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

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

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

Clinical profile of acutely ill psychiatric patients admitted to a general hospital psychiatric unit

Objectives: Helen Joseph Hospital in southern Gauteng Province is one of five specialist hospitals on the academic circuit of the University of theWitwatersrand. Against a background of new mental health legislation, implemented in South Africa during December 2004 with no formal mechanisms in place to monitor mental health services on different levels of care or in regions, a study with three objectives was undertaken, namely: (I) to provide a baseline on psychiatric morbidity and treatment outcome; (II) to establish the state of affairs analysis for mental health care and (III) to establish a framework for cost centre management. The current study focuses on objective one. Method: A retrospective clinical audit was undertaken of mental health service delivery, teaching and research at Helen Joseph Hospital over a one-year period from September 2003 to August 2004. This article reports on the two service delivery datasets identified: the “Inpatient Discharge Summary Report” and the “Consultation/Liaison Report”. Results: A total number of 438 service users were admitted and a monthly average of 80 consultation/liaison assessments was conducted during the study period. Persistent unfavourable nursing staff ratios continued, while the number of service users from other African countries was generally underrated. Non-compliance and substance abuse contributed significantly to the admission of service users. Schizophrenia was indicated as the most likely diagnosis in almost a quarter of cases. Conclusion: Morbidity and treatment outcome at Helen Joseph Hospital will only be contextualized after the implementation of a regular clinical audit process in all the facilities of its referral network. Keywords: Psychiatric morbidity; Treatment outcome; Referral network; Clinical profile; Service delivery; Clinical audit African Journal of Psychiatry Vol. 10 (3) 2007: pp. 159-16

A framework for current public mental health care practice in South Africa

One of the main aims of the new Mental Health Care Act, Act No. 17 of 2002 (MHCA) is to promote the human rights of people with mental disabilities in South Africa. However, the upholding of these rights seems to be subject to the availability of resources. Chapter 2 of the MHCA clarifies the responsibility of the State to provide infrastructure and systems. Chapters 5, 6 and 7 of the Act define and regulate the different categories of mental health care users, clarify the procedures around these categories and spell out mental health practitioners' roles and responsibilities in this regard. Also according to the National Health Act No. 61 of 2003, the State remains the key role player in mental health care provision, being responsible for adequate mental health infrastructure and resource allocation. Due to “limited resources” practitioners however often work in environments where staff ratios may be fractional of what should be expected and in units of which the physical structure and security is totally inadequate. The interface between professional responsibility of clinical workers versus the inadequacy of clinical interventions resulting from infrastructure and staffing constraints needs to be defined. This paper considered recent legislation currently relevant to mental health care practice in order to delineate the legal, ethical and labour framework in which public sector mental health practitioners operate as state employees. These included the Mental Health Care Act, No.17 of 2002; the National Health Act, No. 61 of 2003 and the proposed Traditional Health Practitioners Act, No. 35 of 2004. Formal legal review of and advice on this legislation as it pertains to public sector mental health practitioners as state employees, is necessary and should form the basis of the principles and standards for care endorsed by organized mental health care practitioner groups such as the South African Society of Psychiatrists (SASOP).African Journal of Psychiatry Vol. 10 (4) 2007: pp. 205-20

Shouldering the blame for impingement: the rotator cuff continuum

The aim of this article was to summarise recent research on shoulder impingement and rotator cuff pathology. A continuum model of rotator cuff pathology is described, and the challenges of accurate clinical diagnosis, imaging and best management discussed.Keywords: shoulder impingement syndrome, subacromial impingement syndrome, rotator cuff, tendinopathy, rehabilitatio

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