An Integrability Condition for Simple Lie Groups II

It is shown that a simple Lie group $G$ ($\neq {\rm SL}_2$) can be locally characterised by an integrability condition on an $\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where $\operatorname{Aut}(\mathfrak{g})$ is the automorphism group of the Lie algebra of $G$. The integrability condition is the vanishing of a torsion tensor of type $(1,2)$. This is a slight improvement of an earlier result proved in [Min-Oo M., Ruh E.A., in Differential Geometry and Complex Analysis, Springer, Berlin, 1985, 205-211]

Interacting two-state Markov chains on undirected networks

It is shown that irreducible two-state continuous-time Markov chains interacting on a network in a bilinear fashion have a unique stable steady state. The proof is elementary and uses the relative entropy function.Comment: 9 pages; minor typos correcte

Cohomogeneity One Special Lagrangian Submanifolds in the Deformed Conifold

In this paper we describe the cohomogeneity one special Lagrangian 3-folds in the cotangent bundle of the 3-sphere, also known in the physics literature as a deformed conifold. Our main result gives a global foliation of the deformed conifold by T^2-invariant special Lagrangian 3-folds, where the generic leaf is topologically T^2 X R. In the limit, these special Lagrangians asymptotically approach a special Lagrangian cone on a torus in the conifold. Using moment map techniques we also recover the family of SO(n)-invariant special Lagrangian n-folds in the cotangent bundle of the n-sphere obtained by H. Anciaux.Comment: 22 pages, 2 figure

Bundle Constructions of Calibrated Submanifolds in R^7 and R^8

We construct calibrated submanifolds of R^7 and R^8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R^4. We construct examples of associative and coassociative submanifolds of R^7 and of Cayley submanifolds of R^8. This construction is a generalization of the Harvey-Lawson bundle construction of special Lagrangian submanifolds of R^{2n}.Comment: 22 pages; for Revised Version: Minor changes, improved notation, streamlined expositio

Determinants of SMEs' Performance: The Case of Kyaing Tong, Eastern Shan State, Myanmar.

This research aims to investigate the correlation between entrepreneurial competencies, external factors, firm characteristics, location, market orientation and the performance of SMEs in the Kyaing Tong area, Myanmar. The target population is SME owners from that area who run their firms with less than 50 workers. 331 participants returned completed and usable questionnaires. A Pearson Correlation Coefficient analysis tool was employed to test the hypotheses. In this study, the researcher has found supports for most of the research hypotheses. The results indicate that organizing competencies, strategic competencies, commitment competencies, external factors, nature of firm, firm knowledge, location, customer orientation, competitor orientation, and inter-functional orientation play have a positive impact on the performance of these SMEs. No association, however, was found between opportunity competencies, relationship competencies, conceptual competencies, and size of firm and SMEs’ performances

Development and Characterization of Tool Compounds Targeting the Runt Domain’s interaction With Cbfβ

RUNX1 and CBFβ, which encode subunits of the core binding factor, are frequent targets of chromosomal aberrations in hematological malignancies. We previously determined that CBFβ (encoded by CBFB) is important for the transforming activity of the chimeric protein AML1-ETO protein (RUNX1-RUNX1T1) generated by the t(8;21), and other studies showed that normal Runx1 functions are essential for survival and maintenance of some leukemias lacking RUNX1 or CBFB mutations. Thus, we hypothesized that we could achieve therapeutic efficacy in multiple leukemias by targeting the Runx1:CBFβinteraction with small molecules. Using the structural information of the DNA binding Runt domain (RD) of Runx1 and its interface with CBFβ, we employed a computational screen for a library of 78,000 drug-like compounds, and further optimized our leads. The Runt domain inhibitors (RDIs) bind directly to the RD and disrupt its interaction with CBFβ. We showed that the RDIs reduced growth and induced apoptosis of t(8;21) acute myeloid leukemia (AML) cell lines, and reduced the progenitor activity of mouse and human leukemia cells harboring the t(8;21), but not normal bone marrow cells. The RDIs had similar effects on murine and human T cell acute lymphocytic leukemia (T-ALL) cell lines that did not harbor the t(8;21). Furthermore, our inclusion of a structurally related and weakly active compound as a control strongly support that the efficacies we observed were due to on target inhibition of RUNX functions. Our results confirmed that the RDIs might prove efficacious in various AMLs, and that a therapeutic window is available to specifically target malignant cells. We developed a pro-drug AI-9-59 with improved solubility and pharmacokinetic properties and assessed whether it has any in vivo efficacies in mouse leukemia models. Our results showed that the pro-drug was toxic to mice at dosage above 50 mg/kg and had no observable growth inhibitory effect on leukemia cells, suggesting that the concentration of the pro-drug necessary to inhibit endogenous core binding factor activity exceeds the maximum tolerated dose in mice. However, the expansion of granulocyte macrophage progenitors, and the gastrointestinal toxicity phenotype we observed suggested that the effects could be from on-target repression of RUNX proteins functions

A Systematic Review on the Effectiveness of Different Functional Treatments for Acute Ankle Sprains

Background: An ankle sprain is a very common sport-related injury and can reduce participation in sports and employment. It can also create further complications in the function of the joint. Purpose: To evaluate the effectiveness of different functional treatments and to ascertain which functional treatment is the most effective method for acute ankle sprains. Study Design: Systematic review. Methods: The design of this systematic review was developed in accordance with PRISMA-P 2015 statement and performed according to its guidelines. A computerized literature search was performed from PubMed Central, MEDLINE via OVID and Cochrane library. Randomized controlled trials or quasi-experimental studies, published within a ten-year period (2007 to 2017), in peer-reviewed journals, with full-text articles and written in English were included in this study. Any type of functional treatments being applied to treat acute ankle sprains were considered as an intervention and only adult participants were included in this review. Surgical methods, unpublished trials, not written in the English language or not experimental research were excluded. Results: From the pooled data of this review, the stocking was more effective at improving pain, swelling, functional outcomes, range of motion, and return to sport/work, and had higher patient satisfaction than the bandage. There was no evidence that the taping and lace-up brace were more effective than other functional interventions in the treatment of acute ankle sprains. Furthermore, the prevalence of complications was greatest for the taping and lace-up brace interventions. The semi-rigid or posterior rigid support group had a better functional recovery and higher patient satisfaction, but some complications were present. Conclusion: The semi-rigid or posterior rigid support group and stocking were the most effective functional interventions for acute ankle sprain treatment. What is known about this subject: The functional treatments are becoming popular due to being effective, inexpensive and simplistic to apply. Different types of functional interventions have been used according to the choice of clinicians and patients in the treatment of ankle sprains. According to the previous researches, semi-rigid support, ankle braces, bandage and lace-up supports have greater advantages than other functional treatments from different perspectives (Example. the elastic bandage had a slower recovery rate than semi-rigid brace but less complications than taping, the lace-up support was better in swelling management than other functional treatments). What this study adds to existing knowledge: This study found that the stocking is an effective treatment for managing acute ankle sprains. It is valuable for the patient because the cost of the stocking is considerably cheaper than other functional treatments and it is very easy to wear. Some popular functional treatments like lace-up support; taping and semi-rigid braces were shown to have some complications