Center for Nonlinear Studies

Dynamics of Complex Networks: Biology, Information and Security (2004-2006)

The dynamics of complex networks in biological and informational systems were studied using a diverse set of tools including mathematical graph theory, statistical mechanics, and numerical simulation. Emphasis was on understanding how the nature of the network determines the evolution of processes on the network. Significant applications were in cell signaling networks that attempt to extend component parts into integrated systems dynamics, in protein folding network, information networks, and in complex network systems relevant to homeland security. There was particular emphasis in the following areas:

Biological networks and epidemiology of disease.
Social networks and interactions.
Network theory including random graphs, small-world networks and scale free graphs.

Highlight Publications:

Anghel, M., Z. Toroczkai, K. E. Bassler, and G. Korniss. Competition-driven network dynamics: emergence of a scale-free leadership structure and collective efficiency. 2004. Physical Review Letters. 92: 058701.
Eubank, S., H. Guclu, V. S. A. Kumar, M. V. Marathe, A. Srinivasan, Z. Toroczkai, and N. Wang. Modelling disease outbreaks in realistic urban social networks. 2004. Nature. 429: 180.
Ben-Naim, E., and S. Redner. Winning quick and dirty: the greedy random walk. 2004. Journal of Physics A (Mathematical and General). 37 (47): 11321.
Ben-Naim, E., F. Vazquez, and S. Redner. On the structure of competitive societies. 2006. European Physical Journal B. 49 (4): 531.
Chen, Y., E. Lopez, S. Havlin, and H. E. Stanley. Universal behavior of optimal paths in weighted networks with general disorder. 2006. Physical Review Letters. 96 (6): 068702.
Chertkov, M., and V. Y. Chernyak. Loop calculus in statistical physics and information science. 2006. Physical Review E. 73 (6): 065102.
Kozma, B., M. B. Hastings, and G. Korniss. Roughness scaling for Edwards-Wilkinson relaxation in small-world networks. 2004. Physical Review Letters. 92: 108701.
Kozma, B., M. B. Hastings, and G. Korniss. Diffusion processes on power-law small-world networks. 2005. Physical Review Letters. 95 (1): 018701.
Redner, S. Citation statistics from 110 years of Physical Review. 2005. Physics Today. 58 (6): 49.
Shalizi, C.R., K. L. Shalizi, and R. Haslinger. Quantifying self-organization with optimal predictors. 2004. Physical Review Letters. 93: 118701.
Sood, V., and S. Redner. Voter model on heterogeneous graphs. 2005. Physical Review Letters. 94 (17): 178701.
Stepanov, M.G., V. Chernyak, M. Chertkov, and B. Vasic. Diagnosis of weaknesses in modern error correction codes: a physics approach. 2005. Physical Review Letters. 95 (22): 228701.
Toroczkai, Z., and K. E. Bassler. Jamming is limited in scale-free systems. 2004. Nature. 428: 716.
Redner, S., and M. R. Petersen. Role of global warming on the statistics of record-breaking temperatures. 2006. Physical Review E. 74 (6): 061114.
Ben-Naim, E., S. Redner, and F. Vazquez. Scaling in tournaments. 2007. Europhysics Letters. 77 (3): 30005.