Complex Networks

On-line learning is one of the most powerful and commonly used techniques for training large layered networks and has been used successfully in many real-world applications. Traditional analytical methods have been recently complemented by ones from statistical physics and Bayesian statistics. This powerful combination of analytical methods provides more insight and deeper understanding of existing algorithms and leads to novel and principled proposals for their improvement. This book presents a coherent picture of the state-of-the-art in the theoretical analysis of on-line learning. An introduction relates the subject to other developments in neural networks and explains the overall picture. Surveys by leading experts in the field combine new and established material and enable non-experts to learn more about the techniques and methods used. This book, the first in the area, provides a comprehensive view of the subject and will be welcomed by mathematicians, scientists and engineers,

Now in its fourth edition, the first part of this book is devoted to the basic material of complex analysis, while the second covers many special topics, such as the Riemann Mapping Theorem, the gamma

The first advanced textbook on this subject. The Structure and Rheology of Complex Fluids provides a multidisciplinary and comprehensive introduction to these fascinating and important substances. It

The Polish Complex takes place on Christmas Eve, from early morning until late in the evening, as a line of people (including the narrator, whose name is Konwicki) stand and wait in front of a jewelr

Provides a framework to account for complex thought processes within and between minds.

An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician.

Complex Pleasure deals with questions of literary feeling in eight major German writers—Lessing, Kant, Holderlin, Nietzsche, Musil, Kafka, Trakl, and Benjamin. On the basis of close readings of these

Over a period of several centuries, Europeans developed an intricate system of plantation agriculture overseas which was quite different from the agricultural system used at home. Though the plantation complex centered on the American tropics, its influence was much wider. Much more than an economic order for the Americas, the plantation complex had an important place in world history. These essays concentrate on the intercontinental impact.

Between 1814 and 1831, the great French mathematician A. L. Cauchy created practically single-handedly a new branch of pure mathematics. Complex function theory was and remains of central importance, and its creation marked the start of one of the most exciting periods in the development of mathematics. In this book Dr Smithies analyses the process whereby Cauchy created the basic structure of complex analysis, describing first the eighteenth-century background before proceeding to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchy's hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchy's thinking during t

Complex fluid flows are encountered widely in nature, in living beings and in engineering practice. These flows often involve both geometric and dynamic complexity and present problems that are difficult to analyse because of their wide range of length and time scales, as well as their geometric configuration. This book describes some computational techniques and modelling strategies for analysing and predicting complex transport phenomena. It summarizes advances in the context of a pressure-based algorithm. Among methods discussed are discretization schemes for treating convection and pressure, parallel computing, multigrid methods, and composite, multiblock techniques. With respect to physical modelling, the book addresses issues of turbulence closure and multiscale, multiphase transport from an engineering viewpoint. Both fundamental and practical issues are considered, along with the relative merits of competing approaches. Numerous examples are given throughout the text. Mechanica

The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organised criticality, are introduced in this book, for a broad range of readers interested in complex natural phenomena. Now in a greatly expanded second edition, this book relates fractals and chaos to a variety of geological and geophysical applications. These include drainage networks and erosion, floods, earthquakes, mineral and petroleum resources, fragmentation, mantle convection and magnetic field generation. Many advances have been made in the field since the first edition was published. In this edition coverage of self-organised criticality is expanded and statistics and time series are included to provide a broad background for the reader. All concepts are introduced at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mat

Why do we make mistakes? Are there certain errors common to failure, whether in a complex enterprise or daily life? In this truly indispensable book, Dietrich Dörner identifies what he calls the

In view of the extensive development of CCS 7 and fast-paced growth of ISDN in telecommunication networks throughout the world, this valuable resource serves as a timely reference and guide. Practical

Optical devices are employed in an ever-increasing range of applications, from simple lenses to complex fibre-optic communication networks. This book provides a detailed introduction to modern optical engineering, covering the fundamental concepts as well as practical techniques and applications. Basic optical principles are presented, particularly reflection, refraction, aberrations, diffraction and interference. Building on this foundation, a wide variety of optical devices and processes are then discussed, including simple optical instruments, photodetectors, spatial light modulators, holography and lasers. Two chapters are devoted to linear system transforms and signal processing, and the book concludes with a chapter on fibre optics. The book contains many worked examples and over 250 problems (solutions manual for instructors available from the publishers). It will be invaluable to electrical engineering and physics undergraduates taking courses in optical engineering, photonics,

Too many laws, too many lawyers--that's the necessary consequence of a complex society, or so conventional wisdom has it. Countless pundits insist that any call for legal simplification smacks of nos

In praise of Prambanan is devoted to the Hindu-Javanese temple complex of Candi Prambanan, also known by its locally more popular name of Candi Loro Jonggrang.

Is the "Oedipus complex" universal? This book examines the controversial question in light of its collection of 139 family complex folktales from every world cultural area and every

Is the “Oedipus complex” universal? This book examines the controversial question in light of its collection of 139 family complex folktales from every world cultural area and every leve

A two-part volume containing a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications, and a detailed review of recent investigations

The major histocompatibility complex (Mhc) is one of the few identified gene systems in domestic animals that is associated with quantitative traits such as disease resistance, immune response, growth

This book is an incisive analysis of Japan's deepening economic presence in Asia. It challenges neoclassical economists, arguing that instead of simply building a 'yen bloc' or responding to market forces, Japanese business and government elites are working together to build an expanded - and potentially exclusive - production zone. The authors suggest that the transplantation of many standard Japanese business practices in Asia is based on the concept of keiretsu (enterprise group) which allows a complex web of production networks to develop. The book shows that such strategic control of technology is a unique model of globalisation. While informed by economic theory, Asia in Japan's Embrace is highly accessible, containing interviews and anecdotal evidence from factory floors and board rooms. It is comprehensive and controversial, outlining policy implications and the impact on global trade.

A basic problem for the interconnection of communications media is to design interconnection networks for specific needs. For example, to minimize delay and to maximize reliability, networks are req

Classic Complex Analysis is a text that has been developed over decades of teaching with an enthusiastic student reception. The first half of the book focuses on the core material. An early chapter

In this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a detailed study of Weil and Cart

There are many different analytical techniques used to identify and quantify a wide range of substances in complex matrices such as the atmosphere, factory air, water, plants, soils, foods and industr

Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Topics inc

Basic treatment of the theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differe

This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats sever

Modern Real and Complex Analysis Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maint

Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity. This is an introduction to the subject suitable for beginning graduate students, concentrating on the important case of two dimensions. This permits a simpler treatment than other books, yet is still sufficient for a wide range of applications to complex analysis; these include Picard's theorem, the Phragmén–Lindelöf principle, the Koebe one-quarter mapping theorem and a sharp quantitative form of Runge's theorem. In addition there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics, and gives a flavour of some recent research. Exercises are provided throughout, enabling the book to be used with advanced courses on complex analysis or potential theory.

Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity. This is an introduction to the subject suitable for beginning graduate students, concentrating on the important case of two dimensions. This permits a simpler treatment than other books, yet is still sufficient for a wide range of applications to complex analysis; these include Picard's theorem, the Phragmén–Lindelöf principle, the Koebe one-quarter mapping theorem and a sharp quantitative form of Runge's theorem. In addition there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics, and gives a flavour of some recent research. Exercises are provided throughout, enabling the book to be used with advanced courses on complex analysis or potential theory.

Drawn from lectures given by Raghavan Narasimhan at the University of Geneva and the University of Chicago, this book presents the part of the theory of several complex variables pertaining to unramif

Richard Day was one of the first economists to recognize the importance of complex dynamics, or chaos theory, in economics and to systematically explore whether a mathematical existence of such behavi

This volume contains a unique, systematic presentation of the general theory of differential equations on complex manifolds. The six chapters deal with questions concerning qualitative (asymptotic

"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is r

A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, w

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solut

Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solut

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such

This text is a beginning graduate-level introduction to neural networks, focussing on current theoretical models, examining what these models can reveal about how the brain functions, and discussing the ramifications for psychology, artificial intelligence and the construction of a new generation of intelligent computers. The book is divided into four parts. The first part gives an account of the anatomy of the central nervous system, followed by a brief introduction to neurophysiology. The second part is devoted to the dynamics of neuronal states, and demonstrates how very simple models may stimulate associative memory. The third part of the book discusses models of learning, including detailed discussions on the limits of memory storage, methods of learning and their associated models, associativity, and error correction. The final part reviews possible applications of neural networks in artificial intelligence, expert systems, optimization problems, and the construction of actual ne