Download Computational Neuroscience: A First Course (Springer Series by Hanspeter A. Mallot PDF

By Hanspeter A. Mallot

Computational Neuroscience - a primary Course presents a necessary creation to computational neuroscience and  equips readers with a primary figuring out of modeling the apprehensive method on the membrane, mobile, and community point. The ebook, 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 medication, takes its readers on a trip via 3 primary domain names of computational neuroscience: membrane biophysics, platforms thought and synthetic neural networks. the necessary mathematical strategies are stored as intuitive and easy as attainable during the publication, making it totally available to readers who're much less conversant in arithmetic. total, Computational Neuroscience - a primary Course represents an important reference advisor for all neuroscientists who use computational tools of their day-by-day paintings, in addition to for any theoretical scientist drawing close the sector of computational neuroscience.

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Mathematically, it rests on integral equations of the convolution type which will be introduced in due course. 1 Correlation and Linear Spatial Summation The Superposition Principle If an electrode is placed in the retina, spikes can be recorded from retinal ganglion cells. e. on the pattern of light shone on the receptor layer of the retina while recording. A. Mallot: Computational Neuroscience, SSBN 2, pp. 23–55. 1007/978-3-319-00861-5_2 24 2 Receptive Fields and the Specificity of Neuronal Firing simplest case, a little spot of light is moved across the retina covering just a few receptors at any one time.

Evaluates to a number) are contained in the Hilbert space L2 . Since the visual field is actually not the infinite plane but rather a finite subset of the sphere, all continuous functions defined on the visual field satisfy this condition. 3 Paul A. M. Dirac (1902 – 1984). English physicist. Nobel Price in Physics (with E. Schr¨ odinger) 1933. 2 28 2 Receptive Fields and the Specificity of Neuronal Firing a second, excitatory stimulation. 1e is also known as “Mexican hat function”. 1. e. stimuli of the form I(x, y) ≡ Io .

English physicist. Nobel Price in Physics (with E. Schr¨ odinger) 1933. 2 28 2 Receptive Fields and the Specificity of Neuronal Firing a second, excitatory stimulation. 1e is also known as “Mexican hat function”. 1. e. stimuli of the form I(x, y) ≡ Io . 9, this amounts to the constraint ∞ ∞ φ (x, y) dy dy ≈ 0. 12) −∞ −∞ This means that for most receptive field functions, the total weights of excitatory and inhibitory regions cancel out. The receptive field function in the correlation operation can also be considered as a template for a particular sub-pattern or “image feature” for which the neuron is a detector.

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