arXiv subjects

I. Mitra

Publications and source records attributed to I. Mitra.

4 recordsLinked to original sources

arXiv2005

Some Theoretical Investigations in EEG Studies

It is well known that Electroencephalography(EEG) and the respective evoked potentials have deep implications corresponding to specific cognitive tasks and in the diagnosis of several diseases such as epilepsy and schizophrenia. Some recent experimental results have already shown some evidence of chaotic activity in the brain. The Hodgekin-Huxley(HH) models, may yield geometrical solutions in terms of limit cycles and basins of attractors, but its implementation requires a priori knowledge of the kinetics of the innumerable conductances acting in a given set of cells. We are of the opinion that the EEG data should reflect the neuronal dynamics, and there should be some mechanism at the neuronal level which generates stochasticity compatible with the recorded data. In this paper we develop a theoretical framework to show that EEG dynamics may be governed by a suitably biased Vander-Pol oscillator which is closely related with the modified version of the FitzHugh-Nagumo(FN) model making extension of the ideas of dynamic causal modelling (DCM). Eventually we also give a prescription to compute the correlation matrices which may be tested empirically, for some small values of the parameters.

q-bio.NC↗

arXiv2004

Neural Graphs and Category of Memory States

The brain as an astonishingly remarkable device has been studied from various angles. It is now well known that neurons are the seat of all activities of the brain function. The dynamical properties pertaining to a single neuron and a collection of neurons may be widely different owing to the clustering properties of a group of neurons. As it can be clearly understood theory of complex physical systems has been more and more employed to study the behaviour of neurons and neuronal circuits. We here mainly discuss neural correlates of memory and cognitive functions utilizing graph theory and ideas from geometry. It has been suggested that stochastic processes being at the helm of affairs in the neuronal level there may exist surfaces to some extent like a hologram for the existence of memory functions.It is also instructive to mention that Amari's developments \cite{amari} as regards information geometry has acted as an important inspiration. Unlike some previous analysis categorization of memory from neural perspectives have been reconsidered at the neuronal level. In essence the main point of discussion here has been to give an alternative model of memory where stochastic geometry and algebraic surfaces is an important ingredient.

q-bio.NC↗

arXiv2004

Quantum Entanglement, Cognition & The Processes of Inference

Church's hypothesis and Godel's theorem may provide constraints on mental processes.As a relief quantum entanglement may lead to a definite proposal as regards the nature of reality and how much of it we are able to know and how do we know it.We deal with these questions and have devised a Gedanken Experiment showing the redundancy of principle of reality. We thereby propose a model describing the processes of making conclusions from a given set of premises though without the reference of neurobiological processes at present. We argue thereafter that the physical laws of nature may not be universal as it seems, being dependent on some physical processes namely computation and the states of neural cognitive states which may be governed yet by some other rule.

physics.gen-ph↗

arXiv2002

On decoupled theories in (5+1) dimensions from (F,D1,NS5,D5) supergravity configuration

It is well-known that ($N$, $M$) 5-branes of type IIB supergravity form a non-threshold bound state with ($N'$, $M'$) strings called the (F, D1, NS5, D5) bound state where the strings lie along one of the spatial directions of the 5-branes (hep-th/9905056). By taking low energy limits in appropriate ways on this supergravity configuration, we obtain the supergravity duals of various decoupled theories in (5+1) dimensions corresponding to noncommutative open string (NCOS) theory, open D-string (OD1) theory and open D5-brane (OD5) theory. We then study the $SL(2, Z)$ transformation properties of these theories. We show that when the asymptotic value of the axion ($χ_0$) is rational (for which $χ_0$ can be put to zero), NCOS theory is always related to OD1 theory by strong-weak or S-duality symmetry. We also discuss the self-duality conjecture (hep-th/0006062) of both NCOS and OD1 theories. On the other hand, when $χ_0$ is irrational, we find that $SL(2, Z)$ duality on NCOS theory gives another NCOS theory with different values of the parameters, but for OD1 theory $SL(2,Z)$ duality always gives an NCOS theory. $SL(2, Z)$ transformation on OD5 theory reveals that it gives rise to Little String Theory (LST) when $χ_0$ = rational, but it gives another OD5 theory with different values of the parameters when $χ_0$ is irrational.

hep-th↗