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

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

On commuting Tonelli Hamiltonians: Autonomous case

We show that the Aubry sets, the Ma\~{n}\'{e} sets, Mather's barrier functions are the same for two commuting autonomous Tonelli Hamiltonians. We also show the quasi-linearity of $\alpha$-functions from the dynamical point of view and the existence of common $C^{1,1}$ critical subsolution for their associated Hamilton-Jacobi equations.Comment: 15 page