The Information Manifold PDF Download

Author: Antonio Badia
Publisher:
ISBN: 9780262355179
Category : Communication
Languages : en
Pages : 408

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Author: Antonio Badia
Publisher: MIT Press
ISBN: 0262043033
Category : Social Science
Languages : en
Pages : 353

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Book Description
An argument that information exists at different levels of analysis—syntactic, semantic, and pragmatic—and an exploration of the implications. Although this is the Information Age, there is no universal agreement about what information really is. Different disciplines view information differently; engineers, computer scientists, economists, linguists, and philosophers all take varying and apparently disconnected approaches. In this book, Antonio Badia distinguishes four levels of analysis brought to bear on information: syntactic, semantic, pragmatic, and network-based. Badia explains each of these theoretical approaches in turn, discussing, among other topics, theories of Claude Shannon and Andrey Kolomogorov, Fred Dretske's description of information flow, and ideas on receiver impact and informational interactions. Badia argues that all these theories describe the same phenomena from different perspectives, each one narrower than the previous one. The syntactic approach is the more general one, but it fails to specify when information is meaningful to an agent, which is the focus of the semantic and pragmatic approaches. The network-based approach, meanwhile, provides a framework to understand information use among agents. Badia then explores the consequences of understanding information as existing at several levels. Humans live at the semantic and pragmatic level (and at the network level as a society), computers at the syntactic level. This sheds light on some recent issues, including “fake news” (computers cannot tell whether a statement is true or not, because truth is a semantic notion) and “algorithmic bias” (a pragmatic, not syntactic concern). Humans, not computers, the book argues, have the ability to solve these issues.

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: Loring W. Tu
Publisher: Springer Science & Business Media
ISBN: 1441974008
Category : Mathematics
Languages : en
Pages : 426

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Book Description
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.

Author: Victor Patrangenaru
Publisher: CRC Press
ISBN: 1439820511
Category : Mathematics
Languages : en
Pages : 534

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Book Description
A New Way of Analyzing Object Data from a Nonparametric ViewpointNonparametric Statistics on Manifolds and Their Applications to Object Data Analysis provides one of the first thorough treatments of the theory and methodology for analyzing data on manifolds. It also presents in-depth applications to practical problems arising in a variety of fields

Author: John M. Lee
Publisher: Springer
ISBN: 3319917552
Category : Mathematics
Languages : en
Pages : 447

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Book Description
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Author: John M. Lee
Publisher: Springer Science & Business Media
ISBN: 0387227261
Category : Mathematics
Languages : en
Pages : 232

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Book Description
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Author: John M. Lee
Publisher: Springer Science & Business Media
ISBN: 0387217525
Category : Mathematics
Languages : en
Pages : 646

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Book Description
Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why

Author: Frank W. Warner
Publisher: Springer Science & Business Media
ISBN: 1475717997
Category : Mathematics
Languages : en
Pages : 283

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Book Description
Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds. The book also provides a proof of the de Rham theorem via sheaf cohomology theory and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem.

Author: Shun-ichi Amari
Publisher: American Mathematical Soc.
ISBN: 9780821843024
Category : Computers
Languages : en
Pages : 220

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Book Description
Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis.