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

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