Matrix Singular Value Decomposition

This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix as a linear combination of rank one partial isometries is applied to image compression by using reduced rank matrix approximations to represent greyscale images. MATLAB results for approximations of JPEG and .bmp images are presented. The results indicate that images can be represented with reasonable resolution using low rank matrix SVD approximations

Testing for the Uncovered Interest Rate Parity (UIP) in Developing Countries: The Case of Rwanda

The aim of this paper is to assess the link between interest rates and exchange rates in Rwanda under the framework of uncovered interest rate parity (UIP) hypothesis.The parity condition states that the difference between the interest rates of two countries is equal to the expected depreciation between the countries’ currencies. The paper uses data spanning the January 2004 to December 2016 period. The paper uses the spot exchange rate, risk premium, deposit interest rates as domestic variables while the USA deposit rates are used as foreign interest rates. Due to its desirable properties especially in terms of handling rational expectations models, the Generalized Method of Moments (GMM) is used to estimate the UIP equation for Rwanda before carrying out several others diagnostic tests to assess the robustness of results. Empirical results show that interest rate differentials, risk premium and the intercept are statistically not significant. These results imply that the UIP condition does not hold for Rwanda under the period of study, which is consistent with other empirical findings in developing countries. The lack of empirical support for the UIP hypothesis in Rwanda may open up arbitrage opportunities for investors with rational expectations.Indeed, the Modelling and forecasting team should review the UIP equation in the Forecasting and Policy Analysis System (FPAS) macro-model so as to give more attention to non-interest sensitive determinants of exchange rate dynamics in Rwanda. Keywords: Uncovered Interest rate Parity (UIP), Generalized Method of Moments (GMM) JEL Classification: C2, E4, E6, F2, F

Rwanda to phase out polluting vehicles by 2040, an efficient strategy to mitigate global warming effects?

Passenger vehicles are major pollutants because on average a typical passenger vehicle emits about 4.6 metric tons of carbon dioxide per year. I highly support the idea that Rwanda joined on November 11, 2021, a group of countries at the COP26 UN climate talks that have made an agreement to end polluting vehicles by 2040. Rwanda is a landlocked country with a 12.95 million population as of 2020(world bank). Rwanda currently has over 221,000 registered vehicles; 83980 are passenger vehicles, 114,900 vehicles (52 percent of those vehicles) are motorcycles and the rest include public transports (buses and minibuses) and trucks for transportation of goods. Because of the high population density and the size of Rwanda, many people use motorcycles and public buses as a mode of transportation to move from place to place

MULTIFUNCTIONAL NANOMATERIALS FOR BLOOD BASED CANCER DIAGNOSTICS

MULTIFUNCTIONAL NANOMATERIALS FOR BLOOD BASED CANCER DIAGNOSTIC

CORRESPONDENCE COURSE PROGRAM AND TEACHER ACHIEVEMENT AT KIGALI, RWANDA

The study was mainly about the effects of correspondence course programs and teachers’ achievement in Kigali City and was led by the following objectives: to examine the effect of correspondence course programs and teachers’ achievement in Kigali City; to examine the problems faced by teachers undertaking correspondence courses or learning programs in Kigali City and to investigate ways through which we can reduce the problems facing correspondence course programs in Kigali City. The study was mainly evaluative and qualitative in nature, although for the purposes of accuracy and clarity, some quantitative aspects were used. The study comprised 227 respondents, who included 10 community leaders, 193 students, and 17 teachers. 3 head teachers, 2 representatives from NGOs, and 12 civil servants, including the chief administrative officer Gasabo, Kicukiro, Nyarugenge district, and Kigali City development officer 5 education officers, who included the district inspector of schools and Kigali City education officer, plus 20 parents whose children were undertaking a correspondence course program. Therefore, the sample population of 350 selected from three sectors of Kigali City made up 227 of the sample size population, which was selected using purposive sampling and simple random sampling. This ponder embraced a survey investigation plan that utilized surveys as a means of information collection and guided meetings. Information was displayed and examined in tables and graphs, applying expressive insights (frequencies, rates, and cruel) as well as utilizing the SPSS bundle. 95% of the respondents who were inquired said that the correspondence course program in Kigali City is confronted by high and steady loss and dropout rates. 73% of the respondents whom the analyst caught up with said that correspondence courses advance great learning involvement because learners are free to connect with other individuals within the communities where they take off and within the dialects that they learn. This has advanced them to distinctive levels in numerous zones where they work.  Article visualizations

A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require renormalization or dressing of these parameters to connect them to the boundary states

Monetary policy, credit growth, and economic activity in Rwanda

The successful conduct of monetary policy requires a thorough assessment of how changes in policy actions arepropagated to the real economy. We employ the Vector Autoregression (VAR) type of models to examine the effect ofmonetary policy on goal variables, namely, credit, output, and inflation in Rwanda. The empirical findings from standardVAR models show that the effect of the interbank rate on goal variables is consistent with theoretical propositions andempirical applications. A positive shock to the interbank rate causes inflation to fall by about five percentage pointsover eight quarters, and credit to fall by about four percentage points in the first four quarters. Consequently, economicgrowth falls by about one percentage point. The Vector Error Correction (VEC) model shows that the previous quarter’sdeviation from long-run equilibrium is corrected for in the current quarter at an adjustment speed of 0.1%. These findingsremain robust when we apply a Structural Vector Autogressive (SVAR) model, and these models capture the essentialmacroeconomic relations between a monetary policy indicator and goal variables, following the recent improvement infinancial markets

Feasibility of the modified sequential organ function assessment score in a resource-constrained setting: a prospective observational study.

BackgroundSub-Saharan Africa has a great burden of critical illness with limited health care resources. We evaluated the feasibility and utility of the modified Sequential Organ Function Assessment (mSOFA) score in assessing morbidity and mortality in the National Referral Hospital's intensive care unit (ICU) for one year.MethodsWe conducted a prospective, observational cohort study on patients above 12 years of age admitted to the ICU at Mulago Hospital (Kampala, Uganda). All SOFA scores were determined at admission and at 48 h. We modified the SOFA score by replacing the PaO2/FiO2 ratio with SPO2/FiO2. The primary outcome was ICU mortality.ResultsThis ICU cohort of 118 patients had a mean age of 37 years and an ICU mortality rate of 46.6%. Non-survivors had higher initial (7.7 SD 3.8 vs. 5.5 SD 3.3; p = 0.007), mean (8.1 SD 3.9 vs 4.7 SD 2.6; p < 0.001) and highest mSOFA scores (9.4 SD 4.2 vs. 5.8 SD 3.2; p < 0.001), with an increase of 1.0 (SD 3.1) mSOFA on average after 48 h when compared to survivors (p < 0.001). The area under the receiver operating characteristic curves for each mSOFA category was: initial-0.68, mean-0.76, highest-0.76 and delta mSOFA-0.74. Multivariate logistic regression analysis showed no significant association between mSOFA scores and mortality.ConclusionOur results confirm that calculation of the mSOFA score is feasible for an ICU population in a resource-limited country. More data are needed to test for an association between mSOFA and mortality

Does tutor subject-matter expertise influence student achievement in the problem based learning curriculum at UNITRA medical school?

Objective. To establish whether or not tutor subject-matter expertise influences student achievement in content-based examinations in the problem-based learning (PBL) curriculum at the University of Transkei (UNITRA) Medical School.Design. A retrospective study of MB ChB III student achievement in end-of-block modified essay questions (MEQ) examinations in microbiology, pathology and pharmacology for the years 1994 - 1999, inclusive. Pooled scores from the expert-tutored groups were compared with those from the groups tutored by non-experts using analysis of variance (ANOVA) or t-test. Subject expert tutors were those with postgraduate specialisation in the given discipline.Setting. The Medical School, Faculty of Health Sciences, UNITRA, Umtata.Outcome measures. Whether pooled mean MEQ scores in end-of-block examinations for microbiology, pathology or pharmacology differ according to the subject-matter expertise of the tutor.Results. There were no significant differences in mean scores obtained for pharmacology (51.1 ± 0.6 versus 52.6 ± 0.7, P = 0.109) and pathology (49.8 ± 0.6 versus 49.9 ± 0.8, P = 0.919). The difference between the scores in microbiology was small (3 percentage points) but statistically significant, with the groups tutored by microbiologists scoring higher than those tutored by pathologists or pharmacologists (54.1 ± 1.0 versus 51.2 ± 0.8, P = 0.032).Conclusions. These data demonstrate that in the UNITRA Medical School PBL curriculum tutor subject-matter expertise has little or no influence on student achievement in the discrete areas of tutor expertise