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# ðŸ“™ A New Foundation for Representation in Cognitive and Brain Science: Category Theory and the Hippocampus by Jaime GÃ³mez-Ramirez (auth.) â€” free download

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**A New Foundation for Representation in Cognitive and Brain Science: Category Theory and the Hippocampus free epub by Jaime GÃ³mez-Ramirez (auth.)**

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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.

- Series:
**Springer Series in Cognitive and Neural Systems 7** - Author:
**Jaime GÃ³mez-Ramirez (auth.)** - Year:
**2014** - Publisher:
**Springer Netherlands** - Language:
**English** - ISBN:
**978-94-007-7737-8,978-94-007-7738-5**

- File size:
**2 811 181** - Format:
**pdf**

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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...

Now more than ever, biology has the potential to contribute practical solutions to many of the major challenges confronting the United States and the world. A New Biology for the 21st Century recommends that a "New Biology" approach--one that depends on g...

Collecting information previously scattered throughout the vast literature, including the authorâ€™s own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition ...

Collecting information previously scattered throughout the vast literature, including the authorÐ²Ð‚â„¢s own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transitio...

The central question addressed in Foundations for the Future in Mathematics Education is this:Â What kind of understandings and abilities should be emphasized to decrease mismatches between the narrow band of mathematical understandings and abilities that ...

Collecting information previously scattered throughout the vast literature, including the authorâ€™s own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition s...

Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within math...

TodayAs practice of psychiatric administration is totally different from that in past years because of the vast changes sweeping the health care and behavioral health care sectors. Reflecting these changes, this completely revamped second edition contains...

The goal of this book is to summarise the recent advances in carbon nanotubes as a new material for electrochemical sensors. Since their discovery in 1991, carbon nanotubes have received considerable attention in different fields. Their special geometry a...