Shapes of hyperbolic triangles and once-punctured torus groups

Let $\Delta$ be a hyperbolic triangle with a fixed area $\varphi$. We prove that for all but countably many $\varphi$, generic choices of $\Delta$ have the property that the group generated by the $\pi$--rotations about the midpoints of the sides of the triangle admits no nontrivial relations. By contrast, we show for all $\varphi\in(0,\pi)\setminus\mathbb{Q}\pi$, a dense set of triangles does afford nontrivial relations, which in the generic case map to hyperbolic translations. To establish this fact, we study the deformation space $\mathfrak{C}_\theta$ of singular hyperbolic metrics on a torus with a single cone point of angle $\theta=2(\pi-\varphi)$, and answer an analogous question for the holonomy map $\rho_\xi$ of such a hyperbolic structure $\xi$. In an appendix by X.~Gao, concrete examples of $\theta$ and $\xi\in\mathfrak{C}_\theta$ are given where the image of each $\rho_\xi$ is finitely presented, non-free and torsion-free; in fact, those images will be isomorphic to the fundamental groups of closed hyperbolic 3--manifolds.Comment: 32 pages. To appear in Math.

The disposition and pharmacokinetics of Dioscorea nipponica Makino extract in rats

This study was aimed to investigate the disposition and pharmacokinetics of the total saponins of dioscorea (TSD) in rats. Male Sprague-Dawley rats were orally administrated with 3H labeled TSD at a single dose ratio of 80 mg TSD per 1 kg rat. Blood samples and feces were collected at different time points to measure the level of TSD activity. At the final time point, determination of the disposition of TSD in lung, kidney, heart, liver, adrenal, and small intestine were performed. From the blood samples' emission of radioactivity, pharmacokinetic parameters were derived as T1/2 = 33.33 ± 4.48 h, T max = 6.5 ± 0.71 h, AUC = 119400 ± 421097.67, and C max = 2643.33 ± 192.26 dpm/ml. There was 51.609% of 3H labeled substance excreted in 24 h. These results suggested that blood concentration of 3H-TSD was extremely low and the majority of TSD was excreted in the feces. The TSD was extensively distributed to multitissues. The radioactivity level was measured to be the highest in the liver, adrenal gland, and wall of the gastrointestinal tract. The radioactivity of TSD was still being detected in blood after 96 h. This showed TSD was excreted in vivo very slowly. © 2008 Academic Journals.published_or_final_versio

The importance of early arthroscopy in athletes with painful cartilage lesions of the ankle: a prospective study of 61 consecutive cases

BACKGROUND Ankle sprains are common in sports and can sometimes result in a persistent pain condition. PURPOSE Primarily to evaluate clinical symptoms, signs, diagnostics and outcomes of surgery for symptomatic chondral injuries of the talo crural joint in athletes. Secondly, in applicable cases, to evaluate the accuracy of MRI in detecting these injuries. Type of study: Prospective consecutive series. METHODS Over around 4 years we studied 61 consecutive athletes with symptomatic chondral lesions to the talocrural joint causing persistent exertion ankle pain. RESULTS 43% were professional full time athletes and 67% were semi-professional, elite or amateur athletes, main sports being soccer (49%) and rugby (14%). The main subjective complaint was exertion ankle pain (93%). Effusion (75%) and joint line tenderness on palpation (92%) were the most common clinical findings. The duration from injury to arthroscopy for 58/61 cases was 7 months (5.7–7.9). 3/61 cases were referred within 3 weeks from injury. There were in total 75 cartilage lesions. Of these, 52 were located on the Talus dome, 17 on the medial malleolus and 6 on the Tibia plafond. Of the Talus dome injuries 18 were anteromedial, 14 anterolateral, 9 posteromedial, 3 posterolateral and 8 affecting mid talus. 50% were grade 4 lesions, 13.3% grade 3, 16.7% grade 2 and 20% grade 1. MRI had been performed pre operatively in 26/61 (39%) and 59% of these had been interpreted as normal. Detection rate of cartilage lesions was only 19%, but subchondral oedema was present in 55%. At clinical follow up average 24 months after surgery (10–48 months), 73% were playing at pre-injury level. The average return to that level of sports after surgery was 16 weeks (3–32 weeks). However 43% still suffered minor symptoms. CONCLUSION Arthroscopy should be considered early when an athlete presents with exertion ankle pain, effusion and joint line tenderness on palpation after a previous sprain. Conventional MRI is not reliable for detecting isolated cartilage lesions, but the presence of subchondral oedema should raise such suspicion

Microtubules gate tau condensation to spatially regulate microtubule functions.

Tau is an abundant microtubule-associated protein in neurons. Tau aggregation into insoluble fibrils is a hallmark of Alzheimer's disease and other types of dementia1, yet the physiological state of tau molecules within cells remains unclear. Using single-molecule imaging, we directly observe that the microtubule lattice regulates reversible tau self-association, leading to localized, dynamic condensation of tau molecules on the microtubule surface. Tau condensates form selectively permissible barriers, spatially regulating the activity of microtubule-severing enzymes and the movement of molecular motors through their boundaries. We propose that reversible self-association of tau molecules, gated by the microtubule lattice, is an important mechanism of the biological functions of tau, and that oligomerization of tau is a common property shared between the physiological and disease-associated forms of the molecule

The nature of localization in graphene under quantum Hall conditions

Particle localization is an essential ingredient in quantum Hall physics [1,2]. In conventional high mobility two-dimensional electron systems Coulomb interactions were shown to compete with disorder and to play a central role in particle localization [3]. Here we address the nature of localization in graphene where the carrier mobility, quantifying the disorder, is two to four orders of magnitude smaller [4,5,6,7,8,9,10]. We image the electronic density of states and the localized state spectrum of a graphene flake in the quantum Hall regime with a scanning single electron transistor [11]. Our microscopic approach provides direct insight into the nature of localization. Surprisingly, despite strong disorder, our findings indicate that localization in graphene is not dominated by single particle physics, but rather by a competition between the underlying disorder potential and the repulsive Coulomb interaction responsible for screening.Comment: 18 pages, including 5 figure

Turnip mosaic potyvirus probably first spread to Eurasian brassica crops from wild orchids about 1000 years ago

Turnip mosaic potyvirus (TuMV) is probably the most widespread and damaging virus that infects cultivated brassicas worldwide. Previous work has indicated that the virus originated in western Eurasia, with all of its closest relatives being viruses of monocotyledonous plants. Here we report that we have identified a sister lineage of TuMV-like potyviruses (TuMV-OM) from European orchids. The isolates of TuMV-OM form a monophyletic sister lineage to the brassica-infecting TuMVs (TuMV-BIs), and are nested within a clade of monocotyledon-infecting viruses. Extensive host-range tests showed that all of the TuMV-OMs are biologically similar to, but distinct from, TuMV-BIs and do not readily infect brassicas. We conclude that it is more likely that TuMV evolved from a TuMV-OM-like ancestor than the reverse. We did Bayesian coalescent analyses using a combination of novel and published sequence data from four TuMV genes [helper component-proteinase protein (HC-Pro), protein 3(P3), nuclear inclusion b protein (NIb), and coat protein (CP)]. Three genes (HC-Pro, P3, and NIb), but not the CP gene, gave results indicating that the TuMV-BI viruses diverged from TuMV-OMs around 1000 years ago. Only 150 years later, the four lineages of the present global population of TuMV-BIs diverged from one another. These dates are congruent with historical records of the spread of agriculture in Western Europe. From about 1200 years ago, there was a warming of the climate, and agriculture and the human population of the region greatly increased. Farming replaced woodlands, fostering viruses and aphid vectors that could invade the crops, which included several brassica cultivars and weeds. Later, starting 500 years ago, inter-continental maritime trade probably spread the TuMV-BIs to the remainder of the world

The Mediating Role of Resilience and Self-Esteem Between Life Events and Coping Styles Among Rural Left-Behind Adolescents in China: A Cross-Sectional Study

Objective: This study aims to explore the association between life events and coping styles, and how resilience and self-esteem mediate the association.Methods: A cross-sectional study was conducted among 981 left-behind adolescents (LBAs) in five junior high schools in Hunan Province, China, from April 13 to April 20, 2020. We utilized self-designed sociodemographic questionnaire, Adolescent Self-Rating Life Events Checklist, Resilience Scale Chinese Adolescent, Rosenberg Self-Esteem Scale, and Simplified Coping Style Questionnaire to assess the mental health of LBAs. Statistic description, Pearson correlation analysis, and structural equation model were adopted to analyze the data.Results: Results revealed that life events could negatively predict resilience (beta = -0.29, P < 0.001) and self-esteem (beta = -0.39, P < 0.001) and positively predict LBAs' positive coping style (beta = 0.28, P < 0.001) and negative coping style (beta = 0.21, P < 0.001). Self-esteem could also positively predict the resilience of LBAs (beta = 0.62, P < 0.001); resilience could negatively predict the negative coping style (beta = -0.21, P < 0.001) and positively predict the positive coping style (beta = 0.79, P < 0.001). Life events not only have direct effects on negative coping style (beta = 0.21) and positive coping style (beta = 0.28) but also have indirect effects on coping styles by affecting resilience (beta = -0.29) and self-esteem (beta = -0.39). The total effect of life events on coping styles was 0.32, where 34.37% was mediated by resilience and self-esteem.Conclusion: We proved that resilience and self-esteem mediated most of the effects of life events on coping styles. The findings had important implications for interventions to promote mental health of LBAs, particularly the enhancement of resilience and self-esteem