A structural and a functional aspect of stable information processing by the brain.
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.
Majumdar
Kaushik Kumar
KK
Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600113, India, kaushik@imsc.res.in.