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

Teaching and learning English as a Home Language in a predominantly non-native English classroom: A study from KwaZulu-Natal1

This study focuses on a secondary school in an Indian-African suburb of Merewent in KwaZulu-Natal, an example of a suburban school where English as a Home Language (EHL) is taught to a majority of non-native English learners from township schools. The EHL classrooms were investigated for ‘communicativeness’ and then compared to English as a Second Language (ESL) classrooms. It might be expected that EHL classrooms would exhibit an affinity with ESL classrooms. However, although non-native EHL has many aspects in common with ESL, there were significant differences between the two. The most important difference from the standpoint of Communicative Language Teaching (CLT) was in the learning content selection, with the EHL settings using more literary works, and so focusing less on the direct teaching of grammatical forms. However, a disturbing pattern was the inability of the learners in both sets of settings to take full advantage of CLT, which suggested that the learners might not be at the appropriate level of language development.Keywords: English as Home Language (EHL), non-native English learners, township schools, English as a Second Language (ESL), Communicative Language Teaching (CLT), language developmen

Blended teaching and learning: Exploring the concept, barriers to implementation and designing of learning resources

With the advent of the coronavirus disease 2019 (COVID-19), several institutions worldwide have adopted the blended mode of teaching and learning. However, literature on this concept in South Africa and on the African continent is scarce. This scoping review explores the concept of blended approach to training and how to design resources for the blended teaching and learning approach. In addition, the review investigates barriers to the implementation of blended learning. The findings of this study demonstrate that the understanding of the concept of blended teaching and learning is not homogenous and is often left to individual academics to decide on the approach. The review identified several hurdles that need to be addressed for successful implementation of blended teaching and learning, however these are not specific to South African institutions. Available literature on studies done elsewhere and in South African, suggest that some of the identified barriers to adoption of blended teaching and learning are real, while others are perceived or imagined. Lastly, the authors observed that there are several approaches to designing learning resources for the blended mode of teaching and learning. The choice of approach is dependent on the intended purpose for which the specific design is adopted. There is a need for studies that specifically investigate blended learning in Universities in South Africa and on the continent to help identify barriers to adopting blended teaching and learning among institutions that are specific to the South African and African context. Institutions adopting the blended teaching and learning mode of delivery, need to be unambiguous in their philosophy of blending teaching and learning and not leave it to the implementing academics. Policymakers can use the information generated in this review to recommend minimum requirements for a blended delivery mode in public institutions of higher learning

Lower Cost Lightweight Cold-formed Portal Frames

Southern Africa has a dire need for housing small industries and people, and concomitantly the creation of employment. It is common to use hot-rolled steel sections for industrial structures, which are pre-manufactured and then bolted together on site. In this paper an alternative structural concept for low-rise portals for light industries is proposed, whereby the total frame is made up of standard cold-formed sections which are cut and welded together on site. The cladding material is employed as an integral structural component through the principles of stressed skin diaphragm action. A short pile footing is proposed to provide a degree of rotational fixity for the colunns of the frame. Different frame configurations are investigated and the practical application of the concept is discussed

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

Building a framework for determining the optimal supplier shipping performance

Thesis (M. Eng. in Logistics)--Massachusetts Institute of Technology, Engineering Systems Division, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 67-69).Most companies aim for perfect on-time delivery from suppliers, since late deliveries can cause supply disruptions and raise the cost of inventory, transportation and coordination. But this assumes that companies do not incur expenses in increasing or maintaining supplier performance. Our thesis looks at the problem faced by those companies that do invest in suppliers to help them achieve a desired performance level. In these special cases, a perfect target may no longer yield the minimum cost incurred over a performance spectrum. Our thesis provides a framework that companies can use to determine an optimal target for timely deliveries by comparing the cost implications of different supplier performance levels. We pursue an empirical approach, using the data and metrics of an industrial equipment manufacturer that uses a hit-or-miss performance measure to evaluate on-time supplier deliveries. Within the scope of this performance management system, we determine the relevant cost categories. Using regression analysis, we create models projecting each category's expected behavior based on data we collect. Combining the models allows us to calculate a system optimal point at which the incremental cost of supplier development towards an improved performance target matches the benefit derived from avoided supply disruption. This performance target minimizes the total cost of the performance management system. While our framework is calibrated to a specific company, the models we create are general enough to be adapted by companies facing similar problems. By laying out our treatment of costs, we hope to make it feasible for other companies to calculate a target that makes sense: one that suppliers can achieve and purchasers can afford.by Maximilian L. Hurd and Izak W. J. van Rensburg.M.Eng.in Logistic

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

Topological Constraints at the Theta Point: Closed Loops at Two Loops

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe, which gives way to a fluctuation-induced first-order transition.Comment: 5 pages, RevTeX, typo