BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices

In this paper the elementary moves of the BFACF-algorithm for lattice polygons are generalised to elementary moves of BFACF-style algorithms for lattice polygons in the body-centred (BCC) and face-centred (FCC) cubic lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC lattices and so expand a similar result for the cubic lattice. Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC lattices

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

Acute mental health care according to recent mental health legislation. Part III. Structuring space for acute mental health care

Objective: This is the third of three reports on the follow-up review of mental health care at Helen Joseph Hospital (HJH). The study reviewed existing South African standards for mental health care facilities. Architectural principles and implications for the use of space were deducted from recent legislation. Objectives were to evaluate the use of space in the existing physical facilities, to identify appropriate architectural solutions considering identified human rights requirements and to provide provisional cost estimates to align the unit towards its designated functions. Method: Personal interviews were conducted. An on-site assessment and survey was made of existing and potential new spaces. Results: Spatial requirements for implementing the Mental Health Act, No. 17 of 2002 (MHCA) were explored. Principles for spatial design of acute facilities include that: - spaces should communicate clear individual identity; - space should be segregated into zones according to user functionality and privacy; - communal leisure spaces should open into safe contained outdoor spaces; - circulation routes should preferably be circular; - sufficient visual connection should exist between circulation space and group activities; and - open lines of sight should be provided to all access points. The potential options for extension included: - an extensive unused single storey structural shell for a potential office wing on the same floor; - a huge vacant double volume space which could be accessed across the existing flat roof for potential occupational therapy activities; and - the existing roof area could be altered and secured to become an adequate outside leisure and garden area. A proposed concept design in two phases – based on these principles - was submitted to hospital and provincial management. Conclusion: To implement the MHCA without violating the human rights of mental health care users at HJH will require specific adjustment and extension of the current use of space at HJH.Key words: Architecture; Hospitals; Mental health services; Human right

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

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

A cross-sectional study of 2550 amateur cyclists shows lack of knowledge regarding relevant sports nutrition guidelines

Background: Amateur cyclists use a wide variety of supplements and nutritional substances to increase performance in addition to their training.Objectives: The intended nutritional supplement use, carbohydrate (CHO) use and hydration practices of amateur cyclists before, during and after endurance cycling were analysed. Evidence of ignorance regarding the use of sports supplements and CHO, as well as the disregard of hydration strategy was hypothesised.Methods: Amateur cyclists, of all age and sex groups, were requested to complete an online survey anonymously on the 2013 Momentum 94.7 Cycle Challenge website, a few days before the event.Results: Responses were received from 2 550 out of 30 640 race entrants (8%); representing a distribution of 75% males, 25% females, with the majority between 25 to 45 years old. Nutritional supplements were used by 59% of respondents, with 77% dose adherence, and 29% with supplement ingredient knowledge. Half of the respondents (48%) planned to carbo-load two-three days before the event, while only five percent used professional advice to scientifically calculate their carbo-loading requirements. CHO were consumed by 81% during the event. Hydration preferences during the race were sports drinks (59%) and water (22%); and after the race 45% preferred a sports drink and 40% water. Ingredients, taste, colour, and temperature were criteria used to choose a sports drink. Only 18% of respondents knew to use both colour of urine and thirstiness to determine post-race fluid requirements.Conclusion: The authors concluded that amateur cyclists had insufficient knowledge regarding nutritional supplement ingredients and usage, CHO requirements and carbo-loading practices, and hydration strategies before, during and after the event.Keywords: ergogenic aids, nutritional supplements, carbohydrate us

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

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