Lattice Knots in a Slab

In this paper the number and lengths of minimal length lattice knots confined to slabs of width $L$, is determined. Our data on minimal length verify the results by Sharein et.al. (2011) for the similar problem, expect in a single case, where an improvement is found. From our data we construct two models of grafted knotted ring polymers squeezed between hard walls, or by an external force. In each model, we determine the entropic forces arising when the lattice polygon is squeezed by externally applied forces. The profile of forces and compressibility of several knot types are presented and compared, and in addition, the total work done on the lattice knots when it is squeezed to a minimal state is determined

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

Sedation for cases without local anaesthetic

No Abstract

Fostering effective governance through intragovernmental networks: a case of a justice, crime prevention and security cluster network

South Africa’s crime challenge remains despite substantial public sector efforts. As wicked problems, including crime, often transcend the conventional capacities of public authorities to address them effectively, the primary aim of this research was to uncover the underlying dimensions that contribute to the effective functioning of an intragovernmental collaboration network. This research adopted a case study approach to delve into the structure and efficacy of the South African Justice, Crime Prevention, and Security Cluster. The chosen methodology and insider access to senior management produced rich descriptions not previously available to offer a conceptual understanding of balances and trade-offs required during a mandated and directed collaboration. Findings offer enhanced understanding, contributing to overcoming traditional barriers in public administration networks and reforming traditional hierarchical structures to offer meaningful governance alternatives or improvements to existing structures. Specifically, this study reveals gaps in the intragovernmental network and offers insights for governance and performance enhancements. Findings emphasize the importance of fostering a collaborative culture based on performance and accountability. The study underscores the need for more robust network directives, clarifying roles and responsibilities, and enhancing leadership attributes. It stresses the importance of efficient coordination, collaborative capability, and shared purpose. The study also suggests cluster-oriented budgeting and greater involvement of key stakeholders, including civil societies, research institutions, and academic establishments. These findings contribute to improving government-led networks in addressing complex challenges

On trivial words in finitely presented groups

We propose a numerical method for studying the cogrowth of finitely presented groups. To validate our numerical results we compare them against the corresponding data from groups whose cogrowth series are known exactly. Further, we add to the set of such groups by finding the cogrowth series for Baumslag-Solitar groups $\mathrm{BS}(N,N) =$ and prove that their cogrowth rates are algebraic numbers.Comment: This article has been rewritten as two separate papers, with improved exposition. The new papers are arXiv:1309.4184 and arXiv:1312.572

A simple model of a vesicle drop in a confined geometry

We present the exact solution of a two-dimensional directed walk model of a drop, or half vesicle, confined between two walls, and attached to one wall. This model is also a generalisation of a polymer model of steric stabilisation recently investigated. We explore the competition between a sticky potential on the two walls and the effect of a pressure-like term in the system. We show that a negative pressure ensures the drop/polymer is unaffected by confinement when the walls are a macroscopic distance apart

A comprehensive programme addressing HIV/AIDS and gender based violence

A survey was administered to 304 respondents participating from three areas near Welkom, South Africa. Face-toface interviews were conducted with women from randomly selected households to evaluate the impact of a service provision programme targeting women living with HIV/AIDS and gender based violence. Gender based violence (GBV) awareness and knowledge was high. Respondents had high perceived levels of risk.They reported making various behavioural changes to avoid GBV.The respondents were aware of their legal rights pertaining to GBV. HIV/AIDS knowledge levels and attitudes were acceptable. Behavioural changes included condom use, abstinence and being faithful to one partner. Disclosure of HIV was lower than disclosure of GBV.Awareness and knowledge of female condoms were high, yet usage low. Participants reported that they would be able to introduce condoms to a relationship and negotiate usage with relative ease. Perceived levels of GBV and HIV were high, and stigma levels towards the affected women were also relatively high.The awareness and knowledge levels of GBV and HIV of older respondents were lower than younger respondents.The key findings of this study support the notion of using a holistic approach, targeting more than one issue.There is lower stigma levels associated with combined conditions, which might allow easier access to vulnerable groups. Coordination and collaboration of services are however needed to enable this benefit. Une étude a été faite auprès de 304 participantes venant de trois quartiers près de Welkom, en Afrique du Sud. Des chercheurs de terrain, bien formés, ont mené des entretiens en tête-à-tête avec des femmes de foyers sélectionnés au hasard avec le but d'évaluer l'impact du programme de service visant des femmes qui vivent avec le VIH/SIDA et la violence contre les femmes. La prise de conscience et la connaissance de la violence contre les femmes étaient élevées. Les participantes montraient des niveaux élevés du risque perçu. Elles avouent avoir changé leur comportement afin d'éviter la violence contre les femmes, ainsi que dénoncer le malfaiteur. Elles connaissaient leurs droits par rapport à la violence contre les femmes. Les niveaux de connaissance du VIH/SIDA et des attitudes étaient satisfaisants. Le changement de comportement inclut entre autres, l'utilisation du préservatif (même si cela n'était pas fait régulièrement), l'abstinence et être fidèle à un seul partenaire. La divulgation de sa séropositivité était plus basse que celle de la violence. La prise de conscience et la connaissance du préservatif féminin était élevé. Cependant, son usage était très bas car il n'est pas facilement disponible. Les participantes ont signalé qu'elles pourraient proposer un préservatif et négocier son usage sans beaucoup de difficulté. Les niveaux perçus de la violence contre les femmes et le VIH étaient élevés. Le niveau de stigmatisation envers des femmes infectées était relativement élevé. Le niveau de conscience et de connaissance de la violence contre les femmes et du SIDA chez les participantes plus âgées était plus bas par rapport à celui de participantes plus jeunes.Tandis que tous les trois quartiers ont montré une évidence de valeur des activités de “LifeLine”, la valeur des interventions à Odendaalsrus était moins importante. Il y a un besoin de réorganiser des activités prioritaires par le biais de “LifeLine”. Les résultats de cette étude soutien la notion de l'utilisation d'une approche holistique visant plus d'un sujet. Le niveau de stigmatisation liée aux conditions complexes est moins élevé. Cela peut permettre l'accès plus facile aux groupes vulnérables. La coordination et la collaboration des services sont toutefois nécessaires afin de permettre la rentabilité. Les résultats des interventions de GBV et de VIH confirment d'autres études. Le manque des documents et davantage d'études sur la rentabilité des interventions compréhensives est abordé dans cette description d'une approche qui a pour but d'aborder la violence contre les femmes et le VIH en se servant d'une approche holistique. Keywords: HIV/AIDS and GBV, holistic, comprehensive programme.SAHARA J Vol. 4 (3) 2007: pp. 695-70

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