Minimal knotted polygons in cubic lattices

An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe

Paulus se liggaam-metafoor in 1 Korintiërs 12 in literêr-historiese konteks

Paul’s body metaphor in 1 Corinthians 12 in literary contextThe purpose of this article is to place and describe Paul’s use of the body metaphor in 1 Corinthians 12 in its literary context. By way of introduction, the importance of a proper understanding of Paul’s use of the body metaphor is indicated. The first part of the article deals with the origin and use of the body metaphor in ancient times, thereby establishing the literary context within which Paul used the metaphor. Greek, Roman and Jewish usage is described. In the second part of the article the focus moves to Paul’s use of the metaphor within its literary context. It is concluded that the body metaphor was well-known to Greek, Roman and Jewish readers, and was thus ideally suited to Paul’s unique communication of the relationship between Christ and his church

Fresh look at randomly branched polymers

We develop a new, dynamical field theory of isotropic randomly branched polymers, and we use this model in conjunction with the renormalization group (RG) to study several prominent problems in the physics of these polymers. Our model provides an alternative vantage point to understand the swollen phase via dimensional reduction. We reveal a hidden Becchi-Rouet-Stora (BRS) symmetry of the model that describes the collapse ($\theta$-)transition to compact polymer-conformations, and calculate the critical exponents to 2-loop order. It turns out that the long-standing 1-loop results for these exponents are not entirely correct. A runaway of the RG flow indicates that the so-called $\theta^\prime$-transition could be a fluctuation induced first order transition.Comment: 4 page

Tuberculosis infection control practices in a high-burden metro in South Africa : a perpetual bane for efficient primary health care service delivery

Background: Tuberculosis (TB) prevention, including infection control, is a key element in the strategy to end the global TB epidemic. While effective infection control requires all health system components to function well, this is an area that has not received sufficient attention in South Africa despite the availability of policy and guidelines. Aim: To describe the state of implementation of TB infection control measures in a high-burden metro in South Africa. Setting: The research was undertaken in a high TB-and HIV-burdened metropolitan area of South Africa. More specifically, the study sites were primary health care facilities (PHC), that among other services also diagnosed TB. Methods: A cross-sectional survey, focusing on the World Health Organization levels of infection control, which included structured interviews with nurses providing TB diagnosis and treatment services as well as observations, at all 41 PHC facilities in a high TB-burdened and HIV-burdened metro of South Africa. Results: Tuberculosis infection control was poorly implemented, with few facilities scoring 80% and above on compliance with infection control measures. Facility controls: 26 facilities (63.4%) had an infection control committee and 12 (29.3%) had a written infection control plan. Administrative controls: 26 facilities (63.4%) reported separating coughing and non-coughing patients, while observations revealed that only 11 facilities (26.8%) had separate waiting areas for (presumptive) TB patients. Environmental controls: most facilities used open windows for ventilation (n = 30; 73.2%); however, on the day of the visit, only 12 facilities (30.3%) had open windows in consulting rooms. Personal protective equipment: 9 facilities (22%) did not have any disposable respirators in stock and only 9 respondents (22%) had undergone fit testing. The most frequently reported barrier to implementing good TB infection control practices was lack of equipment (n = 22; 40%) such as masks and disposable respirators, as well as the structure or layout of the PHC facilities. The main recommendation to improve TB infection control was education for patients and health care workers (n = 18; 33.3%). Conclusion: All levels of the health care system should be engaged to address TB prevention and infection control in PHC facilities. Improved infection control will address the nosocomial spread of TB in health facilities and keep health care workers and patients safe from infection

Resources and infrastructure for the delivery of antiretroviral therapy at primary health

There are concerns as to whether South Africa\'s public health system has sufficient resources, human and otherwise, to ensure universal access to antiretroviral treatment (ART). We report on public sector implementation of the Comprehensive Care Management and Treatment (CCMT) programme in the Free State Province, South Africa, in particular whether the primary health care (PHC) infrastructure was able to mobilise the necessary inputs to effectively provide ART, without undermining other services within facilities. A longitudinal study was conducted of the first 16 PHC facilities accredited to provide ART in the province. The facilities were visited on three occasions over 2 years, involving both structured and open-ended interviews with professional and lay staff, and observations of available resources. The resources assessed were staffing, space, essential equipment, drug supplies and laboratory systems. Approximately one-fifth (20%) of professional nurses were allocated to the CCMT programme in the facilities, although the overall number of professional nurses increased by only 14%. This process resulted in some displacement of professional nurses towards the CCMT Programme away from other services in the facilities. However, this could have been partially compensated for by task shifting towards community health workers and the appointment of additional support staff. Staff were largely positive about the programme. Drug supplies, availability of equipment and laboratory systems, although good at the baseline, improved further over the period of observation. The lack of adequate space to accommodate the new programme was a frequently reported problem. Overall, our assessment is that the PHC infrastructure in the Free State\'s public health system is capable of implementing and benefiting from the CCMT programme. Nevertheless, constraints in the availability of professional staff threaten future implementation of both the CCMT and other PHC programmes. Keywords: Resources, infrastructure, antiretroviral therapy, primary health care facilities.SAHARA-J Vol. 5 (3) 2008: pp.106-11

Partially directed paths in a wedge

The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$. The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.Comment: 26 pages, 5 figures. Submitted to JCT

Forcing Adsorption of a Tethered Polymer by Pulling

We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a second-order thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a non-zero vertical component this transition becomes first-order. Strikingly, we find that if the angle between the pulling force and the surface is beneath a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for small temperature, which has been observed previously for this model in the presence of pure vertical pulling. Interestingly, the reentrance phenomenon vanishes under certain pulling angles, with details depending on how the three-dimensional polymer is modeled

A qualitative exploration of resilience in pre-adolescent AIDS orphans living in a residential care facility

This article presents the findings of a study among a small group of South African AIDS orphans living in a residential care facility, Lebone Land. The research was conducted between June and September 2006. A qualitative, exploratory study consisting of in-depth, semistructured interviews with eight children and seven key informants aimed to identify and investigate developmental assets operating in the children’s lives to help them cope amid exposure to adversities. The findings indicate that the  developmental assets that facilitate coping and foster resilience in these children relate to four main components: external stressors and challenges, external supports, inner strengths and interpersonal and problem-solving skills. Emerging key themes relate to the experience of illness, death, poverty and violence, as well as the important roles of morality, social values, resistance skills, religion and faith in assisting these children in defining their purpose in life. To this end, constructive use of time, commitment to learning, goal-setting, problem-solving ability and self-efficacy are fundamental in the children’s attainment of their future projections. Therefore, qualities such as optimism, perseverance and hope seem to permeate the children’s process of recovery. Strong networks of support, particularly friendships with other children, also seemto contribute to developing and sustaining resilience

Rare event sampling with stochastic growth algorithms

We discuss uniform sampling algorithms that are based on stochastic growth methods, using sampling of extreme configurations of polymers in simple lattice models as a motivation. We shall show how a series of clever enhancements to a fifty-odd year old algorithm, the Rosenbluth method, led to a cutting-edge algorithm capable of uniform sampling of equilibrium statistical mechanical systems of polymers in situations where competing algorithms failed to perform well. Examples range from collapsed homo-polymers near sticky surfaces to models of protein folding.Comment: First International Conference on Numerical Physic

Management of anterior vaginal prolapse in South Africa : national survey

LetterThe original publication is available at http://www.samj.org.zaTo the Editor: A national survey was done on the management of anterior vaginal prolapse (AVP) by registered gynaecologists and urologists in South Africa. Of 822 questionnaires posted, 30.2% were returned completed (23.2% from gynaecologists and 7.0% from urologists). The information supplied was anonymous and is probably a true reflection of current practice. Of concern were the 36.3% of respondents who did not use a recognised staging system, a low rate of pre-operative urodynamic investigation by gynaecologists (8.4%) and a high rate of synthetic mesh use by urologists (75.9%), even for primary procedures. This first survey among South African prolapse surgeons provides valuable insight into clinical practice.Publishers’ versio