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On Representation Of Function By Means Of Superpositions And Related Topics
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Book Synopsis On Representation of Functions by Means of Superpositions and Related Topics by : Anatoliĭ Georgievich Vitushkin
Download or read book On Representation of Functions by Means of Superpositions and Related Topics written by Anatoliĭ Georgievich Vitushkin and published by . This book was released on 1978 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical En cyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977 - 1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivision has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathe matics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, engineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Efficiency and Scalability Methods for Computational Intellect by : Igelnik, Boris
Download or read book Efficiency and Scalability Methods for Computational Intellect written by Igelnik, Boris and published by IGI Global. This book was released on 2013-04-30 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational modeling and simulation has developed and expanded into a diverse range of fields such as digital signal processing, image processing, robotics, systems biology, and many more; enhancing the need for a diversifying problem solving applications in this area. Efficiency and Scalability Methods for Computational Intellect presents various theories and methods for approaching the problem of modeling and simulating intellect in order to target computation efficiency and scalability of proposed methods. Researchers, instructors, and graduate students will benefit from this current research and will in turn be able to apply the knowledge in an effective manner to gain an understanding of how to improve this field.
Book Synopsis Elements of Artificial Neural Networks by : Kishan Mehrotra
Download or read book Elements of Artificial Neural Networks written by Kishan Mehrotra and published by MIT Press. This book was released on 1997 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Artificial Neural Networks provides a clearly organized general introduction, focusing on a broad range of algorithms, for students and others who want to use neural networks rather than simply study them. The authors, who have been developing and team teaching the material in a one-semester course over the past six years, describe most of the basic neural network models (with several detailed solved examples) and discuss the rationale and advantages of the models, as well as their limitations. The approach is practical and open-minded and requires very little mathematical or technical background. Written from a computer science and statistics point of view, the text stresses links to contiguous fields and can easily serve as a first course for students in economics and management. The opening chapter sets the stage, presenting the basic concepts in a clear and objective way and tackling important -- yet rarely addressed -- questions related to the use of neural networks in practical situations. Subsequent chapters on supervised learning (single layer and multilayer networks), unsupervised learning, and associative models are structured around classes of problems to which networks can be applied. Applications are discussed along with the algorithms. A separate chapter takes up optimization methods. The most frequently used algorithms, such as backpropagation, are introduced early on, right after perceptrons, so that these can form the basis for initiating course projects. Algorithms published as late as 1995 are also included. All of the algorithms are presented using block-structured pseudo-code, and exercises are provided throughout. Software implementing many commonly used neural network algorithms is available at the book's website. Transparency masters, including abbreviated text and figures for the entire book, are available for instructors using the text.
Book Synopsis Tame Geometry with Application in Smooth Analysis by : Yosef Yomdin
Download or read book Tame Geometry with Application in Smooth Analysis written by Yosef Yomdin and published by Springer. This book was released on 2004-02-07 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation.
Download or read book Bulletin Mathématique written by and published by . This book was released on 1979 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Vladimir I. Arnold - Collected Works by : Vladimir I. Arnold
Download or read book Vladimir I. Arnold - Collected Works written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2009-10-22 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Arnold is one of the greatest mathematical scientists of our time, as well as one of the finest, most prolific mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics and KAM theory.
Book Synopsis St. Petersburg Mathematical Journal by :
Download or read book St. Petersburg Mathematical Journal written by and published by . This book was released on 1996 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Soviet Mathematics by : Soviet Union. Ministerstvo vysshego i srednego spet︠s︡ialʹnogo obrazovanii︠a︡
Download or read book Soviet Mathematics written by Soviet Union. Ministerstvo vysshego i srednego spet︠s︡ialʹnogo obrazovanii︠a︡ and published by . This book was released on 1985 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cumulative Book Index written by and published by . This book was released on 1979 with total page 3010 pages. Available in PDF, EPUB and Kindle. Book excerpt: A world list of books in the English language.
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.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 906 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Russian Mathematical Surveys written by and published by . This book was released on 2002 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Real Analysis by : Andrew M. Bruckner
Download or read book Real Analysis written by Andrew M. Bruckner and published by ClassicalRealAnalysis.com. This book was released on 1997 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introductory chapter containing background material as well as a mini-overview of much of the course, making the book accessible to readers with varied backgrounds. It uses a wealth of examples to introduce topics and to illustrate important concepts.KEY TOPICS:Explains the ideas behind developments and proofs -- showing that proofs come not from "magical methods" but from natural processes. Introduces concepts in stages, and features applications of abstract theorems to concrete settings -- showing the power of an abstract approach in problem solving.
Download or read book Brain Theory written by Adrianus Aertsen and published by . This book was released on 1993-05-28 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emerging from the Fourth International Meeting on Brain Theory, Held in Trento, Italy, April 1992, this collection of papers brings together new insights and concepts from various branches of experimental and theoretical neuroscience, partly in the form of review chapters, partly in short, focused contributions, or critical essays. The volume is divided into four sections: space-time aspects of brain function--sensory perception; space-time aspects of brain function--control of action; space-time dynamics of neuronal activity in the working brain; and the brain--the organization of perception and action. No index. Annotation copyright by Book News, Inc., Portland, OR
Book Synopsis Conditional Inference and Logic for Intelligent Systems by : Irwin R. Goodman
Download or read book Conditional Inference and Logic for Intelligent Systems written by Irwin R. Goodman and published by North Holland. This book was released on 1991 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is concerned with addressing an anomoly involving probability and logic. This includes the interpretation and evaluation of implicative statements in natural language, compatible with conditional probability. One of the chief motivations for investigating this problem has been the need to formalize rigorously the appropriate connections between conditional probabilities and the underlying production rules in expert sytems. This is accomplished through the development of a comprehensive theory of conditional events and an associated logic. The results of this effort should be of prime use in the design and evaluation of inference rules in expert systems, and also, allow for a new expansion of probability to include at the syntactic level the concept of conditioning. The monograph is intended for two audiences: AI researchers who are primarily interested in the management of uncertainty in expert systems, and mathematicians in the fields of probabilistic modeling, logic, and algebra.
Book Synopsis Exploring Brain Functions by : T. A. Poggio
Download or read book Exploring Brain Functions written by T. A. Poggio and published by . This book was released on 1993-04-27 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring Brain Functions Models in Neuroscience Edited by T. A. Poggio and D. A. Glaser This volume consists of the background papers and reports of discussion from the Dahlem Workshop. It focuses on the identification of appropriate models for brain functions and ways of evaluating them. A unique combination of key researchers involved in theoretical and experimental neurobiology addressed these issues from the following perspectives: Molecular and biophysical mechanisms of information processing; Forms and mechanisms of learning; Models of visual perception: case studies in brain functions; and Architectures of intelligent systems. This book provides a timely assessment of the state of theories involving the brain and their role in neuroscience today and tomorrow, from the point of view of theoreticians and experimentalists alike.
