The Fermat-Torricelli problem in normed planes and spaces

We investigate the Fermat-Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat-Torricelli locus in a geometric way. We present many new results, as well as give an exposition of known results that are scattered in various sources, with proofs for some of them. Together, these results can be considered to be a minitheory of the Fermat-Torricelli problem in Minkowski spaces and especially in Minkowski planes. This demonstrates that substantial results about locational problems valid for all norms can be found using a geometric approach

Movement patterns and athletic performance of leopards in the Okavango Delta

Although leopards are the most widespread of all the big cats and are known for their adaptability, they are elusive and little is known in detail about their movement and hunting energetics. We used high-resolution GPS/IMU (inertial measurement unit) collars to record position, activity and the first high-speed movement data on four male leopards in the Okavango Delta, an area with high habitat diversity and habitat fragmentation. Leopards in this study were generally active and conducted more runs during the night, with peaks in activity and number of runs in the morning and evening twilight. Runs were generally short (less than 100 m) and relatively slow (maximum speed 5.3 m s−1, mean of individual medians) compared to other large predators. Average daily travel distance was 11 km and maximum daily travel distance was 29 km. No direct correlation was found between average daily temperature and travel distance or between season and travel distance. Total daily energy requirements based on locomotor cost and basal metabolic rate varied little between individuals and over time. This study provides novel insights into movement patterns and athletic performance of leopards through quantitative high-resolution measurement of the locomotor, energetic, spatial and temporal movement characteristics. The results are unbiased by methodological and observational limitations characteristic of previous studies and demonstrate the utility of applying new technologies to field studies of elusive nocturnal species

Supplemented low-protein diets : are they superior in chronic renal failure?

CITATION: Herselman, M. G. et al 1995. Supplemented low-protein diets : are they superior in chronic renal failure? South African Medical Journal, 85(5):361-365.The original publication is available at http://www.samj.org.zaTwenty-two patients with chronic renal failure were randomly assigned to a conventional low-protein diet containing 0,6g protein/kg/day or a very-low-protein diet containing 0,6g protein/kg/day supplemented with essential amino acids; they were followed up for 9 months. There were no significant changes in body mass index, arm muscle area, percentage body fat, serum albumin and transferrin levels in any of the groups; neither was there any difference between the groups in respect of these parameters. Renal function, as measured by the reciprocal of serum creatinine over time, stabilised in both groups during intervention, with no significant difference between the groups. There was however no correlation between changes in renal function and changes in blood pressure, or dietary intake of protein, phosphorus, cholesterol, polyunsaturated and saturated fatty acids. There were also no significant changes and no significant differences between the groups in serum levels of parathyroid hormone and alkaline phosphatase, urine cyclic adenosine monophosphate, tubular reabsorption of phosphate, and the theoretical renal threshold for phosphate. The results of this study suggest that the supplemented very-low-protein diet was not superior to the conventional low-protein diet in terms of its effect on protein-energy status, renal function and biochemical parameters of renal osteodystrophy.Publisher’s versio

Supplemented low-protein diets : are they superior in chronic renal failure?

CITATION: Herselman, M. G. et al 1995. Supplemented low-protein diets : are they superior in chronic renal failure? South African Medical Journal, 85(5):361-365.The original publication is available at http://www.samj.org.zaTwenty-two patients with chronic renal failure were randomly assigned to a conventional low-protein diet containing 0,6g protein/kg/day or a very-low-protein diet containing 0,6g protein/kg/day supplemented with essential amino acids; they were followed up for 9 months. There were no significant changes in body mass index, arm muscle area, percentage body fat, serum albumin and transferrin levels in any of the groups; neither was there any difference between the groups in respect of these parameters. Renal function, as measured by the reciprocal of serum creatinine over time, stabilised in both groups during intervention, with no significant difference between the groups. There was however no correlation between changes in renal function and changes in blood pressure, or dietary intake of protein, phosphorus, cholesterol, polyunsaturated and saturated fatty acids. There were also no significant changes and no significant differences between the groups in serum levels of parathyroid hormone and alkaline phosphatase, urine cyclic adenosine monophosphate, tubular reabsorption of phosphate, and the theoretical renal threshold for phosphate. The results of this study suggest that the supplemented very-low-protein diet was not superior to the conventional low-protein diet in terms of its effect on protein-energy status, renal function and biochemical parameters of renal osteodystrophy.Publisher’s versio

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

Changes in neutrophil count, creatine kinases and muscle soreness after repeated bouts of downhill running

Objective. A primary objective was to examine circulating neutrophil count after repeated bouts of downhill running. An additional aim was to determine creatine kinase (CK) levels during the initial 12 hours, after repeated DHRs. Design. Eleven healthy, untrained Caucasian males performed 2 x 60 min bouts of DHR (-13.5%), spaced 14 days apart, at a speed equal to 75% VO2max on a level grade. Blood was collected before, after, and every hour for 12 hours, and every 24 hours for 6 days. Absolute neutrophil count, CK, and delayed-onset muscle soreness (DOMS) were assessed. Results were analysed using repeated measures ANOVA (

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter $D=\Omega(\sqrt n)$, and at most $\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr)$ edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

A renal registry for Africa: first steps.

There is a dearth of data on end-stage renal disease (ESRD) in Africa. Several national renal registries have been established but have not been sustainable because of resource limitations. The African Association of Nephrology (AFRAN) and the African Paediatric Nephrology Association (AFPNA) recognize the importance of good registry data and plan to establish an African Renal Registry. This article reviews the elements needed for a successful renal registry and gives an overview of renal registries in developed and developing countries, with the emphasis on Africa. It then discusses the proposed African Renal Registry and the first steps towards its implementation. A registry requires a clear purpose, and agreement on inclusion and exclusion criteria, the dataset and the data dictionary. Ethical issues, data ownership and access, the dissemination of findings and funding must all be considered. Well-documented processes should guide data collection and ensure data quality. The ERA-EDTA Registry is the world's oldest renal registry. In Africa, registry data have been published mainly by North African countries, starting with Egypt and Tunisia in 1975. However, in recent years no African country has regularly reported national registry data. A shared renal registry would provide participating countries with a reliable technology platform and a common data dictionary to facilitate joint analyses and comparisons. In March 2015, AFRAN organized a registry workshop for African nephrologists and then took the decision to establish, for the first time, an African Renal Registry. In conclusion, African nephrologists have decided to establish a continental renal registry. This initiative could make a substantial impact on the practice of nephrology and the provision of services for adults and children with ESRD in many African countries

Ethical and practical issues to consider in the governance of genomic and human research data and data sharing in South Africa: a meeting report

Genomic research and biobanking has undergone exponential growth in Africa and at the heart of this research is the sharing of biospecimens and associated clinical data amongst researchers in Africa and across the world. While this move towards open science is progressing, there has been a strengthening internationally of data protection regulations that seek to safeguard the rights of data subjects while promoting the movement of data for the benefit of research. In line with this global shift, many jurisdictions in Africa are introducing data protection regulations, but there has been limited consideration of the regulation of data sharing for genomic research and biobanking in Africa. South Africa (SA) is one country that has sought to regulate the international sharing of data and has enacted the Protection of Personal Information Act (POPIA) 2013 that will change the governance and regulation of data in SA, including health research data, once it is in force. To identify and discuss challenges and opportunities in the governance of data sharing for genomic and health research data in SA, a two-day meeting was convened in February 2019 in Cape Town, SA with over 30 participants with expertise in law, ethics, genomics and biobanking science, drawn from academia, industry, and government. This report sets out some of the key challenges identified during the workshop and the opportunities and limitations of the current regulatory framework in SA