Prime Graphs and Exponential Composition of Species

In this paper, we enumerate prime graphs with respect to the Cartesian multiplication of graphs. We use the unique factorization of a connected graph into the product of prime graphs given by Sabidussi to find explicit formulas for labeled and unlabeled prime graphs. In the case of species, we construct the exponential composition of species based on the arithmetic product of species of Maia and M\'endez and the quotient species, and express the species of connected graphs as the exponential composition of the species of prime graphs.Comment: 30 pages, 7 figures, 1 tabl

Design & Evaluation of Path-based Reputation System for MANET Routing

Most of the existing reputation systems in mobile ad hoc networks (MANET) consider only node reputations when selecting routes. Reputation and trust are therefore generally ensured within a one-hop distance when routing decisions are made, which often fail to provide the most reliable, trusted route. In this report, we first summarize the background studies on the security of MANET. Then, we propose a system that is based on path reputation, which is computed from reputation and trust values of each and every node in the route. The use of path reputation greatly enhances the reliability of resulting routes. The detailed system architecture and components design of the proposed mechanism are carefully described on top of the AODV (Ad-hoc On-demand Distance Vector) routing protocol. We also evaluate the performance of the proposed system by simulating it on top of AODV. Simulation experiments show that the proposed scheme greatly improves network throughput in the midst of misbehavior nodes while requires very limited message overhead. To our knowledge, this is the first path-based reputation system proposal that may be implemented on top of a non-source based routing scheme such as AODV

Gendered aspects of perceived and internalized HIV-related stigma in China.

Although studies have demonstrated that females experience more HIV-related stigma than males do, questions remain regarding the different dimensions of the stigma (i.e., perceived versus internalized) in China. The present study investigated gender differences in perceived and internalized HIV-related stigma, taking into account the potential influence of education. The study was conducted between October 2011 and March 2013. A total of 522 people living with HIV (PLH) were recruited from Anhui Province, China. The PLH participated in a survey using the Computer Assisted Personal Interview (CAPI) method. The gender differences in perceived and internalized HIV-related stigma were calculated with and without stratifying by education level. Female participants had significantly less education than the male participants. No significant difference was observed between females and males with respect to perceived stigma. However, females reported significantly higher internalized stigma than males did (p < .001). When socio-demographic characteristics were controlled, the gender difference in internalized stigma remained significant among educated participants (p = .038). The findings suggested that gender differences in HIV-related stigma were primarily found for internalized stigma. Heightened intervention efforts are encouraged to reduce internalized HIV-related stigma, particularly among female PLH in China and other regions with similar gender dynamics

On Relaxed Averaged Alternating Reflections (RAAR) Algorithm for Phase Retrieval from Structured Illuminations

In this paper, as opposed to the random phase masks, the structured illuminations with a pixel-dependent deterministic phase shift are considered to derandomize the model setup. The RAAR algorithm is modified to adapt to two or more diffraction patterns, and the modified RAAR algorithm operates in Fourier domain rather than space domain. The local convergence of the RAAR algorithm is proved by some eigenvalue analysis. Numerical simulations is presented to demonstrate the effectiveness and stability of the algorithm compared to the HIO (Hybrid Input-Output) method. The numerical performances show the global convergence of the RAAR in our tests.Comment: 17 pages, 26 figures, submitting to Inverse Problem