Algebraic Approach to Data Processing PDF Download
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Author: Julio C. Urenda
Publisher: Springer Nature
ISBN: 3031167805
Category : Computers
Languages : en
Pages : 246
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Book Description
The book explores a new general approach to selecting—and designing—data processing techniques. Symmetry and invariance ideas behind this algebraic approach have been successful in physics, where many new theories are formulated in symmetry terms. The book explains this approach and expands it to new application areas ranging from engineering, medicine, education to social sciences. In many cases, this approach leads to optimal techniques and optimal solutions. That the same data processing techniques help us better analyze wooden structures, lung dysfunctions, and deep learning algorithms is a good indication that these techniques can be used in many other applications as well. The book is recommended to researchers and practitioners who need to select a data processing technique—or who want to design a new technique when the existing techniques do not work. It is also recommended to students who want to learn the state-of-the-art data processing.
Author: Julio C. Urenda
Publisher: Springer Nature
ISBN: 3031167805
Category : Computers
Languages : en
Pages : 246
Get Book Here
Book Description
The book explores a new general approach to selecting—and designing—data processing techniques. Symmetry and invariance ideas behind this algebraic approach have been successful in physics, where many new theories are formulated in symmetry terms. The book explains this approach and expands it to new application areas ranging from engineering, medicine, education to social sciences. In many cases, this approach leads to optimal techniques and optimal solutions. That the same data processing techniques help us better analyze wooden structures, lung dysfunctions, and deep learning algorithms is a good indication that these techniques can be used in many other applications as well. The book is recommended to researchers and practitioners who need to select a data processing technique—or who want to design a new technique when the existing techniques do not work. It is also recommended to students who want to learn the state-of-the-art data processing.
Author: Ernest G. Manes
Publisher: Springer Science & Business Media
ISBN: 1461249627
Category : Computers
Languages : en
Pages : 358
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Book Description
In the 1930s, mathematical logicians studied the notion of "effective comput ability" using such notions as recursive functions, A-calculus, and Turing machines. The 1940s saw the construction of the first electronic computers, and the next 20 years saw the evolution of higher-level programming languages in which programs could be written in a convenient fashion independent (thanks to compilers and interpreters) of the architecture of any specific machine. The development of such languages led in turn to the general analysis of questions of syntax, structuring strings of symbols which could count as legal programs, and semantics, determining the "meaning" of a program, for example, as the function it computes in transforming input data to output results. An important approach to semantics, pioneered by Floyd, Hoare, and Wirth, is called assertion semantics: given a specification of which assertions (preconditions) on input data should guarantee that the results satisfy desired assertions (postconditions) on output data, one seeks a logical proof that the program satisfies its specification. An alternative approach, pioneered by Scott and Strachey, is called denotational semantics: it offers algebraic techniques for characterizing the denotation of (i. e. , the function computed by) a program-the properties of the program can then be checked by direct comparison of the denotation with the specification. This book is an introduction to denotational semantics. More specifically, we introduce the reader to two approaches to denotational semantics: the order semantics of Scott and Strachey and our own partially additive semantics.
Author: Francis Borceux
Publisher: Springer Science & Business Media
ISBN: 3319017330
Category : Mathematics
Languages : en
Pages : 440
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Book Description
This is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natural link between linear geometry at an undergraduate level and algebraic geometry at a graduate level, and it is also an important topic in geometric applications, such as cryptography. 380 years ago, the work of Fermat and Descartes led us to study geometric problems using coordinates and equations. Today, this is the most popular way of handling geometrical problems. Linear algebra provides an efficient tool for studying all the first degree (lines, planes) and second degree (ellipses, hyperboloids) geometric figures, in the affine, the Euclidean, the Hermitian and the projective contexts. But recent applications of mathematics, like cryptography, need these notions not only in real or complex cases, but also in more general settings, like in spaces constructed on finite fields. And of course, why not also turn our attention to geometric figures of higher degrees? Besides all the linear aspects of geometry in their most general setting, this book also describes useful algebraic tools for studying curves of arbitrary degree and investigates results as advanced as the Bezout theorem, the Cramer paradox, topological group of a cubic, rational curves etc. Hence the book is of interest for all those who have to teach or study linear geometry: affine, Euclidean, Hermitian, projective; it is also of great interest to those who do not want to restrict themselves to the undergraduate level of geometric figures of degree one or two.
Author: Hartmut Ehrig
Publisher: Springer Science & Business Media
ISBN: 3540311882
Category : Computers
Languages : en
Pages : 383
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Book Description
This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. It contains an introduction to classical graphs. Basic and advanced results are first shown for an abstract form of replacement systems and are then instantiated to several forms of graph and Petri net transformation systems. The book develops typed attributed graph transformation and contains a practical case study.
Author: Miklós Rédei
Publisher: Springer Science & Business Media
ISBN: 9401590265
Category : Science
Languages : en
Pages : 244
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Book Description
This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J.
Author: Darrell Williamson
Publisher: Springer Science & Business Media
ISBN: 1447105419
Category : Technology & Engineering
Languages : en
Pages : 432
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Book Description
This comprehensive and up-to-date book focuses on an algebraic approach to the analysis and design of discrete-time signal processors, including material applicable to numeric and symbolic computation programs such as MATLAB. Written with clarity, it contains the latest detailed research results.
Author: L. Beran
Publisher: Springer Science & Business Media
ISBN: 9400952155
Category : Computers
Languages : en
Pages : 412
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Book Description
Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. Bowever, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programmi ng profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-s.cale order", which are almost impossible to fit into the existing classifica tion schemes. They draw upon widely different sections of mathe matics.
Author: Philippa Pattison
Publisher: Cambridge University Press
ISBN: 0521365686
Category : Psychology
Languages : en
Pages : 334
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Book Description
The book should be of interest to all researchers interested in using social network methods.
Author: Alessandro Aldini
Publisher: Springer Science & Business Media
ISBN: 1848002238
Category : Computers
Languages : en
Pages : 316
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Book Description
Inthe?eldofformalmethodsincomputerscience,concurrencytheoryisreceivinga constantlyincreasinginterest.Thisisespeciallytrueforprocessalgebra.Althoughit had been originally conceived as a means for reasoning about the semantics of c- current programs, process algebraic formalisms like CCS, CSP, ACP, ?-calculus, and their extensions (see, e.g., [154,119,112,22,155,181,30]) were soon used also for comprehendingfunctionaland nonfunctionalaspects of the behaviorof com- nicating concurrent systems. The scienti?c impact of process calculi and behavioral equivalences at the base of process algebra is witnessed not only by a very rich literature. It is in fact worth mentioningthe standardizationprocedurethat led to the developmentof the process algebraic language LOTOS [49], as well as the implementation of several modeling and analysis tools based on process algebra, like CWB [70] and CADP [93], some of which have been used in industrial case studies. Furthermore, process calculi and behavioral equivalencesare by now adopted in university-levelcourses to teach the foundations of concurrent programming as well as the model-driven design of concurrent, distributed, and mobile systems. Nevertheless, after 30 years since its introduction, process algebra is rarely adopted in the practice of software development. On the one hand, its technica- ties often obfuscate the way in which systems are modeled. As an example, if a process term comprises numerous occurrences of the parallel composition operator, it is hard to understand the communicationscheme among the varioussubterms. On the other hand, process algebra is perceived as being dif?cult to learn and use by practitioners, as it is not close enough to the way they think of software systems.
Author: Kulik, Boris
Publisher: IGI Global
ISBN: 1522527834
Category : Mathematics
Languages : en
Pages : 317
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Book Description
Mathematics has been used as a tool in logistical reasoning for centuries. Examining how specific mathematic structures can aid in data and knowledge management helps determine how to efficiently and effectively process more information in these fields. N-ary Relations for Logical Analysis of Data and Knowledge is a critical scholarly reference source that provides a detailed study of the mathematical techniques currently involved in the progression of information technology fields. Featuring relevant topics that include algebraic sets, deductive analysis, defeasible reasoning, and probabilistic modeling, this publication is ideal for academicians, students, and researchers who are interested in staying apprised of the latest research in the information technology field.
