Faculty of Science (Research Outputs)

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Forward scattering on the line with a transfer condition
(SpringerOpen [Commercial Publisher], 2013-12) Currie, Sonja; Nowaczyk, Marlena; Watson, Bruce A.
We consider scattering on the line with a transfer condition at the origin. Under suitable growth conditions on the potential, the spectrum consists of a finite number of eigenvalues which are negative real numbers, while the remainder is continuous spectrum which is comprised of the positive real axis. Asymptotics are provided for the Jost solutions. Conditions which characterize transfer conditions resulting in self-adjoint problems are found. Properties are given of the scattering coefficient linking it to the spectrum.
Self-adjoint higher order differential operators with eigenvalue parameter dependent boundary conditions.
(SpringerOpen [Commercial Publisher], 2015-12) Möller, Manfred; Zinsou, Bertin
Eigenvalue problems for even order regular quasi-differential equations with boundary conditions which depend linearly on the eigenvalue parameter λ can be represented by an operator polynomial (Formula presented.) where M is a self-adjoint operator. Necessary and sufficient conditions are given such that also K and A are self-adjoint.
Survival analysis of bank loans in the presence of long-term survivors
(South African Statistical Association, 2017-04) Marimo, M; Chimedza, C
In this paper we model competing risks, default and early settlement events, in the presence of long term survivors and compare survival and logistic methodologies. Cause specific Cox regression models were fitted and adjustments were made to accommodate a proportion of long term survivors. Methodologies were compared using ROC curves and area under the curves. The results show that survival methods perform better than logistic regression methods when modelling lifetime data in the presence of competing risks and in the presence of long term survivors.
Insights into the genetics of blood pressure in black South African individuals: the Birth to Twenty cohort
(BMC, 2018) Hendry, Liesl M.; Sahibdeen, Venesa; Choudhury, Ananyo; Norris, Shane A.; Ramsay, Michèle; Lombard, Zané
Background: Cardiovascular diseases (CVDs) are the leading cause of non-communicable disease deaths globally, with hypertension being a major risk factor contributing to CVDs. Blood pressure is a heritable trait, with relatively few genetic studies having been performed in Africans. This study aimed to identify genetic variants associated with variance in systolic (SBP) and diastolic (DBP) blood pressure in black South Africans. Methods: Genotyping was performed using the Metabochip in a subset of participants (mixed sex; median age 17.9) and their adult female caregivers (median age 41.0) from the Birth to Twenty cohort (n = 1947). Data were analysed as a merged dataset (all participants and caregivers together) in GEMMA (v0.94.1) using univariate linear mixed models, incorporating a centered relatedness matrix to account for the relatedness between individuals and with adjustments for age, sex, BMI and principal components of the genotype information. Results: Association analysis identified regions of interest in the NOS1AP (DBP: rs112468105 - p = 7.18 × 10−5 and SBP: rs4657181 - p = 4.04 × 10−5), MYRF (SBP: rs11230796 - p = 2.16 × 10−7, rs400075 - p = 2.88 × 10−7) and POC1B (SBP: rs770373 - p = 7.05 × 10−5, rs770374 - p = 9.05 × 10−5) genes and some intergenic regions (DACH1|LOC440145 (DBP: rs17240498 - p = 4.91 × 10−6 and SBP: rs17240498 - p = 2.10 × 10−5) and INTS10|LPL (SBP: rs55830938 - p = 1.30 × 10−5, rs73599609 - p = 5.78 × 10−5, rs73667448 - p = 6.86×10−5)). Conclusions: The study provided further insight into the contribution of genetic variants to blood pressure in black South Africans. Future functional and replication studies in larger samples are required to confirm the role of the identified loci in blood pressure regulation and whether or not these variants are African-specific.
Entanglement beating in free space through spin–orbit coupling
(Springer Nature, 2018) Rosales-Guzmán, Carmelo; Denz, Cornelia; Otte, Eileen; Ndagano, Bienvenu; Forbes, Andrew
It is well known that the entanglement of a quantum state is invariant under local unitary transformations. This rule dictates, for example, that the entanglement of internal degrees of freedom of a photon remains invariant during free-space propagation. Here, we outline a scenario in which this paradigm does not hold. Using local Bell states engineered from classical vector vortex beams with non-separable degrees of freedom, the so-called classically entangled states, we demonstrate that the entanglement evolves during propagation, oscillating between maximally entangled (purely vector) and product states (purely scalar). We outline the spin–orbit interaction behind these novel propagation dynamics and confirm the results experimentally, demonstrating spin–orbit coupling in paraxial beams. This demonstration highlights a hitherto unnoticed property of classical entanglement and simultaneously offers a device for the on-demand delivery of vector states to targets, for example, for dynamic laser materials processing, switchable resolution within stimulated emission depletion (STED) systems, and a tractor beam for entanglement.
Platinum-bearing chromite layers are caused by pressure reduction during magma ascent
(Nature Research, 2018) Latypov, Rais; Costin, Gelu; Chistyakova, Sofya; Hunt, Emma J.; Mukherjee, Ria; Naldrett, Tony
Platinum-bearing chromitites in mafic-ultramafic intrusions such as the Bushveld Complex are key repositories of strategically important metals for human society. Basaltic melts saturated in chromite alone are crucial to their generation, but the origin of such melts is controversial. One concept holds that they are produced by processes operating within the magma chamber, whereas another argues that melts entering the chamber were already saturated in chromite. Here we address the problem by examining the pressure-related changes in the topology of a Mg2SiO4–CaAl2Si2O8–SiO2–MgCr2O4 quaternary system and by thermodynamic modelling of crystallisation sequences of basaltic melts at 1–10 kbar pressures. We show that basaltic melts located adjacent to a so-called chromite topological trough in deep-seated reservoirs become saturated in chromite alone upon their ascent towards the Earth’s surface and subsequent cooling in shallow-level chambers. Large volumes of these chromite-only-saturated melts replenishing these chambers are responsible for monomineralic layers of massive chromitites with associated platinum-group elements.
Assessing runs of Homozygosity: a comparison of SNP Array and whole genome sequence low coverage data
(BMC, 2018) Ceballos, Francisco C.; Hazelhurst, Scott; Ramsay, Michèle
Background: Runs of Homozygosity (ROH) are genomic regions where identical haplotypes are inherited from each parent. Since their first detection due to technological advances in the late 1990s, ROHs have been shedding light on human population history and deciphering the genetic basis of monogenic and complex traits and diseases. ROH studies have predominantly exploited SNP array data, but are gradually moving to whole genome sequence (WGS) data as it becomes available. WGS data, covering more genetic variability, can add value to ROH studies, but require additional considerations during analysis. Results: Using SNP array and low coverage WGS data from 1885 individuals from 20 world populations, our aims were to compare ROH from the two datasets and to establish software conditions to get comparable results, thus providing guidelines for combining disparate datasets in joint ROH analyses. By allowing heterozygous SNPs per window, using the PLINK homozygosity function and non-parametric analysis, we were able to obtain non-significant differences in number ROH, mean ROH size and total sum of ROH between data sets using the different technologies for almost all populations. Conclusions: By allowing 3 heterozygous SNPs per ROH when dealing with WGS low coverage data, it is possible to establish meaningful comparisons between data using SNP array and WGS low coverage technologies.
A metagenomic viral discovery approach identifies potential zoonotic and novel mammalian viruses in Neoromicia bats within South Africa
(Public Library of Science, 2018-03) Geldenhuys, M.; Mortlock, M.; Weyer, J.; Bezuidt, O.; Seamark, E.C.J.; Kearney, T.
Species within the Neoromicia bat genus are abundant and widely distributed in Africa. It is common for these insectivorous bats to roost in anthropogenic structures in urban regions. Additionally, Neoromicia capensis have previously been identified as potential hosts for Middle East respiratory syndrome (MERS)-related coronaviruses. This study aimed to ascertain the gastrointestinal virome of these bats, as viruses excreted in fecal material or which may be replicating in rectal or intestinal tissues have the greatest opportunities of coming into contact with other hosts. Samples were collected in five regions of South Africa over eight years. Initial virome composition was determined by viral metagenomic sequencing by pooling samples and enriching for viral particles. Libraries were sequenced on the Illumina MiSeq and NextSeq500 platforms, producing a combined 37 million reads. Bioinformatics analysis of the high throughput sequencing data detected the full genome of a novel species of the Circoviridae family, and also identified sequence data from the Adenoviridae, Coronaviridae, Herpesviridae, Parvoviridae, Papillomaviridae, Phenuiviridae, and Picornaviridae families. Metagenomic sequencing data was insufficient to determine the viral diversity of certain families due to the fragmented coverage of genomes and lack of suitable sequencing depth, as some viruses were detected from the analysis of reads-data only. Follow up conventional PCR assays targeting conserved gene regions for the Adenoviridae, Coronaviridae, and Herpesviridae families were used to confirm metagenomic data and generate additional sequences to determine genetic diversity. The complete coding genome of a MERS-related coronavirus was recovered with additional amplicon sequencing on the MiSeq platform. The new genome shared 97.2% overall nucleotide identity to a previous Neoromicia-associated MERS-related virus, also from South Africa. Conventional PCR analysis detected diverse adenovirus and herpesvirus sequences that were widespread throughout Neoromicia populations in South Africa. Furthermore, similar adenovirus sequences were detected within these populations throughout several years. With the exception of the coronaviruses, the study represents the first report of sequence data from several viral families within a Southern African insectivorous bat genus; highlighting the need for continued investigations in this regard.
Temporal shifts in landscape connectivity for an ecosystem engineer, the roe deer, across a multiple-use landscape
(Springer, 2018-04) Martin, Jodie; Vourc’h, Gwenae¨l; Bonnot, Nade`ge; Cargnelutti, Bruno; Chaval, Yannick; Lourte, Bruno; Goulard, Michel; Hoch, Thierry; Plantard, Olivier; Hewison, A. J. Mark; Morellet, Nicolas
Context: Routine movements of large herbivores, often considered as ecosystem engineers, impact key ecological processes. Functional landscape connectivity for such species influences the spatial distribution of associated ecological services and disservices. Objectives: We studied how spatio-temporal variation in the risk-resource trade-off, generated by fluctuations in human activities and environmental conditions, influences the routine movements of roedeer across a heterogeneous landscape, generating shifts in functional connectivity at daily and seasonal time scales. Methods: We used GPS locations of 172 adult roedeer and step selection functions to infer landscape connectivity. In particular, we assessed the influence of six habitat features on fine scale movements across four biological seasons and three daily periods, based on variations in the risk-resource trade-off. Results: The influence of habitat features on roe deer movements was strongly dependent on proximity to refuge habitat, i.e. woodlands. Roe deer confined their movements to safe habitats during daytime and during the hunting season, when human activity is high.
Knock-down of LRP/LR promotes apoptosis in early and late stage colorectal carcinoma cells via caspase activation
(BioMed Central, 2018-05) Vania, Leila; Rebelo, Thalia M.; Ferreira, Eloise; Weiss, Stefan F. T.
Background: Cancer remains one of the leading causes of death around the world, where incidence and mortality rates are at a constant increase. Tumourigenic cells are characteristically seen to over-express the 37 kDa/67 kDa laminin receptor (LRP/LR) compared to their normal cell counterparts. This receptor has numerous roles in tumourigenesis including metastasis, angiogenic enhancement, telomerase activation, cell viability and apoptotic evasion. This study aimed to expose the role of LRP/LR on the cellular viability of early (SW-480) and late (DLD-1) stage colorectal cancer cells. Methods: siRNA were used to down-regulate the expression of LRP/LR in SW-480 and DLD-1 cells which was assessed using western blotting. Subsequently, cell survival was evaluated using the MTT cell survival assay and confocal microscopy. Thereafter, Annexin V-FITC/PI staining and caspase activity assays were used to investigate the mechanism underlying the cell death observed upon LRP/LR knockdown. The data was analysed using Student’s ttest with a confidence interval of 95%, with p-values of less than 0.05 seen as significant. Results: Here we reveal that siRNA-mediated knock-down of LRP led to notable decreases in cell viability through increased levels of apoptosis, apparent by compromised membrane integrity and significantly high caspase-3 activity. Down-regulated LRP resulted in a significant increase in caspase-8 and -9 activity in both cell lines. Conclusions: These findings show that the receptor is critically implicated in apoptosis and that LRP/LR downregulation induces apoptosis in early and late stage colorectal cancer cells through both apoptotic pathways. Thus, this study suggests that siRNA-mediated knock-down of LRP could be a possible therapeutic strategy for the treatment of early and late stage colorectal carcinoma.
Compositions with a fixed number of inversions
(Springer, 2018-05) Knopfmacher, A.; Mays, M. E.; Wagner, S.
A composition of the positive integer n is a representation of n as an ordered sum of positive integers n = a1 + a2 + ··· + am. There are 2n−1 unrestricted compositions of n, which can be sorted according to the number of inversions they contain. (An inversion in a composition is a pair of summands {ai, aj} for which i aj .) The number of inversions of a composition is an indication of how far the composition is from a partition of n, which by convention uses a sequence of nondecreasing summands and thus has no inversions. We count compositions of n with exactly r inversions in several ways to derive generating function identities, and also consider asymptotic results.
Kondo effect and enhanced magnetic properties in gadolinium functionalized carbon nanotube supramolecular complex
(Nature Research, 2018-05) Ncube, S.; Coleman, C.; Strydom, A.; Flahaut, E.; de Sousa, A.
We report on the enhancement of magnetic properties of multiwalled carbon nanotubes (MWNTs) functionalized with a gadolinium based supramolecular complex. By employing a newly developed synthesis technique, we find that the functionalization method of the nanocomposite enhances the strength of magnetic interaction, leading to a large effective moment of 15.79µB and nonsuperparamagnetic behavior, unlike what has been previously reported. Saturating resistance at low temperatures is ftted with the numerical renormalization group formula, verifying the Kondo effect for magnetic impurities on a metallic electron system. Magnetoresistance shows devices fabricated from aligned gadolinium functionalized MWNTs (Gd-Fctn-MWNTs) exhibit spin-valve switching behaviour of up to 8%. This study highlights the possibility of enhancing magnetic interactions in carbon systems through chemical modification, moreover, we demonstrate the rich physics that might be useful for developing spin based quantum computing elements based on one-dimensional (1D) channels.
Genetic risk score for adult body mass index associations with childhood and adolescent weight gain in an African population
(BioMed Central, 2018-08) Munthali, Richard J.; Sahibdeen, Venesa; Kagura, Juliana; Hendry, Liesl M.; Norris, Shane A.; Ong, Ken K.; Lombard, Zané; Day, Felix R.
Background: Ninety-seven independent single nucleotide polymorphisms (SNPs) are robustly associated with adult body mass index (BMI kg/m2) in Caucasian populations. The relevance of such variants in African populations at different stages of the life course (such as childhood) is unclear. We tested whether a genetic risk score composed of the aforementioned SNPs was associated with BMI from infancy to early adulthood. We further tested whether this genetic effect was mediated by conditional weight gain at different growth periods. We used data from the Birth to Twenty Plus Cohort (Bt20+), for 971 urban South African black children from birth to 18 years. DNA was collected at 13 years old and was genotyped using the Metabochip (Illumina) array. The weighted genetic risk score (wGRS) for BMI was constructed based on 71 of the 97 previously reported SNPs. Results: The cross-sectional association between the wGRS and BMI strengthened with age from 5 to 18 years. The significant associations were observed from 11 to 18 years, and peak effect sizes were observed at 13 and 14 years of age. Results from the linear mixed effects models showed significant interactions between the wGRS and age on longitudinal BMI but no such interactions were observed in sex and the wGRS. A higher wGRS was associated with an increased relative risk of belonging to the early onset obese longitudinal BMI trajectory (relative risk = 1.88; 95%CI 1.28 to 2.76) compared to belonging to a normal longitudinal BMI trajectory. Adolescent conditional relative weight gain had a suggestive mediation effect of 56% on the association between wGRS and obesity risk at 18 years. Conclusions: The results suggest that genetic susceptibility to higher adult BMI can be tracked from childhood in this African population. This supports the notion that prevention of adult obesity should begin early in life. The genetic risk score combined with other non-genetic risk factors, such as BMI trajectory membership in our case, has the potential to be used to screen for early identification of individuals at increased risk of obesity and other related NCD risk factors in order to reduce the adverse health risk outcomes later.
Free field primaries in general dimensions: counting and construction with rings and modules
(Springer, 2018-08) de Mello Koch, Robert
We define lowest weight polynomials (LWPs), motivated by so(d, 2) representation theory, as elements of the polynomial ring over d × n variables obeying a system of first and second order partial differential equations. LWPs invariant under Sn correspond to primary fields in free scalar field theory in d dimensions, constructed from n fields. The LWPs are in one-to-one correspondence with a quotient of the polynomial ring in d × (n − 1) variables by an ideal generated by n quadratic polynomials. The implications of this description for the counting and construction of primary fields are described: an interesting binomial identity underlies one of the construction algorithms. The product on the ring of LWPs can be described as a commutative star product. The quadratic algebra of lowest weight polynomials has a dual quadratic algebra which is non-commutative. We discuss the possible physical implications of this dual algebra.
Dimethylformamide is a novel nitrilase inducer in Rhodococcus rhodochrous
(Springer, 2018-09) Chhiba-Govindjee, V. P.; Brady, D.; Mathiba, K.; van der Westhuyzen, C. W.; Steenkamp, P.; Rashamuse, J. K.; Stoychev, S.
Nitrilases are of commercial interest in the selective synthesis of carboxylic acids from nitriles. Nitrilase induction was achieved here in three bacterial strains through the incorporation of a previously unrecognised and inexpensive nitrilase inducer, dimethylformamide (DMF), during cultivation of two Rhodococcus rhodochrous strains (ATCC BAA-870 and PPPPB BD1780), as well as a closely related organism (Pimelobacter simplex PPPPB BD-1781). Benzonitrile, a known nitrilase inducer, was ineffective in these strains. Biocatalytic product profiling, enzyme inhibition studies and protein sequencing were performed to distinguish the nitrilase activity from that of sequential nitrile hydratase-amidase activity. The expressed enzyme, a 40-kDa protein with high sequence similarity to nitrilase protein Uniprot Q-03217, hydrolyzed 3-cyanopyridine to produce nicotinic acid exclusively in strains BD-1780 and BD-1781. These strains were capable of synthesising both the vitamin nicotinic acid as well as β-amino acids, a compound class of pharmaceutical interest. The induced nitrilase demonstrated high enantioselectivity (>99%) in the hydrolysis of 3-amino-3-phenylpropanenitrile to the corresponding carboxylic acid.
Towards multiscale and multisource remote sensing mineral exploration using rpas: A case study in the lofdal carbonatite-hosted ree deposit, Namibia
(MDPI, Basel, Switzerland, 2019) Booysen, René; Nex, Paul A.M.; Zimmermann, Robert; Lorenz, Sandra; Gloaguen, Richard; Andreani, Louis; Möckel, Robert
Traditional exploration techniques usually rely on extensive field work supported by geophysical ground surveying. However, this approach can be limited by several factors such as field accessibility, financial cost, area size, climate, and public disapproval. We recommend the use of multiscale hyperspectral remote sensing to mitigate the disadvantages of traditional exploration techniques. The proposed workflow analyzes a possible target at different levels of spatial detail. This method is particularly beneficial in inaccessible and remote areas with little infrastructure, because it allows for a systematic, dense and generally noninvasive surveying. After a satellite regional reconnaissance, a target is characterized in more detail by plane-based hyperspectral mapping. Subsequently, Remotely Piloted Aircraft System (RPAS)-mounted hyperspectral sensors are deployed on selected regions of interest to provide a higher level of spatial detail. All hyperspectral data are corrected for radiometric and geometric distortions. End-member modeling and classification techniques are used for rapid and accurate lithological mapping. Validation is performed via field spectroscopy and portable XRF as well as laboratory geochemical and spectral analyses. The resulting spectral data products quickly provide relevant information on outcropping lithologies for the field teams. We show that the multiscale approach allows defining the promising areas that are further refined using RPAS-based hyperspectral imaging. We further argue that the addition of RPAS-based hyperspectral data can improve the detail of field mapping in mineral exploration, by bridging the resolution gap between airplane- and ground-based data. RPAS-based measurements can supplement and direct geological observation rapidly in the field and therefore allow better integration with in situ ground investigations. We demonstrate the efficiency of the proposed approach at the Lofdal Carbonatite Complex in Namibia, which has been previously subjected to rare earth elements exploration. The deposit is located in a remote environment and characterized by difficult terrain which limits ground surveys.
Thermal analysis of natural convection and radiation heat transfer in moving porous fins
(Global Digital Central, 2019) Ndlovu, P.L.; Moitsheki, R.J.
In this article, the Differential Transform Method (DTM) is used to perform thermal analysis of natural convective and radiative heat transfer in moving porous fins of rectangular and exponential profiles. This study is performed using Darcy’s model to formulate the governing heat transfer equations. The effects of porosity parameter, irregular profile and other thermo-physical parameters, such as Peclet number and the radiation parameter are also analyzed. The results show that the fin rapidly dissipates heat to the surrounding temperature with an increase in the values of the porosity parameter and the dimensionless time parameter. The results also show that the heat transfer rate in an exponential profile with negative power factor is much higher than the rectangular profile.
Evidence for igneous differentiation in Sudbury Igneous Complex and impact-driven evolution of terrestrial planet proto-crusts
(Nature Research, 2019-01) Latypov, Rais; Chistyakova, Sofya; Grieve, Richard; Huhma, Hannu
Bolide impact is a ubiquitous geological process in the Solar System, which produced craters and basins filled with impact melt sheets on the terrestrial planets. However, it remains controversial whether these sheets were able to undergo large-scale igneous differentiation, or not. Here, we report on the discovery of large discrete bodies of melanorites that occur throughout almost the entire stratigraphy of the 1.85-billion-year-old Sudbury Igneous Complex (SIC) – the best exposed impact melt sheet on Earth – and use them to reaffirm that conspicuous norite-gabbro-granophyre stratigraphy of the SIC is produced by fractional crystallization of an originally homogeneous impact melt of granodioritic composition. This implies that more ancient and compositionally primitive Hadean impact melt sheets on the Earth and other terrestrial planets also underwent large-volume igneous differentiation. The near-surface differentiation of these giant impact melt sheets may therefore have contributed to the evolution and lithological diversity of the proto-crust on terrestrial planets.
Stabilization of ODE with hyperbolic equation actuator subject to boundary control matched disturbance
(Taylor and Francis Ltd., 2019-01-02) Zhou, H.C.; Guo, B.Z.
In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation with external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By ADRC approach, the disturbance is estimated through a disturbance estimator with both time-varying high gain and constant high gain, and the disturbance is canceled online in the feedback loop. It is shown that the resulting closed-loop system with time-varying high gain is asymptotically stable and is practically stable with constant high gain. By SMC approach, the existence and uniqueness of the solution for the closed loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented. The resulting closed-loop system is shown to be exponentially stable. The numerical experiments are carried out to illustrate effectiveness of the proposed control law. © 2016, © 2016 Informa UK Limited, trading as Taylor & Francis Group.
Wishart exponential families on cones related to tridiagonal matrices
(Springer Tokyo, 2019-04-01) Graczyk, P; Ishi, H; Mamane, S
Let G be the graph corresponding to the graphical model of nearest neighbor interaction in a Gaussian character. We study Natural Exponential Families (NEF) of Wishart distributions on convex cones Q G and P G , where P G is the cone of tridiagonal positive definite real symmetric matrices, and Q G is the dual cone of P G . The Wishart NEF that we construct include Wishart distributions considered earlier for models based on decomposable(chordal) graphs. Our approach is, however, different and allows us to study the basic objects of Wishart NEF on the cones Q G and P G . We determine Riesz measures generating Wishart exponential families on Q G and P G , and we give the quadratic construction of these Riesz measures and exponential families. The mean, inverse-mean, covariance and variance functions, as well as moments of higher order, are studied and their explicit formulas are given. © 2018, The Institute of Statistical Mathematics, Tokyo.