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An Introduction to the Modeling of Neural Networks
This book is a beginning graduate-level introduction to neural networks which is divided into four parts.
Introduction to Random Matrices
Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
Ageing and the Glass Transition
Understanding cooperative phenomena far from equilibrium is one of the fascinating challenges of present-day many-body physics. Glassy behaviour and the physical ageing process of such materials are paradigmatic examples. The present volume, primarily intended as introduction and reference, collects six extensive lectures addressing selected experimental and theoretical issues in the field of glassy systems.
Mathematical Constants II
Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson-Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl-Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton-Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Nonequilibrium Statistical Mechanics in One Dimension
Self-contained and up-to-date guide to one-dimensional reactions, dynamics, diffusion and adsorption.
Theory of Financial Risk and Derivative Pricing
Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.
Solids Far from Equilibrium
Originally published in 1991, this book, based on the 1989 Beg-Rohu summer school, contains six sets of pedagogical lectures by internationally respected researchers on the statistical physics of crystal growth. Providing a course in which the phenomena of shape and growth are viewed from a fresh vantage point, the lectures cover a variety of developments in the field and reflect on problems that have received inadequate attention. Statistical physicists, condensed matter physicists, metallurgists, and applied mathematicians will find this a stimulating and valuable book on an important topic.
New Visions on Form and Growth
There exists a wide variety of patterns in nature, from inert matter such as crystalline dendrites and flames, to filamentous fungi and neurones in the living world. Their structural evolution during growth can be theoretically modeled in order to predict the shape of their forms, their dimensions and their growth rate. 'New Visions on Growth and Form' aims at answering such questions by employing different theoretical approaches and providing a critical appraisal. The book belongs to the wide field of non-equilibrium statistical physics, and explores different mechanisms such as transport, interfacial tension, and chemical reactions, which govern the growth of a material. It explains the fundamental equations relating different morphological quantities, as well as the relevant experimental control parameters. From the unifying concepts arising in the theoretical approach the author proposes a tentative description of cell morphogenesis as a further application of the theory.
From Statistical Physics to Statistical Inference and Back
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.
First-passage Phenomena And Their Applications
The book contains review articles on recent advances in first-passage phenomena and applications contributed by leading international experts. It is intended for graduate students and researchers who are interested in learning about this intriguing and important topic.
