Articles: Department of Mathematics and Statistics
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Item Mixed model analysis using R.(World Agroforestry Centre, 2009) Mbunzi, Stephen M; Nagda, SonalItem Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered Pairs and on Ordered Triples(UoEm, 2014) Kimani, Patrick; Rimberia, Jane; Muthoka, Geoffrey; Lao, HusseinRanks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply the concept of marks to compute the ranks and subdegrees of the symmetric group Sn (n = 5,6,7) and Sn (n = 6,7,8) acting on ordered pairs and triples respectively.Item Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered Pairs and on Ordered Triples(Uoem, 2014) Kimani, Patrick; Rimberia, Jane; Muthoka, Geoffrey; Muthoka, GeoffreyRanks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply the concept of marks to compute the ranks and subdegrees of the symmetric group 𝑆𝑛(𝑛 = 5,6,7) and 𝑆𝑛 (𝑛 = 6,7,8) acting on ordered pairs and triples respectively.Item A model for childhood Pneumonia Dynamics(Asian online journals, 2014) Ngari, Cyrus G.; Malonza, David M.; Muthuri, Grace G.This paper presents a deterministic model for pneumonia transmission and uses the model to assess the potential impact of therapy. The model is based on the Susceptible-Infected-Treatment-Susceptible compartmental structure with the possibility of infected individual recovering from natural immunity. Important epidemiological thresholds such as the basic and control reproduction numbers ( 𝑅𝑜and 𝑅𝑐 respectively) and a measure of treatment impact are derived. Infection free point was found to be locally stable but globally unstable. We found that if the control reproduction number is greater than unity, then there is a unique endemic equilibrium point and it is less than unity, the endemic equilibrium point is globally asymptotically stable, and pneumonia will be eliminated. Numerical simulations using Matlab software suggest that, besides the parameters that determine the basic reproduction number, natural immunity plays an important role in pneumonia transmissions and magnitude of the public health impact of therapy. Further, treatment regimens with better efficacy holds great promise for lowering the public health burden of pneumonia disease.Item Determinants of Electronic Health in Developing Countries(2014-04) Mugo, David M.; Nzuki, DavidLimitations of paper-based records are influencing a transition across the globe towards Electronic Health Records (EHRs) and in general electronic health (eHealth). However, despite the well documented benefits of eHealth, adoption particularly in developing countries remains a great challenge. Lessons learned from widespread implementation efforts can be used to encourage and inform the use of eHealth. This study evaluates the most current literature to establish the extent to which electronic health has been adopted in developing countries. The study has shown various determinants of electronic health adoption which will help countries particularly the developing ones come up with necessary interventions to accelerate the adoption. As part of future work, more studies need to be done, firstly to confirm the effect of the mentioned determinants in this paper in each developing country, secondly to find out other determinants of eHealth adoption and thirdly to show how developing countries’ cooperation on eHealth strategies can affect the journey towards eHealth adoption by these countries.Item An Assessment framework for Internet banking system reliability(2014-09) Musyoka, Faith M.E-banking technology is very widespread in banking sector while in Kenya; banks are striving to achieve social and economic development. Banks are investing in Internet for better financial services to their customers though these systems are believed to have critical challenges in terms of reliability yet have become modern means of performing business transactions. Therefore, there is a great need to maintain reliability, which has been investigated shallowly in developing countries given the many challenges such countries face. This paper therefore sought to define a framework that can be used for assessing Internet banking system reliability. The study used multi case study design with study population being two banks in Kenya. Data was collected from a key informant using a questionnaire and document analysis guide and was analysed using both descriptive and inferential statistics. The study found out that documentation and size internal properties had significant positive effect on reliability. Further researches are required to establish effect of internal properties of Internet banking system on other software qualities.Item Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered 4-Element and 5- Element Subsets(UoEm, 2015) Kimani, Patrick; Rimberia, Jane; Muthoka, Geoffrey; Lao, Hussein; Kimani, JacobRanks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply the concept of marks to compute the ranks and subdegrees of the symmetric group Sn (n = 7,8,9) acting on ordered 4-element subsets and Sn (n = 8,9,10) acting on ordered 5-element subsets.Item Transitivity Action of An on (n=4,5,6,7) on Unordered and Ordered Quadrupples(UoEm, 2015) kimani, Gachago j; N, Kinyanjui J.; j, Rimberia; kimani, Patrick; muchemi, Jacob kiboiIn this paper, we study some transitivity action properties of the alternating group An(n=4,5,6,7 ,) acting on unordered and ordered pairs from the set X = {1,2,...,n} through determination of the number of disjoint equivalence classes called orbits.when n≤ 7 ,the alternating group acts transitively on both X (4) and X [4] . key words : Orbits ,alternating group An , An on unordered and ordered quadruples from the set X.Item Application of Marks to Computation of Ranks and Subdegrees of the Symmetric Group Acting on Ordered 4-Element and 5- Element Subsets(UoEm, 2015) Kimani, Patrick; Rimberia, Jane; Muthoka, Geoffrey; Lao, Hussein; Kimani, JacobRanks and subdegrees can be computed using combinatorial arguments, the Cauchy-Frobenius lemma and use of the concept of marks. However the concept of Marks has been given very little attention. In this paper we will apply the concept of marks to compute the ranks and subdegrees of the symmetric group 𝑆𝑛(𝑛 = 7,8,9) acting on ordered 4-element subsets and 𝑆𝑛 (𝑛 = 8,9,10) acting on ordered 5-element subsets .Item Cycle Index Formulas for D n Acting on Unordered Pairs(Uoem, 2015) Muthoka, Geoffrey; Kamuti, Ireri; Lao, Hussein; Kimani, Patrick MwangiThe cycle index of dihedral group D n acting on the set of X the vertices of a regular n- gon was studied (See [1]). In this paper we study the cycle index formulas of D n acting on unordered pairs from the set . In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of and an odd value of .1.Item Cycle Index Formulas for Dn Acting on Unordered Pairs(UoEm, 2015) Muthoka, Geoffrey; Kamuti, Ireri; Lao, Hussein; kimani, patrickThe cycle index of dihedral group Dn acting on the set X of the vertices of a regular -gon was studied (See [1]). In this paper we study the cycle index formulas of Dn acting on unordered pairs from the set x . In each case the actions of the cyclic part and the reflection part are studied separately for both an even value of n and an odd value of n .Item Localization of Overlaid Text Based on Noise Inconsistencies(2015-04) Too, Boaz K.; Prabhakar, C. J.In this paper, we present a novel technique for localization of caption text in video frames based on noise inconsistencies. Text is artificially added to the video after it has been captured and as such does not form part of the original video graphics. Typically, the amount of noise level is uniform across the entire captured video frame, thus, artificially embedding or overlaying text on the video introduces yet another segment of noise level. Therefore detection of various noise levels in the video frame may signify availability of overlaid text. Hence we exploited this property by detecting regions with various noise levels to localize overlaid text in video frames. Experimental results obtained shows a great improvement in line with overlaid text localization, where we have performed metric measure based on Recall, Precision and f-measure.Item Localization of Overlaid Text Based on Noise Inconsistencies(2015-04) Too, Boaz K.; Prabhakar, C. J.In this paper, we present a novel technique for localization of caption text in video frames based on noise inconsistencies. Text is artificially added to the video after it has been captured and as such does not form part of the original video graphics. Typically, the amount of noise level is uniform across the entire captured video frame, thus, artificially embedding or overlaying text on the video introduces yet another segment of noise level. Therefore detection of various noise levels in the video frame may signify availability of overlaid text. Hence we exploited this property by detecting regions with various noise levels to localize overlaid text in video frames. Experimental results obtained shows a great improvement in line with overlaid text localization, where we have performed metric measure based on Recall, Precision and f-measure.Item Enumeration of cyclic codes over GF(17)(UoEm, 2015-05) Hussein, Lao; Kivunge, Benard; Muthoka, Geoffrey; Mwangi, PatrickIn this paper we seek the number of irreducible polynomials of xn− 1 over GF(17). We factorize Xn− 1 over GF(17)into irreducible polynomials using cyclotomic cosets of 17 modulo n . The number of irreducible polynomials factors of Xn− 1 over fq is equal to the number of q cyclotomic cosets of modulo n. Each monic divisor of Xn− 1 is a generator polynomial of cyclic code in Fqn. We show that the number of cyclic codes of length n over a finite field f is equal to Xn− 1. Lastly, the number of cyclic codes of length n , when n= 17 , = the number of polynomials that divide 17k ,n = 17k,n=17k − 1, ( , 17) = 1 are enumerated.Item Segmentation and Alignment of Multi-oriented and Curved Text Lines from Document Images(2015-06) Too, Boaz K.; Prabhakar, C. J.In this paper, we present a novel approach to segment and align multi-oriented and curved text-lines from document images. We assumed that the input document image contains text-lines with arbitrary orientation and identified the arbitrary text string based on projection profile. We employed anisotropic Gaussian filter bank on the identified arbitrary text region in order to smooth the text region, which helps to detect the ridges which is a representative of a text-line path. The ridges are then labeled and a cubic B-spline is fitted to the text-line path points. The orientation and curvature features of the text-line path is estimated using orientated gradients for each point and corresponding curvature to these text-line path are computed. Text is aligned along the horizontally transformed line by rotating individual characters based on the computed curvature information. Finally, the aligned text-lines are extracted, which can be fed into OCR for recognition. The evaluation metrics was evaluated at text-line segmentation level and the results posted show a significant improvement. The resulting system is proven to provide better results than most state of the art algorithmsItem Socio-Economic Determinants of Low Birth Weight in Kenya: An Application of Logistic Regression Model(Science Publishing Group, 2015-11) Atitwa, Edwine B.Babies born with Low-birth weight are at increased risk for serious health problems which are accompanied by disabilities and even death. The purpose of this study was to determine socio-economic factors that lead to low birth weight of children in Kenya. Data used was from Kdhs 2003 and the significant effect of socio-economic determinants on low birth weight was examined using logistic regression analysis data is categorical and continuous in nature, where predictor variables being socio-economic determinants and birth weight being dependent variable. Results indicate that out of six socio-economic factors involved in the study, four (Religion, Time Wanted Pregnancy, Marital Status and Economic Status) revealed some significant effects on the children with low birth weight. Therefore Socio-economic determinants have a significant effect on Low birth weight which suggests a strong negative associated with infant survival in Kenya independent of other risk factors. The logistic function revealed a statistically significant association between the birth weight, Religion, Time Wanted Pregnancy, Marital Status and Economic Status. Predicted probability is 11.4% low birth weight. Researcher recommends that respondents should avoid conceiving unexpectedly since it was associated with high low birth weight. Also to effectively enhance normal birth weight in Kenya, then expectant mothers should keenly focus on the socio-economic determinants by avoiding marital problems like divorce.Item Analytical model for childhood pneumonia, a case study of Kenya(Science Domain International, 2016) Ngari, Cyrus G.; Pokhariyal, G. P.; Koske, J. K.Pneumonia is an infection of the lungs that is caused by bacteria, viruses, fungi, or parasites. For a long time to the best of our knowledge there have not been reliable mathematical model for childhood pneumonia in Kenya. This research study developed a deterministic model based on the Susceptible- Vaccinated-Infected-Treated-Recovered-Susceptible compartment classes. The study used the partial differentiation of control reproduction number toinvestigate effects of; environment, efficacy of vaccination drug and treatment. Model analysis indicates the system lie in feasible region, it is bounded, has no backward bifurcation and there exists unique endemic equilibrium point when control reproduction number is greater than unity. Local and global stability of the equilibrium points indicated that control reproduction has to be maintained at less than unity to eradicate the disease. Sensitivity analysis of the control reproduction number indicates that improved vaccination drug’s efficacy, attaining herd immunity, higher treatment rates and lower effects of environment are the best intervention strategies to lower impact of the pneumonia of the children under the age of five years in Kenya.Item Tuberculosis model, a case study of tigania west, Kenya(2016) Muthuri, Grace G.; Malonza, David; Ngari, Cyrus G.Tuberculosis (TB) is a bacterial disease caused by mycobacterium tuberculosis. Many mathematical models for TB have been developed but not specifically for Kenya. This study develops a deterministic model based on Susceptible–Exposed–Active–Treated compartments classes. The model analyses the stability of the disease free equilibrium by analyzing the basic (R0) and control (RC) reproduction number and the endemic equilibrium point (EEP) which shows that the model is stable when RC< 1 and there exist an EEP when RC is less than one. Sensitivity analysis of the model was investigated using the partial derivatives of (RC) with respect to treatment which shows that high rate of treatment reduces the control reproduction number so is the best intervention method in Kenya.Item Modeling Kenya Domestic Radicalization like A Disease Incorporating Rehabilitation Centers(Academic Research Publishing Group, 2016) Ngari, Cyrus G.The study presents a deterministic model for radicalization process in Kenya and use the model to assess impact of rehabilitation centers to radicalization burden. The possibility of other drivers of radicalization to individuals who are not religious fanatics, and also individuals in rehabilitated subclass continuing being violent was considered. The model incorporated rehabilitation of the radicalized but peaceful individuals in subclass R (t), and also radicalized but violent individuals in subclass T (t), allowing recovery of individuals in subclass R (t) from the intervention of good clergies. The stationary points were computed, their stabilities investigated and important thresholds determining the progression of the radicalization evaluated. The model sensitivity indices indicate that high intervention rates hold great promise to reduce the radicalization burden.Item Numerical simulation of the deterministic model of the under-five year’s pneumonia in Kenya(2016) Ngari, Cyrus G.; Pokhariyal, G. P.; Koske, J. K.In this paper the numerical simulation of the childhood pneumonia deterministic model are determined. The estimated parameters and the under-five year’s population data for year 2013 was used to simulate the developed deterministic model, using Matlab inbuilt ordinary differential equation (ode) solver. Graphical results predicting the dynamics of the under-five year’s pneumonia were obtained for a period of twenty years. Simulations indicated that sustained vaccination and treatment are likely to reduce the burden of the under-five year’s pneumonia over a period twenty years.