Showing papers by "Sarika Jalan published in 2008"
TL;DR: Analyses of random networks, scale-free networks and small-world networks show that the nearest neighbor spacing distribution of the Laplacian of these networks follow Gaussian orthogonal ensemble statistics of the random matrix theory.
Abstract: We analyse the eigenvalue fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that the nearest neighbor spacing distribution of the Laplacian of these networks follow Gaussian orthogonal ensemble statistics of the random matrix theory. Furthermore, we study the nearest neighbor spacing distribution as a function of the random connections and find that the transition to the Gaussian orthogonal ensemble statistics occurs at the small-world transition.
29 citations
TL;DR: An exact mapping is provided between this model and the zero-range process, and it is argued that this mapping can be used to infer a possible evolution rule for any given network.
Abstract: We introduce a stochastic model of growing networks where both the number of new nodes which join the network and the number of connections vary stochastically. We provide an exact mapping between this model and the zero-range process, and calculate analytically the degree distribution for any given evolution rule. We argue that this mapping can be used to infer a possible evolution rule for any given network. This is being demonstrated for a protein-protein interaction network of Saccharomyces cerevisiae.
20 citations
TL;DR: In this paper, the authors analyzed complex networks under random matrix theory framework and showed that the long range correlations among eigenvalues provide a qualitative measure of randomness in networks, and that as networks deviate from the regular structure, $\Delta_3$ follows random matrix prediction of linear behavior, in semi-logarithmic scale with the slope of $1/pi^2.
Abstract: We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in networks. As networks deviate from the regular structure, $\Delta_3$ follows random matrix prediction of linear behavior, in semi-logarithmic scale with the slope of $1/\pi^2$, for the longer scale.
14 citations
Posted Content•
13 May 2008
TL;DR: In this paper, symbolic dynamics is used to study discrete-time dynamical systems with multiple time delays, where the authors exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of certain symbol sequences related to the characteristics of the dynamics.
Abstract: We use symbolic dynamics to study discrete-time dynamical systems with multiple time delays. We exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of certain symbol sequences related to the characteristics of the dynamics. In particular, we show that the resulting forbidden sequences are closely related to the time delays in the system. We present two applications to coupled map lattices, namely (1) detecting synchronization and (2) determining unknown values of the transmission delays in networks with possibly directed and weighted connections and measurement noise. The method is applicable to multi-dimensional as well as set-valued maps, and to networks with time-varying delays and connection structure.