000			03102nam a22003017a 4500
003			OSt
005			20250226152619.0
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020			_a9783030984946
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a616.8:514 _bCLE-M
100			_aClement, Richard A.
245			_aMathematical tools for neuroscience : _ba geometric approach
260			_aCham, Switzerland : _bSpringer, _c2022.
300			_ax, 162 pages : _billustrations (15 b/w illustrations, 106 illustrations in colour)
490			_aLecture notes on morphogenesis _x2195-1934
504			_aIncludes bibliographical references and index
520			_aThis 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. Just as tangent planes can be used to analyse the local linear behaviour of points on a surface, so the extension to tangent spaces can be used to investigate the local linear behaviour of manifolds. The majority of the geometric techniques introduced are all about how to do things with tangent spaces. Examples of the geometric approach to neuroscience include the analysis of colour and spatial vision measurements and the control of eye and arm movements. Additional examples are used to extend the applications of the approach and to show that it leads to new techniques for investigating neural systems. An advantage of following a geometric approach is that it is often possible to illustrate the concepts visually and all the descriptions of the examples are complemented by comprehensively captioned diagrams. The book is intended for a reader with an interest in neuroscience who may have been introduced to calculus in the past but is not aware of the many insights obtained by a geometric approach to the brain. Appendices contain brief reviews of the required background knowledge in neuroscience and calculus.
650			_aNeuroscience _xMathematics
650			_aMorse theory
650			_aEye movements
650			_aNeural integrator
650			_aHebbian learning
650			_aGeodesic
856			_3Table of content _uhttps://link.springer.com/content/pdf/bfm:978-3-030-98495-3/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/60875539-mathematical-tools-for-neuroscience#CommunityReviews
942			_2udc _cBK
999			_c35783 _d35783