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.
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.
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.
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.
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.
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.
Detection of REEs with lightweight UAV‑based hyperspectral imaging
(Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations., 2020) Booysen, René; Nex, Paul A.M.; Zimmermann, Robert; Loren, Sandra; Kirsch, Moritz; Jackish, Robert; Gloaguen, Richard
Rare earth elements (REEs) supply is important to ensure the energy transition, e-mobility and ultimately to achieve the sustainable development goals of the United Nations. Conventional exploration techniques usually rely on substantial geological field work including dense in-situ sampling with long delays until provision of analytical results. However, this approach is limited by land accessibility, financial status, climate and public opposition. Efficient and innovative methods are required to mitigate these limitations. The use of lightweight unmanned aerial vehicles (UAVs) provides a unique opportunity to conduct rapid and non-invasive exploration even in socially sensitive areas and in relatively inaccessible locations. We employ drones with hyperspectral sensors to detect REEs at the earth’s surface and thus contribute to a rapidly evolving field at the cutting edge of exploration technologies. We showcase for the first time the direct mapping of REEs with lightweight hyperspectral UAV platforms. Our solution has the advantage of quick turn-around times (< 1 d), low detection limits (< 200 ppm for Nd) and is ideally suited to support exploration campaigns. This procedure was successfully tested and validated in two areas: Marinkas Quellen, Namibia, and Siilinjärvi, Finland. This strategy should invigorate the use of drones in exploration and for the monitoring of mining activities.
Accurate hyperspectral imaging of mineralised outcrops: An example from lithium-bearing pegmatites at Uis, Namibia
(Elsevier Inc, 2021) Booysen, René; Nex, Paul A.M.; Lorenz, Sandra; Thiele, Samuel T.; Fuchsloch, Warrick C.; Marais, Timothy; Gloaguen, Richard
Efficient, socially acceptable and rapid methods of exploration are required to discover new deposits and enable the green energy transition. Sustainable exploration requires a combination of innovative thinking and new technologies. Hyperspectral imaging (HSI) is a rapidly developing technology and allows for fast and systematic mineral mapping, facilitating exploration of the Earth’s surface at various scales on a variety of platforms. Newly available sensors allow data capture over a wide spectral range, and provide information about the abundance and spatial location of ore and pathfinder minerals in drill-core, hand samples and outcrops with mm to cm precision. Conversely, the complex geometries of the imaged surfaces affect the spectral quality and signal-to-noise ratio (SnR) of HSI data at these very narrow spatial samplings. Additionally, the complex mineral assemblages found in hydrothermally altered ore deposits can make interpretation of spectral results a challenge. In this contribution, we propose an innovative approach that integrates multiple sensors and scales of data acquisition to help disentangle complex mineralogy associated with lithium and tin mineralisation in the Uis pegmatite complex, Namibia. We train this method using hand samples and finally produce a three-dimensional (3D) point cloud for mapping lithium mineralisation in the open pit. We were able to identify and map lithium-bearing cookeite and montebrasite at outcrop scale. The accuracy of the approach was validated by drill-core data, XRD analysis and LIBS measurements. This approach facilitates efficient mapping of complex terrains, as well as important monitoring and optimisation of ore extraction. Our method can easily be adapted to other minerals relevant to the mining industry.
Geological Remote Sensing
(Acdemic Press, United Kingdom, 2021) Booysen, René; Nex, Paul A.M.; Gloaguen, Richard; Lorenz, Sandra; Zimmermann, Robert; Alderton, David; Elias, Scott A.
The field of remote sensing has recently witnessed major innovations that have been translated to Earth science applications. Before they can be used, remote sensing data must be corrected for effects originating from the sensors, the platforms on which they are deployed, atmospheric characteristics, and geometrical constraints. When the data are calibrated and geolocated, they can be used either as physical quantities, such as reflectance and temperatures, or as images. The recent development of new sensors has permitted the remote measurement of a large area of the Earth's surface, with direct geological applications. Additionally, advances in machine vision, machine learning and artificial intelligence, combined with an unprecedented increase in computer processing power, have led to innovative remote sensing data processing techniques that simplify the handling of large amounts of complex data. As a consequence, it is now possible to characterize the geological settings of large areas with precision and even their changes through time. Remote sensing data are now directly integrated into modelling algorithms that describe surface and subsurface processes at different scales. Geological remote sensing currently encompasses multi temporal, multi-source and multi scale approaches. The retrieval of big data in disseminated archives, as well as (near) real time processing are the challenges that remain to be solved. These new applications in geology ensure cost efficient, safe, and rapid surveys and monitoring that not only benefit the research community but society at large.
Analysis of urban sprawl dynamics using machine learning, CA-Markov chain, and the Shannon entropy model: a case study in Mbombela City, South Africa
(SpringerOpen, 2024) Mhangara, Paidamwoyo; Gidey, Eskinder; Rabia Manjoo
Over half of the world’s population resides in urban areas. We anticipate that this pattern will become more evident, notably in South Africa. Therefore, research on urban spirals, both past and projected, is necessary for efficient urban land use planning and management. This study aims to assess the spatio-temporal urban sprawl dynamics from 2003 to 2033 in Mbombela, South Africa. We employed robust approaches such as machine learning, the cellular automata-Markov chain, and the Shannon entropy model to look at how urban sprawl changes over time using both the Landsat 4–5 Thematic Mapper and the 8 Operational Land Imagers. We conducted this study to bridge the gaps in existing research, which primarily focuses on past and current urban growth trends rather than future trends. The findings indicated that the coverage of built-up areas and vegetation has expanded by 1.98 km2 and 13.23 km2 between the years 2003 and 2023. On the other hand, the amount of land continues to decrease by -12.56 km2 and − 2.65 km2 annually, respectively. We anticipate an increase in the built-up area and vegetation to a total of 7.60 km2 and 0.57 km2, respectively, by the year 2033. We anticipate a total annual decline of -7.78 km2 and − 0.39 km2 in water bodies and open land coverage, respectively. This work has the potential to assist planners and policymakers in improving sustainable urban land-use planning.

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