A structural and a functional aspect of stable information processing by the brain |
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Authors: | Kaushik Kumar Majumdar |
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Institution: | (1) Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600113, India |
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Abstract: | Brain is an expert in producing the same output from a particular set of inputs, even from a very noisy environment. In this
article a model of neural circuit in the brain has been proposed which is composed of cyclic sub-circuits. A big loop has
been defined to be consisting of a feed forward path from the sensory neurons to the highest processing area of the brain
and feed back paths from that region back up to close to the same sensory neurons. It has been mathematically shown how some
smaller cycles can amplify signal. A big loop processes information by contrast and amplify principle. How a pair of presynaptic
and postsynaptic neurons can be identified by an exact synchronization detection method has also been mentioned. It has been
assumed that the spike train coming out of a firing neuron encodes all the information produced by it as output. It is possible
to extract this information over a period of time by Fourier transforms. The Fourier coefficients arranged in a vector form
will uniquely represent the neural spike train over a period of time. The information emanating out of all the neurons in
a given neural circuit over a period of time can be represented by a collection of points in a multidimensional vector space.
This cluster of points represents the functional or behavioral form of the neural circuit. It has been proposed that a particular
cluster of vectors as the representation of a new behavior is chosen by the brain interactively with respect to the memory
stored in that circuit and the amount of emotion involved. It has been proposed that in this situation a Coulomb force like
expression governs the dynamics of functioning of the circuit and stability of the system is reached at the minimum of all
the minima of a potential function derived from the force like expression. The calculations have been done with respect to
a pseudometric defined in a multidimensional vector space. |
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Keywords: | Brain circuit Cyclic directed subgraphs Contrast and amplify principle Spike trains Fast Fourier Transform (FFT) Minimization of potential function |
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