, but the author does a fairly good job of presenting the material for the advanced reader.

I was very disappointed with this book. I try to reserve judgement on books until I've read at least 50 pages. However, when I reached page 50 and the author stated "Although I still am not sure how CIM (and DEN for that matter) will affect network and systems management ...", I gave up. If the author doesn't know how DEN will affect network and systems management, then why is he writing a book? This is the whole reason I bought the book. Oh well ... $$$ down the tubes.

I'm reading the book and enjoying it very much. The author also was very accessible for questions I had on the book, something not always found out there.

This book provides essential information on DEN specifications. It provides up-to-date information on complex DEN issues. Rather than a descriptive work, the author does offer his own opinions and forecasting on the theme and industry that is yet to be seen. For the most part his predictions do make sense. Worth the money.

This is the first book I see on the subject. Although it provides a great overview of DEN and major players, the technology is still too new and very shake at the moment. Of course, I can't blame the author, which I'm sure, had to rely on RFCs and white papers. As long as readers have that perspective in mind, the book is worth reading.

This book is unquestionably the worst technical book I have ever had the misfortune to waste my time on in my 14-year career in the computer industry. The author flaunts a complete lack of understanding of some of the very basic concepts that he attempts to discuss. The book is a hastily slapped together regurgitation of a variety of materials about DEN. The author seems to have cut and pasted content from several sources without any regard for the coherence or even the completeness of what he cut and pasted (e.g. on p. 96, he states "This section defines the dynamic attributes used by RADIUS"; but it doesn't! This leads me to the conclusion that the author hasn't the faintest idea of what he is writing about; and that he grabbed a bunch of relevant material in electronic format, cut and pasted portions of these materials with little regard for the coherence of the resulting text, and called it a book. The book is replete with typos (it is amazing that someone so well-versed in the art of cutting and pasting has not yet discovered the spell-checker :-)) and sheer careless mistakes (e.g. on page xvi, the preface describes Chapters 9 as dealing with "Protecting Mission-Critical Application" and Chapter 10 as describing "Remote Access Schema", whereas in reality Chapter 9 is entitled "DEN and Network Services Security" and Chapter 10 is entitled "LDAP(v3): Dynamic Attributes for RADIUS". Mr. Goncalves does a deplorable job of hiding his complete ignorance of some of the topics that he attempts to discuss. E.g. he mentions SNMP and then refers to RFC 1089 as the source for more information about SNMP (anyone who is familiar with SNMP will know that if one is to cite ONE RFC as a reference to SNMP, it will not be RFC 1089!!). He talks about X.500 and then lists 6 object classes, viz. Network Device, Network Protocol, Network Media, Profile, Policy, and Network Service as the "X.500 six base class hierarchies" (these six classes actually form the basis of the DEN model and were never defined by X.500!). In the last section of the book, entitled "DEN at work: Challenges and the latest developments", one would expect to find a discussion of the current challenges being faced by the DMTF; instead, one finds a reprint of most of B. Aboba's Internet Draft on Dynamic Attributes for RADIUS! The list goes on and on, but I believe that my point has been made. My rating for this book would have been zero stars if Amazon had permitted it. In summary: Don't bother.

With a background in chemistry, biology, psychology, and neuroscience, I believed a course on simulating the the brain to understand the mind would be incredibly fascinating. However, this book, in spite of various claims to be an introduction to cognitive neuroscience, is full of technical jargon that is mostly likely only understood by those familiar with the subject.

The book itself comes off as extremely condescending to any beginner who is frustrated with the book because throughout the text, the authors repeat over and over and over again some variation of, "Here is a SIMPLE example..."

****ALSO IMPORTANT TO NOTE: As for the free software you can download online, PDP++, it is prone to errors (random quitting, functions not working properly) and DOES NOT work on many newer versions of Mac OS X. You have to download a different program called Emergent, which is not compatible with what you read in this text; this is also an annoying problem.

The aspects of the book that focus on the biology of the mind are like breaths of fresh air, but every chapter inevitably leads into mind-numbing instructions and equations that are difficult to comprehend.

This is by far the most frustrating book I've had to deal with. The other one-star review was shrewd in warning undergrad students and beginners about this text.

"Computational Explorations in Cognitive Neuroscience" provides a very readable overview of state-of-the-art neural network models for human cognition with an emphasis on both biological plausibility and experimental (psychological/cognitive) evidence.

In this book, research themes, which include perception, memory, language as well as high-level cognition, are explained in terms of computation. Their theory is based on brain science, computer science, and psychology. Though the authors speculate about the functions of each part of the brain and the relation among them to some extent, the authors propose a new paradigm to existing sciences. Their integrative approach and method are very simulative, and I've got a lot of hints from this book. But I don't need the usageof particular software, PDP++ in such a theoretical book. The authors explain and demonstrate their models and theories using PDP++ at the end of each chapter. If you want to study how to use PDP++ as well as their theories, this book will be extremely good one.

In this book, research themes including perception, memory, and language as well as high-level cognition are explained in terms of computation. Their theories are based on brain science, computer science, and psychology. Though the authors speculate about the functions of the brain and the relation among them to some extent, the authors propose a new paradigm to existing sciences. Their integrative approach and method are very simulative, and I've got a lot of hints from this book. But I don't need the usage of particular software, PDP++ in such a theoretical book. The authors explain and demonstrate their models and theories using PDP++ at the end of each chapter. If you want to study how to use PDP++ as well as their theories, this book will be truly excellent.

I am currently taking a honors psych class which utilizes this textbook as a lab handout (we solve the exercises closing out each chapter). I find this book very hard to read due to the language and the explanations the authors use to explain certain topics. The book reads more like a guide for those already familiar with the subject matter, and the questions closing out each chapter are even harder to understand than the chapter text itself. If the authors wish the book to be of any help to undergrads who are not already familiar with the topic they should take a step back and revise the text so that it is understandable for all. NOTE TO UA STUDENTS THINKING OF TAKING THE CLASS WHICH UTILIZES THIS BOOK
---->dont.

"A First Look at Fuzzy Logic and Neural Networks..." might be a lot more accurate. It does a good job of covering the concepts. What it doesn't do is address any of the issues of implementing a fuzzy system in an embedded environment. If you don't know what a fuzzy set is then you should consider this book. If you want some tips or ideas for creating an inference engine for an 8 or 16 bit processor I suggest you look elsewhere.

The book is written in a language that makes it accessible to beginners in the field of fuzzy logic as well as experts, since it contains top notch research on the state of the art of the topic.
Embedded system design using fuzzy logic algorithms is made easy through practical examples.
I thoroughly enjoyed the book. If you want a concise, well written book that is not overbearing and is actually very user friendly and you are interested in fuzzy logic application algorithms this is your book.

While this book does provide a reasonable overview, I found it rather disappointing.

It has too many errors. With highly technical material, it is imperative that the information is correct or else you can't trust it. For example a minus instead of a plus does not help when explaining terminology.

Only half the book is really about fuzzy logic. There is far too much padding eg. 1.large diagrams showing Moore's Law and the layers in an IC gate. These are not subjects that should be covered in a book on fuzzy logic and one is forced to conclude that the author had a page quota to be reached and did it by adding these secions and large verbose reference sections.

A worked example or an appendix showing an algorithm in C would have been far more useful.

For someone looking for fuzzy modeling and control into embedded systems this book is excellent. The author provides a firm fuzzy concepts necessary to design intelligent systems and gives the reader a solid background for further studies and real world applications. Embedded systems design case studies overview is something that all embedded system developers should understand but many don't take the time. It is thorough, without being arcane or pedantic.

In summary the book contains the right material, it is presented in an easy to absorb manor and is practically oriented. I highly recommended it to embedded engineering students, or engineers and managers facing the challenges of fuzzy logic based project. I'll consider five stars for this book.

Good introduction about fuzzy logic plus a ton of web resources. I gave it 3 stars because so many wording errors in this book.

This is one of the worst books on data mining available. It is not intended for marketers nor researchers. You don't need any knowledge about neural networks and -even worse- you will not learn anything. It only talks about the IBM Neural Network Utility. If you are a business man look for 'Data Mining Techniques' from Michael J. A. Berry If you are a math man looking for a good text on neural networks see 'Neural Networks' from Simon Haykin.

If you do not like math and would like to know about neural networks, then this is it. The book is very explanatory, it is designed for starters and you get a very good feeling about what neural networks are and how they work. Do not expect, however, that you will be able to design one after reading the book.

The cover of this book clearly states that it is intended for "Solving Business Problems - from Application Development to Decision Support". The back of the book states that it is a "practical, accessible guide for business executives..."

This is not a book for developers unless they are just getting started and have never heard of neural nets or data mining. I found this little book helpful for providing easy-to-understand reviews for beginning AI students and non-technical business people.

Some of the other reviewers of this book are unfairly slamming this book for not being technical enough, when clearly that is not the intention of the book. There are no formulae in this book, but there are some nice diagrams that get the point across for beginners. The chapter on agents seemed a little misplaced, but otherwise, for learning about neural nets, this is not a bad book. For a pure biz-oriented "intro to data mining" I prefer the Adriaans book, however.

The Amazon.com review of this book (see above) says "are you personally more interested in strategic applications and general overviews than mind-numbing equations and printouts of code?". A good general overview does not have to contain printouts of code and mind-numbing equations, but it does have more substance and conceptual information than this "business week" like book long article. That's the point. The contents of this book would be fine for a business magazine article but not for a book. Too much prose and at the end not even an intelligent reader can make sense of what is really feasible with this technology and how it can be approached. There are much better general data mining books in the market, books without codes and weird equations for the mathematical illiterate, but with strong conceptual explanations and fundations. See, for instance, "Data Mining" by Pieter Adriaans for a much better book.

Presents clearly the problems and the method. The introductory part was helpful in understanding the ICA theoretical model although more detail on kurtosis description would have been beneficial. I liked the infomax algorithm and the way it was presented. On the down side: some minor erroneus explanations found. I have the feeling that ICA is more than just infomax approach and that the title "Independent Component Analysis - an Infomax Approach" would have been more appropiate. On the application section, very good presentation of the signal separation but very succint explanation on natural images for example. Being the first book I see in the field, I think, a thorough presentation would have been helpful.

The first part of the book is the best part, it deals with ICA in the information theoretic framework and shows how the (ML) and (infomax) are closely related. However, it is not for beginners since the background material is abbreviated as well as the mathematical exposition of this book assumes the preknowledge in ICA theory.The overall impression one gets is that the book is too short, knowing that the book is more or less a collection of the author's papers, this should not be surprising at all.

I rate it 4/5 because of its expensive price.

This book is not what you expect at all because :

(1) It is merely a collection of papers for the same author lacking proper organization;

(2) Blank pages are deliberately left between chapters, also figures are placed on separate pages this can tell you a lot regarding the quality you expect;

(3) The book is expensive ,I think the author should make it the half or less ;

(4) A researcher in this field hardly sees the book as a reference;

(5) Other topics are ignored ex:Tensoral methods;ICA is not only about Infomax;

(6) The first pages compose the climax of the book ,the rest is just loose and even abscent concepts;

(7) Finally,I think that the book was published too early ,it seems a lot of maturity could have been witnessed if the author waited instead.

Anyone new will be presented to the name of the subject but not the subject itself .The book by Hyvarinen should be available ... ,go for it.I believe life will be a lot easier .The latter is divided into four parts which clearly puts the reader in the right place to start and are : (I) Mathematical Preliminaries (II) Basic Independent Component Analysis (III) Extensions and related Methods (IV) Applications of ICA ,also after reading the sample chapter and contents I think you will not be disappointed . ....

If the newcomer is expecting a textbook which gives a thorough and rigorous introduction to the subject, he will not find it here. Essentially, Independent Component Analysis by T. Lee is a compendium of Lee's work on the subject, being, for the most part, a regurgitation of his papers. This in itself is no cause for distress; however, I feel that perhaps some more detail and work could have gone into other researchers' avenues to the problem. For instance, cumulant based methods hardly make it into the book. The derivation of the most important formulas for multiple decorrelation algorithms are omitted. The Fixed-Point Method of Hyvarinen is omitted. A paragraph is given to algorithms which work entirely in the frequency domain. Short shrift is given to JADE.

The applications side is dominated nearly entirely by the biomedical applications to which Lee is associated with, with a small foray into the world of feature extraction.

The introduction and conclusions are well written, though more detail could have helped. There are a few errata throughout though this is normal for a first book. All in all a book with a rather narrow focus.

This book provides a systematic overview of a beautiful theoretical apparatus that the author and collaborators have developed for describing the computational power of neural networks. It addresses neural networks from the standpoint of computational complexity theory, not machine learning.

A central issue that arises is what values the neural couplings can take on. The book outlines the consequences of various choices. Rational-valued neural networks turn out to be Turing machines, a contribution of general significance. The book shows (and perhaps unduly emphasizes) that irrational-valued couplings can yield Superturing computation, a result which has been controversial.

If irrational numbers can arise in a computational setting, then the work outlined here is clearly a major landmark that deserves the careful, systematic exposition the book provides. On the other hand, maybe irrational numbers are just not relevant to actual computational devices. (They certainly aren't yet.) If so, the book is still a worthwhile theoretical exercise leading to an elegant set of results. Even if one leans toward the latter option - and I would say that this is probably the vast majority - I don't think any of us really _know_ where the irrational numbers stand vis-a-vis our computational universe.

Even if you intuitively see that an infinitely rich source of information, which is what an irrational number provides, should yield Super-Turing computation, the book is still valuable. (If you don't have this intuition, think about it more!) There is a lot to be gleaned from the non-obvious (at least to me) details of how that intuition works itself out.

The book has more technical flaws. The author periodically states results without really explaining fully, or even at all. This leaves a good deal of work to the reader. I would expect to spend a few hours per page, here and there, though usually it will move quicker. A major issue is also the challenging notation, which is often more difficult than it needs to be. The book's introduction to advice turing machines is also insufficient; you'll need to do a bit of background reading if you don't know much about them.

A computer is an artifact. Through specific control mechanisms of electric currents it was possible to domesticate natural phenomena, and put them at men service, giving rise to the levels of automation that characterize the world in the turning of the millennium. But a computer is an analog artifact. Paul Cull, from Oregon State University, states this computational anecdote in the following terms: «That analog devices behave digitally is the basis for a large part of electronics engineering and allows for the construction of electronic computers. It is part of the engineering folklore that when the gain is high enough any circuit from a large class will eventually settle into one of two states, which can be used to represent booleans 0 and 1. As far as we can tell, this theorem and its proof has never been published, but it probably appears in a now unobtainable MIT technical report of the1950s.» Recently much work have been done to show that digital computers are a particular class of analog computers that exhibit greater computational power. In fact, digital computers are extreme (weak) analog computers. A book was needed to introduce these ideas to the graduate student on Theoretical Computer Science and to the general researcher on the new field of Non-standard Models of Computation. Hava Siegelmann's book partially fills this gap in the computational literature.

Over the last decade, researchers have speculated that although the Turing model is indeed able to simulate a large class of computations, it does not necessarily provide a complete picture of the computations possible in nature. As pointed out by Hava Siegelmann, the most famous proposals of new models were made by Richard Feynman and Roger Penrose. Feynman suggested making use of the non-locality of quantum physics. Penrose, who was motivated by the model of the human brain, argued that the Turing model of computing is not strong enough to model biological intelligence. In response, several novel models of computation have been put forth: among them the quantum Turing machine and the DNA computer. These models compute faster than Turing machines and thus are richer under time constraints. However they cannot compute non-recursive functions, and in this sense are not inherently more powerful than the classical model. The analog recurrent neural network model of Hava Siegemann computes more than the Turing machine, not only under time-constraints, but also in general. In this sense it can be referred to as a hypercomputation model.

The use of analog recurrent neural networks for computability analysis is due to Hava Siegelmann and Eduardo Sontag. In Hava Siegelmann's book, she used them to establish lower bounds on their computational power. These systems satisfy the classical constraints of computation theory, namely, (a) input is discrete (binary) and finite, (b) output is discrete (binary) and finite, and (c) the system is itself finite (control is finite). The infiniteness may originate from two different sources: the system is influenced by a real value, which can be a physical constant, directly affecting the computation, a probability of a biased binary random coin or any other process; the infiniteness may also come from the operations of an adaptive process interleaved with the computation process, like is the case in our brains. Neurons may hold values within [0,1] with unbounded precision. To work with such analog systems, binary input is encoded into a rational number between 0 and 1, and the rational output is decoded into an output binary sequence. The technique used in this book consists of an encoding of binary words into the Cantor Set of base 4. Within this (number-theoretic) model, finite binary words are encoded as rational numbers in [0,1]. We may then identify the set of computable functions by analog recurrent neural nets, provided that the type of the weights is given. This research program has been systematically pursued by Hava Siegelmann at the Technion and her collaborators.

The first level of nets is NET[integers]. These nets are historically related with the work of Warren McCulloch and Walter Pitts. As the weights are integer numbers, each processor can only compute a linear combination of integer coefficients applied to zeros and ones. The activation values are thus always zero or one. In this case the nets 'degenerate' into classical devices called finite automata. It was Kleene who first proved that McCulloch and Pitts nets are equivalent to finite automata and therefore they were able to recognize all regular languages. But they are not capable of recognizing well-formed parenthetic expressions or to recognize the nucleic acids for these structures are not regular...

The second relevant class Hava Siegelmann considers is NET[rationals]. Rationals are indeed computable numbers in finite time, and NET[rationals] turn to be equivalent to Turing machines. Twofold equivalent: rational nets compute the same functions as Turing machines and, under appropriate encoding of input and output, they are able to compute the same functions in exactly the same time. Even knowing that rationals are provided for free in nature, rationals of increasing complexity, this ressource do not even speed up computations with regard to Turing machines. The class NET[rationals] coincide with the class of (partial) recursive functions of Kurt Gödel and Kleene. About them it is said that they constitute the whole concrete, realizable, mathematical universe.

The third relevant (and maybe surprising to the reader) class is NET[reals]. Reals are indeed in general non computable. But theories of physics abound that consider real variables. If the reader look at these theories from a more epistemological point of view as approximative models, then we argue that while some alternative theories are not available, if the old models can encode hypercomputations, then they are not simulable in digital computers. The advantage of making a theory of computation on top of these systems is that nonuniform classes of computation, namely the classes that arise in complexity theory using Turing machines with advice, are uniformly described in NET[reals]. As shown in Hava Siegelmann's book all sets over finite alphabets can be represented as reals that encode the families of boolean circuits that recognize them. Under efficient time computation, these networks compute not only all efficient computations by Turing machines but also some non-recursive functions such as (a unary encoding of) the halting problem of Turing machines.

A novel connection between the complexity of the networks in terms of information theory and their computational complexity is developed, spanning a hierarchy of computation from the Turing to the fully analog model. This leads to the statement of the Siegelmann-Sontag thesis of 'hypercomputation by analog systems' analogously to the Church-Turing thesis of 'computation by digital systems'.

A beautiful non-standard theory of computation is presented in 'Neural Networks and Analog Computation'. I strongly recommend the careful reading of Hava Siegelmann's book, to enjoy the uniformity of nets description and to ponder where hypercomputation begins in the limits of classical physical reality.

This book certainly claims to give much much more than what It actually provides. Trying to read this book, you'll have to swallow a formalism that unfortunately does not pay off. There is absolutely no revolutionary idea, just well known facts and pretention to do better than a TM but based on assumptions that by their sole existence, suffice to do better than any Turing machine, you don't need a whole book to say this. (namely, working with arbitrary precision).

Some of this book is an interesting discussion of the boundries of computability. However, the book's central claim, that you can exceed the Turing limit, requires the storing of infinitely precise variables in a physical device. This is a physical impossibility which no amount of gratuitous logical notation will make go away. Even if you put aside the difficulties of measuring a value to infinite precision, quantum indeterminance and discontinuity will not allow any physical object to store or encode an infinitely precise value in any fashion. Once this premise is seen to be false, most of the other interesting claims in the book, and all the hypercomputational ones, immediately collapse.

Anyone who can help me get this book, please email me wr1230_99@hotmail.com
THANKS A LOT!

Well written workbook for the interested general reader to gain an understanding of neural networks. Although some workbooks come with neural network simulator software for a personal computer (mine did not, and I was unable to evaluate the simulator), the printed workbook itself is extremely interactive and has the reader work through simulations of simple neural networks. This workbook covers the perceptron, minimum error learning, Hebbian learning, competitive learning, attractor networks (single layer, double layer and statistical), and back propagation networks.

Don't waste your money. This isn't a bad text, in terms of explaining the theory, but it includes a 3.5" floppy disk that is so old my computer couldn't even read the files. It's not worth the money without the software. The author does not appear to have published any related work in the last four or five years, and I have not found any pointers to updated software on the Web (probably because the book predates the web). I guess this might make a good museum item, if you don't take the cellophane off it.

A fairly good text in terms of explanation of theory and so on, but the accompanying disk contains neural network simulation software that is six or eight years old. I bought the Macintosh version, and I couldn't even read some of the files (either because the file format was ancient or because the floppy disk was so old the files had been corrupted by ambient radiation). I had to dig out my old PowerBook so I had a floppy disk drive to use. Big surprise - I bought it in a bookstore and the publication date was not displayed on the outside of the cellophane wrapped package.

This is an enthusiastically written and nicely illustrated book, but the order of presentation is strange, possibly a result of bad editing. You might find it helpful to skip straight to pages 63-66 and study the introductory material that appears, for some reason, a quarter of the way through the text. It explains how the PET scanning technique works. The book nods at other technologies that produce and/or record signals from the brain, including MRI and electroencephalography, but it is basically a book about PET. The acronym stands for Positron Emission Tomography.

PET scanning is a low resolution technique that produces a computed picture of oxygen uptake by tissues in the brain. The experimental idea is to get the brain of a human experimental volunteer to do something - recite the multiplication tables, say - and then try to notice whether and how the given project changes the relative oxygen demand of brain tissue in various regions of the brain.

The hope would be to identify local volumes of brain tissue which are associated with and thus perhaps even perform some basic psychological function. In practice, the brain obligingly lights up here and there - presumably consuming oxygen in order to energize its thinking.

From the explanations given in the book, it appears that the PET scanned pictures, which are quite beautiful, are thought to reflect heightened metabolic activity in the nerves of the brain, and only in the nerves. The book speaks often about functional brain "modules" and "assemblages of nerves." It is not clear to me, from the text, just how the scanner distinguishes between the nerves and all the other types of tissue in the brain. The glia, for example, outnumber the nerve cells about 9 to 1 in the brain, and these cells breathe oxygen too. In other words it is not clear, from the book, how the scanner somehow selectively singles out nerve cells and snaps their picture.

And maybe it doesn't. I was left wondering what a PET scan of some other complex organ, such as the liver, looks like. The PET technique may just be fine, brilliant in fact, but if it is, then maybe it deserves a clearer explanation that I could find in here.

Once a month we get a book on somebody else's view of the mind, the brain, or both.

Instead of more theory, Images Of Mind describes the machinery neuroscientists use to take all the pictures that have sparked all the theories about how the brain works. Complete with lush illustrations and lucid descriptions, Images takes the reader on a historical tour of the devices scientists have used to "watch" the mind work. From EEGs to PET scanners, Raichle and Posner describe how neurotechnological devices work and what they measure.

The writing is direct and elegant, meant for the pro and the layperson.

The problem with using brain imaging to understand how it works is that currently all the published papers contain irreproducible data. This means that these nice papers show us more noise than real data, and 'contribute' confusion rather than understanding. This book, like the rest of the literature, 'deals' with this problem by simply ignoring it.