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Author: Vugar E. Ismailov
Publisher: American Mathematical Society
ISBN: 1470467658
Category : Mathematics
Languages : en
Pages : 186
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Book Description
Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed. This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.
Author: Vugar E. Ismailov
Publisher: American Mathematical Society
ISBN: 1470467658
Category : Mathematics
Languages : en
Pages : 186
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Book Description
Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed. This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.
Author: Allan Pinkus
Publisher: Cambridge University Press
ISBN: 1107124395
Category : Computers
Languages : en
Pages : 218
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Book Description
Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.
Author: Charles K. Chui
Publisher: SIAM
ISBN: 0898712262
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Subject of multivariate splines presented from an elementary point of view; includes many open problems.
Author: George William Irwin
Publisher: IET
ISBN: 9780852968529
Category : Computers
Languages : en
Pages : 320
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Book Description
The aim is to present an introduction to, and an overview of, the present state of neural network research and development, with an emphasis on control systems application studies. The book is useful to a range of levels of reader. The earlier chapters introduce the more popular networks and the fundamental control principles, these are followed by a series of application studies, most of which are industrially based, and the book concludes with a consideration of some recent research.
Author: N. Sundararajan
Publisher: World Scientific
ISBN: 9789810237714
Category : Science
Languages : en
Pages : 236
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Book Description
A review of radial basis founction (RBF) neural networks. A novel sequential learning algorithm for minimal resource allocation neural networks (MRAN). MRAN for function approximation & pattern classification problems; MRAN for nonlinear dynamic systems; MRAN for communication channel equalization; Concluding remarks; A outline source code for MRAN in MATLAB; Bibliography; Index.
Author: Tommy Wai-shing Chow
Publisher: World Scientific
ISBN: 1908979372
Category : Computers
Languages : en
Pages : 322
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Book Description
This book covers neural networks with special emphasis on advanced learning methodologies and applications. It includes practical issues of weight initializations, stalling of learning, and escape from a local minima, which have not been covered by many existing books in this area. Additionally, the book highlights the important feature selection problem, which baffles many neural networks practitioners because of the difficulties handling large datasets. It also contains several interesting IT, engineering and bioinformatics applications./a
Author: Tadashi Ochiai
Publisher: American Mathematical Society
ISBN: 1470456737
Category : Mathematics
Languages : en
Pages : 228
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Book Description
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.
Author: Leszek Rutkowski
Publisher: Springer Science & Business Media
ISBN: 3790819026
Category : Computers
Languages : en
Pages : 935
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Book Description
This volume presents new trends and developments in soft computing techniques. Topics include: neural networks, fuzzy systems, evolutionary computation, knowledge discovery, rough sets, and hybrid methods. It also covers various applications of soft computing techniques in economics, mechanics, medicine, automatics and image processing. The book contains contributions from internationally recognized scientists, such as Zadeh, Bubnicki, Pawlak, Amari, Batyrshin, Hirota, Koczy, Kosinski, Novák, S.-Y. Lee, Pedrycz, Raudys, Setiono, Sincak, Strumillo, Takagi, Usui, Wilamowski and Zurada. An excellent overview of soft computing methods and their applications.
Author: Tadashi Ochiai
Publisher: American Mathematical Society
ISBN: 1470456729
Category : Mathematics
Languages : en
Pages : 167
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Book Description
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation of this book is an update of the classical theory for class groups taking into account the changed point of view on Iwasawa theory. The goal of this first part of the two-part publication is to explain the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt–Kubota $L$-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects. The second part of the book will be published as a separate volume in the same series, Mathematical Surveys and Monographs of the American Mathematical Society.
Author: Simon Foucart
Publisher: Springer Nature
ISBN: 3031664973
Category :
Languages : en
Pages : 294
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Book Description
