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Artificial neural networks, learning, statistical mechanics; background material in mathematics and physics; examples and exercises; textbook/reference.
Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.
Statistical Mechanics is an integral part of theoretical physics, and this book aims at presenting the fundamentals of statistical mechanics in a clear and concise manner. The book begins with a clear exposition of classical as well as quantal equilibrium statistical mechanics. Then it moves on to give insights into the Gibbs canonical distribution, the grand canonical distribution, ideal Bose gas, ideal fermi gas, and imperfect gases. The text also delves into certain topics of special interest, such as phase-transitions, Ising model, and liquid Helium. The book concludes with a discussion of some selected topics of non-equilibrium statistical mechanics. Primarily intended as a text for postgraduate students of physics, it would also prove useful for students at the undergraduate level.

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