The epidemiology of traumatic brain injuries sustained by children under 10 years of age presenting to a tertiary hospital in Soweto, South Africa

Background. Traumatic brain injury (TBI) in the paediatric population is a significant contributor to death and disability worldwide. In sub-Saharan Africa, death and disability from TBI are still superseded by infectious disease. Mechanisms of injury differ by region and socioeconomics, but in general, falls, road traffic collisions (RTCs), being ‘struck by/against objects’ and non-accidental injuries (NAIs) are responsible for most cases.Objectives. To: (i) quantify the burden of TBI in terms of demographics, causes and severity; (ii) explore resource utilisation regarding length of stay, computed tomography (CT) brain scan use and multidisciplinary participation; (iii) interrogate possible temporal patterns of injury; and (iv) thus identify potential targets for community-based prevention strategies.Methods. In a 5-year retrospective review of all children aged <10 years admitted with TBI between September 2013 and August 2018, demographics, date of injury, mechanism of injury, severity of TBI based on the Glasgow Coma Scale, and requirement for a CT brain scan were collected for each patient. Outcomes were reported as discharge, transfer or death. Outcomes for children sustaining isolated TBI were compared with those for children sustaining TBI with polytrauma.Results. A total of 2 153 patients were included, with a mean (standard deviation) age of 4.6 (2.7) years and a male/female ratio of 1.7:1. RTCs were the most frequent cause of injury at 59% (80% of these were pedestrian-vehicle collisions), followed by falls at 24%. Mild TBIs accounted for 87% of admissions, moderate injuries for 6%, and severe injuries for 7%. Polytrauma was associated with increased severity of TBI. The cohort had a 2.3% mortality. NAIs accounted for 6% of injuries and carried a 4% mortality. The median (interquartile range) duration of hospitalisation was 1 (1 - 3) days, ranging from <24 hours to 132 days. CT scans were performed on 43% of admitted patients, and 48% of patients had consultations with another medical or allied medical discipline. Injuries were more frequent during the summer months and over weekends. Infants aged <1 year were identified as a group particularly vulnerable to injury, specifically NAI.Conclusions. Paediatric TBI was demonstrated to be a resource-intensive public health concern. From the results, we identified potential primary prevention targets that could perhaps be incorporated into broader community-based intervention programmes. We also identified a need to study long-term consequences of mild TBI further in our paediatric population

Knotting probabilities after a local strand passage in unknotted self-avoiding polygons

We investigate the knotting probability after a local strand passage is performed in an unknotted self-avoiding polygon on the simple cubic lattice. We assume that two polygon segments have already been brought close together for the purpose of performing a strand passage, and model this using Theta-SAPs, polygons that contain the pattern Theta at a fixed location. It is proved that the number of n-edge Theta-SAPs grows exponentially (with n) at the same rate as the total number of n-edge unknotted self-avoiding polygons, and that the same holds for subsets of n-edge Theta-SAPs that yield a specific after-strand-passage knot-type. Thus the probability of a given after-strand-passage knot-type does not grow (or decay) exponentially with n, and we conjecture that instead it approaches a knot-type dependent amplitude ratio lying strictly between 0 and 1. This is supported by critical exponent estimates obtained from a new maximum likelihood method for Theta-SAPs that are generated by a composite (aka multiple) Markov Chain Monte Carlo BFACF algorithm. We also give strong numerical evidence that the after-strand-passage knotting probability depends on the local structure around the strand passage site. Considering both the local structure and the crossing-sign at the strand passage site, we observe that the more "compact" the local structure, the less likely the after-strand-passage polygon is to be knotted. This trend is consistent with results from other strand-passage models, however, we are the first to note the influence of the crossing-sign information. Two measures of "compactness" are used: the size of a smallest polygon that contains the structure and the structure's "opening" angle. The opening angle definition is consistent with one that is measurable from single molecule DNA experiments.Comment: 31 pages, 12 figures, submitted to Journal of Physics

Rooted Spiral Trees on Hyper-cubical lattices

We study rooted spiral trees in 2,3 and 4 dimensions on a hyper cubical lattice using exact enumeration and Monte-Carlo techniques. On the square lattice, we also obtain exact lower bound of 1.93565 on the growth constant $\lambda$. Series expansions give $\theta=-1.3667\pm 0.001$ and $\nu = 1.3148\pm0.001$ on a square lattice. With Monte-Carlo simulations we get the estimates as $\theta=-1.364\pm0.01$, and $\nu = 1.312\pm0.01$. These results are numerical evidence against earlier proposed dimensional reduction by four in this problem. In dimensions higher than two, the spiral constraint can be implemented in two ways. In either case, our series expansion results do not support the proposed dimensional reduction.Comment: replaced with published versio

Knot localization in adsorbing polymer rings

We study by Monte Carlo simulations a model of knotted polymer ring adsorbing onto an impenetrable, attractive wall. The polymer is described by a self-avoiding polygon (SAP) on the cubic lattice. We find that the adsorption transition temperature, the crossover exponent $\phi$ and the metric exponent $\nu$, are the same as in the model where the topology of the ring is unrestricted. By measuring the average length of the knotted portion of the ring we are able to show that adsorbed knots are localized. This knot localization transition is triggered by the adsorption transition but is accompanied by a less sharp variation of the exponent related to the degree of localization. Indeed, for a whole interval below the adsorption transition, one can not exclude a contiuous variation with temperature of this exponent. Deep into the adsorbed phase we are able to verify that knot localization is strong and well described in terms of the flat knot model.Comment: 27 pages, 10 figures. Submitter to Phys. Rev.

Scaling prediction for self-avoiding polygons revisited

We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the bicritical point. We also consider the shape of the critical curve near the bicritical point, which describes the crossover to the branched polymer phase. Our recently conjectured expression for the scaling function of rooted self-avoiding polygons is further supported. For (unrooted) self-avoiding polygons, the analysis reveals the presence of an additional additive term with a new universal amplitude. We conjecture the exact value of this amplitude.Comment: 17 pages, 3 figure

Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer

The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang-Landau sampling method for integers up to 8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where p(n) is the number of solid partitions of the integer n. This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex

On the Dominance of Trivial Knots among SAPs on a Cubic Lattice

The knotting probability is defined by the probability with which an $N$-step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum models of the SAP as a function of $N$. In particular the characteristic length of the trivial knot that corresponds to a `half-life' of the knotting probability is estimated to be $2.5 \times 10^5$ on the cubic lattice.Comment: LaTeX2e, 21 pages, 8 figur

Area distribution of the planar random loop boundary

We numerically investigate the area statistics of the outer boundary of planar random loops, on the square and triangular lattices. Our Monte Carlo simulations suggest that the underlying limit distribution is the Airy distribution, which was recently found to appear also as area distribution in the model of self-avoiding loops.Comment: 10 pages, 2 figures. v2: minor changes, version as publishe

Task shifting and integration of HIV care into primary care in South Africa: The development and content of the streamlining tasks and roles to expand treatment and care for HIV (STRETCH) intervention

Background: Task shifting and the integration of human immunodeficiency virus (HIV) care into primary care services have been identified as possible strategies for improving access to antiretroviral treatment (ART). This paper describes the development and content of an intervention involving these two strategies, as part of the Streamlining Tasks and Roles to Expand Treatment and Care for HIV (STRETCH) pragmatic randomised controlled trial. Methods: Developing the intervention: The intervention was developed following discussions with senior management, clinicians, and clinic staff. These discussions revealed that the establishment of separate antiretroviral treatment services for HIV had resulted in problems in accessing care due to the large number of patients at ART clinics. The intervention developed therefore combined the shifting from doctors to nurses of prescriptions of antiretrovirals (ARVs) for uncomplicated patients and the stepwise integration of HIV care into primary care services. Results: Components of the intervention: The intervention consisted of regulatory changes, training, and guidelines to support nurse ART prescription, local management teams, an implementation toolkit, and a flexible, phased introduction. Nurse supervisors were equipped to train intervention clinic nurses in ART prescription using outreach education and an integrated primary care guideline. Management teams were set up and a STRETCH coordinator was appointed to oversee the implementation process. Discussion: Three important processes were used in developing and implementing this intervention: active participation of clinic staff and local and provincial management, educational outreach to train nurses in intervention sites, and an external facilitator to support all stages of the intervention rollout

Abundance of unknots in various models of polymer loops

A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of $N$ segments follows a decaying exponential form, $\sim \exp (-N/N_0)$, where $N_0$ marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of $N_0$ for a variety of polymer models. Among models examined, $N_0$ is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.Comment: 13 pages, 6 color figure