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

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

Case Study: An unusual case of Wernicke’s encephalopathy - Thiamin deficiency in advanced gastric adenocarcinoma

No Abstract

The epidemiology of traumatic brain injuries sustained by children under 10 years of age presenting to a tertiary hospital in Soweto, South Africa

Background. Traumatic brain injury (TBI) in the paediatric population is a significant contributor to death and disability worldwide. In sub-Saharan Africa, death and disability from TBI are still superseded by infectious disease. Mechanisms of injury differ by region and socioeconomics, but in general, falls, road traffic collisions (RTCs), being ‘struck by/against objects’ and non-accidental injuries (NAIs) are responsible for most cases.Objectives. To: (i) quantify the burden of TBI in terms of demographics, causes and severity; (ii) explore resource utilisation regarding length of stay, computed tomography (CT) brain scan use and multidisciplinary participation; (iii) interrogate possible temporal patterns of injury; and (iv) thus identify potential targets for community-based prevention strategies.Methods. In a 5-year retrospective review of all children aged <10 years admitted with TBI between September 2013 and August 2018, demographics, date of injury, mechanism of injury, severity of TBI based on the Glasgow Coma Scale, and requirement for a CT brain scan were collected for each patient. Outcomes were reported as discharge, transfer or death. Outcomes for children sustaining isolated TBI were compared with those for children sustaining TBI with polytrauma.Results. A total of 2 153 patients were included, with a mean (standard deviation) age of 4.6 (2.7) years and a male/female ratio of 1.7:1. RTCs were the most frequent cause of injury at 59% (80% of these were pedestrian-vehicle collisions), followed by falls at 24%. Mild TBIs accounted for 87% of admissions, moderate injuries for 6%, and severe injuries for 7%. Polytrauma was associated with increased severity of TBI. The cohort had a 2.3% mortality. NAIs accounted for 6% of injuries and carried a 4% mortality. The median (interquartile range) duration of hospitalisation was 1 (1 - 3) days, ranging from <24 hours to 132 days. CT scans were performed on 43% of admitted patients, and 48% of patients had consultations with another medical or allied medical discipline. Injuries were more frequent during the summer months and over weekends. Infants aged <1 year were identified as a group particularly vulnerable to injury, specifically NAI.Conclusions. Paediatric TBI was demonstrated to be a resource-intensive public health concern. From the results, we identified potential primary prevention targets that could perhaps be incorporated into broader community-based intervention programmes. We also identified a need to study long-term consequences of mild TBI further in our paediatric population

Control of rheumatoid arthritis with conventional disease-modifying antirheumatic drugs in a tertiary hospital in central South Africa

Background. Rheumatoid arthritis (RA) is a highly prevalent disease with a significant impact on morbidity and life expectancy. There is a paucity of literature relating to the current state of disease control in South Africa, and none on Free State Province.Objectives. To evaluate control of RA with conventional disease-modifying antirheumatic drugs (DMARDs) in the rheumatology outpatient department of Universitas Academic Hospital, Bloemfontein, and to determine the relative impact of various factors contributing to the prevention of disease control.Methods. A cross-sectional study was undertaken over a period of 8 months from December 2016 to August 2017 in the rheumatology outpatient department of Universitas Academic Hospital. Data were collected by means of information sheets and questionnaires completed by attending doctors. The information pertained to disease activity, possible factors contributing to poor control, and relevant demographic data.Results. Information was collected from 169 patients, and data analysis was performed on 161. The results revealed that RA was controlled in 34 patients (21.1%). Of the 127 patients with uncontrolled disease, 61 (48.0%) reported dispensing issues relating to poor drug availability. Seventy-two (56.7%) of the patients with uncontrolled disease were deemed to be on insufficient treatment for their disease state, of whom 33 (45.8%) also reported concomitant dispensing issues. Other factors such as transport/access problems, administrative issues, adverse events and poor compliance/insight contributed to the inadequate control of RA to a minor extent. In terms of monthly dispensing, 159 patients (98.8%) reported receiving all their DMARDs during the first month. The vast majority of these drugs were dispensed from Universitas Hospital. This figure decreased to 119 patients (73.9%) who received all their DMARDs during the second month, mostly from district units. Only 55.3% (n=89) of the patients reported receiving all of their DMARDs from their down-referral units.Conclusions. Control of RA at this institution is suboptimal compared with national and international standards. The main contributors to poor control appear to be problems relating to dispensing of medication and inadequate escalation of therapy by doctors. Most of the concern with the dispensing of medication lies with the poor availability of DMARDs in peripheral unit pharmacies. These factors are remediable and should be attended to

The peripartum management of a 32-year-old patient presenting at 34 weeks’ gestation with unrepaired cyanotic heart disease

CITATION: Rossouw, J. N., et al. 2018. The peripartum management of a 32-year-old patient presenting at 34 weeks’ gestation with unrepaired cyanotic heart disease. South African Journal of Obstetrics and Gynaecology, 24(2):36-39, doi:10.7196/sajog.1265.The original publication is available at http://www.sajog.org.zaENGLISH ABSTRACT: Unrepaired cyanotic heart disease is considered a high-risk lesion owing to the consequent increase in maternal and fetal complications. In the presence of pulmonary hypertension, maternal mortality approaching 50% has been reported, and pregnancy is therefore considered contraindicated. We present a case of a 32-year-old woman presenting at 34 weeks’ gestation in heart failure due to newly diagnosed cyanotic complex cardiac disease. The diagnosis of left atrial isomerism with a common atrium, single atrioventricular valve, and a restrictive ventricular septum defect was made. Cyanosis was due to mixing at atrial level, without features of Eisenmenger’s syndrome. Her intrapartum multidisciplinary management is described in detail. The patient was discharged home in a condition similar to her baseline, together with her healthy neonate.http://www.sajog.org.za/index.php/SAJOG/article/view/1265Publisher's versio

Experimental and theoretical study of vibrations of a cantilevered beam using a ZnO piezoelectric sensor

Piezoelectric sensors can measure vibrations of solid structures very accurately. A model of a cantilevered beam, with a ZnO film on one side is presented. Both viscous and internal damping are considered. The output of the sensor is modeled and matched with experimental results by adjusting the damping parameters. A theoretical formulation for damage is introduced. Experimental results for a damaged beam confirm the shift in frequencies to lower values. The model is used to identify the extent of the damage

Punctured polygons and polyominoes on the square lattice

We use the finite lattice method to count the number of punctured staircase and self-avoiding polygons with up to three holes on the square lattice. New or radically extended series have been derived for both the perimeter and area generating functions. We show that the critical point is unchanged by a finite number of punctures, and that the critical exponent increases by a fixed amount for each puncture. The increase is 1.5 per puncture when enumerating by perimeter and 1.0 when enumerating by area. A refined estimate of the connective constant for polygons by area is given. A similar set of results is obtained for finitely punctured polyominoes. The exponent increase is proved to be 1.0 per puncture for polyominoes.Comment: 36 pages, 11 figure

Collapsing lattice animals and lattice trees in two dimensions

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second order transitions from an extended to a collapsed phase in the resulting 2-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into two different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees, but the other is {\it not yet} bond driven and does not contain the Derrida-Herrmann model as special point. Instead it ends at a multicritical point $P^*$ where a transition line between two collapsed phases (one bond-driven and the other contact-driven) sparks off. The Derrida-Herrmann model is representative for the bond driven collapse, which then forms the fourth universality class on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.Comment: 11 pages, 16 figures, 1 tabl