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Monday, February 19, 2018
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2:00pm [2:30pm]Prof. Karmeshu, JNU, Delhi
Description:
Title: Stochastic Modelling and Simulation of Neuronal System with Distributed Delay Speaker: Prof. Karmeshu, JNU, Delhi Day & Date: Monday, 19th February 2018 Time: 2.30 pm Venue: Ramanujan Hall Brief Bio: Professor Karmeshu has been with the School of Computer and Systems Sciences (SC&SS) at the Jawaharlal Nehru University, New Delhi since 1986. He is a recipient of the Shanti Swarup Bhatnagar Award in Mathematical Sciences for the year 1993, a Fellow of the National Academy of Sciences (India) and several other organisations. His primary research interests are in Mathematical Modelling and Computer Simulation. Abstract: Modelling of neuronal dynamics aims to capture the mechanisms that generate empirically observed inter-spike interval (ISI) patterns. The time-interval between spikes gives ISI distribution which requires solution of the first passage time problem of the stochastic differential equation governing the dynamics of membrane potential when it reaches the threshold for the first time. The empirical spiking patterns exhibit both unimodal and bimodal/multimodal patterns. A theoretical model based on generalized neuronal model with distributed delay (GNMDD) is proposed to generate multimodal/ bimodal inter spike interval (ISI) distribution. Further the effect of external damped oscillatory current in neuronal model is investigated. It is found that with increasing amplitude of damped oscillatory current, the multimodal ISI distribution changes to unimodal ISI distribution when the magnitude of external current reaches some critical value. It is noted that the entropy also shows a sudden transition around the critical point. This phenomenon is akin to phase transition. This work is done jointly with Sudheer Sharma and Sanjeev Yadav.

3:00pm [3:30pm]Ronnie Sebastian
Description:
CACAAG (Combinatorial Aspects of Commutative Algebra and Algebraic Geometry) seminar Speaker: Ronnie Sebastian Date & Time : 19th February, 3:30pm Venue : Ramanujan Hall Abstract: This talk will be based on the following elementary and nice exposition http://www.math.stonybrook.edu/~roblaz/Reprints/Green. Laz.Simple.Pf.Petri.pdf Using some simple facts about projective space, cohomology, cohomology of line bundles on projective space, we shall prove the following theorems: 1. Noether's theorem - Projective normality of the canonical embedding of non-hyperelliptic curves. 2. Petri's -theorem - Let X be a smooth and projective curve of genus g \geq 5. Assume that X carries a line bundle A of degree g-1 with h^0(A)=2. Further assume that both A and \Omega_X\otimes A^* are generated by their global sections. Then the homogeneous ideal of X in its canonical embedding is generated by degree 2 elements.

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