دانلود کتاب Mathematical Tools for Neuroscience: A Geometric Approach (Lecture Notes in Morphogenesis)

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Preface
Acknowledgements
Contents
1 Mind and Brain
1.1 Objects in Mind
1.2 Objects on the Brain
1.3 Using Your Grey Matter
1.4 About This Book
References
2 Biological Objects
2.1 Configuration Spaces
2.2 Tangent Spaces
2.3 Moving Around
References
3 Measurements
3.1 Linear Transformations
3.2 Principal Components Analysis
3.3 Hebbian Learning
3.4 Anti-Hebbian Learning
References
4 From Local to Global
4.1 Critical Points
4.2 Receptive and Association Fields
4.3 Bump Functions
4.4 Gradient Space
References
5 Actions
5.1 Slow-Fast Systems
5.2 Velocity Commands
5.3 Deciding What to interact With
5.4 Unexpected Consequences of Nonlinear Behaviour
References
6 Brain and Body
6.1 Mechanics of Biological Tissue
6.2 Linear Behaviour
6.3 Nonlinear Behaviour
6.4 Production of Voice Sounds
6.5 Heteroclinic Cycles
References
7 Analysis of Experimental Measurements
7.1 Delay Embedding
7.2 An Unstable Neural Pathway
7.3 Topological Data Analysis
References
8 Where Are We Going With All This?
8.1 Review of the Geometric Approach
8.2 Alternative Approaches
8.3 Mathematics for Neurons
8.4 Further Reading
8.4.1 Brain
8.4.2 Geometry
References
9 Appendix: Background Material
9.1 Brains
9.2 Calculus
Glossary of Terms with Hidden Assumptions
Index