ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 05 Mar 2021 15:13:32 GMT2021-03-05T15:13:32Z5051- Randomness of random networks: A random matrix analysishttps://scholarbank.nus.edu.sg/handle/10635/97751Title: Randomness of random networks: A random matrix analysis
Authors: Jalan, S.; Bandyopadhyay, J.N.
Abstract: We analyze complex networks under the random matrix theory framework. Particularly, we show that Δ3 statistics, which gives information about the long-range correlations among eigenvalues, provides a measure of randomness in networks. As networks deviate from the regular structure, Δ3 follows the random matrix prediction of logarithmic behavior (i.e., ) for longer scale. © 2009 Europhysics Letters Association.
Sat, 01 Aug 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/977512009-08-01T00:00:00Z
- Symbolic dynamics and synchronization of coupled map networks with multiple delayshttps://scholarbank.nus.edu.sg/handle/10635/98156Title: Symbolic dynamics and synchronization of coupled map networks with multiple delays
Authors: Atay, F.M.; Jalan, S.; Jost, J.
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. © 2010 Elsevier B.V.
Wed, 01 Dec 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/981562010-12-01T00:00:00Z
- Spectral analysis of deformed random networkshttps://scholarbank.nus.edu.sg/handle/10635/97978Title: Spectral analysis of deformed random networks
Authors: Jalan, S.
Abstract: We study spectral behavior of sparsely connected random networks under the random matrix framework. Subnetworks without any connection among them form a network having perfect community structure. As connections among the subnetworks are introduced, the spacing distribution shows a transition from the Poisson statistics to the Gaussian orthogonal ensemble statistics of random matrix theory. The eigenvalue density distribution shows a transition to the Wigner's semicircular behavior for a completely deformed network. The range for which spectral rigidity, measured by the Dyson-Mehta Δ3 statistics, follows the Gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure. The spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure, whereas the density distribution and the Δ3 statistics remain identical to the undeformed network. On the other hand the Δ3 statistics is useful for the larger deformation strengths. Finally, we analyze the spectrum of a protein-protein interaction network for Helicobacter, and compare the spectral behavior with those of the model networks. © 2009 The American Physical Society.
Thu, 01 Oct 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/979782009-10-01T00:00:00Z
- Spectral properties of directed random networks with modular structurehttps://scholarbank.nus.edu.sg/handle/10635/97981Title: Spectral properties of directed random networks with modular structure
Authors: Jalan, S.; Zhu, G.; Li, B.
Abstract: We study spectra of directed networks with inhibitory and excitatory couplings. We investigate in particular eigenvector localization properties of various model networks for different values of correlation among their entries. Spectra of random networks with completely uncorrelated entries show a circular distribution with delocalized eigenvectors, whereas networks with correlated entries have localized eigenvectors. In order to understand the origin of localization we track the spectra as a function of connection probability and directionality. As connections are made directed, eigenstates start occurring in complex-conjugate pairs and the eigenvalue distribution combined with the localization measure shows a rich pattern. Moreover, for a very well distinguished community structure, the whole spectrum is localized except few eigenstates at the boundary of the circular distribution. As the network deviates from the community structure there is a sudden change in the localization property for a very small value of deformation from the perfect community structure. We search for this effect for the whole range of correlation strengths and for different community configurations. Furthermore, we investigate spectral properties of a metabolic network of zebrafish and compare them with those of the model networks. © 2011 American Physical Society.
Tue, 18 Oct 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/979812011-10-18T00:00:00Z
- Random matrix analysis of localization properties of gene coexpression networkhttps://scholarbank.nus.edu.sg/handle/10635/97750Title: Random matrix analysis of localization properties of gene coexpression network
Authors: Jalan, S.; Solymosi, N.; Vattay, G.; Li, B.
Abstract: We analyze gene coexpression network under the random matrix theory framework. The nearest-neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral rigidity test follows random matrix prediction for a certain range and deviates afterwards. Eigenvector analysis of the network using inverse participation ratio suggests that the statistics of bulk of the eigenvalues of network is consistent with those of the real symmetric random matrix, whereas few eigenvalues are localized. Based on these IPR calculations, we can divide eigenvalues in three sets: (a) The nondegenerate part that follows RMT. (b) The nondegenerate part, at both ends and at intermediate eigenvalues, which deviates from RMT and expected to contain information about important nodes in the network. (c) The degenerate part with zero eigenvalue, which fluctuates around RMT-predicted value. We identify nodes corresponding to the dominant modes of the corresponding eigenvectors and analyze their structural properties. © 2010 The American Physical Society.
Wed, 28 Apr 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/977502010-04-28T00:00:00Z