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Books > Science & Mathematics > Mathematics > Mathematical foundations
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A New Foundation for Representation in Cognitive and Brain Science - Category Theory and the Hippocampus (Paperback, Softcover reprint of the original 1st ed. 2014)
Loot Price: R2,504
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A New Foundation for Representation in Cognitive and Brain Science - Category Theory and the Hippocampus (Paperback, Softcover reprint of the original 1st ed. 2014)
Series: Springer Series in Cognitive and Neural Systems, 7
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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.
General
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