We consider circular ensembles with nonuniform weight functions. We investigate the universality of short-range and long-range level fluctuations, which are important in the study of quantum chaotic systems. We analyze a set of hierarchic relations among the correlation functions to obtain the level density for a wide class of potentials and to demonstrate universality of correlation functions in the case of weak periodic potentials (where the term potential refers to the logarithm of the weight function). Analytic study of circular unitary ensemble is done with the help of orthogonal polynomials on the unit circle. For circular orthogonal and symplectic ensembles, we introduce skew-orthogonal polynomials on the unit circle. We consider the asymptotic forms of the polynomials for the three types of ensembles with weak potentials to give a proof of the universality. The analytic results are verified by Monte Carlo simulations of the ensembles with different weight functions. We also discuss the implications of these results in the context of conductance fluctuations in mesoscopic systems and show that the universality breaks down for strong potentials.

We discuss the long-range spectral correlations in random matrices. Their universality for one-band spectra and its breakdown for multiband spectra are investigated and characterized. The long-range properties are complementary to the usual short-range properties, and are important for conductance fluctuations in mesoscopic systems. However, unlike short-range properties, they are not ubiquitous in model quantum-chaotic systems. We formulate a system of multiply-kicked quantum rotors, and show that it exhibits both long-range and short-range correlations.

Wireless Mesh Networks (WMNs) are the evolutionary self-organizing multi-hop wireless networks to promise last mile access. Due to the emergence of stochastically varying network environments, routing in WMNs is critically affected. In this paper, we first propose a fuzzy logic based hybrid performance metric comprising of link and node parameters. This Integrated Link Cost (ILC) is computed for each link based upon throughput, delay, jitter of the link and residual energy of the node and is used to compute shortest path between a given source-terminal node pair. Further to address the optimal routing path selection, two soft computing based approaches are proposed and analyzed along with a conventional approach. Extensive simulations are performed for various architectures of WMNs with varying network conditions. It was observed that the proposed approaches are far superior in dealing with dynamic nature of WMNs as compared to Adhoc On-demand Distance Vector (AODV) algorithm

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Multi radio, multi hop, self organizing and self configuring wireless technology are the characteristic features of wireless mesh networks (WMNs) to offer last mile access to end users. The emergence of stochastically varying network environments critically affects routing in WMNs. Any routing policy meant for WMNs must be quickly adaptive and evolve in a decentralized self organizing and self configuring manner. This paper firstly proposes formulation of a soft computing i.e. fuzzy logic based hybrid performance metric which includes per flow (throughput, delay and jitter) as well as per node (residual energy of the node) parameters. This fuzzy logic based hybrid performance metric enumerates the integrated link cost (ILC) which is used as distance measure between two adjacent nodes. The paper further proposes three routing algorithms based upon nature inspired computing approaches namely firefly algorithm, Big Bang Big Crunch and Ant Colony Optimization. The proposed routing approaches aim at finding the minimal ILC path within a stipulated time constraint. The time constraint is governed by the mobility of network nodes. Extensive simulations were conducted for various WMN topologies. The results of the proposed approaches have been compared with two commonly used conventional approaches and were found to be far more superior. It was also observed that the self organizing capability of the proposed nature inspired routing approaches effectively reduces the complexity and makes a network quite adaptive to the dynamic network behavior found in WMNs.