Mon, February 19, 2018
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- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- 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.
- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- 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.