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

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

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

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

An assessment of the quality of randomised controlled trials conducted in China

Background: Despite the rapid increase in research in China, little is known about the quality of clinical trials conducted there.Methods: A systematic review and critical appraisal of randomised controlled trials (RCTs) conducted in China and published in 2004 was undertaken to describe their characteristics, assess the quality of their reporting, and where possible, the quality of their conduct. Randomised controlled trials in all disease areas and types of interventions, which took place in China and included Chinese citizens were identified using PubMed and hand searching the Journal Series of the Chinese Medical Association. Quality was assessed against a subset of criteria adapted from the CONSORT statement.Results: Three hundred and seven RCTs were included. One hundred and ninety-nine (64.8%) failed to report methods of randomization and 254 (82.4%) did not mention blinding of either participants or investigators. Reporting of baseline characteristics, primary outcome and length of follow-up was inadequate in a substantial proportion of studies. Fewer than 11% of RCTs mentioned ethical approval and only 18.0% adequately discussed informed consent. However, dropout rates were very favourable with nearly 44% of trials reporting a zero dropout rate.Conclusion: Reporting of RCTs in China requires substantial improvement to meet the targets of the CONSORT statement. The conduct of Chinese RCTs cannot be directly inferred from the standard of reporting; however without good reporting the methods of the trials cannot be clearly ascertained

The sudden change phenomenon of quantum discord

Even if the parameters determining a system's state are varied smoothly, the behavior of quantum correlations alike to quantum discord, and of its classical counterparts, can be very peculiar, with the appearance of non-analyticities in its rate of change. Here we review this sudden change phenomenon (SCP) discussing some important points related to it: Its uncovering, interpretations, and experimental verifications, its use in the context of the emergence of the pointer basis in a quantum measurement process, its appearance and universality under Markovian and non-Markovian dynamics, its theoretical and experimental investigation in some other physical scenarios, and the related phenomenon of double sudden change of trace distance discord. Several open questions are identified, and we envisage that in answering them we will gain significant further insight about the relation between the SCP and the symmetry-geometric aspects of the quantum state space.Comment: Lectures on General Quantum Correlations and their Applications, F. F. Fanchini, D. O. Soares Pinto, and G. Adesso (Eds.), Springer (2017), pp 309-33

Dynamical Mean-Field Theory

The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.Comment: Chapter in "Theoretical Methods for Strongly Correlated Systems", edited by A. Avella and F. Mancini, Springer (2011), 31 pages, 5 figure

Gene expression clines reveal local adaptation and associated trade-offs at a continental scale

Local adaptation, where fitness in one environment comes at a cost in another, should lead to spatial variation in trade-offs between life history traits and may be critical for population persistence. Recent studies have sought genomic signals of local adaptation, but often have been limited to laboratory populations representing two environmentally different locations of a species' distribution. We measured gene expression, as a proxy for fitness, in males of Drosophila subobscura, occupying a 20° latitudinal and 11 °C thermal range. Uniquely, we sampled six populations and studied both common garden and semi-natural responses to identify signals of local adaptation. We found contrasting patterns of investment: transcripts with expression positively correlated to latitude were enriched for metabolic processes, expressed across all tissues whereas negatively correlated transcripts were enriched for reproductive processes, expressed primarily in testes. When using only the end populations, to compare our results to previous studies, we found that locally adaptive patterns were obscured. While phenotypic trade-offs between metabolic and reproductive functions across widespread species are well-known, our results identify underlying genetic and tissue responses at a continental scale that may be responsible for this. This may contribute to understanding population persistence under environmental change

Experimental studies of e + e -→ some charmless processes containing K S0 at √s = 3.773 and 3.65 GeV

We measure the observed cross sections for the charmless processes e + e -→K S0 K - K - K + π ++ c.c., K S0 K - π + η+c.c., K S0 K - π + π + π - η+c.c., K S0 K - K - K + π + η+c.c., K S0 K - K - K + π + π 0+c.c., K S0 K - ρ ++c.c. and K S0 K - π + ρ 0+c.c. We also extract upper limits on the branching fractions for ψ(3770) decays into these final states at 90% C.L. Analyzed data samples correspond to 17.3 pb-1 and 6.5 pb-1 integrated luminosities registered, respectively, at √s = 3.773 and 3.65 GeV, with the BES-II detector at the BEPC collider. © 2009 Springer-Verlag / Società Italiana di Fisica.published_or_final_versionSpringer Open Choice, 21 Feb 201