Disjunctive Total Domination in Graphs

Let $G$ be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, $\gamma_t(G)$. A set $S$ of vertices in $G$ is a disjunctive total dominating set of $G$ if every vertex is adjacent to a vertex of $S$ or has at least two vertices in $S$ at distance2 from it. The disjunctive total domination number, $\gamma^d_t(G)$, is the minimum cardinality of such a set. We observe that $\gamma^d_t(G) \le \gamma_t(G)$. We prove that if $G$ is a connected graph of order$n \ge 8$, then $\gamma^d_t(G) \le 2(n-1)/3$ and we characterize the extremal graphs. It is known that if $G$ is a connected claw-free graph of order$n$, then $\gamma_t(G) \le 2n/3$ and this upper bound is tight for arbitrarily large$n$. We show this upper bound can be improved significantly for the disjunctive total domination number. We show that if $G$ is a connected claw-free graph of order$n > 10$, then $\gamma^d_t(G) \le 4n/7$ and we characterize the graphs achieving equality in this bound.Comment: 23 page

The socioeconomic and environmental health situation of international migrants in Johannesburg, South Africa

Background. Around the world, cities are dealing with growing numbers of international migrants (IMs). Many migrants are likely to have encountered exceptional challenges through the migration process, with implications for their health. Nevertheless, studies conducted in several developed countries point to a pattern of better health in migrant groups – the ‘healthy migrant’ effect. However, little is known about the health of migrants in poorly resourced destination countries, especially in African settings.Objectives. To compare living conditions and environmental health status in IMs relative to South African (SA) households, both living in settings of poverty in Johannesburg, SA.Methods. Data were extracted from a long-term panel study underway in five neighbourhoods of Johannesburg. Cross-sectional studies, undertaken annually from 2006 to 2010, involved the annual administration of questionnaires to around 500 households to obtain information on living conditions and health.Results. Most of the differences observed through univariate analyses in living conditions and health status between IM and SA households were explained by controlling for socioeconomic and neighbourhood factors.Conclusion. This study revealed that SA respondents and IMs in settings of urban poverty in Johannesburg had remarkably similar health status, with little evidence of a ‘healthy migrant’ effect. Nevertheless the authors argue for vigilance and a finer understanding of the unique sociocultural dimensions of health in migrant communities in Johannesburg as they continue to transform the profile of urban health in SA and other African cities

Nephrolithiasis (part 1): Epidemiology, causes and pathogenesis of recurrent nephrolithiasis

A recent increase in the incidence of recurrent renal calcium oxalate calculi has been demonstrated. Although a few advances have shown that the increase in incidence of these stones is due to genetic causes, it is mostly associated with a change in environmental factors. Global warming and weather changes, some medications administered to young children and eating habits play a pivotal role in increasing stone incidence. By far the most important single factor in stone incidence involves the increased ingestion of red meat and salt. So much so that it is anticipated that calcium oxalate stone occurrence will increase pari passu with dietary changes in the South African black community. The reasons for the difference in the incidence between males and females (12% v. 6%) remain controversial, and should be further studied

Development of an energy-dense biscuit suitable for primary school learners for the South African National School Nutrition Programme

South Africa has a well established National School Nutrition Programme (NSNP). Despite rescheduling the mealtime to two hours after the start of the school day to accommodate learners who come to school on an empty stomach, a gap still exists as many children start their learning day with low energy and concentration levels. A cost-effective, energy-dense snack served at the start of the school day can be a solution to sustain learners until the main meal is served. Cross-sectional surveys were used to determine the snack preferences of children and the product development process was used to develop a suitable snack. An energy-dense peanut butter biscuit was developed based on those surveys as well as a scoping review of previous snack studies. The energy-dense developed product provided 1388kJ (61.0%) of energy from fat, 688kJ (30.2%) of energy from carbohydrates and 201kJ (8.8%) of energy from protein per 100g. The biscuit conformed to microbial testing standards. Shelf-life analysis projected a shelf-life of five weeks fresh and five months in food grade packaging. Sensory results showed that there was no significant difference in sensory scores across gender (p=0.691) and age (p=0.706). More of the learners (n=56, 69.1%) found the biscuit to be ‘Super good’ than the other ratings (p<.0005). When compared with similar biscuit products currently on the market, it was found that the developed biscuit was the most reasonably priced. The developed biscuit has the potential to serve as a solution to hidden hunger for children that come to school on an empty stomach. This versatile snack solution has potential for continuity of use even during periods of national crisis as with COVID-19, when learners’ nutritional needs may be most vulnerable

Food insecurity in households in informal settlements in urban South Africa

Food insecurity in the urban poor is a major public health challenge. The Health, Environment and Development study assessed trends in food insecurity and food consumption over a period of 7 years in an informal settlement in Johannesburg, South Africa (SA). Annual cross-sectional surveys were conducted in the informal settlement (Hospital Hill). The degree of household food insecurity decreased significantly from 2006 (85%) to 2012 (70%). There was a spike in 2009 (91%), possibly owing to global food price increases. Childhood food insecurity followed the same trend as household food insecurity. During the first 3 study years, consumption of protein, vegetables and fruit decreased by 10 - 20%, but had returned to previous levels by 2012. In this study, although declining, food insecurity remains unacceptably high. Hunger relief and poverty alleviation need to be more aggressively implemented in order to improve the quality of life in poor urban communities in SA

A cross-sectional analytical study of geophagia practices and blood metal concentrations in pregnant women in Johannesburg, South Africa

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Outcomes following aortic valve replacement for isolated aortic stenosis with left ventricular dysfunction

Background: Severe aortic stenosis (AS) is associated with a poor prognosis in patients with left ventricular dysfunction (LVD). Survival is estimated at less than 2 years without aortic valve replacement (AVR). Limited data are available on the effects and outcomes of AVR in such patients, especially in the absence of concomitant coronary artery disease (CAD). Methods: This was a retrospective study which identified 33 patients over an approximate 10 year period who underwent surgical AVR for severe isolated AS and LVD(LVEF ≤50%). Patients were excluded if they had a prior valve replacement, mixed valve disease, <18 years old or the presence of CAD. Overall survival was analysed using the Kaplan-Meier curve and Cox proportional hazards model. The changes in postoperative LVEF and NYHA functional class, following AVR, was assessed using the Friedman test and ANOVA.  Results: Operative mortality was 15% with 5 deaths.  Female sex and hyperlipidaemia were identifi ed as predictors of early mortality by univariate analysis. LVEF improved in survivors from a mean of 39 ± 10% - 49.8 ± 8.7% at a 1 year follow-up (p=0.04). Younger age was identifi ed as an independent predictor of LVEF recovery (p=0.04). There was no difference in outcomes in patients with low baseline transvalvular gradients compared to those with higher gradients. There was signifi cant symptomatic improvement noted in all survivors following AVR (p<0.01).  Conclusion: Left ventricular function has a slower rateof recovery, compared to an earlier improvement of NYHA functional class after AVR for severe isolated AS and pre-operative LVD. In this high-risk group thefi ndings support AVR in patients with LVD