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

Jin-Gu-Lian Capsule Did Not Significantly Improve Clinical Value in Rheumatoid Arthritis Therapy: A Real-World Study

Yong Chen,1 Mang He,1 Si-Jin Zhao,2 Yan-Juan Chen,1 Yong-Qiao Zhang,2 Xiao-Long Chen,2 Chuan-Jie Yang,2 Yu-Zhuo Luo,2 Kutty Selva Nandakumar,3 Zhou-Xiong Xing,4 Mei Tian1 1Department of Rheumatology and Immunology, Affiliated Hospital of Zunyi Medical University, Zunyi, Guizhou, People’s Republic of China; 2Undergraduate Students of Zunyi Medical University, Zunyi, Guizhou, People’s Republic of China; 3Docent, Department of Medical Biochemistry and Biophysics, Karolinska Institute, Stockholm, Sweden; 4Department of Critical Care Medicine, Affiliated Hospital of Zunyi Medical University, Zunyi, Guizhou, People’s Republic of ChinaCorrespondence: Mei Tian; Zhou-Xiong Xing, Affiliated Hospital of Zunyi Medical University, 149 Dalian Road, Huichuan District, Zunyi City, Guizhou Province, People’s Republic of China, Email [email protected]; [email protected]: To investigate the clinical value of adding Jin-gu-lian (JGL) capsules into rheumatoid arthritis (RA) treatment by examining its impact on disease activity and quality of life (QoL) through a real-world study (RWS).Patients and methods: RWS was conducted to compare the inflammatory markers, including IgM-RF, ESR, and CRP, between RA patients treated with only Western medicine (reference group) and Western medicine plus JGL (study group) during one-year follow-up. The clinical data was acquired from the hospital information system (HIS). Telephone call-based follow-up on QoL (SF-36) and accompanying symptoms, including gastrointestinal complaints, attacks of pneumonia, herpes zoster, URTIs, UTIs, and LTBIs. Finally, the anti-rheumatic drugs given to both groups were also compared. RWS was further validated for its feasibility by performing studies with hydroxychloroquine (HCQ) treatment, which is a commonly used anti-rheumatic drug for RA with mild effect.Results: The study group failed to show a significant effect on inflammatory markers, especially on the CRP levels, indicating no additional clinical value of supplementing with JGL. Similarly, at the endpoint, no significant differences between the two groups on QoL and related symptoms were observed. Our study suggests that the patients in the study group might need more anti-rheumatic drugs to fill the treatment insufficiency, and the application ratio of NSAIDs would be significantly higher than the reference group. By conducting this study on HCQ treatment, the positive aspects of controlling disease activity and reducing NSAIDs application were found, which demonstrates the utility of performing the RWS to evaluate the effect of JGL.Conclusion: Adding JGL did not significantly improve the clinical efficacy of RA treatment by this RWS. Folk herbal prescriptions such as JGL are suggested to underwent strict clinical trials before application.Keywords: real-world study, rheumatoid arthritis, traditional Chinese medicine, disease activity, hydroxychloroquin