Computational Neuroscience: A First Course by Hanspeter A Mallot

By Hanspeter A Mallot

Computational Neuroscience - a primary Course presents an important creation to computational neuroscience and equips readers with a primary knowing of modeling the apprehensive method on the membrane, mobile, and community point. The publication, 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, structures conception and synthetic neural networks. the mandatory mathematical thoughts are saved as intuitive and straightforward as attainable through the publication, making it absolutely available to readers who're much less accustomed to arithmetic. total, Computational Neuroscience - a primary Course represents an important reference consultant for all neuroscientists who use computational equipment of their day-by-day paintings, in addition to for any theoretical scientist forthcoming the sphere of computational neuroscience.

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42 2 Receptive Fields and the Specificity of Neuronal Firing Input ✲ linear filter w(x, y,t) I(x, y,t) Potential✲non-linearity e = f (u) u(t) Output ✲ e(x, y,t) Fig. 8 An important class of non-linear system can be described as a cascade of a linear system, followed by a static non-linearity. In neuroscience, L–NL-cascades are considered as a coarse model of dendritic summation followed by spike initiation at the axon hillock. λ , with a λ -fold activity λ e. Clearly, this will work only for small positive values of λ , since the activity of the neuron is limited and cannot become negative.

The physical power (irradiance) impinging per unit area on the retinal receptors, the response of a neuron can never be strictly linear. Consider for example a stimulus leading to some excitation e. 38 becomes a mapping from a set of functions (input images) into another set of functions (pattern of neural excitation). Such mappings are called operators. The definition of linearity is extended to operators in a straight-forward way. 42 2 Receptive Fields and the Specificity of Neuronal Firing Input ✲ linear filter w(x, y,t) I(x, y,t) Potential✲non-linearity e = f (u) u(t) Output ✲ e(x, y,t) Fig.

Pierre-Simon Marquis de Laplace (1749 – 1827). French mathematician. 32 2 Receptive Fields and the Specificity of Neuronal Firing e(x, y) = I(x , y )φ (x − x, y − y) dx dy . e. the point-spread function and the receptive field function are mirrored versions of each other. Note that this result holds only for translation-invariant systems. In this case, the point-spread function describes the divergence in a network and the receptive field functions the convergence in the same network. e. lateral connectivity (cf.

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