Approximation of conformal mappings using conformally equivalent triangular lattices

Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be approximated by such discrete conformal maps $f^\epsilon$. In particular, let $T$ be an infinite regular triangulation of the plane with congruent triangles and only acute angles (i.e.\ $<\pi/2$). We scale this tiling by $\epsilon>0$ and approximate a compact subset of the domain of $f$ with a portion of it. For $\epsilon$ small enough we prove that there exists a conformally equivalent triangle mesh whose scale factors are given by $\log|f'|$ on the boundary. Furthermore we show that the corresponding discrete conformal maps $f^\epsilon$ converge to $f$ uniformly in $C^1$ with error of order $\epsilon$.Comment: 14 pages, 3 figures; v2 typos corrected, revised introduction, some proofs extende

Schizophrenia trials in China: a survey

OBJECTIVE: China's biomedical research activity is increasing and this literature is becoming more accessible online. Our aim was to survey all randomized control schizophrenia trials (RCTs) in one Chinese bibliographic database. METHOD: Chinese Academic Journals was electronically searched for RCTs and all relevant citations were also sought on PubMed to ascertain global accessibility. RESULTS: The search identified 3275 records, of which 982 were RCTs relevant to schizophrenia. A total of 71% (699) could be found by using English phrases. All the main body of text of the 982 papers was in Mandarin. On average, these trials involved about 100 people, with interventions and outcome measures familiar to schizophrenia trialists worldwide. Four of the 982 records (<1%) were identified on PubMed. CONCLUSION: Those undertaking systematic reviews should search the Chinese literature for relevant material. Failing to do this will leave the results of systematic reviews prone to random error or bias, or both

Alisertib, an Aurora kinase A inhibitor, induces apoptosis and autophagy but inhibits epithelial to mesenchymal transition in human epithelial ovarian cancer cells.

Ovarian cancer is a leading killer of women, and no cure for advanced ovarian cancer is available. Alisertib (ALS), a selective Aurora kinase A (AURKA) inhibitor, has shown potent anticancer effects, and is under clinical investigation for the treatment of advanced solid tumor and hematologic malignancies. However, the role of ALS in the treatment of ovarian cancer remains unclear. This study investigated the effects of ALS on cell growth, apoptosis, autophagy, and epithelial to mesenchymal transition (EMT), and the underlying mechanisms in human epithelial ovarian cancer SKOV3 and OVCAR4 cells. Our docking study showed that ALS, MLN8054, and VX-680 preferentially bound to AURKA over AURKB via hydrogen bond formation, charge interaction, and &pi;-&pi; stacking. ALS had potent growth-inhibitory, proapoptotic, proautophagic, and EMT-inhibitory effects on SKOV3 and OVCAR4 cells. ALS arrested SKOV3 and OVCAR4 cells in G2/M phase and induced mitochondria-mediated apoptosis and autophagy in both SKOV3 and OVCAR4 cell lines in a concentration-dependent manner. ALS suppressed phosphatidylinositol 3-kinase/protein kinase B (Akt)/mammalian target of rapamycin (mTOR) and p38 mitogen-activated protein kinase pathways but activated 5\u27-AMP-dependent kinase, as indicated by their altered phosphorylation, contributing to the proautophagic activity of ALS. Modulation of autophagy altered basal and ALS-induced apoptosis in SKOV3 and OVCAR4 cells. Further, ALS suppressed the EMT-like phenotype in both cell lines by restoring the balance between E-cadherin and N-cadherin. ALS downregulated sirtuin 1 and pre-B cell colony enhancing factor (PBEF/visfatin) expression levels and inhibited phosphorylation of AURKA in both cell lines. These findings indicate that ALS blocks the cell cycle by G2/M phase arrest and promotes cellular apoptosis and autophagy, but inhibits EMT via phosphatidylinositol 3-kinase/Akt/mTOR-mediated and sirtuin 1-mediated pathways in human epithelial ovarian cancer cells. Further studies are warranted to validate the efficacy and safety of ALS in the treatment of ovarian cancer

Fully gapped topological surface states in Bi2_2Se3_3 films induced by a d-wave high-temperature superconductor

Topological insulators are a new class of materials, that exhibit robust gapless surface states protected by time-reversal symmetry. The interplay between such symmetry-protected topological surface states and symmetry-broken states (e.g. superconductivity) provides a platform for exploring novel quantum phenomena and new functionalities, such as 1D chiral or helical gapless Majorana fermions, and Majorana zero modes which may find application in fault-tolerant quantum computation. Inducing superconductivity on topological surface states is a prerequisite for their experimental realization. Here by growing high quality topological insulator Bi$_2$Se$_3$ films on a d-wave superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ using molecular beam epitaxy, we are able to induce high temperature superconductivity on the surface states of Bi$_2$Se$_3$ films with a large pairing gap up to 15 meV. Interestingly, distinct from the d-wave pairing of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, the proximity-induced gap on the surface states is nearly isotropic and consistent with predominant s-wave pairing as revealed by angle-resolved photoemission spectroscopy. Our work could provide a critical step toward the realization of the long sought-after Majorana zero modes.Comment: Nature Physics, DOI:10.1038/nphys274

Disparities and risks of sexually transmissible infections among men who have sex with men in China: a meta-analysis and data synthesis.

BACKGROUND: Sexually transmitted infections (STIs), including Hepatitis B and C virus, are emerging public health risks in China, especially among men who have sex with men (MSM). This study aims to assess the magnitude and risks of STIs among Chinese MSM. METHODS: Chinese and English peer-reviewed articles were searched in five electronic databases from January 2000 to February 2013. Pooled prevalence estimates for each STI infection were calculated using meta-analysis. Infection risks of STIs in MSM, HIV-positive MSM and male sex workers (MSW) were obtained. This review followed the PRISMA guidelines and was registered in PROSPERO. RESULTS: Eighty-eight articles (11 in English and 77 in Chinese) investigating 35,203 MSM in 28 provinces were included in this review. The prevalence levels of STIs among MSM were 6.3% (95% CI: 3.5-11.0%) for chlamydia, 1.5% (0.7-2.9%) for genital wart, 1.9% (1.3-2.7%) for gonorrhoea, 8.9% (7.8-10.2%) for hepatitis B (HBV), 1.2% (1.0-1.6%) for hepatitis C (HCV), 66.3% (57.4-74.1%) for human papillomavirus (HPV), 10.6% (6.2-17.6%) for herpes simplex virus (HSV-2) and 4.3% (3.2-5.8%) for Ureaplasma urealyticum. HIV-positive MSM have consistently higher odds of all these infections than the broader MSM population. As a subgroup of MSM, MSW were 2.5 (1.4-4.7), 5.7 (2.7-12.3), and 2.2 (1.4-3.7) times more likely to be infected with chlamydia, gonorrhoea and HCV than the broader MSM population, respectively. CONCLUSION: Prevalence levels of STIs among MSW were significantly higher than the broader MSM population. Co-infection of HIV and STIs were prevalent among Chinese MSM. Integration of HIV and STIs healthcare and surveillance systems is essential in providing effective HIV/STIs preventive measures and treatments. TRIAL REGISTRATION: PROSPERO NO: CRD42013003721