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• Archive: https://archive.is/wip/sMYgn Richard A Clement - Mathematical Tools for Neuroscience: A Geometric ApproachThis book provides a brief but accessible introduction to a set of related, mathematical ideas that have proved useful in understanding the brain and behaviour.
• If you record the eye movements of a group of people watching a riverside scene then some will look at the river, some will look at the barge by the side of the river, some will look at the people on the bridge, and so on, but if a duck takes off then everybody will look at it.
• How come the brain is so adept at processing such biological objects?
• In this book it is shown that brains are especially suited to exploiting the geometric properties of such objects.Central to the geometric approach is the concept of a manifold, which extends the idea of a surface to many dimensions.
• The manifold can be specified by collections of n-dimensional data points or by the paths of a system through state space.