Ridge Functions And Applications In Neural Networks

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Ridge Functions and Applications in Neural Networks

Author : Vugar E. Ismailov
Publisher : American Mathematical Society
ISBN 13 : 1470467658
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Ridge Functions and Applications in Neural Networks by : Vugar E. Ismailov

Download or read book Ridge Functions and Applications in Neural Networks written by Vugar E. Ismailov and published by American Mathematical Society. This book was released on 2021-12-17 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ridge Functions

Author : Allan Pinkus
Publisher : Cambridge University Press
ISBN 13 : 1107124395
Total Pages : 218 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Ridge Functions by : Allan Pinkus

Download or read book Ridge Functions written by Allan Pinkus and published by Cambridge University Press. This book was released on 2015-08-07 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.

Ridge Functions

Author : Allan Pinkus
Publisher :
ISBN 13 : 9781316439685
Total Pages : 207 pages
Book Rating : 4.4/5 (396 download)

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Book Synopsis Ridge Functions by : Allan Pinkus

Download or read book Ridge Functions written by Allan Pinkus and published by . This book was released on 2016 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis and Applications of Artificial Neural Networks

Author : Leo P. J. Veelenturf
Publisher :
ISBN 13 :
Total Pages : 284 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Analysis and Applications of Artificial Neural Networks by : Leo P. J. Veelenturf

Download or read book Analysis and Applications of Artificial Neural Networks written by Leo P. J. Veelenturf and published by . This book was released on 1995 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Neural Network Applications in Control

Author : George William Irwin
Publisher : IET
ISBN 13 : 9780852968529
Total Pages : 320 pages
Book Rating : 4.9/5 (685 download)

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Book Synopsis Neural Network Applications in Control by : George William Irwin

Download or read book Neural Network Applications in Control written by George William Irwin and published by IET. This book was released on 1995 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Neural Networks and Computing

Author :
Publisher :
ISBN 13 : 1908979372
Total Pages : pages
Book Rating : 4.9/5 (89 download)

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Book Synopsis Neural Networks and Computing by :

Download or read book Neural Networks and Computing written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Process Neural Networks

Author : Xingui He
Publisher : Springer Science & Business Media
ISBN 13 : 3540737626
Total Pages : 240 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Process Neural Networks by : Xingui He

Download or read book Process Neural Networks written by Xingui He and published by Springer Science & Business Media. This book was released on 2010-07-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Machine Learning for the Physical Sciences

Author : Carlo Requião da Cunha
Publisher : CRC Press
ISBN 13 : 1003821146
Total Pages : 289 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Machine Learning for the Physical Sciences by : Carlo Requião da Cunha

Download or read book Machine Learning for the Physical Sciences written by Carlo Requião da Cunha and published by CRC Press. This book was released on 2023-12-05 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Recent Advances in Harmonic Analysis and Applications

Author : Dmitriy Bilyk
Publisher : Springer Science & Business Media
ISBN 13 : 1461445647
Total Pages : 400 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Recent Advances in Harmonic Analysis and Applications by : Dmitriy Bilyk

Download or read book Recent Advances in Harmonic Analysis and Applications written by Dmitriy Bilyk and published by Springer Science & Business Media. This book was released on 2012-10-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theory of Ridge Regression Estimation with Applications

Author : A. K. Md. Ehsanes Saleh
Publisher : John Wiley & Sons
ISBN 13 : 1118644611
Total Pages : 384 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Theory of Ridge Regression Estimation with Applications by : A. K. Md. Ehsanes Saleh

Download or read book Theory of Ridge Regression Estimation with Applications written by A. K. Md. Ehsanes Saleh and published by John Wiley & Sons. This book was released on 2019-02-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multivariate Approximation and Splines

Author : Günther Nürnberger
Publisher : Birkhäuser
ISBN 13 : 3034888716
Total Pages : 329 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Multivariate Approximation and Splines by : Günther Nürnberger

Download or read book Multivariate Approximation and Splines written by Günther Nürnberger and published by Birkhäuser. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Amenability of Discrete Groups by Examples

Author : Kate Juschenko
Publisher : American Mathematical Society
ISBN 13 : 1470470322
Total Pages : 180 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Amenability of Discrete Groups by Examples by : Kate Juschenko

Download or read book Amenability of Discrete Groups by Examples written by Kate Juschenko and published by American Mathematical Society. This book was released on 2022-06-30 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, amenability has been actively studied and a number of different approaches resulted in many examples of amenable and non-amenable groups. In the book, the author puts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results; those are presented after analyzing the main examples. The techniques that are used for proving amenability in this book are mainly a combination of analytic and probabilistic tools with geometric group theory.

Advances in Computational Mathematics

Author : H P Dikshit
Publisher : World Scientific
ISBN 13 : 9814552062
Total Pages : 332 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Advances in Computational Mathematics by : H P Dikshit

Download or read book Advances in Computational Mathematics written by H P Dikshit and published by World Scientific. This book was released on 1994-05-18 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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:

Automorphic Forms Beyond $mathrm {GL}_2$

$Download Automorphic Forms Beyond $mathrm {GL}_2$ PDF Online Free$

Author : Ellen Elizabeth Eischen
Publisher : American Mathematical Society
ISBN 13 : 1470474921
Total Pages : 199 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Automorphic Forms Beyond $mathrm {GL}_2$ by : Ellen Elizabeth Eischen

Download or read book Automorphic Forms Beyond $mathrm {GL}_2$ written by Ellen Elizabeth Eischen and published by American Mathematical Society. This book was released on 2024-03-26 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Residuated Structures in Algebra and Logic

Author : George Metcalfe
Publisher : American Mathematical Society
ISBN 13 : 1470469855
Total Pages : 282 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Residuated Structures in Algebra and Logic by : George Metcalfe

Download or read book Residuated Structures in Algebra and Logic written by George Metcalfe and published by American Mathematical Society. This book was released on 2023-11-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Iwasawa Theory and Its Perspective, Volume 2

Author : Tadashi Ochiai
Publisher : American Mathematical Society
ISBN 13 : 1470456737
Total Pages : 228 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Iwasawa Theory and Its Perspective, Volume 2 by : Tadashi Ochiai

Download or read book Iwasawa Theory and Its Perspective, Volume 2 written by Tadashi Ochiai and published by American Mathematical Society. This book was released on 2024-04-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Inverse Problems and Zero Forcing for Graphs

Author : Leslie Hogben
Publisher : American Mathematical Society
ISBN 13 : 1470466554
Total Pages : 302 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Inverse Problems and Zero Forcing for Graphs by : Leslie Hogben

Download or read book Inverse Problems and Zero Forcing for Graphs written by Leslie Hogben and published by American Mathematical Society. This book was released on 2022-07-21 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas. The IEP-$G$ asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP-$G$ also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP-$G$ is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP-$G$. The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.