Ridge Functions And Applications In Neural Networks

Author : Vugar E. Ismailov
Publisher : American Mathematical Society
Page : 186 pages
File Size : 55,7 Mb
Release : 2021-12-17
Category : Mathematics
ISBN : 9781470467654

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Ridge Functions and Applications in Neural Networks by Vugar E. Ismailov Pdf

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 : Unknown
Page : 207 pages
File Size : 51,6 Mb
Release : 2016
Category : MATHEMATICS
ISBN : 1316439682

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Ridge Functions by Allan Pinkus Pdf

Ridge functions are a rich class of simple multivariate functions which have found applications in a variety of areas. These include partial differential equations (where they are sometimes termed 'plane waves'), computerised tomography, projection pursuit in the analysis of large multivariate data sets, the MLP model in neural networks, Waring's problem over linear forms, and approximation theory. Ridge Functions is the first book devoted to studying them as entities in and of themselves. The author describes their central properties and provides a solid theoretical foundation for researchers working in areas such as approximation or data science. He also includes an extensive bibliography and discusses some of the unresolved questions that may set the course for future research in the field.

Author : Allan Pinkus
Publisher : Cambridge University Press
Page : 218 pages
File Size : 50,7 Mb
Release : 2015-08-07
Category : Computers
ISBN : 9781107124394

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Ridge Functions by Allan Pinkus Pdf

Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.

Author : Leo P. J. Veelenturf
Publisher : Unknown
Page : 284 pages
File Size : 53,9 Mb
Release : 1995
Category : Computers
ISBN : UOM:39015034225659

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Analysis and Applications of Artificial Neural Networks by Leo P. J. Veelenturf Pdf

This volume is an analysis of the behaviour of the three types of neural networks: the binary perceptron, the continuous perceptron and the self-organizing neural network. Analysis is largely mathematical but concepts are also explained through practical examples.

Author : George William Irwin,K. Warwick,Kenneth J. Hunt
Publisher : IET
Page : 320 pages
File Size : 49,9 Mb
Release : 1995
Category : Computers
ISBN : 0852968523

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Neural Network Applications in Control by George William Irwin,K. Warwick,Kenneth J. Hunt Pdf

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 : Xingui He,Shaohua Xu
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 53,8 Mb
Release : 2010-07-05
Category : Computers
ISBN : 9783540737629

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Process Neural Networks by Xingui He,Shaohua Xu Pdf

For the first time, this book sets forth the concept and model for a process neural network. You’ll discover how a process neural network expands the mapping relationship between the input and output of traditional neural networks and greatly enhances the expression capability of artificial neural networks. Detailed illustrations help you visualize information processing flow and the mapping relationship between inputs and outputs.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,5 Mb
Release : 2024-06-27
Category : Electronic
ISBN : 9781908979377

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Neural Networks and Computing by Anonim Pdf

Author : Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 48,9 Mb
Release : 2012-10-16
Category : Mathematics
ISBN : 9781461445647

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Recent Advances in Harmonic Analysis and Applications by Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick Pdf

Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations. Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.

Author : Carlo Requião da Cunha
Publisher : CRC Press
Page : 289 pages
File Size : 53,6 Mb
Release : 2023-12-05
Category : Computers
ISBN : 9781003821144

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Machine Learning for the Physical Sciences by Carlo Requião da Cunha Pdf

Machine learning is an exciting topic with a myriad of applications. However, most textbooks are targeted towards computer science students. This, however, creates a complication for scientists across the physical sciences that also want to understand the main concepts of machine learning and look ahead to applica- tions and advancements in their fields. This textbook bridges this gap, providing an introduction to the mathematical foundations for the main algorithms used in machine learning for those from the physical sciences, without a formal background in computer science. It demon- strates how machine learning can be used to solve problems in physics and engineering, targeting senior undergraduate and graduate students in physics and electrical engineering, alongside advanced researchers. Key Features: Includes detailed algorithms Supplemented by codes in Julia: a high-performing language and one that is easy to read for those in the natural sciences All algorithms are presented with a good mathematical background

Author : A. K. Md. Ehsanes Saleh,Mohammad Arashi,B. M. Golam Kibria
Publisher : John Wiley & Sons
Page : 384 pages
File Size : 48,5 Mb
Release : 2019-02-12
Category : Mathematics
ISBN : 9781118644614

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Theory of Ridge Regression Estimation with Applications by A. K. Md. Ehsanes Saleh,Mohammad Arashi,B. M. Golam Kibria Pdf

A guide to the systematic analytical results for ridge, LASSO, preliminary test, and Stein-type estimators with applications Theory of Ridge Regression Estimation with Applications offers a comprehensive guide to the theory and methods of estimation. Ridge regression and LASSO are at the center of all penalty estimators in a range of standard models that are used in many applied statistical analyses. Written by noted experts in the field, the book contains a thorough introduction to penalty and shrinkage estimation and explores the role that ridge, LASSO, and logistic regression play in the computer intensive area of neural network and big data analysis. Designed to be accessible, the book presents detailed coverage of the basic terminology related to various models such as the location and simple linear models, normal and rank theory-based ridge, LASSO, preliminary test and Stein-type estimators. The authors also include problem sets to enhance learning. This book is a volume in the Wiley Series in Probability and Statistics series that provides essential and invaluable reading for all statisticians. This important resource: Offers theoretical coverage and computer-intensive applications of the procedures presented Contains solutions and alternate methods for prediction accuracy and selecting model procedures Presents the first book to focus on ridge regression and unifies past research with current methodology Uses R throughout the text and includes a companion website containing convenient data sets Written for graduate students, practitioners, and researchers in various fields of science, Theory of Ridge Regression Estimation with Applications is an authoritative guide to the theory and methodology of statistical estimation.

Author : A Browne
Publisher : CRC Press
Page : 294 pages
File Size : 54,5 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 0750304995

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Neural Network Analysis, Architectures and Applications by A Browne Pdf

Neural Network Analysis, Architectures and Applications discusses the main areas of neural networks, with each authoritative chapter covering the latest information from different perspectives. Divided into three parts, the book first lays the groundwork for understanding and simplifying networks. It then describes novel architectures and algorithms, including pulse-stream techniques, cellular neural networks, and multiversion neural computing. The book concludes by examining various neural network applications, such as neuron-fuzzy control systems and image compression. This final part of the book also provides a case study involving oil spill detection. This book is invaluable for students and practitioners who have a basic understanding of neural computing yet want to broaden and deepen their knowledge of the field.

Author : Günther Nürnberger,Jochen W. Schmidt,Guido Walz
Publisher : Birkhäuser
Page : 329 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034888714

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Multivariate Approximation and Splines by Günther Nürnberger,Jochen W. Schmidt,Guido Walz Pdf

This book contains the refereed papers which were presented at the interna tional conference on "Multivariate Approximation and Splines" held in Mannheim, Germany, on September 7-10,1996. Fifty experts from Bulgaria, England, France, Israel, Netherlands, Norway, Poland, Switzerland, Ukraine, USA and Germany participated in the symposium. It was the aim of the conference to give an overview of recent developments in multivariate approximation with special emphasis on spline methods. The field is characterized by rapidly developing branches such as approximation, data fit ting, interpolation, splines, radial basis functions, neural networks, computer aided design methods, subdivision algorithms and wavelets. The research has applications in areas like industrial production, visualization, pattern recognition, image and signal processing, cognitive systems and modeling in geology, physics, biology and medicine. In the following, we briefly describe the contents of the papers. Exact inequalities of Kolmogorov type which estimate the derivatives of mul the paper of BABENKO, KOFANovand tivariate periodic functions are derived in PICHUGOV. These inequalities are applied to the approximation of classes of mul tivariate periodic functions and to the approximation by quasi-polynomials. BAINOV, DISHLIEV and HRISTOVA investigate initial value problems for non linear impulse differential-difference equations which have many applications in simulating real processes. By applying iterative techniques, sequences of lower and upper solutions are constructed which converge to a solution of the initial value problem.

Author : H P Dikshit,C A Micchelli
Publisher : World Scientific
Page : 332 pages
File Size : 46,6 Mb
Release : 1994-05-18
Category : Electronic
ISBN : 9789814552066

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Advances in Computational Mathematics by H P Dikshit,C A Micchelli Pdf

Contents:Finite Elements for Kirchhoff and Mindlin-Reissner Plates (D Braess)A Multiscale Method for the Double Layer Potential Equation on a Polyhedron (W Dahmen et al)Shape Preserving GC2-Rational Cubic Splines (A Bhatt et al)Affine Operators and Frames of Multivariate Wavelets (C K Chui & X L Shi)Compressed Representations of Curves and Images Using a Multiresolution Box-Spline Framework (H Diamond et al)Wavelet Transformations and Matrix Compression (S L Lee et al)Using the Refinement Equation for the Construction of Pre-Wavelets VII: Strömberg Wavelets (C A Micchelli)An Extension of a Result of Rivilin on Walsh Equiconvergence (R Brück et al)Rational Complex Planar Splines (H P Dikshit et al)Constructive Aspects in Complex Analysis (D Gaier)Applications and Computation of Orthogonal Polynomials (W Gautschi)Approximation of Multivariate Functions (V Ya Lin & A Pinkus)Some Algorithms for Thin Plate Spline Interpolation to Functions of Two Variables (M J D Powell)and other papers Readership: Applied mathematicians. keywords:

Author : Ellen Elizabeth Eischen,Wee Teck Gan,Aaron Pollack,Zhiwei Yun
Publisher : American Mathematical Society
Page : 199 pages
File Size : 41,6 Mb
Release : 2024-03-26
Category : Mathematics
ISBN : 9781470474928

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Automorphic Forms Beyond $mathrm {GL}_2$ by Ellen Elizabeth Eischen,Wee Teck Gan,Aaron Pollack,Zhiwei Yun Pdf

The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.

Author : George Metcalfe,Francesco Paoli,Constantine Tsinakis
Publisher : American Mathematical Society
Page : 282 pages
File Size : 40,7 Mb
Release : 2023-11-06
Category : Mathematics
ISBN : 9781470469856

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Residuated Structures in Algebra and Logic by George Metcalfe,Francesco Paoli,Constantine Tsinakis Pdf

This book is an introduction to residuated structures, viewed as a common thread binding together algebra and logic. The framework includes well-studied structures from classical abstract algebra such as lattice-ordered groups and ideals of rings, as well as structures serving as algebraic semantics for substructural and other non-classical logics. Crucially, classes of these structures are studied both algebraically, yielding a rich structure theory along the lines of Conrad's program for lattice-ordered groups, and algorithmically, via analytic sequent or hypersequent calculi. These perspectives are related using a natural notion of equivalence for consequence relations that provides a bridge offering benefits to both sides. Algorithmic methods are used to establish properties like decidability, amalgamation, and generation by subclasses, while new insights into logical systems are obtained by studying associated classes of structures. The book is designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field.