Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking's singularity theorem.Comment: 15 pages, LaTe

Characteristics of Conservation Laws for Difference Equations

Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether's Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not derivations and do not obey the chain rule for derivatives. We show how these problems may be resolved and illustrate various uses of the characteristic. In particular, we establish the converse of Noether's Theorem for difference equations, we show (without taking a continuum limit) that the conservation laws in the infinite family generated by Rasin and Schiff are distinct, and we obtain all five-point conservation laws for the potential Lotka-Volterra equation

Development and mechanical characterisation of self-compressed collagen gels

Collagen gels are considered a promising biomaterial for the manufacturing of tissue engineering scaffolds, however, their mechanical properties often need to be improved to enable them to provide enough mechanical support during the course of tissue regeneration process. In this paper, we present a simple self-compression technique for the improvement of the mechanical properties of collagen gels, identified by the fitting of bespoke biphasic finite element models. Radially-confined highly hydrated gels were allowed to self-compress for 18 hours, expelling fluid, and which were subsequently subjected to unconfined ramp-hold compression. Gels, initially of 0.2%, 0.3% and 0.4% (w/v) collagen and 13mm thickness, transformed to 2.9 ± 0.2%, 3.2 ± 0.3% and 3.6 ± 0.1% (w/w) collagen and 0.45 ± 0.06 mm, 0.69 ± 0.04 mm and 0.99 ± 0.07 mm thickness. Young's moduli of the compressed gels did not increase with increasing collagen fibril density, whilst zero-strain hydraulic permeability significantly decreased from 51 to 21 mm4/Ns. The work demonstrates that biphasic theory, applied to unconfined compression, is a highly appropriate paradigm to mechanically characterise concentrated collagen gels and that confined compression of highly hydrated gels should be further investigated to enhance gel mechanical performance

The wave equation on singular space-times

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.Comment: Latex, 19 pages, 1 figure. Discussion of class of metrics covered by our results and some examples added. Conclusion more detailed. Version to appear in Communications in Mathematical Physic

Dust Devil Tracks

Dust devils that leave dark- or light-toned tracks are common on Mars and they can also be found on the Earth’s surface. Dust devil tracks (hereinafter DDTs) are ephemeral surface features with mostly sub-annual lifetimes. Regarding their size, DDT widths can range between ∼1 m and ∼1 km, depending on the diameter of dust devil that created the track, and DDT lengths range from a few tens of meters to several kilometers, limited by the duration and horizontal ground speed of dust devils. DDTs can be classified into three main types based on their morphology and albedo in contrast to their surroundings; all are found on both planets: (a) dark continuous DDTs, (b) dark cycloidal DDTs, and (c) bright DDTs. Dark continuous DDTs are the most common type on Mars. They are characterized by their relatively homogenous and continuous low albedo surface tracks. Based on terrestrial and martian in situ studies, these DDTs most likely form when surficial dust layers are removed to expose larger-grained substrate material (coarse sands of ≥500 μm in diameter). The exposure of larger-grained materials changes the photometric properties of the surface; hence leading to lower albedo tracks because grain size is photometrically inversely proportional to the surface reflectance. However, although not observed so far, compositional differences (i.e., color differences) might also lead to albedo contrasts when dust is removed to expose substrate materials with mineralogical differences. For dark continuous DDTs, albedo drop measurements are around 2.5 % in the wavelength range of 550–850 nm on Mars and around 0.5 % in the wavelength range from 300–1100 nm on Earth. The removal of an equivalent layer thickness around 1 μm is sufficient for the formation of visible dark continuous DDTs on Mars and Earth. The next type of DDTs, dark cycloidal DDTs, are characterized by their low albedo pattern of overlapping scallops. Terrestrial in situ studies imply that they are formed when sand-sized material that is eroded from the outer vortex area of a dust devil is redeposited in annular patterns in the central vortex region. This type of DDT can also be found in on Mars in orbital image data, and although in situ studies are lacking, terrestrial analog studies, laboratory work, and numerical modeling suggest they have the same formation mechanism as those on Earth. Finally, bright DDTs are characterized by their continuous track pattern and high albedo compared to their undisturbed surroundings. They are found on both planets, but to date they have only been analyzed in situ on Earth. Here, the destruction of aggregates of dust, silt and sand by dust devils leads to smooth surfaces in contrast to the undisturbed rough surfaces surrounding the track. The resulting change in photometric properties occurs because the smoother surfaces have a higher reflectance compared to the surrounding rough surface, leading to bright DDTs. On Mars, the destruction of surficial dust-aggregates may also lead to bright DDTs. However, higher reflective surfaces may be produced by other formation mechanisms, such as dust compaction by passing dust devils, as this may also cause changes in photometric properties. On Mars, DDTs in general are found at all elevations and on a global scale, except on the permanent polar caps. DDT maximum areal densities occur during spring and summer in both hemispheres produced by an increase in dust devil activity caused by maximum insolation. Regionally, dust devil densities vary spatially likely controlled by changes in dust cover thicknesses and substrate materials. This variability makes it difficult to infer dust devil activity from DDT frequencies. Furthermore, only a fraction of dust devils leave tracks. However, DDTs can be used as proxies for dust devil lifetimes and wind directions and speeds, and they can also be used to predict lander or rover solar panel clearing events. Overall, the high DDT frequency in many areas on Mars leads to drastic albedo changes that affect large-scale weather patterns

A comparison between the cardio-stress indices of an active and a sedentary population

Die moderne leefwyse bring dikwels mee dat ons die belangrikheid van liggaamlike oefening uit die oog verloor. Ons toenemend passiewe leefwyse het gelei tot ’n aansienlike toename in die voorkoms van lewenstylsiektes soos hipertensie en verskeie vorme van vaskulêre patologie. In hierdie studie word die kardiostres-indekse (KSI’e) van aktiewe en sedentêre individue met mekaar vergelyk ten einde insig te verkry in die uitwerking van die aansienlike veranderinge wat in die gemoderniseerde samelewing plaasgevind het. Die aktiewe populasie het bestaan uit 217 weermagrekrute wat reeds 20 weke van hul basiese weermagopleiding voltooi het. Die (n = 126) lede van die sedentêre populasie is gewerf uit ’n tradisionele tersiêre onderwysinstansie. Die deelnemers uit beide populasies moes drie toetssessies bywoon wat gedurende week 1, week 12 en week 20 gehou is. Hulle het ’n nie-ingrypende ViportTMtoets ondergaan om hul KSI, harttempo en QRS-duur te bepaal. Die resultate het getoon dat alhoewel die basislyn vir KSI, bloeddruk en harttempo aanvanklik hoër was onder die aktiewe populasie, die aanvang van die liggaamsoefeningprogram ten opsigte van hierdie drie faktore ’n geleidelike afname en dus ’n verandering in die rigting, en uiteindelik gesonder marges tot gevolg gehad het. Die KSI het egter nie die normale reikwydte ten opsigte van een van die twee groepe bereik nie, wat daarop gedui het dat alhoewel liggaamlike aktiwiteit fisiologiese stresvlakke verminder, ander sleutelfaktore, te wete leefwyse en stresvlakke, ook in ag geneem moet word. Die studie onderskryf die idee dat ’n toename in liggaamlike aktiwiteit die potensiaal het om ’n individu se vatbaarheid vir kardiovaskulêre siektes te verminder. Die studie ondersoek ook die uitwerking van oefening op die hart deur die gebruik van KSI as ’n meetinstrument.A comparison between the cardio-stress indices of an active and a sedentary population. Our modern lifestyle often results in the importance of physical exercise being overlooked. The increasingly passive way of life has resulted in a notable increase in the prevalence of lifestyle disorders, such as hypertension and some forms of vascular pathology. This study compares the cardio-stress indices (CSIs) of active and sedentary individuals to provide insight into the impact of the significant changes that have taken place in the modernised society. The active population consisted of 217 military recruits who had completed 20 weeks of basic military training. The sedentary population (n = 126) was sourced from a traditional tertiary institution where the focus is on attending lectures. Participants from both populations were required to attend three testing sessions, which were held during Week 1, Week 12 and Week 20. Subjects underwent a non-invasive ViportTM test to measure their CSI, heart rate and QRS duration. The results showed that although baseline readings for CSI, blood pressure (BP) and heart rate (HR) were initially higher among the active population, the commencement of the physical training programme resulted in a steady decline in respect of these three factors to approach healthier margins. However, the CSI for neither population reached the normal range, indicating that although physical activity reduces physiological stress levels, other key factors, namely lifestyle stress levels, must also be taken into account.The study supports the notion that increased physical activity has the potential to reduce the predisposition of an individual to cardiovascular disorders and contributes towards establishing the effect of training on heart health by using CSI as a means of measurementhttp://www.satnt.ac.zaay201

Postural variations in Cardio Stress Index scores

Numerous factors influence heart rate variability, including age, exercise and posture. The Cardio Stress Index (CSI) is a transformed measure of heart rate variability that is determined via a miniature digital multi-channel electrocardiogram system. Although the CSI and heart rate variability are reportedly analogous, little is known about how the two concepts compare in peer-reviewed research. The aim of this study was to examine the differences between CSI and heart rate as measured on a mini- electrocardiogram device when subjects were sitting upright and when they were lying down (in supine position). This is a case-series study with no intervention or follow-up. Sitting and supine CSI and heart rate readings were compared in a random sample of 55 women volunteers recruited through advertising in Pretoria, South Africa. The mean age of the sample was 25.01 years (SD = 7.56). After completing a biographical questionnaire, subjects’ CSI and heart rates were evaluated using a digital medical device, the ViportTM. The combined CSI for the group was elevated above the normative value of 20% (31.00%; SD = 14.03). The seated, supine and combined CSI all differed significantly from one another (p<0.05) and the CSI was significantly correlated with heart rate (p=0.41). In conclusion, the CSI readings, like heart rate variability measurements taken in different postures, cannot be used interchangeably in clinical practice or in research. The CSI appears to mirror existing research evidence on heart rate variability and posture.http://www.ajol.info/journal_index.php?jid=153&ab=ajpher

The correlation between the health-related fitness of healthy participants measured at home as opposed to fitness measured by sport scientists in a laboratory

BACKGROUND : Fitness is defined in the health context as a state of good health or physical condition, primarily as a result of exercise and proper nutrition. Conventional methods of measuring fitness are expensive, time consuming and require specialised methods. There is a need for noninvasive, fast methods of assessing health-related fitness and activity in athlete and non-athlete populations. The aim of this study was to establish any correlation between participants’ self-assessed health-related fitness (HRF) index and the HRF index determined by sports scientists, as well as the laboratory-assessed HRF index and maximum oxygen uptake (VO2max) determined by sports scientists via direct methods in a laboratory, and finally, to determine any potential correlation between an activity-recall questionnaire (Kasari) and VO2max. METHOD : The participants consisted of 169 male and female volunteers between the ages of 18 and 55 years, taking neither supplements nor medication. The University of Pretoria’s HRF index protocol was first carried out by participants on their own at home, and then in the laboratory under the supervision of sport scientists. The complete datasets of 150 participants were statistically analysed to establish correlations. RESULTS : The results indicated highly significant and substantial correlations (ρ = 0.696, p < 0.001) between the participants’ self-assessed HRF index and measurements by the sports scientists. There were moderate correlations between the laboratoryassessed HRF index and the direct VO2max (ρ = 0 512, p < 0.005), as well as the indirect VO2max (ρ = 0.588; p < 0.001). A significant correlation was found between the self-assessed HRF index and the indirect VO2max (ρ = 0.454; p < 0.001). The Kasari questionnaire correlated only weakly with the indirect VO2max (ρ = 0.278, p < 0.002) and not at all with the direct VO2max (ρ = 0.072, p = 0.731). CONCLUSION : Indications are that this test protocol may be conducted at home by individuals, without supervision, to determine exercise ability or fitness, or to monitor changes in physical fitness, thereby limiting expenses and costs.Momentum Interactivehttp://www.safpj.co.za/index.php/safpjhb201

Functional genomics analysis identifies T and NK cell activation as a driver of epigenetic clock progression

Background Epigenetic clocks use DNA methylation (DNAm) levels of specific sets of CpG dinucleotides to accurately predict individual chronological age. A popular application of these clocks is to explore whether the deviation of predicted age from chronological age is associated with disease phenotypes, where this deviation is interpreted as a potential biomarker of biological age. This wide application, however, contrasts with the limited insight in the processes that may drive the running of epigenetic clocks. Results We perform a functional genomics analysis on four epigenetic clocks, including Hannum's blood predictor and Horvath's multi-tissue predictor, using blood DNA methylome and transcriptome data from 3132 individuals. The four clocks result in similar predictions of individual chronological age, and their constituting CpGs are correlated in DNAm level and are enriched for similar histone modifications and chromatin states. Interestingly, DNAm levels of CpGs from the clocks are commonly associated with gene expression in trans. The gene sets involved are highly overlapping and enriched for T cell processes. Further analysis of the transcriptome and methylome of sorted blood cell types identifies differences in DNAm between naive and activated T and NK cells as a probable contributor to the clocks. Indeed, within the same donor, the four epigenetic clocks predict naive cells to be up to 40 years younger than activated cells. Conclusions The ability of epigenetic clocks to predict chronological age involves their ability to detect changes in proportions of naive and activated immune blood cells, an established feature of immuno-senescence. This finding may contribute to the interpretation of associations between clock-derived measures and age-related health outcomes.Molecular Epidemiolog