Quantitative Approximations
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Intelligent Systems Approximation By Artificial Neural Networks
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Author : George A. Anastassiou
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-02
Intelligent Systems Approximation By Artificial Neural Networks written by George A. Anastassiou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-02 with Computers categories.
This brief monograph is the first one to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Here we study with rates the approximation properties of the "right" sigmoidal and hyperbolic tangent artificial neural network positive linear operators. In particular we study the degree of approximation of these operators to the unit operator in the univariate and multivariate cases over bounded or unbounded domains. This is given via inequalities and with the use of modulus of continuity of the involved function or its higher order derivative. We examine the real and complex cases. For the convenience of the reader, the chapters of this book are written in a self-contained style. This treatise relies on author's last two years of related research work. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The exposed results are expected to find applications in many areas of computer science and applied mathematics, such as neural networks, intelligent systems, complexity theory, learning theory, vision and approximation theory, etc. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science libraries.
Quantitative Approximations
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Author : George Anastassiou
language : en
Publisher: CRC Press
Release Date : 2000-09-15
Quantitative Approximations written by George Anastassiou and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-15 with Mathematics categories.
Quantitative approximation methods apply in many diverse fields of research-neural networks, wavelets, partial differential equations, probability and statistics, functional analysis, and classical analysis to name just a few. For the first time in book form, Quantitative Approximations provides a thorough account of all of the significant developm
Trigonometric And Hyperbolic Generated Approximation Theory
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Author : George A Anastassiou
language : en
Publisher: World Scientific
Release Date : 2024-11-28
Trigonometric And Hyperbolic Generated Approximation Theory written by George A Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-28 with Mathematics categories.
This monograph is a testimony of the impact over Computational Analysis of some new trigonometric and hyperbolic types of Taylor's formulae with integral remainders producing a rich collection of approximations of a very wide spectrum.This volume covers perturbed neural network approximations by themselves and with their connections to Brownian motion and stochastic processes, univariate and multivariate analytical inequalities (both ordinary and fractional), Korovkin theory, and approximations by singular integrals (both univariate and multivariate cases). These results are expected to find applications in the many areas of Pure and Applied Mathematics, Computer Science, Engineering, Artificial Intelligence, Machine Learning, Deep Learning, Analytical Inequalities, Approximation Theory, Statistics, Economics, amongst others. Thus, this treatise is suitable for researchers, graduate students, practitioners and seminars of related disciplines, and serves well as an invaluable resource for all Science and Engineering libraries.
Quaternionic Approximation
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Author : Sorin G. Gal
language : en
Publisher: Springer
Release Date : 2019-04-12
Quaternionic Approximation written by Sorin G. Gal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-12 with Mathematics categories.
This book presents the extensions to the quaternionic setting of some of the main approximation results in complex analysis. It also includes the main inequalities regarding the behavior of the derivatives of polynomials with quaternionic cofficients. With some few exceptions, all the material in this book belongs to recent research of the authors on the approximation of slice regular functions of a quaternionic variable. The book is addressed to researchers in various areas of mathematical analysis, in particular hypercomplex analysis, and approximation theory. It is accessible to graduate students and suitable for graduate courses in the above framework.
Rough Sets
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Author : Rafael Bello
language : en
Publisher: Springer Nature
Release Date : 2020-07-07
Rough Sets written by Rafael Bello and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-07 with Computers categories.
The volume LNAI 12179 constitutes the proceedings of the International Joint Conference on Rough Sets, IJCRS 2020, which was due to be held in Havana, Cuba, in June 2020. The conference was held virtually due to the COVID-19 pandemic. The 37 full papers accepted were carefully reviewed and selected from 50 submissions. The papers are grouped in the following topical sections: general rough sets; three-way decision theory; attribute reduction; granular computing; formal concept analysis; data summarization; community detection; fuzzy cognitive maps; tutorials.
The Demography Of Roman Italy
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Author : Saskia Hin
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-14
The Demography Of Roman Italy written by Saskia Hin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-14 with History categories.
This book investigates demographic behaviour and population trends in Italy during the emergence of the Roman Empire. It unites literary and epigraphic sources with demographic theory, archaeological surveys, climatic and skeletal evidence, models and comparative data. Also featured is a chapter on climate change in Roman times.
Intelligent Systems Ii Complete Approximation By Neural Network Operators
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Author : George A. Anastassiou
language : en
Publisher: Springer
Release Date : 2015-06-23
Intelligent Systems Ii Complete Approximation By Neural Network Operators written by George A. Anastassiou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-23 with Technology & Engineering categories.
This monograph is the continuation and completion of the monograph, “Intelligent Systems: Approximation by Artificial Neural Networks” written by the same author and published 2011 by Springer. The book you hold in hand presents the complete recent and original work of the author in approximation by neural networks. Chapters are written in a self-contained style and can be read independently. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The book’s results are expected to find applications in many areas of applied mathematics, computer science and engineering. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science and engineering libraries.
Generalized Fractional Calculus
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2020-11-25
Generalized Fractional Calculus written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Technology & Engineering categories.
This book applies generalized fractional differentiation techniques of Caputo, Canavati and Conformable types to a great variety of integral inequalities e.g. of Ostrowski and Opial types, etc. Some of these are extended to Banach space valued functions. These inequalities have also great impact in numerical analysis, stochastics and fractional differential equations. The book continues with generalized fractional approximations by positive sublinear operators which derive from the presented Korovkin type inequalities and also includes abstract cases. It presents also multivariate complex Korovkin quantitative approximation theory. It follows M-fractional integral inequalities of Ostrowski and Polya types. The results are weighted so they provide a great variety of cases and applications. The second part of the book deals with the quantitative fractional Korovkin type approximation of stochastic processes and lays there the foundations of stochastic fractional calculus. The book considers both Caputo and Conformable fractional directions and derives regular and trigonometric results. The positive linear operators can be expectation operator commutative or not. This book results are expected to find applications in many areas of pure and applied mathematics and stochastics. As such this monograph is suitable for researchers, graduate students, and seminars of the above disciplines, also to be in all science and engineering libraries.
Fuzziness Democracy Control And Collective Decision Choice System A Theory On Political Economy Of Rent Seeking And Profit Harvesting
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Author : Kofi Kissi Dompere
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-03-15
Fuzziness Democracy Control And Collective Decision Choice System A Theory On Political Economy Of Rent Seeking And Profit Harvesting written by Kofi Kissi Dompere and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-15 with Technology & Engineering categories.
This volume presents an analysis of the problems and solutions of the market mockery of the democratic collective decision-choice system with imperfect information structure composed of defective and deceptive structures using methods of fuzzy rationality. The book is devoted to the political economy of rent-seeking, rent-protection and rent-harvesting to enhance profits under democratic collective decision-choice systems. The toolbox used in the monograph consists of methods of fuzzy decision, approximate reasoning, negotiation games and fuzzy mathematics. The monograph further discusses the rent-seeking phenomenon in the Schumpeterian and Marxian political economies where the rent-seeking activities transform the qualitative character of the general capitalism into oligarchic socialism and making the democratic collective decision-choice system as an ideology rather than social calculus for resolving conflicts in preferences in the collective decision-choice space without violence.
Parametrized Deformed And General Neural Networks
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Author : George A. Anastassiou
language : en
Publisher: Springer Nature
Release Date : 2023-09-29
Parametrized Deformed And General Neural Networks written by George A. Anastassiou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-29 with Technology & Engineering categories.
In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.