Complex-Valued Neural Networks With Multi-Valued Neurons

本書以複雜神經網絡定性穩定性研究為核心, 並結合定量研究深入展開, 形成容納複雜網絡和多智能體系統的動態特性的研究脈絡。本書的特點是在動力系統和穩定性之間的關係上進行了詳盡的闡述, 傳統的動力神經網絡和當下的複雜神經網絡及多智能體之間的關係進行闡述, 揭示了大規模系統之間的演化關係。同時, 針對單穩定性、多穩定性、週期解和不變集等動態特性進行相互關係研究, 並將所得到的結果用到動力系統的同步性和一致性方面。結合動力系統的這些特點, 將神經網絡的動態特性應用到聯想記憶、模式識別、在線計算及進化學習等方面具體的應用方面, 實現神經網絡理論和實際問題的零距離結合。

This book focuses on the stability of the dynamical neural system, synchronization of the coupling neural system and their applications in automation control and electrical engineering. The redefined

This book covers the hot topics and applications surrounding complex-valued neural networks. It demonstrates advanced theories with a wide range of applications, including optoelectronics systems, ima

Recent advancements in the field of telecommunications, medical imaging and signal processing deal with signals that are inherently time varying, nonlinear and complex-valued. The time varying, nonlin

This book is the second enlarged and revised edition of the first successful monograph on complex-valued neural networks (CVNNs) published in 2006, which lends itself to graduate and undergraduate cou

Complex-Valued Neural Networks have higher functionality, learn faster and generalize better than their real-valued counterparts.This book is devoted to the Multi-Valued Neuron (MVN) and MVN-based neu

This book was written in response to the growing demand for a text that provides a unified treatment of linear and nonlinear complex valued adaptive filters, and methods for the processing of general

Written for graduate students and researchers in computer science fields, this collection of research articles on complex-valued neural networks with high- dimensional parameters concentrates on how t

What are the principles behind intelligent systems? How are they built? What are intelligent systems useful for? How do we choose the right tool for the job? These questions are answered by Michael Negnevitsky’s Artificial Intelligence: A Guide to Intelligent Systems.Unlike many books on computer intelligence, which use complex computer science terminology and are crowded with complex matrix algebra and differential equations, this text demonstrates that the ideas behind intelligent systems are simple and straightforward. This text assumes little or no programming experience as it tackles topics like expert systems, fuzzy systems, artificial neural networks, evolutionary computation, knowledge engineering, and data mining.TABLE OF CONTENTS1. Introduction to Intelligent Systems 1.1 Intelligent Machines, or What Machines Can Do 1.2 The History of Artificial Intelligence, or From the ‘Dark Ages’ to Knowledge-based Systems 1.3 Generative AI 1.4 Summary Questions fo

The analysis and understanding of multilingualism, and its relationship to identity in the face of globalization, migration and the increasing dominance of English as a lingua franca, makes it a complex and challenging problem that requires insights from a range of disciplines. With reference to a variety of languages and contexts, this book offers fascinating insights into multilingual identity from a team of world-renowned scholars, working from a range of different theoretical and methodological perspectives. Three overarching themes are explored – situatedness, identity practices, and investment – and detailed case studies from different linguistic and cultural contexts are included throughout. The chapter authors' consideration of 'multilingualism-as-resource' challenges the conception of 'multilingualism-as-problem', which has dogged so much political thinking in late modernity. The studies offer a critical lens on the types of linguistic repertoire that are celebrated and valued

The illegal trade in live apes, ape meat and body parts occurs across all ape range states and poses a significant and growing threat to the long-term survival of wild ape populations worldwide. What was once a purely subsistence and cultural activity, now encompasses a global multi-million-dollar trade run by sophisticated trans-boundary criminal networks. The challenge lies in teasing apart the complex and interrelated factors that drive the ape trade, while implementing strategies that do not exacerbate inequality. This volume of State of the Apes brings together original research and analysis with topical case studies and emerging best practices, to further the ape conservation agenda around killing, capture and trade. This title is also available as Open Access via Cambridge Core.

The illegal trade in live apes, ape meat and body parts occurs across all ape range states and poses a significant and growing threat to the long-term survival of wild ape populations worldwide. What was once a purely subsistence and cultural activity, now encompasses a global multi-million-dollar trade run by sophisticated trans-boundary criminal networks. The challenge lies in teasing apart the complex and interrelated factors that drive the ape trade, while implementing strategies that do not exacerbate inequality. This volume of State of the Apes brings together original research and analysis with topical case studies and emerging best practices, to further the ape conservation agenda around killing, capture and trade. This title is also available as Open Access via Cambridge Core.

Data-driven computational neuroscience facilitates the transformation of data into insights into the structure and functions of the brain. This introduction for researchers and graduate students is the first in-depth, comprehensive treatment of statistical and machine learning methods for neuroscience. The methods are demonstrated through case studies of real problems to empower readers to build their own solutions. The book covers a wide variety of methods, including supervised classification with non-probabilistic models (nearest-neighbors, classification trees, rule induction, artificial neural networks and support vector machines) and probabilistic models (discriminant analysis, logistic regression and Bayesian network classifiers), meta-classifiers, multi-dimensional classifiers and feature subset selection methods. Other parts of the book are devoted to association discovery with probabilistic graphical models (Bayesian networks and Markov networks) and spatial statistics with po

Understand the benefits of robust statistics for signal processing with this authoritative yet accessible text. The first ever book on the subject, it provides a comprehensive overview of the field, moving from fundamental theory through to important new results and recent advances. Topics covered include advanced robust methods for complex-valued data, robust covariance estimation, penalized regression models, dependent data, robust bootstrap, and tensors. Robustness issues are illustrated throughout using real-world examples and key algorithms are included in a MATLAB Robust Signal Processing Toolbox accompanying the book online, allowing the methods discussed to be easily applied and adapted to multiple practical situations. This unique resource provides a powerful tool for researchers and practitioners working in the field of signal processing.

For students with disabilities, including those with complex support needs, inclusion means more than just physical presence in a classroom—it means full participation and valued members

The auditory system is a complex neural system composed of many types of neurons connected into networks. One feature that sets the auditory system apart from other sensory systems, such as somatosens

The book is an authoritative collection of contributions by leading experts on the topics of fuzzy logic, multi-valued logic and neural network. Originally written as an homage to Claudio Moraga, seen

This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between super-reflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of non-commutative martingales, which has natural connections with quantum physics and quantum information theory. Requiring few prerequisites and providing fully detailed proofs for the main results, this self-contained study is accessible to graduate students with a basic knowledge of real and complex analysis and functional analysis. Chapters can be read independently, with each building from the introductory notes, and the diversity of topics included also means this book can serve as the basis for a variety of graduate courses.

Reproducing kernel Hilbert spaces have developed into an important tool in many areas, especially statistics and machine learning, and they play a valuable role in complex analysis, probability, group representation theory, and the theory of integral operators. This unique text offers a unified overview of the topic, providing detailed examples of applications, as well as covering the fundamental underlying theory, including chapters on interpolation and approximation, Cholesky and Schur operations on kernels, and vector-valued spaces. Self-contained and accessibly written, with exercises at the end of each chapter, this unrivalled treatment of the topic serves as an ideal introduction for graduate students across mathematics, computer science, and engineering, as well as a useful reference for researchers working in functional analysis or its applications.

Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors. This book addresses topics of importance when dealing with s

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in the first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. Volume 1 focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. Volume 2 goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. Volume 3 covers complex analysis and the theory of measure and integration.

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.

The nervous system is made up of a large number of interacting elements. To understand how such a complex system functions requires the construction and analysis of computational models at many different levels. This book provides a step-by-step account of how to model the neuron and neural circuitry to understand the nervous system at all levels, from ion channels to networks. Starting with a simple model of the neuron as an electrical circuit, gradually more details are added to include the effects of neuronal morphology, synapses, ion channels and intracellular signalling. The principle of abstraction is explained through chapters on simplifying models, and how simplified models can be used in networks. This theme is continued in a final chapter on modelling the development of the nervous system. Requiring an elementary background in neuroscience and some high school mathematics, this textbook is an ideal basis for a course on computational neuroscience.

This book is devoted to some mathematical methods that arise in two domains of artificial intelligence: neural networks and qualitative physics. Professor Aubin makes use of control and viability theory in neural networks and cognitive systems, regarded as dynamical systems controlled by synaptic matrices, and set-valued analysis that plays a natural and crucial role in qualitative analysis and simulation. This allows many examples of neural networks to be presented in a unified way. In addition, several results on the control of linear and nonlinear systems are used to obtain a 'learning algorithm' of pattern classification problems, such as the back-propagation formula, as well as learning algorithms of feedback regulation laws of solutions to control systems subject to state constraints. This book will be of value to anyone with an interest in neural networks and cognitive systems.

Random walks, Markov chains and electrical networks serve as an introduction to the study of real-valued functions on finite or infinite graphs, with appropriate interpretations using probability theo

In this complete introduction to the theory of finding derivatives of scalar-, vector- and matrix-valued functions with respect to complex matrix variables, Hjørungnes describes an essential set of mathematical tools for solving research problems where unknown parameters are contained in complex-valued matrices. The first book examining complex-valued matrix derivatives from an engineering perspective, it uses numerous practical examples from signal processing and communications to demonstrate how these tools can be used to analyze and optimize the performance of engineering systems. Covering un-patterned and certain patterned matrices, this self-contained and easy-to-follow reference deals with applications in a range of areas including wireless communications, control theory, adaptive filtering, resource management and digital signal processing. Over 80 end-of-chapter exercises are provided, with a complete solutions manual available online.

In this 1961 text, Professor Mason examines the complex of ambiguous attitudes which Rilke had towards Europe, in particular his hostility towards England and the English language. He proves that Rilke knew more English than he admitted, had English friends, and valued his English admirers. Professor Mason also shows that the heart of the matter is also at the heart of Rilke's poetry; that he identified England and above all America with forces which were robbing his Europe of its spiritual significance. The central passages of the Duino Elegies are thus seen from a fresh perspective. Professor Mason is writing of a genius who was also tiresome, and there is a pleasant astringent touch in many parts of the book. For readers of Rilke it is essential: written at a time when the European ideal had to be given life in England and substance in Europe, it provides any European with something to consider.

This 2002 book investigates the opportunities in building intelligent decision support systems offered by multi-agent distributed probabilistic reasoning. Probabilistic reasoning with graphical models, also known as Bayesian networks or belief networks, has become increasingly an active field of research and practice in artificial intelligence, operations research and statistics. The success of this technique in modeling intelligent decision support systems under the centralized and single-agent paradigm has been striking. Yang Xiang extends graphical dependence models to the distributed and multi-agent paradigm. He identifies the major technical challenges involved in such an endeavor and presents the results. The framework developed in the book allows distributed representation of uncertain knowledge on a large and complex environment embedded in multiple cooperative agents, and effective, exact and distributed probabilistic inference.

Complex-valued random signals are embedded in the very fabric of science and engineering, yet the usual assumptions made about their statistical behavior are often a poor representation of the underlying physics. This book deals with improper and noncircular complex signals, which do not conform to classical assumptions, and it demonstrates how correct treatment of these signals can have significant payoffs. The book begins with detailed coverage of the fundamental theory and presents a variety of tools and algorithms for dealing with improper and noncircular signals. It provides a comprehensive account of the main applications, covering detection, estimation, and signal analysis of stationary, nonstationary, and cyclostationary processes. Providing a systematic development from the origin of complex signals to their probabilistic description makes the theory accessible to newcomers. This book is ideal for graduate students and researchers working with complex data in a range of resear

The authoritative reference on NEURON, the simulation environment for modeling biological neurons and neural networks that enjoys wide use in the experimental and computational neuroscience communities. This book shows how to use NEURON to construct and apply empirically based models. Written primarily for neuroscience investigators, teachers, and students, it assumes no previous knowledge of computer programming or numerical methods. Readers with a background in the physical sciences or mathematics, who have some knowledge about brain cells and circuits and are interested in computational modeling, will also find it helpful. The NEURON Book covers material that ranges from the inner workings of this program, to practical considerations involved in specifying the anatomical and biophysical properties that are to be represented in models. It uses a problem-solving approach, with many working examples that readers can try for themselves.

J-contractive and J-inner matrix valued functions have a wide range of applications in mathematical analysis, mathematical physics, control engineering and theory of systems and networks. This book provides a comprehensive introduction to the theory of these functions with respect to the open upper half-plane, and a number of applications are also discussed. The first chapters develop the requisite background material from the geometry of finite dimensional spaces with an indefinite inner product, and the theory of the Nevanlinna class of matrix valued functions with bounded characteristic in the open upper half-plane (with attention to special subclasses). Subsequent chapters develop this theory to include associated pairs of inner matrix valued functions and reproducing kernel Hilbert spaces. Special attention is paid to the subclasses of regular and strongly regular J-inner matrix valued functions, which play an essential role in the study of the extension and interpolation problem

Focusing on concepts rather than techniques, this text deals primarily with real-valued functions of a real variable. Complex numbers appear only in supplements and the last two chapters. 1968 edition