I am a theoretical physicist working in the general area of Non-equilibrium Statistical Physics and its applications to  some interdisciplinary fields.  My interests include Non-equilibrium phase transitions, Novel correlations in  non-equilibrium steady state , Exactly solvable  driven diffusive systems,  Structure and functionig  of Networks. I would  like to  pursue future research in the follwing three  important  directions :

Novel-correlations in non-equilibrium steady states:

Classical non-equilibrium systems  do not ensure existence of the  state functions like Hamiltonian and entropy as these systems are known to have non-zero current in the configutaion space.  Thus the steady states of these systems posses interesting and non-trivial correlations which are usually absent in equilibrium.  One of my main research interests is to unfold these  novel correlations. Recently we proposed a method, which can provide an exact steady state and  spatial correlations in a class of non-equilibrium models. The method has been used successfully in Extended Katz Lebowitz Spoon (EKLS) model, Restricted Assymetric Exclusion Process (RASEP), Exclusion process with internal degrees of freedom, Tonks gas, DNA denaturation transition etc.

Absorbing state phase transitions beyond DP :

One of the most interesting properties of non-equilibrium systems is the possibility of phase transition, even in one spatial dimensions. Transition from an active phase to an absorbing state is one such phenomenon which has no counterpart in equilibrium statistical mechanics. The idea of universality classes, characterised by only a few critical exponents,  extends to  the non-equilibrium transitions too.  Generic absorbing state phase transitions  (APT), governed by a fluctuating scalar orderparameter  belong to  the  Directed percolation (DP) universality class, the queen of non-equilibrium phase transitions. However, there are  several  exceptions. APT beyond DP is a less understood  area of research and  we are trying to understand  these sytems  by studying some simple and analytically tractable models.  Recently we have introduced a model, namely RASEP, where hard core particles on a ring can move to  one of the neighbouring vacant sites when the other neighbour is occupied. This model shows AAPT different from DP at density r=1/2.  The  spatial correlations and the exact critical exponents are obtained analytically. The orderparameter of the model satisfies the requirements of DP-conjecture and we are trying to reason why  this class of models shows non-DP behaviour.  Are there perturbations  which   makes this critical point flow to DP ?    

miRNA co-target network :

One of the main research activity which  I am  going to pursue in future is the  microRNA co-target  networks in Biology. microRNAs (miRNA) are small  (about 23 base long) RNAs transcribed from the DNA. These miRNAs  usually downregulate gene-expression  by binding  themselves to the UTRs of the mRNAs which translates into  proteins. The diversity of miRNA targets offer enormous level of combinatorial possibilities by forming  complex regulatory networks;  constructed  from the pairwise co-targets of miRNAs. It turns out that these relevant set of miRNAs  form several small  clusters. We  claim  that the miRNA clusters are building blocks of biological functions as  many of these clusters are expressed maximally in specific tissues. Those miRNAs which are known to deregulate  the genes involved in  genetic diseases are also found to be  cluster specific. Our recent study of  20 other animals also indicate that the clustering  of miRNAs is a universal feature. Thus, we propose that the genes are better regulated by co-targeting of clusters of miRNAs, compared to individual regulation. We are planning some experiments here (SINP) to verify this.  We sincerely believe that  these studies  will help biologists in their search for miRNAs that  target  the genes involved in any specicific phenotypes. Recently we started  collaborating with U. Kolthur in TIFR, India  on glucose  metabolism. We are also trying to study (with A. Erzan and E. Gungor , ITU, Istanbul)  the the relevant set of miRNAs  involved in Mediterian Fever.  

In all these studies the weighted network of miRNA pairs  is created from the  number of common targets (genes) they have. One can construct similar networks from the common disease or the common Transcription factors and obtain miRNA clusters.  It is important to compare these clusters  obtained from different scenarios.  We are planning to built a database of miRNA clusters at SINP.