Knot theory and matrix integrals

The large size limit of matrix integrals with quartic potential may be used to count alternating links and tangles. The removal of redundancies amounts to renormalizations of the potential. This extends into two directions: higher genus and the counting of "virtual" links and tangles; and the counting of "coloured" alternating links and tangles. We discuss the asymptotic behavior of the number of tangles as the number of crossings goes to infinity.Comment: chapter of the book Random Matrix Theory, Eds Akemann, Baik and Di Francesc

Determinant Formulae for some Tiling Problems and Application to Fully Packed Loops

We present determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration

Constraining Big Bang lithium production with recent solar neutrino data

The 3He({\alpha},{\gamma})7Be reaction affects not only the production of 7Li in Big Bang nucleosynthesis, but also the fluxes of 7Be and 8B neutrinos from the Sun. This double role is exploited here to constrain the former by the latter. A number of recent experiments on 3He({\alpha},{\gamma})7Be provide precise cross section data at E = 0.5-1.0 MeV center-of-mass energy. However, there is a scarcity of precise data at Big Bang energies, 0.1-0.5 MeV, and below. This problem can be alleviated, based on precisely calibrated 7Be and 8B neutrino fluxes from the Sun that are now available, assuming the neutrino flavour oscillation framework to be correct. These fluxes and the standard solar model are used here to determine the 3He(alpha,gamma)7Be astrophysical S-factor at the solar Gamow peak, S(23+6-5 keV) = 0.548+/-0.054 keVb. This new data point is then included in a re-evaluation of the 3He({\alpha},{\gamma})7Be S-factor at Big Bang energies, following an approach recently developed for this reaction in the context of solar fusion studies. The re-evaluated S-factor curve is then used to re-determine the 3He({\alpha},{\gamma})7Be thermonuclear reaction rate at Big Bang energies. The predicted primordial lithium abundance is 7Li/H = 5.0e-10, far higher than the Spite plateau.Comment: Final accepted version, some typos corrected, in the press at Phys. Rev.

A Bijection between classes of Fully Packed Loops and Plane Partitions

It has recently been observed empirically that the number of FPL configurations with 3 sets of a, b and c nested arches equals the number of plane partitions in a box of size a x b x c. In this note, this result is proved by constructing explicitly the bijection between these FPL and plane partitions

Diabetes and kidney cancer: A direct or indirect association?

A positive association between diabetes and kidney cancer has been reported in several investigations, but it is unclear whether diabetes or its complications account for this association. Recent advances in estimating direct associations may be useful for elucidating the association between diabetes and kidney cancer. Therefore, we performed a case-control analysis to evaluate whether the direct association between diabetes and kidney cancer is the primary concern in this exposure-outcome relation. Discharge data (with International Classification of Diseases – 9 codes) from 2001 for hospitals throughout Florida were used to construct a case-control population of inpatients aged ≥45 years. Cases (n=1,909) were inpatients with malignant kidney cancer and controls (n=6,451) were inpatients with motor vehicle injuries. Diabetes status was ascertained for cases and controls. Covariates that required adjustment to estimate the total (age, gender, ethnicity, obesity, and smoking) and direct (age, gender, ethnicity, obesity, smoking, hypertension, and kidney disease) associations were identified in a directed acyclic graph. Binary logistic regression was used to estimate the adjusted total and direct odds ratios (ORs) and corresponding 95% confidence intervals (CIs) of kidney cancer for diabetics. The odds of kidney cancer were higher for inpatients with diabetes than inpatients without diabetes when estimating the total association (OR=1.27, 95%CI: 1.10, 1.47) but attenuated when estimating the direct association (OR=1.08, 95%CI: 0.93, 1.25). Our findings provide preliminary insight that the direct association between diabetes and kidney cancer may not be the primary concern in this exposure-outcome relation; indirect pathways (i.e. diabetic complications) may have greater influence on this relation. A similar analysis using longitudinal data with appropriately measured covariates may provide more definitive conclusions and could have implications for kidney cancer prevention among diabetics

Ideal and reality: do countries adopt and follow recommended procedures in comprehensive multiyear planning guidelines for national immunization programmes?

BACKGROUND: Meticulous steps and procedures are proposed in planning guidelines for the development of comprehensive multiyear plans for national immunization programmes. However, we know very little about whether the real-life experience of those who adopt these guidelines involves following these procedures as expected. Are these steps and procedures followed in practice? We examined the adoption and usage of the guidelines in planning national immunization programmes and assessed whether the recommendations in these guidelines are applied as consistently as intended. METHODS: We gathered information from the national comprehensive multiyear plans developed by 77 low-income countries. For each of the 11 components, we examined how each country applied the four recommended steps of situation analysis, problem prioritization, selection of interventions, and selection of indicators. We then conducted an analysis to determine the patterns of alignment of the comprehensive multiyear plans with those four recommended planning steps. RESULTS: Within the first 3 years following publication of the guidelines, 66 (86%) countries used the tool to develop their comprehensive multiyear plans. The funding conditions attached to the use of these guidelines appeared to influence their rapid adoption and usage. Overall, only 33 (43%) countries fully applied all four recommended planning steps of the guidelines. CONCLUSIONS: Adoption and usage of the guidelines for the development of comprehensive multiyear plans for national immunization programmes were rapid. However, our findings show substantial variation between the proposed planning ideals set out in the guidelines and actual use in practice. A better understanding of factors that influence how recommendations in public health guidelines are applied in practice could contribute to improvements in guidelines design. It could also help adjust strategies used to introduce them into public health programmes, with the ultimate goal of a greater health impact