The development of the quaternion normal distribution

In this dissertation an overview on the real representation of quaternions in distribution theory is given. The density functions of the p-variate and matrix-variate quaternion normal distributions are derived from first principles, while that of the quaternion Wishart distribution is derived from the real associated Wishart distribution via the characteristic function. Applications of this theory in hypothesis testing is presented, and the density function of Wilks's statistic is derived for quaternion Wishart matrices.Dissertation (MSc)--University of Pretoria, 2010.Statisticsunrestricte

A statistical scheme to forecast the daily lightning threat over southern Africa using the Unified Model

Cloud-to-ground lightning data from the Southern Africa Lightning Detection Network and numerical weather prediction model parameters from the Unified Model are used to develop a lightning threat index (LTI) for South Africa. The aim is to predict lightning for austral summer days (September to February) by means of a statistical approach. The austral summer months are divided into spring and summer seasons and analysed separately. Stepwise logistic regression techniques are used to select the most appropriate model parameters to predict lightning. These parameters are then utilized in a rare-event logistic regression analysis to produce equations for the LTI that predicts the probability of the occurrence of lightning. Results show that LTI forecasts have a high sensitivity and specificity for spring and summer. The LTI is less reliable during spring, since it over-forecasts the occurrence of lightning. However, during summer, the LTI forecast is reliable, only slightly over-forecasting lightning activity. The LTI produces sharp forecasts during spring and summer. These results show that the LTI will be useful early in the morning in areas where lightning can be expected during the day.http://www.elsevier.com/locate/atmos2018-09-15Geography, Geoinformatics and Meteorolog

SWAPDT : a method for short-time withering assessment of probability for drought tolerance in Camellia sinensis validated by targeted metabolomics

Climate change is causing droughts affecting crop production on a global scale. Classical breeding and selection strategies for drought-tolerant cultivars will help prevent crop losses. Plant breeders, for all crops, need a simple and reliable method to identify drought-tolerant cultivars, but such a method is missing. Plant metabolism is often disrupted by abiotic stress conditions. To survive drought, plants reconfigure their metabolic pathways. Studies have documented the importance of metabolic regulation, i.e. osmolyte accumulation such as polyols and sugars (mannitol, sorbitol); amino acids (proline) during drought. This study identified and quantified metabolites in drought tolerant and drought susceptible Camellia sinensis cultivars under wet and drought stress conditions. For analyses, GC-MS and LC-MS were employed for metabolomics analysis. %RWC results show how the two drought tolerant and two drought susceptible cultivars differed significantly (p ≤ 0.05) from one another; the drought susceptible exhibited rapid water loss compared to the drought tolerant. There was a significant variation (p < 0.05) in metabolite content (amino acid, sugars) between drought tolerant and drought susceptible tea cultivars after short-time withering conditions. These metabolite changes were similar to those seen in other plant species under drought conditions, thus validating this method. The Short-time Withering Assessment of Probability for Drought Tolerance (SWAPDT) method presented here provides an easy method to identify drought tolerant tea cultivars that will mitigate the effects of drought due to climate change on crop losses.The financial support to conduct this research, and study grants for CN and RK from James Finlay (Kenya) Ltd, George Williamson (Kenya) Ltd, Sotik Tea Company (Kenya) Ltd, Mcleod Russell (Uganda) Ltd, and the Tea Research Institute of Kenya. The C. sinensis cultivars used in this study were provided by the Tea Research Foundation of Central Africa (Malawi) and the Tea Research Institute of Kenya. Supplementary funding was provided by, the Technology and Human Resources for Industry Programme (THRIP), an initiative of the Department of Trade and Industries of South Africa (dti), the National Research Foundation (NRF) of South Africa, and the University of Pretoria (South Africa).http://www.elsevier.com/locate/jplph2017-07-31hb2016BiochemistryStatistic

Towards developing a metabolic-marker based predictive model for Phytophthora nicotianae tolerance in citrus rootstocks

Root rot of citrus trees caused by Phytophthora nicotianae is responsible for severe economic losses in citriculture. Use of resistant rootstocks is an effective method of managing this problem, however, breeding and selection of new citrus rootstocks is a time-consuming undertaking. The objective was to develop a method for the rapid assessment of rootstocks for P. nicotianae tolerance, using a metabolomics approach to identify metabolic markers for the phenotypic trait of tolerance. Sixteen citrus rootstocks were inoculated with P. nicotianae in the greenhouse for determination of relative tolerance/susceptibility. Healthy citrus roots from four tolerant and four susceptible rootstocks were used for metabolite analysis with the objective of identifying potential biomarkers. Organic solvent extractions of the roots were prepared and analysed by mass-spectrometry based liquid chromatography, which produced 367 ion features (retention time and m/z). Orthogonal partial least squares discriminant analysis of peak abundance using MarkerLynx software allowed for the identification of ion features that differentiate tolerant and susceptible rootstocks. Using descriptive and inferential statistics based on the ion features of uninoculated tolerant vs. susceptible rootstocks, applying logistic regression, 14 top markers were identified and two of them (22.03_259.0975 and 22.21_313.1445: retention time (rt) and mass to charge ratio (m/z) were accepted as potential metabolic markers. A model that can potentially predict tolerance in citrus rootstocks with >98% accuracy is presented.The authors acknowledge financial support to conduct this research from Citrus Research International, South Africa. Supplementary funding was provided by the University of Pretoria (South Africa). We also thank Dr. Wilhelm Botha for the morphological and molecular characterisation of the pathogen (Pathogen Accession Number: Ph 453 PPRI 23883 Agricultural Research Council, Plant Protection Research Institute, Pretoria, South Africa).https://link.springer.com/journal/421612019-07-01am2019BiochemistryPlant ScienceStatistic

Integral representation of quaternion elliptical density and its applications

In this paper, an integral representation for the density of a matrix variate quaternion elliptical distribution is proposed. To this end, a weight func- tion is used, based on the inverse Laplace transform of a function of a Hermitian quaternion matrix. Examples of well-known members of the family of quaternion elliptical distributions are given as well as their respective weight functions. It is shown that under some conditions, the proposed formula can be applied for the scale mixture of quaternion normal models. Applications of the proposed method are also given.StatDisT group. This work is based upon research supported by the National Research Foundation Grant(Re:2007043000003) and the UP Vice-chancellor's post-doctoral fellowship programme.http://www.tandfonline.com/loi/lsta202016-04-30hb201

On the real representation of quaternion random variables

For the first time, the matrix-variate quaternion normal and quaternion Wishart distributions are derived from first principles, i.e. from their real counterparts, exposing the relations between their respective densities and characteristic functions. Applications of this theory in hypothesis testing are presented, and the density function of Wilks’ statistic is derived for quaternion Wishart matrices.The South African Department of Labour (DoL) and National Research Foundation (NRF) (GRANT: FA2007043000003)http://tandfonline.com/loi/gsta2

Temporal and spatial variation of Botryosphaeriaceae associated with Acacia karroo in South Africa

The Botryosphaeriaceae are common and diverse members of fungal communities infecting woody plants. They are also increasingly being used as model organisms to understand patterns in the global movement of latent pathogens. The aim of this study was to consider the species richness of the Botryosphaeriaceae associated with the native Acacia (Vachellia) karroo across South Africa, and the variation of species at specific local sites over time. The diversity of these fungi associated with different tissues of this host plant was also considered. These questions were addressed by sampling healthy A. karroo from 23 sites in South Africa and by more intensive hierarchical sampling conducted at 40 sites in one area over 3 yr. In total, 13 species of the Botryosphaeriaceae were identified, including seven that were isolated only from the more intensively sampled area. There was a clear geographical influence, with some species occurring only in some parts of the country. Significant variation in the species richness over time for the intensively sampled area was found and there was no evidence of tissue specificity for this group of fungi in leaves, branches and branchlets. Results of pathogenicity trials showed highly variable lesion sizes for the isolated species in comparison to the control, with Sphaeropsis variabilis, Lasiodiplodia theobromae and Neofusicoccumaustrale being the most pathogenic. The overall results revealed a rich diversity of Botryosphaeriaceae on this native host, which varied significantly both geographically and on individual trees, even in the absence of obvious disease.Members of the Tree Protection Cooperative Programme (TPCP), the DST/ NRF Centre of Excellence in Tree Health Biotechnology (CTHB) and the University of Pretoria, South Africa.http://www.elsevier.com/locate/funeco2016-06-30hb201

Kinetic interpretation of log-logistic dose-time response curves

A Hill-type time-response curve was derived using a single-step chemical kinetics approximation. The rate expression for the transformation is a differential equation that provides an interpolation formula between the logistic growth curve and second order kinetics. The solution is equivalent to the log-logistic cumulative distribution function with the time constant expressed in terms of a kinetic rate constant. This expression was extended to a full dose-time-response equation by postulating a concentration dependence for the rate constant. This was achieved by invoking a modified form of Haber’s law that connects an observed toxic effect with the concentration of the active agent and the elapsed exposure time. Analysis showed that the concept of Concentration Addition corresponds to a special case where the rate constant for the overall transformation rate is proportional to the sum of the rate constants that apply when the agents act individually. Biodiesel “survival” curves were measured and used to test the applicability of the empirical model to describe the effects of inhibitor dosage and binary inhibitor mixtures. Positive results suggest that the proposed dose-response relationship for the toxicity of agents to organisms can be extended to inanimate systems especially in cases where accurate mechanistic models are lacking.The Energy Institutional Research Theme of the University of Pretoriahttp://www.nature.com/srepam2017Chemical EngineeringStatistic

Integrated analysis and transcript abundance modelling of H3K4me3 and H3K27me3 in developing secondary xylem

Despite the considerable contribution of xylem development (xylogenesis) to plant biomass accumulation, its epigenetic regulation is poorly understood. Furthermore, the relative contributions of histone modifications to transcriptional regulation is not well studied in plants. We investigated the biological relevance of H3K4me3 and H3K27me3 in secondary xylem development using ChIPseq and their association with transcript levels among other histone modifications in woody and herbaceous models. In developing secondary xylem of the woody model Eucalyptus grandis, H3K4me3 and H3K27me3 genomic spans were distinctly associated with xylogenesis-related processes, with (late) lignification pathways enriched for putative bivalent domains, but not early secondary cell wall polysaccharide deposition. H3K27me3-occupied genes, of which 753 (~31%) are novel targets, were enriched for transcriptional regulation and flower development and had significant preferential expression in roots. Linear regression models of the ChIP-seq profiles predicted ~50% of transcript abundance measured with strand-specific RNA-seq, confirmed in a parallel analysis in Arabidopsis where integration of seven additional histone modifications each contributed smaller proportions of unique information to the predictive models. This study uncovers the biological importance of histone modification antagonism and genomic span in xylogenesis and quantifies for the first time the relative correlations of histone modifications with transcript abundance in plants.The Department of Science and Technology (Strategic Grant for the Eucalyptus Genomics Platform), the National Research Foundation (Bioinformatics and Functional Genomics Programme Grant IUD 86936 and 97911), Incentive Funding Grant (AAM) (UID 8111), Mondi Ltd. and Sappi Ltd.http://www.nature.com/srepam2017Forestry and Agricultural Biotechnology Institute (FABI)GeneticsPlant ScienceStatistic

Microporous polyolefin strands as controlled-release devices for mosquito repellents

The main vectors of malaria in Africa, i.e. An. arabiensis, An. gambiae s.s. and An. funestus, are attracted by human foot odour and they tend to bite victims in the ankle area. Hence, affordable mosquito-repellent polymer-foot bracelets with long lasting protection could reduce infective lower limb bites and therefore help to reduce the overall malaria transmission rate. This study investigated the possibility of increasing the duration of repellence activity by incorporating repellents into inexpensive thermoplastic polymers, namely poly(ethylene-co-vinyl acetate) (EVA) and linear low-density polyethylene (LLDPE). Volatile repellents need to be released into the surrounding air to be effective, i.e. they are continuously lost to the atmosphere. This means that the bracelet should also act as a reservoir for relatively large quantities of the active compound. Towards this goal, polymer strands containing mosquito repellent were prepared by twin-screw extrusion compounding. A co-continuous phase structure was achieved by rapid quenching in an ice bath of the homogeneous polymer-repellent melt mixture exiting the extruder. Phase separation occurred through spinodal decomposition that trapped the liquid repellent in the microporous polymer matrix. A skin-like membrane that covered the extruded polymer strands controlled the release rate. Strands that contained up to 30 wt-% of either DEET or Icaridin provided effective protection against mosquito bites even after 12 weeks of ageing at 50 °C.The Deutsche Forschungsgemeinschaft (DFG), Germany, under Grant AN 212/22-1.http://http://www.elsevier.com/locate/cej2020-03-15hj2019Chemical EngineeringMedical VirologyStatistic