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Springer Series in Cognitive and Neural Systems

A New Foundation for Representation in Cognitive and Brain Science

Category Theory and the Hippocampus

Authors: Gómez Ramirez, Jaime

  • It is a truly multidisciplinary book that provides interesting insights into mathematics, philosophy and neurobiology
  • The book establishes a common working theoretical framework for mathematicians, philosophers and cognitive scientists
  • It is a unique opportunity for cognitive scientists to understand how the mathematical theory of category works
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Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-94-007-7738-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-94-007-7737-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-94-024-0215-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

The purpose of the book is to advance in the understanding of brain function by defining a general framework for representation based on category theory. The idea is to bring this mathematical formalism into the domain of neural representation of physical spaces, setting the basis for a theory of mental representation, able to relate empirical findings, uniting them into a sound theoretical corpus.

The innovative approach presented in the book provides a horizon of interdisciplinary collaboration that aims to set up a common agenda that synthesizes mathematical formalization and empirical procedures in a systemic way. Category theory has been successfully applied to qualitative analysis, mainly in theoretical computer science to deal with programming language semantics. Nevertheless, the potential of category theoretic tools for quantitative analysis of networks has not been tackled so far. Statistical methods to investigate graph structure typically rely on network parameters. Category theory can be seen as an abstraction of graph theory. Thus, new categorical properties can be added into network analysis and graph theoretic constructs can be accordingly extended in more fundamental basis. By generalizing networks using category theory we can address questions and elaborate answers in a more fundamental way without waiving graph theoretic tools. The vital issue is to establish a new framework for quantitative analysis of networks using the theory of categories, in which computational neuroscientists and network theorists may tackle in more efficient ways the dynamics of brain cognitive networks.

The intended audience of the book is researchers who wish to explore the validity of mathematical principles in the understanding of cognitive systems. All the actors in cognitive science: philosophers, engineers, neurobiologists, cognitive psychologists, computer scientists etc. are akin to discover along its pages new unforeseen connections through the development of concepts and formal theories described in the book. Practitioners of both pure and applied mathematics e.g., network theorists, will be delighted with the mapping of abstract mathematical concepts in the terra incognita of cognition.

Reviews

From the book reviews:

“This is a comprehensive textbook of brain theory as it relates to what I will call Neuro-logic. The author does a credible job of describing the role of mathematics, topology, set theory, topology, and other neural representations in alphanumeric digital language. … I recommend this book very highly to the neuroscience community, from the viewpoint of research on cognition, brain theories, systems neuroscience, and mathematics.” (Joseph J. Grenier, Amazon.com, March, 2015)


Table of contents (1 chapters)

  • Towards a Theory of Brain Structure and Function

    Jaime Gómez-Ramirez

    Pages 109-140

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-94-007-7738-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-94-007-7737-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-94-024-0215-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A New Foundation for Representation in Cognitive and Brain Science
Book Subtitle
Category Theory and the Hippocampus
Authors
Series Title
Springer Series in Cognitive and Neural Systems
Series Volume
7
Copyright
2014
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-007-7738-5
DOI
10.1007/978-94-007-7738-5
Hardcover ISBN
978-94-007-7737-8
Softcover ISBN
978-94-024-0215-5
Series ISSN
2363-9105
Edition Number
1
Number of Pages
XXIII, 193
Number of Illustrations and Tables
33 b/w illustrations, 40 illustrations in colour
Topics