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Research

I am working in the Condensed Matter Theory Group of the Physics department.

I am also presently collaborating with other scientists:

1. Rui Carvalho (University College of London, London, United Kingdom)
2. Guido Germano (Philipp's University of Marburg, Marburg, Germany)
3. Giulia Iori (City University, London, United Kingdom)
4. Kimmo Kaski (Laboratory of Computational Engineering, Helsinki University of Technology, Finland)
   
5. Marco Patriarca (Philipp's University of Marburg, Marburg, Germany)
6. Tadeusz Platkowski  (University of Warsaw, Warsaw, Poland)
7. Madabushi Srinivasan Santhanam (Physical Research Laboratory, Ahmedabad, India)
8. Anirvan Mayukh Sengupta (Rutgers University, New Jersey, USA)

For a complete list of my past and present collaborators, please click here.

• 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