Strathmore International Mathematics Conference
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The Strathmore International Mathematics Conference provides mathematics researchers from around the world, working in various mathematical disciplines, a forum to discuss latest developments and share their research results in contemporary areas of mathematics research and applications. This conference also aims to forge new cross-disciplinary interactions among participants and further existing partnerships among the international mathematics community and in particular, young researchers in Eastern Africa. The conference provides a unique opportunity for in-depth technical discussions and exchange of ideas in mathematical sciences, as well as explores the potential of their applications in natural and social sciences, engineering and technology and industry and finance.
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- ItemA 2D-approach towards the detection of distress using Fuzzy K-Nearest Neighbor(Strathmore University, 2019-08) Machanje, Daniel; Orero, JosephThis research focuses on a novel approach of distress detection referred to as the 2D approach, using the fuzzy K-NN classification model. Unlike the traditional approach where single emotions were qualified to depict distress such as fear, anxiety, or anger, the 2D approach introduces two phases of classification, with the first one checking the speech excitement level, otherwise referred to as arousal in previous researches, and the second one checking the speech polarity (negative or positive). Speech features are obtained from the Berlin Database of Emotional Studies (BDES), and feature selection done using the forward selection (FS) method. Attaining a distress detection accuracy of 86.64% using fuzzy K-NN, the proposed 2D approach shows promise in enhancing the detection of emotional states having at least two emotions that could qualify the emotion in question based on their original descriptions just as distress can be either one or many of a number of emotions. Application areas for distress detection include health and security for hostage scenario detection and faster medical response respectively
- Item3-Group divisible designs with block size 4 and 2 groups(Strathmore University, 2019-08) Bezire, WilbroadOne of the main problems in design theory is to find construction methods to obtain unknown designs. In this paper we give fundamental constructions of group divisible SBS designs with block size 4 and 2 groups. We give necessary conditions for their existence and prove that these conditions are sufficient. We use tools from graph theory and finite fields, for example-designs, Steiner quadruple systems (SQSs), 1 and 2-factorisations of complete graphs.
- ItemA Study on the role of reflection in the pedagogical competence development of Zambian mathematics teachers : focusing on qualitative analysis using lesson diaryChikara, KinonePaper presented at Strathmore International Mathematics Research Conference on July 23 - 27, 2012
- ItemAccelerated circularity of consumer electronics using Block Chain and Optimized Machine Learning Algorithms(Strathmore University, 2019-08) Mwongela, StanslausAt the heart of our economy lies a linear take, make, dispose model, relying on consuming big amounts of finite products and fossil fuels. The challenge of consumer electronic waste is colossal, and is continuously growing. In 2016 alone, there was a global generation of 44.7 million tons of e-waste, with an estimated raw material value of EUR 55 billion. 435 thousand tonnes of the 44.7 million tonnes were mobile phones. Only 20 percent of e-waste is documented to be collected and recycled under appropriate conditions, whereas the remaining 80 percent is either thrown into the waste stream or dumped, traded or treated under substandard conditions. The consequences of this linear electronics system pose environmental and health impacts both at the production and disposal ends. At the same time, the economic opportunity is significant. Taking smartphones as an example, almost 1.5 billion are shipped every year, with each unit containing components worth over USD 100. This represents a potential USD 150 billion of value that enters the market each year. This value should remain in the system. Even if the materials present in smartphones were recovered through recycling the least valuable loop of a circular economy they could be worth up to USD 11.5 billion. The need to rethink the system is clear, but solutions so far have been limited. The circular economy coupled with the Al opportunity presents a vision and a workable path forwards to meet these challenges, by redesigning our economy to be one that creates rather than extracts value, and keeps the finite technical resources in flow within the economy. The main purpose of this study is to build a Block Chain Circularity Incentive System that facilitates the accelerated circularity of consumer electronics. The main focus being a decision system that processes the block chain data of consumer electronics use and disposal needs to allow circular product and material flows as well as operate circular business models. A formal experimental design is proposed, more specifically, a simple factorial design. As opposed to having one learning algorithm to process electronic products usage on a Big Chain DB, this research proposes to run multiple algorithms and aggregate the results into a single score. The research also proposes to collect primary data from consumer electronics manufacturers, consumers of electronics, and E-waste recovery firms. The primary data would be used to identify the challenges this stake holders face, train the learning algorithms based on consumer electronics use and disposal needs and additionally test the Block Chain Circularity Incentive System developed.
- ItemAdaptation of a RAS pathway activation signature from FF to FFPE tissues in colorectal cancer(Strathmore University, 2017) Omolo, Bernard; Yang, Mingli; Lo, Fang Yin; Schell, Michael J.; Austin, Sharon; Howard, Kellie; Madan, Anup; Yeatman, Timothy J.Background: The KRAS gene is mutated in about 40 % of colorectal cancer (CRC) cases, which has been clinically validated as a predictive mutational marker of intrinsic resistance to anti-EGFR inhibitor (EGFRi) therapy. Since nearly 60 % of patients with a wild type KRAS fail to respond to EGFRicombination therapies, there is a need to develop more reliable molecular signatures to better predict response. Here we address the challenge of adapting a gene expression signature predictive of RAS pathway activation, created using fresh frozen (FF) tissues, for use with more widely available formalinfixed paraffin-embedded (FFPE) tissues. Methods: In this study, we evaluated the translation of an 18-gene RAS pathway signature score from FF to FFPE in 54 CRC cases, using a head-to- head comparison of five technology platforms. FFPE-based technologies included the Affymetrix Gene Chip (Affy), NanoString nCounter™ (NanoS),Illumina whole genome RNASeq (RNA-Acc), Illumina targeted RNASeq (t-RNA), and Illuminastranded Total RNA-rRNA- depletion (rRNA). Results: Using Affy_FF as the “gold” standard, initial analysis of the 18-gene RAS scores on all 54samples shows varying pairwise Spearman correlations, with (1) Affy_FFPE (r= 0.233, p = 0.090); (2)NanoS_FFPE (r= 0.608, p < 0.0001); (3) RNA-Acc_FFPE (r= 0.175, p = 0.21); (4) t-RNA_FFPE (r=−0.237, p = 0.085); (5) and t-RNA (r= −0.012, p = 0.93). These results suggest that only NanoString has successful FF to FFPE translation. The subsequentremoval of identified “problematic” samples (n= 15) and genes (n= 2) further improves the correlations of Affy_FF with three of the five technologies: Affy_FFPE (r= 0.672, p < 0.0001); NanoS_FFPE (r= 0.738, p < 0.0001); and RNA-Acc_FFPE (r= 0.483, p = 0.002). Conclusions: Of the five technology platforms tested, Nano String technology provides a more faithful translation of the RAS pathway gene expression signature from FF to FFPE than the Affymetrix GeneChip and multiple RNASeq technologies. Moreover, Nano String was the most forgiving technology in the analysis of samples with presumably poor RNA quality. Using this approach, the RAS signature score may now be reasonably applied to FFPE clinical samples.
- ItemAggregational gaussuanity in the Southern African equity markets - implications for the pricing of riskPolakow, Daniel; Taylor, DavidPaper presented at Strathmore International Mathematics Research Conference on July 23 - 27, 2012
- ItemAIDS-related Kaposis sarcoma pathogenesis(Strathmore University, 2019-08) Chimbola, Obias; Lungu, Edward M.Kaposis sarcoma (KS), the most common tumor associated with human immunodeficiency virus- I (HIV-I) and human herpesvirus-8 (HHV-8) (also referred to as Kaposis associated herpesvirus (KSHV) infection, develops in approximately 20 percent of patients infected with HIV-I. The lesions of this multicentric vascular neoplasm are purplish patches, plaques, or nodules. Although highly active antiretroviral therapy (HAART) can prolong the time to treatment failure in patients with KS, nearly every patient with AIDS-related (or epidemic) KS eventually develops disseminated disease. Progression usually occurs in an orderly fashion from new localized or widespread mucocutaneous lesions to more numerous lesions and generalized skin disease with involvement of lyrnph nodes, gastrointestinal tract (GIT), lungs and other organs. Studies have shown that KS cells themselves are not infected with HIV-I; therefore, it is widely accepted than HIV-I does not play a direct oncogenic role in AIDS-KS. However, the precise role of HIV-I in AIDS-KS is still not completely understood, and there is considerable debate over whether HIVI plays a passive role (through the induction of immunosuppression) or a more direct role in the pathogenesis of this disease. We formulate a mathematical model to study the dynamics of HIVI related KS pathogenesis. In this model, it is assumed that HIV-I infects only the CD4 + T cells and HHV-8 infects the B- cells, which largely remain latently infected and only become reactivated after exposure to inflammatory cytokines and other growth factors secreted from HIV-I infected cells. The Infection free and Infection persistent equilibria have been found and their stability established. It is found that the disease can exist even if both sub-group reproduction numbers, relating to HIV-I and HHV-8, are less than unity.
- ItemAnalysis of a mathematical model of influenza dynamics with drug resistance aspect(Strathmore University, 2017) Kanyiri, Caroline W.; Kimathi, MarkInfluenza has posed a terrific public health concern. It has led to unacceptably high mortality rates especially to immune compromised persons worldwide. Efforts to effectively treat and combat the spread of influenza can be put in place if its dynamics are well understood. Numerous challenges have been faced in the event of controlling the spread and eradicating this pandemic, a major impediment being the rise of drug resistance. In light of this, a deterministic model is formulated and used to analyze the transmission dynamics of influenza having incorporated the aspect of drug resistance. A system of differential equations that models the transmission dynamics of influenza is developed. The basic reproduction number (R0) is calculated and stability of the equilibrium points analyzed. Results of the analysis show that there exists a locally stable disease free equilibrium point, E0 when R0 < 1 and a unique endemic equilibrium E*, when R0 > 1. The effect of drug resistance and transmission rate of the resistant virus on the infected and the recovered is discussed.
- ItemAnalysis of categorical data in presence of latent random effects using Structural Equation Modeling: an application(Strathmore University, 2017) Keli, Robert; Mwambi, Henry; Okango, ElphasIn most medical research, of interest is to establish the causal relationships that exist between variables which may be direct or indirect. This research intends to use structural equation modeling technique to analyze the effect of categorical latent variable(s) when assumed to follow a normal random effect model. The statistical inference is carried out under the Mplus statistical software and the developed models validated using empirical data from Kenya Aids Indicator Survey (2007).
- ItemAnti-N-Order Polynomial Daugavet Property on Banach Spaces(Strathmore University, 2019-08) Emenyu, JohnWe generalize the notion of the anti-Daugavet property (a-DP) to the anti-N-order Almasi room, polynomial Daugavet property (a-NPDP) for Banach spaces. The characterization SBS of the a-NPDP is through the spectral information; however, it is well-known in nonlinear theory that there is no suitable notion of the spectra for nonlinear operators resulting into enormous structural challenges to the known characterization techniques for the a-DP. To bypass some of the problems, we establish that a good spectrum of a nonlinear operator is one whose associated eigenvectors are of unit norm and study the a-NPDP for locally uniformly convex or smooth Banach spaces (luacs); in particular, we prove that locally convex or smooth finite dimensional Banach spaces have the a-mDP for rank-I polynomials and then extend this result to innite dimensional luacs Banach spaces. Besides, we prove that locally uniformly convex Banach spaces have the a-NPDP for compact polynomials if and only if their norms are eigenvalues, and moreover, uniformly convex Banach spaces have the a-NPDP for continuous polynomials if and only if their norms belong to the approximate spectra. As a consequence of these results, we conclude that all continuous In-homogeneous polynomials that satisfy the N-order polynomial Daugavet equation on a uniformly convex Banach space such as Lr-spaces for 1 < r < 1 and Hilbert spaces have nontrivial invariant subspaces; this result was not known.
- ItemApplied arithmetic geometry(Strathmore University, 2019-08-12) Dr. Ambrus, PalThe aim of this lecture series is to introduce some methods of arithmetic geometry which are applied in cryptographic research. Cryptography, including more sophisticated versions such as elliptic curve cryptography, allows for efficient protocols for information security, and is widely used in the banking sector including mobile money transfers, an industry in which Africa is a world leader. The methods presented can be used by African research groups to tackle a range of problems arising in technological challenges relevant to the African development context. Arithmetic geometry is a rather modern, highly prestigious and very developed area of pure mathematics, developed originally for studying Diophantine equations. I has very efficient methods to count points on algebraic varieties over finite fields which is closely related to the original motivating problem of finding rational points on varieties over number fields, a geometric reformulation of Diophantine equations. The former problem is very important in cryptography and related areas of secure communication, network building and hash functions. The lecture series will cover the necessary background on cryptography and point counting, and will introduce such tools as p-adic numbers, differential forms and Monsky-Washnitzer cohomology, from the ground up.
- ItemAn Assessment of select market timing strategies performance in Nairobi Securities Exchange(Strathmore University, 2019-08) Ng'ang'a, JudahHerding behavior among Kenyan traders in the capital markets has been majorly attributed to low levels of income and lack of knowledge in trading principles. This focus of this study was on the latter challenge. The study sought to avail information to traders in NSE regarding the profitability of select market timing strategies. The study evaluated the performance of three market timing strategies namely the relative strength index (RSI), simple moving averages (SMA) and hidden Markov model (HMM). The data considered in this study included the share price of the NSE-20 index over the period 2004-2018 triangulated to the perceptions and opinions of trading experts in Kenyan fund manager firms. The performance of market-timing strategies in this study was determined by a strategy's ability to generate above market returns as well as the accompanying Sharpe ratio. Using Henrikson and Merton market timing model, this study shows that all the market timing strategies have positive market timing strategies, with HMM having the best market timing ability. By accommodating the autoregressive nature of financial prices this study examined the ability of the strategies to time the market using an ARDL model. The model shows that all the strategies lack the ability to time the market but just like in HM model, HMM performances ranks best among the three strategies. Over the period 2004-2018 the Sharpe ratio of all the market timing strategies exceed that of SBH. The profitability is still the same when the period is split into two halves (2011-2018). The profitability persists when the trading points determined using the market index are used to trade five randomly selected securities. This confirms the profitability of trading based on patterns of historical prices. This negates the principles of EMH Theory but is in harmony with the FMH Theory, this study, therefore, provides support of FMH Theory as a more relevant market theory. In Kenya, this study found that investors are averse to market timing and tend to herd towards buy and hold strategy. Given the low profitability of the SBH strategy in NSE, this study should provoke the traders in NSE to reconsider their approach in determining optimal trading points.
- ItemBanana Xanthomonas Wilt dynamics with mixed cultivars in a periodic environment(Strathmore University, 2017) Nakakawa, Juliet; Mugisha, Joseph; Shaw, Michael; Karamura, EldadIn this study, a non-autonomous model for the spread of Banana Xanthomonas Wilt disease (BXW) in a seasonally fluctuating environment is considered. Two categories of cultivars with different susceptible levels for inflorescence infection (AAA-genome and ABB-genome (highly susceptible)) were considered. Through mathematical and numerical analysis, threshold condition for existence and stability of both the disease-free equilibrium and periodic solution were obtained. From the sensitivity analysis of key parameters with respect to time-averaged basic reproduction number (R0), it was noted that R0 increases linearly with transmission parameters and declines exponentially with roguing parameters. It was also noted that the critical roguing rate of AAA-genome cultivars was less than that of ABB genome cultivar. The peaks in disease prevalence indicate the importance of effective implementation of controls during the rainy season. Controlling same cultivars via roguing and debudding led to much lower values of R0 as compared to between different cultivars. We conclude that highly susceptible cultivars play an important role in the spread of BXW and control measures should be effectively implemented during the rainy season if BXW is to be eradicated.
- ItemBayesian (hierarchical) spatial modeling in epidemiologyAchia, ThomasPaper presented at Strathmore International Maths Research Conference on July 23 - 27, 2012
- ItemBayesian analysis of Multivariate Stochastic Volatility models(Strathmore University, 2017) Agasa, Lameck; Shitandi, AnakaloMultivariate stochastic volatility (MSV) models have gained applicability in Time Series (TS) data for analyzing multivariate financial and economic time series because they capture the volatility dynamics. Bayesian prior works allow analysis of MSV models to provide parsimonious skew structure and to easily scale up for high-dimensional problem. Bayesian MCMC estimation are used for high dimensional problems because it’s a very efficient estimation method, however, it is associated with a considerable computational burden when the dimensionality of the data is moderate to large. Forward-filtering backward-sampling (FFBS) algorithm by sampling is used as it considers reparameterizations. This is applied directly to heteroscedasticity estimation for latent variables. To show the effectiveness of this approach, we apply the model to a vector of daily exchange rate data from Central Bank of Kenya.
- ItemBayesian belief netsIngleby, MichaelPaper presented at Strathmore International Mathematics Research Conference on July 23 - 27, 2012
- ItemBayesian estimation of Multivariate Stochastic Volatility by applying state space models(Strathmore University, 2017) Agasa, Lameck; Ombasa, KiameThis work seeks to apply a Bayesian analysis in estimating multivariate stochastic volatility (MSV) using state space models. A multiplicative model based on inverted Wishart and multivariate singular beta distributions is proposed for the evolution of the volatility, and a flexible sequential volatility updating is employed. Being computationally fast, the resulting estimation procedure is particularly suitable for on-line forecasting. Bayesian MCMC is applied to estimate high dimensional problems. Three test are conducted on estimates: the log likelihood criterion, the mean of standardized one-step forecast errors, and sequential Bayes factors. The test and procedure are applied in real data set that will comprise ten exchange rate Kenyan shillings versus other currencies in Nairobi stock exchange.
- ItemBeliefs of secondary school mathematics teachers about problem solving skills and instruction practices(Strathmore University, 2019-08) Dorimana, Aline; Uworwabayeho, Alphonse; Nizeyimana, GabrielProblem solving Skill is for long highly considered as a skill that negotiates with the complex demand of 21st century labour market. Its importance is recognized by many countries around the world, including Rwanda. This is reflected in national education systems whereby national curriculums are consistently reviewed with regard to equip young children with problem solving skills at all level of education. Concerning with the case of Rwanda, educational curriculum for pre/primary and secondary levels are developed and reviewed at national level(Rwanda Education Board, 2015). At glance, it is recognized that teachers are the key component in allowing the learning to happen. The literature related to curriculum change points out that belief and perceptions of teachers seem to have considerable effects on the nature of classroom practice which is in line with student’s attitudes, beliefs and learning outcomes. Since the launch of the competence based curriculum in Rwanda, few studies if any have been conducted to understand how teachers perceive its requirements. The current study intends to provide insights about how Rwandan mathematics teachers view problem solving in the teaching and learning of mathematics after four years of the use of competence based curriculum that includes problem solving skill among generic skills that learners must acquire during their schooling. Specifically, the study will explore what upper secondary mathematics teachers believe and perceive about (a) Mathematical problem solving (b) Problem solving instructions (C) Problem solving in classroom practice (d) The kind of mathematics instruction emphasized in Rwandan Competence Based Curriculum (e) Difficulties about problem solving. In addition, the study will give insight on the relationship about beliefs and perceptions and classroom teaching practice. A questionnaire, interview and classroom observation will be used for data collection.
- ItemBernoulli collocation method for solving linear multi-dimensional diusion and wave equations with Dirichlet boundary conditions(Strathmore University, 2017) Zogheib, Bashar; Tohidi, Emran; Shateyi, StanfordIn this paper, a numerical approach is proposed for solving multi-dimensional parabolic diusion and hyperbolic wave equations subject to the appropriate initial and boundary conditions. The considered numerical solutions of these equations are considered as linear combinations of the shifted Bernoulli polynomials with unknown coecients. By collocating the main equations together with the initial and boundary conditions at some special points, equations will be transformed into the associated systems of linear algebraic equations which can be solved by robust Krylov subspace iterative methods such as GMRES. Operational matrices of dierentiation are implemented for speeding up the operations. In both of the one-dimensional and two-dimensional diffusion and wave equations, the geometrical distributions of the collocation points are depicted for clarity of presentation. Several numerical examples are provided to show the eciency and spectral (exponential) accuracy of the proposed method.
- ItemBlood perfusion flow of an electro-kinetic fluid through a porous medium with viscous dissipation(Strathmore University, 2017) B.A., Peter; O.D, .Makinde; A.W., OgunsolaIn this work, we considered a mathematical model of an electro-kinetic fluid flow through a porous medium with blood perfusion and viscous dissipation. The fluid is assumed to poses temperature-dependent variable viscosity and thermal conductivity. The nonlinear governing partial differential equations were obtained and solved numerically using Garlekin weighted residue method coupled with fourth order Runge-Kutta technique. The results obtained were presented graphically and discussed.