Evidence, Decision and Causality

Author: Arif Ahmed

Publisher: Cambridge University Press

ISBN: 1107020891

Category: Mathematics

Page: 258

View: 8692

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An explanation and defence of evidential decision theory, which emphasises the symptomatic value of options over their causal role.
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Vision and Brain

How We Perceive the World

Author: Dr James V Stone

Publisher: MIT Press

ISBN: 0262517736

Category: Health & Fitness

Page: 243

View: 9079

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In this accessible and engaging introduction to modern vision science, James Stone uses visual illusions to explore how the brain sees the world. Understanding vision, Stone argues, is not simply a question of knowing which neurons respond to particular visual features, but also requires a computational theory of vision. Stone draws together results from David Marr's computational framework, Barlow's efficient coding hypothesis, Bayesian inference, Shannon's information theory, and signal processing to construct a coherent account of vision that explains not only how the brain is fooled by particular visual illusions, but also why any biological or computer vision system should also be fooled by these illusions. This short text includes chapters on the eye and its evolution, how and why visual neurons from different species encode the retinal image in the same way, how information theory explains color aftereffects, how different visual cues provide depth information, how the imperfect visual information received by the eye and brain can be rescued by Bayesian inference, how different brain regions process visual information, and the bizarre perceptual consequences that result from damage to these brain regions. The tutorial style emphasizes key conceptual insights, rather than mathematical details, making the book accessible to the nonscientist and suitable for undergraduate or postgraduate study.
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Probability Theory

The Logic of Science

Author: E. T. Jaynes,G. Larry Bretthorst

Publisher: Cambridge University Press

ISBN: 9780521592710

Category: Mathematics

Page: 727

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index
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Mathematical Logic

Author: Stephen Cole Kleene

Publisher: Courier Corporation

ISBN: 0486317072

Category: Mathematics

Page: 416

View: 1817

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Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
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Introduction to Symbolic Logic and Its Applications

Author: Rudolf Carnap

Publisher: Courier Corporation

ISBN: 048614349X

Category: Mathematics

Page: 272

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Clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. Hundreds of problems, examples, and exercises. 1958 edition.
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Additive Number Theory: Inverse Problems and the Geometry of Sumsets

Author: Melvyn B. Nathanson

Publisher: Springer Science & Business Media

ISBN: 9780387946559

Category: Mathematics

Page: 296

View: 3551

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Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.
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Gleason's Theorem and Its Applications

Author: Anatolij Dvurecenskij

Publisher: Springer Science & Business Media

ISBN: 9780792319900

Category: Mathematics

Page: 325

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This volume deals with Gleason's theorem and Gleason's measures and indicates the many ways in which they can be applied. The book comprises five chapters. Chapter 1 is devoted to elements of Hilbert space theory. Chapter 2 is devoted to quantum logic theory. Gleason's theorem is described and proved in Chapter 3, together with proofs for measures that can attain infinite values. In Chapter 4 the possibility of applying Gleason's theorem to the completeness criteria of inner product spaces is addressed. Chapter 5 discusses orthogonal measures and the unexpected possibility of describing states on Keller spaces, as well as other applications. Throughout the book, important facts and concepts are illustrated exercises. For mathematicians and physicists interested in the mathematical foundations of quantum mechanics, and those whose work involves noncommutative measure theory, orthomodular lattices. Hilbert space theory and probability theory.
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Models and Methods in the Philosophy of Science: Selected Essays

Author: Patrick Suppes

Publisher: Springer Science & Business Media

ISBN: 9780792322115

Category: Mathematics

Page: 510

View: 3886

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This book publishes 31 of the author's selected papers which have appeared, with one exception, since 1970. The papers cover a wide range of topics in the philosophy of science. Part I is concerned with general methodology, including formal and axiomatic methods in science. Part II is concerned with causality and explanation. The papers extend the author's earlier work on a probabilistic theory of causality. The papers in Part III are concerned with probability and measurement, especially foundational questions about probability. Part IV consists of several papers, including two historical ones, on the foundations of physics, with the main emphasis being on quantum mechanics. Part V, the longest part, is on the foundations of psychology and includes papers mainly on learning and perception. The book is aimed at philosophers of science, scientists concerned with the methodology of the social sciences, and mathematical psychologists interested in theories of learning, perception and measurement.
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