A Unified Signal Algebra Approach To Two Dimensional Parallel Digital Signal Processing
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A Unified Signal Algebra Approach To Two Dimensional Parallel Digital Signal Processing
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Author : Louis A. D'Alotto
language : en
Publisher: CRC Press
Release Date : 1998-01-09
A Unified Signal Algebra Approach To Two Dimensional Parallel Digital Signal Processing written by Louis A. D'Alotto and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-09 with Technology & Engineering categories.
Aims to bridge the gap between parallel computer architectures and the creation of parallel digital signal processing (DSP) algorithms. This work offers an approach to digital signal processing utilizing the unified signal algebra environment to develop naturally occurring parallel DSP algorithms.;College or university book shops may order five or more copies at a special student price. Price is available on request.
Many Sorted Algebras For Deep Learning And Quantum Technology
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Author : Charles R. Giardina
language : en
Publisher: Elsevier
Release Date : 2024-02-03
Many Sorted Algebras For Deep Learning And Quantum Technology written by Charles R. Giardina and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-03 with Science categories.
Many-Sorted Algebras for Deep Learning and Quantum Technology presents a precise and rigorous description of basic concepts in Quantum technologies and how they relate to Deep Learning and Quantum Theory. Current merging of Quantum Theory and Deep Learning techniques provides a need for a text that can give readers insight into the algebraic underpinnings of these disciplines. Although analytical, topological, probabilistic, as well as geometrical concepts are employed in many of these areas, algebra exhibits the principal thread. This thread is exposed using Many-Sorted Algebras (MSA). In almost every aspect of Quantum Theory as well as Deep Learning more than one sort or type of object is involved. For instance, in Quantum areas Hilbert spaces require two sorts, while in affine spaces, three sorts are needed. Both a global level and a local level of precise specification is described using MSA. At a local level operation involving neural nets may appear to be very algebraically different than those used in Quantum systems, but at a global level they may be identical. Again, MSA is well equipped to easily detail their equivalence through text as well as visual diagrams. Among the reasons for using MSA is in illustrating this sameness. Author Charles R. Giardina includes hundreds of well-designed examples in the text to illustrate the intriguing concepts in Quantum systems. Along with these examples are numerous visual displays. In particular, the Polyadic Graph shows the types or sorts of objects used in Quantum or Deep Learning. It also illustrates all the inter and intra sort operations needed in describing algebras. In brief, it provides the closure conditions. Throughout the text, all laws or equational identities needed in specifying an algebraic structure are precisely described. - Includes hundreds of well-designed examples to illustrate the intriguing concepts in quantum systems - Provides precise description of all laws or equational identities that are needed in specifying an algebraic structure - Illustrates all the inter and intra sort operations needed in describing algebras
Probability For Deep Learning Quantum
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Author : Charles R. Giardina
language : en
Publisher: Elsevier
Release Date : 2025-01-21
Probability For Deep Learning Quantum written by Charles R. Giardina and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-21 with Computers categories.
Probability for Deep Learning Quantum provides readers with the first book to address probabilistic methods in the deep learning environment and the quantum technological area simultaneously, by using a common platform: the Many-Sorted Algebra (MSA) view. While machine learning is created with a foundation of probability, probability is at the heart of quantum physics as well. It is the cornerstone in quantum applications. These applications include quantum measuring, quantum information theory, quantum communication theory, quantum sensing, quantum signal processing, quantum computing, quantum cryptography, and quantum machine learning. Although some of the probabilistic methods differ in machine learning disciplines from those in the quantum technologies, many techniques are very similar. Probability is introduced in the text rigorously, in Komogorov's vision. It is however, slightly modified by developing the theory in a Many-Sorted Algebra setting. This algebraic construct is also used in showing the shared structures underlying much of both machine learning and quantum theory. Both deep learning and quantum technologies have several probabilistic and stochastic methods in common. These methods are described and illustrated using numerous examples within the text. Concepts in entropy are provided from a Shannon as well as a von-Neumann view. Singular value decomposition is applied in machine learning as a basic tool and presented in the Schmidt decomposition. Besides the in-common methods, Born's rule as well as positive operator valued measures are described and illustrated, along with quasi-probabilities. Author Charles R. Giardina provides clear and concise explanations, accompanied by insightful and thought-provoking visualizations, to deepen your understanding and enable you to apply the concepts to real-world scenarios. - Provides readers with a resource that is loaded with hundreds of well-crafted examples illustrating the difficult concepts pertaining to quantum and stochastic processes - Addresses probabilistic methods in the deep learning environment and in the quantum technological area - Includes a rigorous and precise presentation of the algebraic underpinning of both quantum and deep learning
C Algebras And Numerical Analysis
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Author : Ronald Hagen
language : en
Publisher: CRC Press
Release Date : 2000-09-07
C Algebras And Numerical Analysis written by Ronald Hagen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-07 with Mathematics categories.
"Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. Covers fractality and Fredholmness. Explains the phenomena of the asymptotic splitting of the singular values, and more."
Hopf Algebra
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Author : Sorin Dascalescu
language : en
Publisher: CRC Press
Release Date : 2000-09-15
Hopf Algebra written by Sorin Dascalescu 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.
This study covers comodules, rational modules and bicomodules; cosemisimple, semiperfect and co-Frobenius algebras; bialgebras and Hopf algebras; actions and coactions of Hopf algebras on algebras; finite dimensional Hopf algebras, with the Nicholas-Zoeller and Taft-Wilson theorems and character theory; and more.
Abstract Algebra
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Author : Claudia Menini
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Abstract Algebra written by Claudia Menini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups.
Monomial Algebras
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Author : Rafael Villarreal
language : en
Publisher: CRC Press
Release Date : 2000-12-05
Monomial Algebras written by Rafael Villarreal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-05 with Mathematics categories.
An introduction to the methods used to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings, and toric varieties. It emphasizes square-free quadratics and effective computational methods, and applies a combinatorial description of the integral closure of the corresponding monomial subring to graph theory.
Hopf Algebras In Noncommutative Geometry And Physics
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Author : Stefaan Caenepeel
language : en
Publisher: CRC Press
Release Date : 2019-05-07
Hopf Algebras In Noncommutative Geometry And Physics written by Stefaan Caenepeel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the
A Primer Of Algebraic Geometry
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Author : Huishi Li
language : en
Publisher: CRC Press
Release Date : 2017-12-19
A Primer Of Algebraic Geometry written by Huishi Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
"Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."
Algebraic Geometry For Associative Algebras
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Author : Freddy Van Oystaeyen
language : en
Publisher: CRC Press
Release Date : 2000-06-06
Algebraic Geometry For Associative Algebras written by Freddy Van Oystaeyen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-06 with Mathematics categories.
This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theor