ADAKU Christopher
Chemical Structure and Properties of Anthocyanins from Selected Plant Species from Uganda.

Mr. ADAKU Christopher investigated a class of bioactive phytochemicals known as anthocyanins from selected indigenous plants, with the purpose of identifying ingredients for the development of nutraceuticals and for application as natural food colourants. This follows the increasing availability of natural health products with unsubstantiated health claims and the health concern associated with the use of synthetic food colourants. During the study, eleven new and seven known compounds were isolated and their properties deciphered. The compounds exhibited colour and stability required for food colourant application and showed remarkable antioxidant activity which is indicative of their potential beneficial health effects. These findings will lead to the development of nutraceuticals and other natural health products with guaranteed safety and efficacy. The isolated compounds can also be used as natural functional food colurants, especially for colouring refrigerated foods such as yoghurt, ice cream and beverages. This study was funded by SIDA through DRGT and MUTHI and supervised by Prof. Byamukama Robert and Prof. Kiremire Bernard (RIP).

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ANYWAR Godwin
Ethnopharmacology, cytotoxicity, antiviral and immunomodulatory profiles of medicinal plant species used by herbalists in treating people living with HIV/AIDS in Uganda

Mr. ANYWAR Godwin investigated the cytotoxicity, antiviral activity and immunomodulatory potential of medicinal plant species used by herbalists to treat people living with HIV/AIDS (PLHIV) in Uganda. The study was motivated by the fact that PLHIV widely use untested herbal medicines even when already on antiretroviral treatment. The results from this study showed several plant species are mainly used to treat opportunistic infections among PLHIV. Two of the most widely used plant species, Albizia coriaria and Warburgia ugandensis were highly toxic to the human glioblastoma cell line used (U87.CD4.CXCR4). Regression analysis also showed that the plant extracts had varying selective anti-HIV-1 activities in vitro. The plant extracts also elicited different immune responses by stimulating different cytokines from Peripheral Mononuclear Blood Cells (PMBCs). Godwin recommend testing of crude plant extract mixtures used by the herbalists, and isolating and testing pure compounds from the most promising plant species. The study was funded by the Consortium for Advanced Research Training in Africa (CARTA), and DAAD and supervised by Prof. Esezah Kakudidi, Dr. Andreas Shubert, Prof. Robert Byamukama and Prof. Christian Jassoy.

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ENEKU John Paul
Optimization of the electrical resistivity of magnetron sputtered aluminium and boron co-doped zinc oxide thin films for solar cells.

Mr. ENEKU John Paul investigated co-doping of zinc oxide thin films with both aluminium and boron elements to develop a transparent thin film material of very low electrical resistivity for application as a transparent front electrode in thin film solar cells. This offers a low cost and eco-friendly alternative to the costly and toxic Indium Tin Oxide (ITO) electrode which currently dominates the solar cell market. The thin film based solar cells have the potential to significantly lower the price of photovoltaics based electricity. The investigation established that the co-doped zinc oxide thin film material can be used effectively as a transparent electrode in thin-film solar cells and can replace the costly standard Indium Tin Oxide (ITO). This study was funded by Makerere Universsity and International Science Program (ISP, Sweden) and supervised by Prof. Tom Otiti and Prof. Julius Mwabora.

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BUTTIBWA Mary
Utilizing heated pollen and androgenesis pathways for the production of haploids in cassava

Ms. BUTTIBWA Mary investigated how heat-treatment of pollen facilitates production of haploids in cassava. Pollen, a fine powdery substance that comes from the male part of flowers and an equivalent of sperms animals, can be heat-inactivated and used hasten cassava embryo development. Because cassava’s reproduction cycle is too long it is difficult to quickly develop new varieties. The haploid technology can shorten this by 50%. Using heated pollen in pollination fostered the development of cassava embryos that further grew into haploid plants in a short time. The heated pollen germinated on the stigma but no fertilization was achieved; however, embryo development was stimulated. Early embryo rescue techniques rescued immature embryos on an artificial growth medium and re-generated into plants. This work contributes to the genetic improvement of cassava. The study was funded by the Bill and Melinda Gates Foundation through The International Centre for Tropical Agriculture and was supervised by Prof. Arthur Tugume and Dr. Robert Kawuki.

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INUWA Badamasi
Effect of xenoestrogenic substances on fish health and reproductive potential of Nile tilapia, Nile perch and lungfish from two-distinctly polluted sites of Lake Victoria: the “more polluted”

Mr. INUWA Badamasi studied the effect of xenoestrogenic substances on fish health and reproductive potential of Nile tilapia, Nile perch and lungfish from two-distinctly polluted sites of Lake Victoria: the “more polluted” (Kasenyi, Ggaba, Port bell, Jinja) and the “less polluted” (Kasensero, Bale, and Bukakata). The motivation for this research was the decline in the wild fish stocks population of Lake Victoria, attributable to several factors, including pollution. Specifically, the study examined the liver conditions and gonadal development of fishes under different levels of pollution. Severe liver alterations were higher in fishes from more polluted compared to those from less polluted areas. Indeed, the chemical contamination of Lake Victoria could have caused the liver lesions and other changes in the fishes. Overtime, such chemical contamination could lead to negative impacts on the consumption of fish and fish products if actions are not taken to mitigate the risks. This study was funded by the Nigerian Federal Ministry of Education and supervised by Assoc Prof Charles Masembe and Dr. Robinson Odong.

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KITO Luliro Silas
The Numerical Range of Linear Relations and Stability Theorems.

Mr. KITO Luliro Silas studied the numerical range and stability theorems of linear maps on some mathematical spaces with the purpose of establishing the existence and uniqueness of solutions (solvability) to linear relation inclusions. In this study, he explored the effects of small alterations on certain maps between special spaces that are of mathematical interest in solving certain differential equations. The study found that within a certain degree of change, a small alteration on the map will not affect a particular set of characteristics of the map. These results are useful but not limited to; solving problems formulated when modelling airflow around an obstruction for example calculation of forces and moments on aircrafts, modelling fission weapon detonation, determination of mass flow rate of petroleum through pipelines, predicting weather patterns and ocean currents, solving fluid dynamics problems that require computation of fluid properties such as flow velocity, pressure, density and fluid temperature as functions of space and time. This study was funded by SIDA and was supervised by Assoc. Prof. Gerald Wanjala, Dr. Saul H. Nsubuga, Dr. Vincent. A. Ssembatya and Dr. Alex B. Tumwesigye.

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KYOMUHANGI Annet
Reduced Modules Relative to Functors

Ms. KYOMUHANGI Annet’s study focused on the description of reduced modules and their dual using functors. She introduced and studied properties of a functor that measures how far a module defined over a commutative ring is from being reduced. She also found a machinery that allows one to associate a nil ideal to every ring. Since reduced modules are dualisable, Annet studied properties of their dual known as coreduced modules. She further introduced functors that describe coreduced modules and studied their properties. Moreover, she found that reduced modules simplify computations of local cohomology while coreduced modules simplify computations of local homology. The study was funded by Makerere-Sida bilateral programme (2015-2020); Project 316: Capacity building in Mathematics and its applications. Ms. Kyomuhangi was supervised by Dr. David Ssevviiri and Dr. Alex Samuel Bamunoba, both from Makerere University.

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MAYANJA Edison
Mathematical Models for HIV-HCV Co-infection Dynamics under Various Control Strategies

Mr. MAYANJA Edison formulated mathematical models to study the dynamics of Human Immunodeficiency Virus (HIV) and Hepatitis C virus (HCV) co-infection. The HIV-HCV co- infection mathematical models which had been developed before, either ignored infection stages or considered HCV in only two stages of infection: the acute and chronic infection. However, the chronic stage of HCV is very long and consists of infected individuals that are asymptomatic yet infectious. Thus, this required deep analysis that had not been fully elucidated. In his study, he analysed the HCV chronic stage split it into: before onset of cirrhosis and its complications (Latent stage) and after onset of cirrhosis (Advanced stage). He used these mathematical models to investigate how HIV infection impacts the dynamics of HCV infection and vice versa. The study revealed that, increasing the rate of enrolment on HIV treatment reduces HCV prevalence and vice versa. Transmission probability per sexual contact and average number of sexual partners acquired per year were equally likely to result into increased HIV and HCV infections and these parameters were the most sensitive in increasing each of HIV and HCV infections. The study was funded by SIDA and was supervised by Prof. Livingstone S. Luboobi, Prof. Juma Kasozi, and Dr. Rebecca N. Nsubuga.

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NABAWANDA Olivia
Flattened partitions: Pattern Avoidance and Behavior of Permutation Statistics.

Ms. NABAWANDA Olivia studied a sorting procedure (run-sort function) on permutations, where runs are rearranged in lexicographic order. The aim of the study was to investigate the behavior of the run-sort function with different permutation statistics namely runs, descents, peak-values and left-right minima. Olivia used Mathematica, a computation/mathematical software to generate the necessary data, which in turn she used in combination with bijective proofs and generating functions as the main tools. New combinatorial interpretations to several counting sequences namely A124324, Catalan, Fibonacci, Motzkin and Powers of two among others were provided as already indexed on the On-line Encyclopedia of Integer Sequences (OEIS) database, hence contributing to the existing body of knowledge. She also proved that the descent generating polynomials for these permutations are real rooted, and satisfy an interlacing property similar to that satisfied by the Eulerian polynomials, which are known to be real-rooted. Moreover, the run-sort function was found to possess interesting probability distribution properties. The research findings exhibited an interplay between discrete mathematics, probability theory and complex analysis. The study was funded by SIDA and supervised by Dr. Alex Samuel Bamunoba, Prof. Paul Vaderlind and Prof. Fanja Rakotondrajao of Antananarivo.

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NALULE Rebecca Muhumuza
Hierarchical Models and Spatio-Temporal Processes In Data Analysis

Ms. NALULE Rebecca Muhumuza studied Hierarchical Models and Spatio-Temporal Processes in Data- Analysis with the aim of analyzing data which possesses both temporal and spatial dependence. She developed a non-linear general spatio-temporal model by extending Serfling’s model. Rebecca applied the theoretical findings to data of an outbreak of influenza in Southern Germany between 2001 and 2007. She also extended the random effect model by introducing the correlation coefficient between random effects in its definition. She again considered the problem of Bayesian estimation of heterogeneity parameter in the generalized random effects model where a comparison between the obtained results with the existing approaches was made. Rebecca used the findings for consensus building in meta-analyses of measurement results for the Newtonian constant of gravitation data and for the effectiveness of antiretroviral pre-exposure prophylaxis in preventing HIV infection. The study was funded by SIDA and was supervised by Prof Olha Bodnar, Dr. John Bosco Asiimwe and Dr. Rebecca N. Nsubuga.

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NANFUKA Mary
The use of Splines for solving ill-posed problems, with application to the Cauchy problems for the Heat and Helmholtz equations

Ms. NANFUKA Mary developed a regularization procedure based on splines. The procedure was used to solve the Cauchy problems for the heat and Helmholtz equations, which are ill posed problems. The Cauchy problem for the heat equation had been previously solved by the Fourier transform method. The method, assumed that the time derivative, represented a periodic function which is not realistic. Thus, as an alternative, Mary approximated the time derivative by a cubic smoothing spline. The spline method effectively bounded the errors in the output solution according to the stability estimates. The Cauchy problem for the Helmholtz equation was regularized, by introducing a bounded approximation of the second derivative in the x-variable using cubic smoothing splines. A bound for the approximate
derivative was derived. The stability estimates, showed that the method worked pretty well and produced accurate results. The newly developed method was applied to an industrial setting for determining the surface temperature of steel and good results were achieved. The method is recommended for use for the solution to inverse problems that occur in the engineering and medical fields. The research was funded by Sida and supervised by Dr. Fredrik Berntsson, Dr.Godwin Kakuba and Assoc Prof. John Mango.

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OCHEN William
Measurement and Modelling of Residual Stress in Porcelain Tiles Formulated from Different Quartz Particle Sizes in Uganda

Mr. OCHEN William studied residual stress in porcelain tiles formulated from different quartz particle sizes in Uganda. He measured residual stress using X-ray diffraction method, and modeling based on finite element method using abaqus software. His study was prompted by numerous complaints concerning the strength of the locally manufactured tiles. His study found out that residual stress decreases with an increase in quartz particle size over a range of 45-200μm. The decline in residual stress is attributed to the formation of cracks, which affects strength and hardness of the tiles. He further noted that upon sintering at 13000C, tiles with quartz particle size of  90μm exhibited properties that satisfied the ISO 13006 standard. His study therefore recommends the idea of fine quartz milling in a range of not more than 90μm. This study was funded by DAAD and supervised by Prof. Florence Mutonyi D’ujanga and Dr. Bosco Oruru.

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OKELLO Omwonylee Joseph
Limiting Behaviours of the Longest Gaps Between Occurrence Epochs in Poisson Processes.

Mr. OKELLO Omwonylee Joseph investigated the asymptotic properties of longest gaps between occurrence epochs in Poisson processes using the theory of large deviations, based on the laws of large numbers. To do this, the global estimation of the distribution functions of longest gaps was derived with the help of discretization argument and the Slivnyak’s formula of Palm theory. The derived global estimation was then used to achieve Laplace transform asymptotics of the longest gaps. Through the application of Fenchel-Legendre transform, it was found out that the longest gaps satisfy two large deviation principles with exponential and power rate functions. Since this study was about the probabilistic analysis of rare events, the results not only fill the literature gaps but also provide a very useful planning tool to insurance companies, risk analyst, department of disaster preparedness, operation managers and others. The study was funded by SIDA and was supervised by Dr. Xiangfeng Yang; Dr. Richard Awichi Opaka and Dr. Fred Mayabala.

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SSENYUNZI Richard Cliffe
Modelling Precipitable Water Vapour Using Global Navigation Satellite System Data over the East African Tropical Region.

Mr. SSENYUNZI Richard investigated the temporal and spatial variability of the zenith total delay and precipitable water vapour (PWV) data over the East African tropical region. The PWV data was collected from 13 geodetic permanent GNSS stations for the years 2013 to 2016. Lack of key variables such as the atmospheric water vapour, has been affecting the accuracy of weather predictions over the East African tropical region. The lack of this important parameter has been partly due to insufficient data and very scarce and unreliable tropospheric water vapour monitoring instruments in the region. In this study, the PWV, pressure and the weighted mean temperature linear models have been developed. The site-specific models developed can be utilized to supplement the GNSS and the weather stations data over the thirteen stations since they can provide estimates of nearly a similar degree of precision compared to the measured values. The study was funded by the African Development Bank and supervised by Prof. Florence Mutonyi D’ujanga and Dr. Bosco Oruru.

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WAMONO Felix
Contributions to reduced rank regression modelling with applications to small area estimation.

Mr. WAMONO Felix studied the problem of decomposing residuals in the GMANOVA-MANOVA model with rank restrictions on parameters with applications in small area estimation. Firstly, Residuals in the GMANOVA-MANOVA model with rank restrictions on the mean parameters was considered. The main objective was to define residuals useful for evaluating the reduced rank restriction model. We decomposed linear spaces into four subspaces as it can be done for the Extended Growth Curve model with two “profiles”. The new residuals were defined by orthogonal projections on these subspaces. It was discussed how the new residuals could be used to test model assumptions. Secondly, Survey data from Uganda, including the 2014 Uganda Population and Housing Census data was analysed using small area estimation methodology. The GMANOVA-MANOVA model with rank restrictions on parameters was used to estimate the small area means. This study was funded by SIDA and was supervised by Prof. Dietrich von Rosen, Prof. Martin Singull, Assoc. Prof. Leonard Atuhaire and Dr. Innocent Ngaruye.

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