The National Health Insurance, the decentralised clinical training platform, and specialist outreach

According to the Constitution of South Africa (SA), citizens living in remote areas are entitled to the same level of healthcare as those with access to tertiary hospitals. Specialist outreach has been shown to achieve this. When SA’s National Health Services Commission convened (1942 - 1944), Gluckman summarised: ‘Where the need is greatest the supply of hospitals is least.’ Primary healthcare (PHC) characterised the Kark’s Pholela Health Centre and was highly regarded. Although PHC underpins National Health Insurance (NHI) planning, both preventive and curative healthcare are needed. The KwaZulu-Natal (KZN) provincial Department of Health and the University of KZN College of Health Sciences’ 5-year plan for a decentralised clinical teaching platform (DCTP) is ambitious, requiring optimum co-operation between health department and university. Reservations can be addressed through sustained specialist outreach. Above all, the patient mustbe the chief beneficiary. The NHI and DCTP overlap with specialist outreach, but cannot do without it

The National Health Insurance, the decentralised clinical training platform, and specialist outreach

According to the Constitution of South Africa (SA), citizens living in remote areas are entitled to the same level of healthcare as those with access to tertiary hospitals. Specialist outreach has been shown to achieve this. When SA’s National Health Services Commission convened (1942 - 1944), Gluckman summarised: ‘Where the need is greatest the supply of hospitals is least.’ Primary healthcare (PHC) characterised the Kark’s Pholela Health Centre and was highly regarded. Although PHC underpins National Health Insurance (NHI) planning, both preventive and curative healthcare are needed. The KwaZulu-Natal (KZN) provincial Department of Health and the University of KZN College of Health Sciences’ 5-year plan for a decentralised clinical teaching platform (DCTP) is ambitious, requiring optimum co-operation between health department and university. Reservations can be addressed through sustained specialist outreach. Above all, the patient must be the chief beneficiary. The NHI and DCTP overlap with specialist outreach, but cannot do without it

Matchings on infinite graphs

Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting parameter via a local recursion defined directly on the limit of the graph sequence. Interestingly, the recursion may admit multiple solutions, implying non-trivial long-range dependencies between the covered vertices. We overcome this lack of correlation decay by introducing a perturbative parameter (temperature), which we let progressively go to zero. This allows us to uniquely identify the correct solution. In the important case where the graph limit is a unimodular Galton-Watson tree, the recursion simplifies into a distributional equation that can be solved explicitly, leading to a new asymptotic formula that considerably extends the well-known one by Karp and Sipser for Erd\"os-R\'enyi random graphs.Comment: 23 page

Random multi-index matching problems

The multi-index matching problem (MIMP) generalizes the well known matching problem by going from pairs to d-uplets. We use the cavity method from statistical physics to analyze its properties when the costs of the d-uplets are random. At low temperatures we find for d>2 a frozen glassy phase with vanishing entropy. We also investigate some properties of small samples by enumerating the lowest cost matchings to compare with our theoretical predictions.Comment: 22 pages, 16 figure

Flip dynamics in octagonal rhombus tiling sets

We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving 3 tiles which sample the tiling sets {\em via} Monte Carlo Markov chains. We determine the ergodic times of these dynamical systems (at infinite temperature): they grow with the system size $N_T$ like $Cst. N_T^2 \ln N_T$; these dynamics are rapidly mixing. We use an inherent symmetry of tiling sets and a powerful tool from probability theory, the coupling technique. We also point out the interesting occurrence of Gumbel distributions.Comment: 5 Revtex pages, 4 figures; definitive versio

Congenital adrenal hyperplasia due to 21-hydroxylase deficiency in South Africa

Background. Congenital adrenal hyperplasia (CAH) caused by deficiency of the 21-hydoxylase (21-OH) enzyme is the most common form of CAH worldwide.Objective. To evaluate the prevalence of CAH due to 21-OH deficiency, and its clinical presentation and biochemical profiles in affected children.Methods. We performed a retrospective subset analysis of 44 children with confirmed CAH.Results. All the children had classic CAH. The majority (59.8%) had classic salt-wasting (CSW) CAH and 40.1% had simple virilising (SV) CAH. The median age of presentation was 8.1 years (interquartile range (IQR) 4.5 - 11) in the SV group and 2 months (IQR 2 weeks - 5 months) in the CSW group (p=0.0001). No difference in age of presentation was noted between males and females (p=0.541). The clinical presentation was significantly different between the CSW and SV groups, and between males and females in the CSW group (p<0.0001). Most of the females with 46,XX CSW CAH (66.7%) presented with disorders of sex development (DSD), while the remaining 33.3% presented with DSD and dehydration and shock. All the males with 46,XY CSW CAH presented with dehydration and shock. Overall, 37.9% (11/29) of the children were obese or overweight at presentation. Gonadotrophin-releasing hormone-dependent central precocious puberty was observed on follow-up in 29.4% (10/34) of the children at a median of 6.7 years (IQR 5 - 7.7).Conclusion. The diagnosis of CAH is delayed in males and females in both SV and CSW forms of the disorder, which probably contributes to under-reporting of cases and a high mortality rate

Expected length of the longest common subsequence for large alphabets

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe

Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs

We show that the infinitesimal generator of the symmetric simple exclusion process, recast as a quantum spin-1/2 ferromagnetic Heisenberg model, can be solved by elementary techniques on the complete, complete bipartite, and related multipartite graphs. Some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models. The degeneracies of the eigenspectra are described in detail, and the Clebsch-Gordan machinery needed to deal with arbitrary spin-s representations of the SU(2) is briefly developed. We mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal.Comment: Final version as published, 19 pages, 4 figures, 40 references given in full forma

The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion

For independent nearest-neighbour bond percolation on Z^d with d >> 6, we prove that the incipient infinite cluster's two-point function and three-point function converge to those of integrated super-Brownian excursion (ISE) in the scaling limit. The proof is based on an extension of the new expansion for percolation derived in a previous paper, and involves treating the magnetic field as a complex variable. A special case of our result for the two-point function implies that the probability that the cluster of the origin consists of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic, and xr package