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Life
is but a playground, however gross the play may be. However we may
receive blows and however knocked about we may be, the Soul is there and
is never injured. We are that Infinite.
-- Swami Vivekananda
Research
I am working in the Condensed
Matter Theory Group of the Physics department.
I am also presently collaborating with other scientists:
- Rui Carvalho
(University College of London, London, United Kingdom)
- Guido
Germano (Philipp's University of Marburg, Marburg, Germany)
- Giulia Iori (City
University, London, United Kingdom)
- Kimmo Kaski
(Laboratory of Computational Engineering, Helsinki University of
Technology, Finland)
- Marco
Patriarca (Philipp's University of Marburg, Marburg, Germany)
- Tadeusz Platkowski (University of Warsaw, Warsaw, Poland)
- Madabushi Srinivasan Santhanam (Physical Research Laboratory, Ahmedabad, India)
- Anirvan
Mayukh Sengupta (Rutgers University, New Jersey, USA)
For a complete list of my past and present collaborators, please click
here.
My research concentrates on
- Econophysics
: Studies consisting of various conceptual approaches of economic
problems using the tools and methods of statistical physics. This has
been a rapidly growing interdisciplinary field. I have been fortunate to
become the first Ph.D. in Econophysics from India. I have contributed to
several interesting and important areas:
- Simulations of agent-based market models and their
relation to different theories in physics such as the kinetic theory of
gases, percolation theory, and theory of self-organization.
- One of the current challenges is to write down the
``microscopic equation'' which would correspond to the century old
Pareto law in Economics, stating that the higher end of the distribution
of income follows a power-law. It has been our general aim to study a
statistical model of closed economy, which can be either solved exactly
or simulated numerically, and analyze the relation between the
microscopic equation and the kind of macroscopic money distribution it
results in, and especially whether it can provide some insight as to
under what conditions the Pareto law arises.
- "Herding behaviour" has been a very important topic in
Economics. Human beings are "social animals" and hence tend to form
"clusters" or stay together in various spheres of life. To study such
behaviour, the percolation theory of Physics has proved to be quite
useful. I have developed a variant of the famous Cont-Bouchaud model in
Econophysics and investigated under which circumstances the "stylized
facts" of empirical return distrbutions can be most successfully
reproduced.
- Self-organized critical (SOC) systems has been one of
the most widely studied topics in statistical physics in the last two
decades. In economics, the notion of a market being such a
self-organizing system of selfish agents has been held since the good
old days of Adam Smith in 1776. We have introduced a self-organizing
model where agents trade with a single commodity with the money they
possess, and studied the role of money in the economic market.
- Analyzes of stock market data and study of the "stylized
facts" of the empirical data.
- Economic taxonomy and Markowitz portfolio optimization:
We studied the time dependence of the recently introduced minimum
spanning tree description of correlations between stocks, called the
"asset tree'' and how it reflects the economic taxonomy. The nodes of
the tree are identified with stocks and the distance between them is a
unique function of the corresponding element of the correlation matrix.
We find that the tree seems to have a scale-free structure where the
scaling exponent of the degree distribution is different for "business
as usual" and "crash" periods. The basic structure of the tree topology
is very robust with respect to time. We also point out that the
diversification aspect of portfolio optimization results in the fact
that the assets of the classic Markowitz portfolio are always located on
the outer leaves of the tree.
- Spectral and related properties (calculation of the
Hurst exponent and exponent from detrended fluctuation analysis) of the
financial time series data in comparison to the random time series, and
other important spatio-temporal time series generated from GARCH
processes and couple-map lattices in chaotic regime.
- Game-theoretical models of market evolution, where we
introduced the adaptation mechanism based on genetic algorithms in
the minority games. If agents find their performances too low, they
modify their strategies in hope to improve their performances and become
more successful. One aim of this study was to find out what happens at
the system as well as at the individual agent level. We observe that
adaptation remarkably tightens the competition among the agents, and
tries to pull the collective system into a state where the aggregate
utility is the largest. These different adaptation mechanisms broaden
the scope of the applications of minority games to the study of complex
systems.
- Travelling
Salesman Problem : Given a certain set of cities and the
distances between them, a travelling salesman must find the shortest
tour in which he visits all the cities and comes back to its starting
point. Simple as it sounds, it is one of the most difficult and
challenging problems, which have been long studied by Mathematicians,
Computer Scientists and Physicists. In the past I have studied several
important aspects of the TSP and also some specific questions which
might help to understand the physics of TSP better :
- Analytical bounds of the
average optimal travel distances in the Euclidean TSP on the continuum
in the Euclidean and Manhattan metrics, and the relation between the
optimized constants (normalized average optimal travel distances per
city) for the two metrics.
- A general question: What is
the form of the average n-th neighbour distance, for any finite n ?
- How many times the n-th
neighbour is chosen along the optimal tour and detemination of the
frequency distribution.
- TSP on randomly dilute
lattices: If one places N cities randomly on a lattice of size L, we
find that the normalized optimal travel distances per city in the
Euclidean and Manhattan metrics vary monotonically with the city
concentration p. We have studied such optimal tours for visiting all the
cities using a branch and bound algorithm. Extrapolating the results for
N tending to infinity, we find that the normalized optimal travel
distances per city in the Euclidean and Manhattan metrics both equal
unity for p=1, and they reduce to 0.73 and 0.93, respectively, as p
tends to zero. Although the problem is trivial for p=1, it certainly
reduces to the standard TSP on continuum (NP-hard problem) for p tending
to zero. We did not observe any irregular behaviour at any intermediate
point. The crossover from the triviality to the NP-hard problem seems to
occur at p=1.
- Complex
Systems : Study of systems with many interacting components, each
component being different, and their adaptation to continuously changing
environment. I have been involved in developing and understanding:
- Simple multi-agent game
model where the agents adapt dynamically to be competitive and perform
better, by modifying the strategies which the agents use to decide their
course of action. I want to further study collective behaviour and
dynamic evolution of multi-agent systems.
- Models which give rise to
the complex network structures such as those observed in the internet,
world wide web, friendship, etc. and their properties. I am specially
interested in the economic interests of forming networks and how the
economic principles influence the network structure and dynamics.
- Biological
Networks (Gene-regulatory) : A transcription factor, its DNA
binding site and the transcription unit it regulates, constitute the
basic unit of gene regulation. Some genes are regulated by more than one
transcription factor and some transcription factors control more than
one gene. This gives rise to a complex gene regulatory network. It is
well established that these complex networks within cells control
critical steps in gene expression. I am mainly interested in the
physical properties or characteristics of the gene-regulatory network.
- Bioinformatics
: Genome-wide expression profiles of organisms can be easily acquired
using, for example, DNA microarray technology. In order to analyze the
vast amount of data generated by microarrays or ChIP experiments, the
development of genome-wide analysis tools is required. Though standard
clustering algorithms have been successful in finding genes that are
co-regulated for a small set of experimental conditions, they have
limitations when applied to large data sets under varying conditions.
Some attempts have been made to identify transcription modules, i.e.
sets of co-regulated genes along with the sets of conditions for which
the genes are strongly correlated in expression, by probabilistic
methods. Other attempts of genome-wide identification of regulatory
motifs have also been made. Motifs in genomic sequence data can be
defined as strings whose probability of occurrence greatly exceeds that
expected for the background (occurring by pure chance). I am mainly
interested in:
- Understanding the performance of motif finding algorithms
and developing them using the phylogenetic tree.
- Understanding evolutionary models governing regulatory
regions.
For further details please refer to the
list of
publications
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