HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations

Explicit answer is given for the HOMFLY polynomial of the figure eight knot $4_1$ in arbitrary symmetric representation R=[p]. It generalizes the old answers for p=1 and 2 and the recently derived results for p=3,4, which are fully consistent with the Ooguri-Vafa conjecture. The answer can be considered as a quantization of the \sigma_R = \sigma_{[1]}^{|R|} identity for the "special" polynomials (they define the leading asymptotics of HOMFLY at q=1), and arises in a form, convenient for comparison with the representation of the Jones polynomials as sums of dilogarithm ratios. In particular, we construct a difference equation ("non-commutative A-polynomial") in the representation variable p. Simple symmetry transformation provides also a formula for arbitrary antisymmetric (fundamental) representation R=[1^p], which also passes some obvious checks. Also straightforward is a deformation from HOMFLY to superpolynomials. Further generalizations seem possible to arbitrary Young diagrams R, but these expressions are harder to test because of the lack of alternative results, even partial.Comment: 14 page

Rapidly measured indicators of recreational water quality and swimming-associated illness at marine beaches: a prospective cohort study

<p>Abstract</p> <p>Introduction</p> <p>In the United States and elsewhere, recreational water quality is monitored for fecal indicator bacteria to help prevent swimming-associated illnesses. Standard methods to measure these bacteria take at least 24 hours to obtain results. Molecular approaches such as quantitative polymerase chain reaction (qPCR) can estimate these bacteria faster, in under 3 hours. Previously, we demonstrated that measurements of the fecal indicator bacteria <it>Enterococcus </it>using qPCR were associated with gastrointestinal (GI) illness among swimmers at freshwater beaches. In this paper, we report on results from three marine beach sites.</p> <p>Methods</p> <p>We interviewed beach-goers and collected water samples at marine beaches affected by treated sewage discharges in Mississippi in 2005, and Rhode Island and Alabama in 2007. Ten to twelve days later, we obtained information about gastrointestinal, respiratory, eye, ear and skin symptoms by telephone. We tested water samples for fecal indicator organisms using qPCR and other methods.</p> <p>Results</p> <p>We enrolled 6,350 beach-goers. The occurrence of GI illness among swimmers was associated with a log₁₀-increase in exposure to qPCR-determined estimates of fecal indicator organisms in the genus <it>Enterococcus </it>(AOR = 2.6, 95% CI 1.3-5.1) and order <it>Bacteroidales </it>(AOR = 1.9, 95% CI 1.3-2.9). Estimates of organisms related to <it>Clostridium perfringens </it>and a subgroup of organisms in the genus <it>Bacteroides </it>were also determined by qPCR in 2007, as was F+ coliphage, but relationships between these indicators and illness were not statistically significant.</p> <p>Conclusions</p> <p>This study provides the first evidence of a relationship between gastrointestinal illness and estimates of fecal indicator organisms determined by qPCR at marine beaches.</p

Off-target effects of bacillus Calmette–Guérin vaccination on immune responses to SARS-CoV-2: implications for protection against severe COVID-19

Background and objectives: Because of its beneficial off-target effects against non-mycobacterial infectious diseases, bacillus Calmette–Guérin (BCG) vaccination might be an accessible early intervention to boost protection against novel pathogens. Multiple epidemiological studies and randomised controlled trials (RCTs) are investigating the protective effect of BCG against coronavirus disease 2019 (COVID-19). Using samples from participants in a placebo-controlled RCT aiming to determine whether BCG vaccination reduces the incidence and severity of COVID-19, we investigated the immunomodulatory effects of BCG on in vitro immune responses to SARS-CoV-2. Methods: This study used peripheral blood taken from participants in the multicentre RCT and BCG vaccination to reduce the impact of COVID-19 on healthcare workers (BRACE trial). The whole blood taken from BRACE trial participants was stimulated with γ-irradiated SARS-CoV-2-infected or mock-infected Vero cell supernatant. Cytokine responses were measured by multiplex cytokine analysis, and single-cell immunophenotyping was made by flow cytometry. Results: BCG vaccination, but not placebo vaccination, reduced SARS-CoV-2-induced secretion of cytokines known to be associated with severe COVID-19, including IL-6, TNF-α and IL-10. In addition, BCG vaccination promoted an effector memory phenotype in both CD4+ and CD8+ T cells, and an activation of eosinophils in response to SARS-CoV-2. Conclusions: The immunomodulatory signature of BCG’s off-target effects on SARS-CoV-2 is consistent with a protective immune response against severe COVID-19

The impact of surgical delay on resectability of colorectal cancer: An international prospective cohort study

Aim The SARS-CoV-2 pandemic has provided a unique opportunity to explore the impact of surgical delays on cancer resectability. This study aimed to compare resectability for colorectal cancer patients undergoing delayed versus non-delayed surgery. Methods This was an international prospective cohort study of consecutive colorectal cancer patients with a decision for curative surgery (January-April 2020). Surgical delay was defined as an operation taking place more than 4 weeks after treatment decision, in a patient who did not receive neoadjuvant therapy. A subgroup analysis explored the effects of delay in elective patients only. The impact of longer delays was explored in a sensitivity analysis. The primary outcome was complete resection, defined as curative resection with an R0 margin. Results Overall, 5453 patients from 304 hospitals in 47 countries were included, of whom 6.6% (358/5453) did not receive their planned operation. Of the 4304 operated patients without neoadjuvant therapy, 40.5% (1744/4304) were delayed beyond 4 weeks. Delayed patients were more likely to be older, men, more comorbid, have higher body mass index and have rectal cancer and early stage disease. Delayed patients had higher unadjusted rates of complete resection (93.7% vs. 91.9%, P = 0.032) and lower rates of emergency surgery (4.5% vs. 22.5%, P &lt; 0.001). After adjustment, delay was not associated with a lower rate of complete resection (OR 1.18, 95% CI 0.90-1.55, P = 0.224), which was consistent in elective patients only (OR 0.94, 95% CI 0.69-1.27, P = 0.672). Longer delays were not associated with poorer outcomes. Conclusion One in 15 colorectal cancer patients did not receive their planned operation during the first wave of COVID-19. Surgical delay did not appear to compromise resectability, raising the hypothesis that any reduction in long-term survival attributable to delays is likely to be due to micro-metastatic disease

Sol-gel synthesized lithium orthosilicate as a reusable solid catalyst for biodiesel production

© 2020 John Wiley & Sons Ltd Lithium orthosilicate (Li4SiO4) is a promising solid catalyst for biodiesel synthesis. However, Li4SiO4 is traditionally prepared by a solid-state reaction, which results in the unstable activity for the reaction. In the present study, Li4SiO4 was successfully prepared using a simple sol-gel method and employed as an efficient solid alkali catalyst for biodiesel synthesis. The molar ratio of precursors and calcination temperature were optimized for the synthesis of Li4SiO4 by using the sol-gel method. The physical and chemical properties were determined using X-ray diffraction, scanning electron microscopy, laser diffraction particle size, and thermogravimetric analysis. The as-prepared Li4SiO4 catalyst had much smaller particle size, pore volume, and pore size, but higher surface area and basicity than Li4SiO4 catalyst prepared by the solid-state reaction. It was then used to transesterify methanol and soybean oil into biodiesel. The effect of reaction factors (reaction time from 1 to 3 hours, catalyst concentration from 3 to 9%; molar ratio of methanol to oil from 6:1 to 18:1, and temperature from 55°C to 75°C) on the Li4SiO4-catalyzed transesterification was systematically examined. The highest biodiesel conversion of 91% was reached under the following conditions: reaction time of 2 hours, Li4SiO4 concentration of 6%, 12:1 methanol:oil molar ratio, and temperature of 65°C. Notably, Li4SiO4 could be efficiently reused for at least 10 times without significant loss of its activity; this suggests that the sol-gel synthesized Li4SiO4 is a potential solid alkali catalyst for biodiesel synthesis

J24335 exerts neuroprotective effects against 6-hydroxydopamine-induced lesions in PC12 cells and mice

202411 bcchVersion of RecordOthersScience and Technology Development Fund (FDCT) of Macau SAR; University of Macau; Shenzhen-Hong Kong-Macao Science and Technology Innovation Project of Shenzhen Science and Technology Innovation Committee; Science and Technology Foundation of Guizhou Province; National Natural Science Foundation of China; Science and Technology Foundation of Guizhou ProvincePublishedC