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New Foundation for Representation in Cognitive and Brain Science: Category Theory and the Hippocampus 2014 ed. [Kietas viršelis]

2.50/5 (3 ratings by Goodreads)
  • Formatas: Hardback, 193 pages, aukštis x plotis: 235x155 mm, weight: 4956 g, 40 Illustrations, color; 33 Illustrations, black and white; XXIII, 193 p. 73 illus., 40 illus. in color., 1 Hardback
  • Serija: Springer Series in Cognitive and Neural Systems 7
  • Išleidimo metai: 09-Dec-2013
  • Leidėjas: Springer
  • ISBN-10: 940077737X
  • ISBN-13: 9789400777378
Kitos knygos pagal šią temą:
New Foundation for Representation in Cognitive and Brain Science: Category Theory and the Hippocampus 2014 ed.Didesnis paveikslėlis
  • Formatas: Hardback, 193 pages, aukštis x plotis: 235x155 mm, weight: 4956 g, 40 Illustrations, color; 33 Illustrations, black and white; XXIII, 193 p. 73 illus., 40 illus. in color., 1 Hardback
  • Serija: Springer Series in Cognitive and Neural Systems 7
  • Išleidimo metai: 09-Dec-2013
  • Leidėjas: Springer
  • ISBN-10: 940077737X
  • ISBN-13: 9789400777378
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9789400777378.html
Raktažodžiai:

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.



This book advances understanding of brain function by defining a framework for representation based on category theory. Brings mathematical formalism into the domain of neural representation of physical spaces, as a basis for a theory of mental representation.

Recenzijos

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)

1 Research Tools and Paradigms
1(10)
1.1 Introduction
1(1)
1.2 Mathematics as a Language and as a Modelling Tool
2(1)
1.3 The Development of Physical Theories
3(3)
1.4 The Development of Brain Science
6(1)
1.5 YAPS! Yet Another Paradigm Shift!
7(2)
1.6 Plan of the Book
9(2)
2 State of the Art: Mathematical Approaches in Brain Science
11(22)
2.1 Introduction
11(1)
2.2 Brain State
12(2)
2.2.1 The Search for the Meaningful Brain States
13(1)
2.3 Modeling Neurons
14(2)
2.3.1 Detailed Biophysical Models of Neurons
15(1)
2.3.2 Models of Neurons Based on Threshold
16(1)
2.4 Modeling Populations of Neurons
16(10)
2.4.1 Artificial Neural Networks
17(2)
2.4.2 Neurodynamics
19(3)
2.4.3 Neural Field Models and Neural Masses
22(1)
2.4.4 Biological Synchronization: The Theory of Coupled Oscillators
23(3)
2.5 Large-Scale Brain Modeling
26(5)
2.5.1 Theory of Attractors in Brain Dynamics
26(2)
2.5.2 Synergetics
28(1)
2.5.3 Dynamic Geometry
29(1)
2.5.4 Network Theory
30(1)
2.6 Conclusions and Future Directions
31(2)
3 The Categorical Imperative: Category Theory in Cognitive and Brain Science
33(32)
3.1 Introduction
33(1)
3.2 Category Theory
34(14)
3.2.1 Examples of Categories
38(3)
3.2.2 Definition of Some Key Concepts in the Theory of Categories
41(7)
3.3 The Cat-Level Avenue
48(3)
3.4 Applications of Category Theory in Cognitive and Brain Science
51(14)
3.4.1 The Origins: Rosen's (M,R-Systems)
51(2)
3.4.2 Category Theory in Perception
53(1)
3.4.3 Memory Evolutive Neuronal Systems
53(4)
3.4.4 Category Theory in Knowledge Acquisition and Representation
57(8)
4 Elementary Principles in Cognitive Systems Modeling
65(20)
4.1 Introduction
65(1)
4.2 On Reductionism
66(2)
4.2.1 What Is Reductionism?
67(1)
4.3 On Formalisation
68(6)
4.3.1 The Limitations of Formalisation
70(4)
4.4 Emergence on Systems Modeling
74(5)
4.4.1 A Few Notes on Complex Systems
75(1)
4.4.2 A Few Notes on Emergent Properties
76(3)
4.5 Three Principles for Cognitive Systems Modelling
79(6)
4.5.1 Principle of Locality
79(1)
4.5.2 Principle of Hierarchy
80(2)
4.5.3 Principle of Multiplicity
82(3)
5 The Shift Towards Structure
85(12)
5.1 Introduction
85(1)
5.2 Defining Structure
85(3)
5.2.1 The Shepherd's Tale
87(1)
5.3 Categorizing Structured Systems
88(4)
5.3.1 Structured Systems
89(2)
5.3.2 Structured Systems as Categories
91(1)
5.4 An Example of Theoretical Hypothesis in Biological Systems: The Brouwer Theorem
92(5)
6 A General Framework for Representation
97(12)
6.1 Introduction
97(1)
6.2 Representation is Triadic
97(4)
6.3 A Theory of Representation in Cognitive Systems
101(4)
6.3.1 Structural Commonality in Representation
101(1)
6.3.2 Representation as a Relation of Similarity Between Structured Entities
102(1)
6.3.3 Representation as a Relation of Isomorphism Between Structured Entities
103(1)
6.3.4 Representation as a Relation of Homomorphism Between Structured Entities
103(1)
6.3.5 Representation Implies Structural Similarity or Homomorphism
104(1)
6.4 Theory of Representation Based on Category Theory
105(4)
7 Towards a Theory of Brain Structure and Function
109(32)
7.1 Introduction
109(1)
7.2 Brain Mappings Have Form and Meaning
110(5)
7.2.1 Sensorimotor Topographic Patterns
111(2)
7.2.2 Meaningful Patterns in the Olfactory Bulb
113(2)
7.3 The Quest for Functional Brain Organization: Historical Account
115(3)
7.3.1 The Old Paradigm: Modularism-Homuncularism
117(1)
7.4 Brain Cognitive Networks
118(6)
7.4.1 Defining Brain Connectivity
119(2)
7.4.2 Brain Causal Maps
121(2)
7.4.3 Cognits, Neurocognitive Networks and Local Populations
123(1)
7.5 Network Based Approach for Brain Connectivity
124(6)
7.5.1 Network Analysis for Brain Connectivity
126(2)
7.5.2 Small World Network
128(1)
7.5.3 Challenges in Network Based Approaches
129(1)
7.6 A Categorical Framework for Network Theory
130(11)
7.6.1 Exploring Motifs with Graph Homomorphisms
131(2)
7.6.2 Category of Paths
133(2)
7.6.3 A Methodology to Study Network Topology via Categories
135(2)
7.6.4 Quantitative Analysis of Clustering and Modularity with Colimits and Limits
137(2)
7.6.5 Seeing Small World and Scale Free Networks with Categorical Lens
139(2)
8 A Theory of Hippocampus Structure and Function Based on Category Theory
141(20)
8.1 Introduction
141(1)
8.2 The Nature of Spatial Representation
141(2)
8.3 The Hippocampus as a Representational Device
143(2)
8.3.1 The Cognitive Map Hypothesis
144(1)
8.4 The Hippocampus: Anatomy and Connectivity
145(1)
8.5 Place Cells
146(2)
8.5.1 Place Cells as Representational Entities
147(1)
8.6 Grid Cells
148(2)
8.6.1 Grid Fields
149(1)
8.7 Head Direction Cells
150(1)
8.8 A Theory of Brain Spatial Representation Based on Category Theory
151(4)
8.8.1 The Category of Neurons
151(1)
8.8.2 The Category of Places
152(2)
8.8.3 Functor Between Neur and Field
154(1)
8.9 A New Framework for Place and Grid Cells
155(6)
8.9.1 Place Field as Colimit of Grid Fields
157(4)
9 From Cells to Memories: A Categorical Approach
161(6)
9.1 Introduction
161(1)
9.2 Types of Memory
161(2)
9.3 A Theory of Declarative Memory Based on Category Theory
163(4)
9.3.1 Categorical Product in Acquisition of Middle Point Concept in 1D Navigation
163(2)
9.3.2 Categorical Pullback in Acquisition of Middle Point Concept in 2D Navigation
165(1)
9.3.3 Pullback and Grid Cell Formation
166(1)
10 Epilogue
167(4)
References 171(18)
Index 189