Complex Networks: Structure and Dynamics

I have classified below the work done by our group in the area of complex systems into various topics. For a short review (4 pages) of some of our work see the write-up of the invited talk I gave at the DAE Solid State Physics Symposium 2007 in Mysore: Physics of Complex Networks.


• ECOLOGY
  
  In a series of papers we have re-examined the question of whether complex ecological networks are more or less stable (which originated with the pioneering work of Robert May in the 1970s)
  
  S. Sinha and S. Sinha, "Evidence of universality for the May-Wigner stability theorem for random networks with local dynamics", Phys. Rev. E 71 (2005) 020902(R) (1-4).
  S. Sinha, "Complexity vs. stability in small-world networks", Physica A 346 (2005) 147-153.
  M. Brede and S. Sinha, "Assortative mixing by degree makes a network more unstable", cond-mat/0507710
  S. Sinha and S. Sinha, "Robust emergent activity in dynamical networks", Phys. Rev. E 74 (2006) 066117 (1-5).
  
  The significance of these papers to ecology has recently been reviewed in C. C. Wilmers, "Understanding ecosystem robustness", Trends in Ecology and Evolution 22 (2007) 504-506.
  Sinha & Sinha (2005) has recently been cited by Robert May in the Nature News & Views article "Ecology for Bankers", Nature 451 (2008) 893-895.
  For more details on our early explorations, look at Ecological Networks: Dynamical Stability vs. Diversity.
  
  
• FINANCIAL MARKETS
  
  We have analysed the evolution of the network arising from stock price correlations in the Indian market and showed evidence that as markets get more mature the network tends to get clustered into tightly coupled subgraphs (corresponding to different business sectors):
  R. K. Pan and S. Sinha, "Collective behavior of stock price movements in an emerging market", Phys. Rev. E 76 (2007) 046116 (1-9).
  
  
• NEUROSCIENCE
  
  We have analyzed the hierarchical structure of the C elegans nervous system, and showed evidence that the assortativity increases as one goes to the innermost core of the network. This is interesting as most other biological networks are disassortative. We speculate that the assortative nature of the inner core helps in increasing communication efficiency while at the same time making the network more robust:
  N. Chatterjee and S. Sinha, "Understanding the Mind of a Worm: Hierarchical network structure underlying nervous system function in C. Elegans", Progress in Brain Research 168 (2007) 145-153.
  
  The dynamical relevance of the small-world structure of neural networks reported in recent neurobiological studies has been analysed in:
  S. Sinha, J. Saramaki and K. Kaski, "Emergence of self-sustained patterns in small-world excitable media", Phys. Rev. E 76 (2007) 015101(R) (1-4).
  We show that the existence of different ratios of long-range connections can result in formation of strikingly different patterns and relate this to the glia-neuron ratio (recent studies suggest the functional role of neuronal-glia ratio in neurodynamical patterns, e.g., epilepsy).
  
  
• We have also recently proposed a biologically plausible mechanism for the genesis of modular networks, that are ubiquitous in nature:
  R. K. Pan and S. Sinha, "Modular networks emerge from multiconstraint optimization", Phys. Rev. E 76 (2007) 045103(R) (1-4).