By Hanspeter A. Mallot
Computational Neuroscience - a primary Course presents an important advent to computational neuroscience and equips readers with a basic realizing of modeling the frightened approach on the membrane, mobile, and community point. The booklet, which grew out of a lecture sequence held frequently for greater than ten years to graduate scholars in neuroscience with backgrounds in biology, psychology and drugs, takes its readers on a trip via 3 basic domain names of computational neuroscience: membrane biophysics, platforms thought and synthetic neural networks. the necessary mathematical innovations are saved as intuitive and easy as attainable during the booklet, making it totally available to readers who're much less acquainted with arithmetic. total, Computational Neuroscience - a primary Course represents a vital reference advisor for all neuroscientists who use computational tools of their day-by-day paintings, in addition to for any theoretical scientist forthcoming the sphere of computational neuroscience.
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Extra info for Computational Neuroscience: A First Course (Springer Series in Bio-/Neuroinformatics)
Nature 440:1060 – 1063. Action potentials in cortical neurons are shown to rise even steeper than predicted in the Hodgkin-Huxley theory (initially developed for the squid). The authors suggest an additional interaction between adjacent sodium channels not considered in the original theory. Rall, W. (1962). Electrophysiology of a dendritic neuron model. Biophysical Journal, 2:145 – 167. Early and influential paper on the electrodynamics of (passive) conduction and their dependence on dendritic geometry.
The receptive field is the total area, from which the neuron’s activity can be modulated. The areas shown in gray are rough estimates of the excitatory and inhibitory parts of the receptive fields. , f. Center-surround receptive field function φ (x, y) for the two neurons depicted in Figures c, d. The gray areas c, d are delimited by contour lines of φ . 26 2 Receptive Fields and the Specificity of Neuronal Firing Linear spatial summation is a theoretical concept defined by the above two equations.
3 Non-linearities in Receptive Fields 43 u ✻ ✲ t a. f1 (u) ✲ e ✻ ✲ u ✻ ✲ ✲ t b. f2 (u) ✲ e ✻ ✻ ✲ u θ ✲ ✲ t c. f3 (u) ✲ e ✻ uo ✻ ✲ u ✲ ✲ t d. f4 (u) ✲ e ✻ ✻ ✲ u −λ /2 ✲ ✲ t e. f5 (u) ✲ e ✻ ✻ ✲ u ✲ ✲ t f. Fig. 9 Static non-linearity applied to a sinusoidal. a. Sinusoidal used as an input in all cases. b. Half-wave rectification. e. f (sin u). Half-wave rectification deletes all negative values and passes the positive values unchanged. c. Binary switching function (Heaviside function) with threshold θ .
Computational Neuroscience: A First Course (Springer Series in Bio-/Neuroinformatics) by Hanspeter A. Mallot