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

The Compressibility of Minimal Lattice Knots

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our results show that the compressibility is generally not monotonic, but in some cases increases with pressure. Differences of the compressibility for different knot types show that topology is a factor determining the compressibility of a lattice knot, and differences between the three lattices show that compressibility is also a function of geometry.Comment: Submitted to J. Stat. Mec

The amalgamation of mechanical, electrical and software technology to remove manual tasks performed in a vehicle rental business

Published ArticleMost operational businesses today are restricted to normal business hours, as it is not cost effective for a business to operate on a 24-hour basis. Not only will operational costs increase substantially, in addition to these increases, the company will be faced with numerous challenges that range from security to staffing. Over the years, technology has proven to be an asset in which businesses could invest and enjoy the rewards of their investment in the form of an increase in employee efficiency, ease of new procedural implementations and the enforcement of governance. This process of continuous refinement has resulted in business systems developing to a point where the input required from an employee has been limited to the bare minimum. With the flexibility, dependability and affordability of technology today any operational business can reduce the need for human input into their systems. This article discusses the techniques employed by the researcher to stratify the hypothesis that the amalgamating of mechanical, electrical and software technologies will remove manual tasks performed by staff in a vehicle rental business

Corticosteroids in sports-related injuries: Friend or Foe

Corticosteroids act as potent anti-inflammatory drugs and have been used in various sport settings for the treatment of both acute and chronic injuries. Basic physiology and mechanisms of action for gluco- and mineralocorticoids are discussed. Methods of administration, the action on the inflammatory response, and potential short and long-term side effects of corticosteroid use are also deliberated. More specifically, corticosteroid use in the treatment and management of sport-related injuries are discussed, elucidating on the ethical boundaries and anti-doping regulations pertaining to corticosteroid use in sports, as well as putting forth suggestions for the use of local steroid injections and their contraindications. In conclusion, it was found that, despite some controversy in the use of corticosteroid treatment in the sports environment, little empirical evidence exists that could conclusively rule for or against its use. It is however clear that, if clinically justified, there is a significant role for corticosteroid treatment in the realm of sports injury and notably with a relatively low risk profile, if administered correctly.Keywords: Steroid hormones, athlete, sports, injury, inflammation

The inadequacy of the Social Grant System available to children in South Africa

The purpose of this article is to examine the current social assistance grant system available to children in South Africa and to indicate its major shortcomings. The new Children’s Bill and Social Assistance Bill, soon to be enacted, will also be examined to establish whether there are any positive changes with regard to the socio-economic situation of children. Proposals made by the South African Law Commission, South African Human Rights Commission, Committee of Inquiry into a Comprehensive System of Social Security for South Africa, the United Nations Committee on the Rights of the Child and several other interested parties will also be considered to establish whether in fact government is in compliance with its constitutional and international duty towards realising the social security and social assistance rights of children. It is submitted that the exclusion of children of the ages of (currently) 11 to 18 from the child support grant infringes on their  constitutional rights to social assistance, human dignity, life and equality. Another problem with the current grants is the unavailability thereof to households where an adult caregiver is absent as well as the complicated means test. The unavailability of these grants to children of refugees is also a cause for concern. Due to the categorical nature of children’s social assistance grants, it is submitted that the state is not currently conforming to the standards set by the Bill of Rights and international law

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

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

Anterior cruciate ligament injuries of the knee: Patterns of association between the mechanism of injury and pathology visualised on magnetic resonance imaging

Background: Anterior cruciate ligament (ACL) injuries are common among athletes and the general public. These injuries may lead to significant absence from all activities with associated financial and social burdens for the patient. No definitive association has been described between the mechanism of injury and the pathology to enable the implementation of preventative measures to limit these injuries.Aim: To determine whether there is an association between the mechanism of injury and the pathology seen on a magnetic resonance imaging (MRI) scan in ACL injuries.Methods: This was a cross-sectional analytical study. Eighty-seven male patients with an ACL injury and who had an MRI scan of the knee within the last two years participated in this study. Participants were contacted to give their informed consent to participate in this study. The mechanism of injury and the pathology seen on the MRI scan was noted and categorised into different groups of injuries and associated pathologies. Statistical analyses included summaries of the data and a test for the association between the mechanism of injury and the pathology. Since there were multiple pathology responses to each mechanism, a modified version of the chi-square test for independence was used. A five percent level of significance was specified.Results: MRI scans of ACL injuries indicated that the mechanism of a solid foot plant with rotation of the knee has a greater tendency to be associated with medial meniscal injuries (77%). There was also a 54% possibility for it to be associated with lateral meniscal injuries. A solid foot plant with a valgus stress on the knee showed a higher incidence of associated medial collateral ligament (MCL) injuries (41%) and femoral bone bruising (62%). These two mechanisms of injury are the most common in ACL injuries and contribute to the clinical significance found in this study. The p-value was, however, not statistically significant (p=0.44, chi-square value=20.27, df=45) for any association between the pathology and the mechanism of injury.Conclusion: Some injury mechanisms causing an ACL injury were more common than others and had more associated pathologies. The most common mechanism of injury noted in this study was a solid foot plant with either rotation of the knee or valgus stress on the knee. Strengthening the tissue structures involved in those movement patterns causing these mechanisms can possibly limit future ACL injuries in athletes and the general public.Keywords: knee injury, mechanism, association, pathology, MRI scan, preventio