Generalized Frame Potential and Problems Related to SIC-POVMs

Frame theory generalizes the idea of bases in Hilbert space, and the frame potential is an important tool when studying frame theory. In this thesis, we first explore the minimization problem of a generalized definition of frame potential, namely the p-frame potential, and show there exists a universal optimizer under certain conditions by applying a method involving ultraspherical polynomials and spherical designs. Next, we further discuss the topic on Grassmannian frames, which are special cases of minimizers of p-frame potentials. We present the construction of equiangular lines in lower dimensions since numerical result showed their connections with Grassmannian frames. We also derive properties of the (6,4)-Grassmannian frame. Then, we obtain lower bounds for the generalized frame potentials in the complex setting. The frame potentials may provide a different approach to determine the existence of Gabor frames that are equiangular. This relates the potential minimization problem to the unsolved Zauner conjecture. In addition, we study the properties of Gramian matrices of Gabor frames in an attempt to search for Gabor frames with a small number of different inner products. We also calculate the number of different inner products in Gabor frames generated by Alltop sequences and Björck sequences. In addition, we also present examples related to a generalized support uncertainty inequality and shift-invariant spaces on LCA groups

Psoriasis-associated variant Act1 D10N with impaired regulation by Hsp90

Act1 is an essential adaptor molecule in IL-17-mediated signaling and is recruited to the IL-17 receptor upon IL-17 stimulation. Here, we report that Act1 is a client protein of the molecular chaperone, Hsp90. The Act1 variant (D10N) linked to psoriasis susceptibility is defective in its interaction with Hsp90, resulting in a global loss of Act1 function. Act1-/- mice modeled the mechanistic link between Act1 loss of function and psoriasis susceptibility. Although Act1 is necessary for IL-17-mediated inflammation, Act1-/- mice exhibited a hyper TH17 response and developed spontaneous IL-22-dependent skin inflammation. In the absence of IL-17-signaling, IL-22 is the main contributor to skin inflammation, providing a molecular mechanism for the association of Act1 (D10N) with psoriasis susceptibility

Pressured HIV testing "in the name of love": a mixed methods analysis of pressured HIV testing among men who have sex with men in China.

INTRODUCTION: HIV testing has rapidly expanded into diverse, decentralized settings. While increasing accessibility to HIV testing is beneficial, it may lead to unintended consequences such as being pressured to test. We examined the frequency, correlates and contexts of pressured HIV testing among Chinese men who have sex with men (MSM) using mixed methods. METHODS: We conducted an online survey of MSM (N = 1044) in May 2017. Pressured HIV testing was defined as being forced to test for HIV. We conducted logistic regression analysis to determine the associations between pressured HIV testing and socio-demographic and sexual behavioural factors. Follow-up interviews (n = 17) were conducted with men who reported pressured testing and we analysed qualitative data using a thematic analysis approach. RESULTS: Ninety-six men (9.2%) reported experiencing pressure to test for HIV. Regular male sex partners were the most common source of pressure (61%, 59/96), and the most common form of pressure was a threat to end a relationship with the one who was being pressured (39%, 37/96). We found a higher risk of pressured testing in men who had only used HIV self-testing compared to men who had never self-tested (AOR 2.39 (95%CI: 1.38 to 4.14)). However, this relationship was only significant among men with low education (AOR 5.88 (95% CI: 1.92 to 17.99)) and not among men with high education (AOR 1.62 (95% CI: 0.85 to 3.10)). After pressured testing, about half of men subsequently tested for HIV (55%, 53/96) without pressure - none reported being diagnosed with HIV. Consistent with this finding, qualitative data suggest that perceptions of pressure existed on a continuum and depended on the relationship status of the one who pressured them. Although being pressured to test was accompanied by negative feelings, men who were pressured into testing often changed their attitude towards HIV testing, testing behaviours, sexual behaviours and relationship with the one who pressured them to test. CONCLUSION: Pressured HIV testing was reported among Chinese MSM, especially from men with low education levels and men who received HIV self-testing. However, in some circumstances, pressure to test helped MSM in several ways, challenging our understanding of the role of agency in the setting of HIV testing

The mHz quasi-regular modulations of 4U 1630--47 during its 1998 outburst

We present the results of a detailed timing and spectral analysis of the quasi-regular modulation (QRM) phenomenon in the black hole X-ray binary 4U 1630--47 during its 1998 outburst observed by Rossi X-ray Timing Explore (RXTE). We find that the $\sim$ 50-110 mHz QRM is flux dependent, and the QRM is detected with simultaneous low frequency quasi-periodic oscillations (LFQPOs). According to the behavior of the power density spectrum, we divide the observations into four groups. In the first group, namely behavior A, LFQPOs are detected, but no mHz QRM. The second group, namely behavior B, a QRM with frequency above $\sim$ 88 mHz is detected and the $\sim$ 5 Hz and $\sim$ 7 Hz LFQPOs are almost overlapping. In the third group, namely behavior C, the QRM frequency below $\sim$ 88 mHz is detected and the LFQPOs are significantly separated. In the forth group, namely behavior D, neither QRM nor LFQPOs are detected. We study the energy-dependence of the fractional rms, centroid frequency, and phase-lag of QRM and LFQPOs for behavior B and C. We then study the evolution of QRM and find that the frequency of QRM increases with hardness, while its rms decreases with hardness. We also analyze the spectra of each observation, and find that the QRM rms of behavior B has a positive correlation with $\rm F_{\rm powerlaw}$ / $\rm F_{\rm total}$. Finally, we give our understanding for this mHz QRM phenomena.Comment: 14pages, 15 figure

Comparing the effectiveness of a crowdsourced video and a social marketing video in promoting condom use among Chinese men who have sex with men: a study protocol

Crowdsourcing has been used to spur innovation and increase community engagement in public health programmes. Crowdsourcing is the process of giving individual tasks to a large group, often involving open contests and enabled through multisectoral partnerships. Here we describe one crowdsourced video intervention in which a video promoting condom use is produced through an open contest. The aim of this study is to determine whether a crowdsourced intervention is as effective as a social marketing intervention in promoting condom use among high-risk men who have sex with men (MSM) and transgender male-to-female (TG) in China

In-orbit background simulation of a type-B CATCH satellite

The Chasing All Transients Constellation Hunters (CATCH) space mission plans to launch three types of micro-satellites (A, B, and C). The type-B CATCH satellites are dedicated to locating transients and detecting their time-dependent energy spectra. A type-B satellite is equipped with lightweight Wolter-I X-ray optics and an array of position-sensitive multi-pixel Silicon Drift Detectors. To optimize the scientific payloads for operating properly in orbit and performing the observations with high sensitivities, this work performs an in-orbit background simulation of a type-B CATCH satellite using the Geant4 toolkit. It shows that the persistent background is dominated by the cosmic X-ray diffuse background and the cosmic-ray protons. The dynamic background is also estimated considering trapped charged particles in the radiation belts and low-energy charged particles near the geomagnetic equator, which is dominated by the incident electrons outside the aperture. The simulated persistent background within the focal spot is used to estimate the observation sensitivity, i.e. 4.22$\times$10$^{-13}$ erg cm$^{-2}$ s$^{-1}$ with an exposure of 10$^{4}$ s and a Crab-like source spectrum, which can be utilized further to optimize the shielding design. The simulated in-orbit background also suggests that the magnetic diverter just underneath the optics may be unnecessary in this kind of micro-satellites, because the dynamic background induced by charged particles outside the aperture is around 3 orders of magnitude larger than that inside the aperture.Comment: 24 pages, 13 figures, 7 tables, accepted for publication in Experimental Astronom

The genetic determinants of recurrent somatic mutations in 43,693 blood genomes

Nononcogenic somatic mutations are thought to be uncommon and inconsequential. To test this, we analyzed 43,693 National Heart, Lung and Blood Institute Trans-Omics for Precision Medicine blood whole genomes from 37 cohorts and identified 7131 non-missense somatic mutations that are recurrently mutated in at least 50 individuals. These recurrent non-missense somatic mutations (RNMSMs) are not clearly explained by other clonal phenomena such as clonal hematopoiesis. RNMSM prevalence increased with age, with an average 50-year-old having 27 RNMSMs. Inherited germline variation associated with RNMSM acquisition. These variants were found in genes involved in adaptive immune function, proinflammatory cytokine production, and lymphoid lineage commitment. In addition, the presence of eight specific RNMSMs associated with blood cell traits at effect sizes comparable to Mendelian genetic mutations. Overall, we found that somatic mutations in blood are an unexpectedly common phenomenon with ancestry-specific determinants and human health consequences