State Complexity of Catenation Combined with Star and Reversal

This paper is a continuation of our research work on state complexity of combined operations. Motivated by applications, we study the state complexities of two particular combined operations: catenation combined with star and catenation combined with reversal. We show that the state complexities of both of these combined operations are considerably less than the compositions of the state complexities of their individual participating operations.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Efficient calculation of the robustness measure R for complex networks

In a recent work, Schneider et al. (2011) proposed a new measure R for network robustness, where the value of R is calculated within the entire process of malicious node attacks. In this paper, we present an approach to improve the calculation efficiency of R, in which a computationally efficient robustness measure R' is introduced when the fraction of failed nodes reaches to a critical threshold qc. Simulation results on three different types of network models and three real networks show that these networks all exhibit a computationally efficient robustness measure R'. The relationships between R' and the network size N and the network average degree are also explored. It is found that the value of R' decreases with N while increases with . Our results would be useful for improving the calculation efficiency of network robustness measure R for complex networks.Peer ReviewedPostprint (author's final draft

Generation multiple vector light modes using beam displacers

Complex vector light modes, characterized by a non-uniform transverse polarization distribution, have pervaded a wide range of research fields. In this study, we propose a novel approach that enables the simultaneous generation of multiple vector beams based on a spatially-segmented digital hologram and two or more cascaded beam displacers. More precisely, an input beam is separated into multiple parallel copies spatially separated, which are then sent to the center of each segmented hologram, enabling independent modulation of each beam. The modulated beams are then judiciously recombined with a beam displacer to generate multiple vector modes in a simultaneous way. We demonstrated our technique with two arbitrary vector modes but the technique can be easily extended to more by inserting additional beam dispalcers. To assess the quality of the generated vector modes, we employed Stokes polarimetry to reconstruct their transverse polarisation distribution and to measure their degree of non-separability. We envision that this technique will find significant applications in various fields, including optical communications, optical sensing, optical tweezers to mention a few