LEADER 04089nam 22006375 450 001 9910564698003321 005 20251204103856.0 010 $a9783030984953$b(electronic bk.) 010 $z9783030984946 024 7 $a10.1007/978-3-030-98495-3 035 $a(MiAaPQ)EBC6961448 035 $a(Au-PeEL)EBL6961448 035 $a(CKB)21605609300041 035 $a(PPN)262169517 035 $a(DE-He213)978-3-030-98495-3 035 $a(EXLCZ)9921605609300041 100 $a20220421d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Tools for Neuroscience $eA Geometric Approach /$fby Richard A. Clement 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (168 pages) 225 1 $aLecture Notes in Morphogenesis,$x2195-1942 300 $aIncludes index. 311 08$aPrint version: Clement, Richard A. Mathematical Tools for Neuroscience Cham : Springer International Publishing AG,c2022 9783030984946 330 $aThis book provides a brief but accessible introduction to a set of related, mathematical ideas that have proved useful in understanding the brain and behaviour. If you record the eye movements of a group of people watching a riverside scene then some will look at the river, some will look at the barge by the side of the river, some will look at the people on the bridge, and so on, but if a duck takes off then everybody will look at it. How come the brain is so adept at processing such biological objects? In this book it is shown that brains are especially suited to exploiting the geometric properties of such objects. Central to the geometric approach is the concept of a manifold, which extends the idea of a surface to many dimensions. The manifold can be specified by collections of n-dimensional data points or by the paths of a system through state space. Just as tangent planes can be used to analyse the local linear behaviour of points on a surface, so the extension to tangent spaces can be used to investigate the local linear behaviour of manifolds. The majority of the geometric techniques introduced are all about how to do things with tangent spaces. Examples of the geometric approach to neuroscience include the analysis of colour and spatial vision measurements and the control of eye and arm movements. Additional examples are used to extend the applications of the approach and to show that it leads to new techniques for investigating neural systems. An advantage of following a geometric approach is that it is often possible to illustrate the concepts visually and all the descriptions of the examples are complemented by comprehensively captioned diagrams. The book is intended for a reader with an interest in neuroscience who may have been introduced to calculus in the past but is not aware of the many insights obtained by a geometric approach to the brain. Appendices contain brief reviews of the required background knowledge in neuroscience and calculus. 410 0$aLecture Notes in Morphogenesis,$x2195-1942 606 $aBiomathematics 606 $aSensorimotor cortex 606 $aComputational neuroscience 606 $aBiometry 606 $aMathematical and Computational Biology 606 $aSensorimotor Processing 606 $aComputational Neuroscience 606 $aBiostatistics 615 0$aBiomathematics. 615 0$aSensorimotor cortex. 615 0$aComputational neuroscience. 615 0$aBiometry. 615 14$aMathematical and Computational Biology. 615 24$aSensorimotor Processing. 615 24$aComputational Neuroscience. 615 24$aBiostatistics. 676 $a612.80151 676 $a612.820151607 700 $aClement$b Richard A.$01223162 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910564698003321 996 $aMathematical Tools for Neuroscience$92837479 997 $aUNINA