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Author: Shun-ichi Amari
Publisher: Springer
ISBN: 4431559787
Category : Mathematics
Languages : en
Pages : 378
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Book Description
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
Author: Shun-ichi Amari
Publisher: Springer
ISBN: 4431559787
Category : Mathematics
Languages : en
Pages : 378
Get Book Here
Book Description
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
Author: Ming Li
Publisher: Springer Science & Business Media
ISBN: 1475726066
Category : Mathematics
Languages : en
Pages : 655
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Book Description
Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).
Author: James J. (Jong Hyuk) Park
Publisher: Springer
ISBN: 3662454025
Category : Technology & Engineering
Languages : en
Pages : 1395
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Book Description
The 6th FTRA International Conference on Computer Science and its Applications (CSA-14) will be held in Guam, USA, Dec. 17 - 19, 2014. CSA-14 presents a comprehensive conference focused on the various aspects of advances in engineering systems in computer science, and applications, including ubiquitous computing, U-Health care system, Big Data, UI/UX for human-centric computing, Computing Service, Bioinformatics and Bio-Inspired Computing and will show recent advances on various aspects of computing technology, Ubiquitous Computing Services and its application.
Author: Francesco Parrino
Publisher: Elsevier
ISBN: 0128204346
Category : Technology & Engineering
Languages : en
Pages : 735
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Book Description
Scientific interest in TiO2-based materials has exponentially grown in the last few decades. Titanium Dioxide (TiO2) and Its Applications introduces the main physicochemical properties of TiO2 which are the basis of its applications in various fields. While the basic principles of the TiO2 properties have been the subject of various previous publications, this book is mainly devoted to TiO2 applications. The book includes contributions written by experts from a wide range of disciplines in order to address titanium dioxide's utilization in energy, consumer, materials, devices, and catalytic applications. The various applications identified include: photocatalysis, catalysis, optics, electronics, energy storage and production, ceramics, pigments, cosmetics, sensors, and heat transfer. Titanium Dioxide (TiO2) and Its Applications is suitable for a wide readership in the disciplines of materials science, chemistry, and engineering in both academia and industry. - Includes a wide range of current and emerging applications of titanium dioxide in the fields of energy, consumer applications, materials, and devices - Provides a brief overview of titanium dioxide and its properties, as well as techniques to design, deposit, and study the material - Discusses the relevant properties, preparation methods, and other apposite considerations in each application-focused chapter
Author: R. McWeeny
Publisher: Elsevier
ISBN: 1483226247
Category : Mathematics
Languages : en
Pages : 263
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Book Description
Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.
Author: Ngoc Thanh Nguyen
Publisher: Springer Nature
ISBN: 3031741277
Category :
Languages : en
Pages : 559
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Book Description
Author: David C. Lay
Publisher:
ISBN: 9781292020556
Category : Algebras, Linear
Languages : en
Pages : 800
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Book Description
NOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value--this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products. xxxxxxxxxxxxxxx For courses in linear algebra.This package includes MyMathLab(R). With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students' understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete "Rn" setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand. Personalize learning with MyMathLabMyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. MyMathLab includes assignable algorithmic exercises, the complete eBook, interactive figures, tools to personalize learning, and more.
Author: J. Eldon Whitesitt
Publisher: Courier Corporation
ISBN: 0486158160
Category : Mathematics
Languages : en
Pages : 194
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Book Description
Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.
Author: Han-Fu Chen
Publisher: Springer Science & Business Media
ISBN: 0306481669
Category : Mathematics
Languages : en
Pages : 369
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Book Description
Estimating unknown parameters based on observation data conta- ing information about the parameters is ubiquitous in diverse areas of both theory and application. For example, in system identification the unknown system coefficients are estimated on the basis of input-output data of the control system; in adaptive control systems the adaptive control gain should be defined based on observation data in such a way that the gain asymptotically tends to the optimal one; in blind ch- nel identification the channel coefficients are estimated using the output data obtained at the receiver; in signal processing the optimal weighting matrix is estimated on the basis of observations; in pattern classifi- tion the parameters specifying the partition hyperplane are searched by learning, and more examples may be added to this list. All these parameter estimation problems can be transformed to a root-seeking problem for an unknown function. To see this, let - note the observation at time i. e. , the information available about the unknown parameters at time It can be assumed that the parameter under estimation denoted by is a root of some unknown function This is not a restriction, because, for example, may serve as such a function.
Author: Morton Hamermesh
Publisher:
ISBN:
Category : Group theory
Languages : en
Pages : 0
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Book Description
