Articles: Department of Mathematics and Statistics
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Item A 24-hour ambulatory blood pressure monitoring system for preeclampsia management in antenatal care(Elsevier, 2019-06) Musyoka, Faith M.; Thiga, Moses M.; Muketha, Geoffrey M.The burden of preeclampsia has been a major concern worldwide both in developed and developing countries, making its prevention and management a major concern. Although motherhood is a fulfilling experience in society, it is connected to ill-health in some women, leading to maternal morbidity and mortality. The United Nations' Sustainable Development Goal (SDG) 3 aims to reduce the global maternal mortality ratio to less than 70 per 100,000 live births. These deaths are caused by among other things, the emergence of conditions such as preeclampsia during pregnancy. Therefore, this study sought to implement a 24-hour ambulatory blood pressure monitoring solution for preeclampsia management, using a smartwatch in conjunction with a mobile and cloudbased application. Upon blood pressure readings from the expectant mother, an alert is sent to the assigned caregiver in order to initiate quick action. The researchers adopted a rapid prototyping approach in the implementation of the 24-hour ambulatory blood pressure monitoring system. An experimental design was adopted in the study to evaluate whether the system functionalities performed as expected. The system, which was evaluated in the context of a sample of 30 expectant mothers from two level 5 hospitals in Kenya, has been able to read blood pressure from expectant mothers' smartwatches. The real-time data is then sent to the caregivers’ smartphone, as well as an alert. The solution has shown great potential for actual adoption in healthcare systems in developing countries, given its simplicity and affordability.Item Action of PGL(2,q) on the Cosets of the Centralizer of an Eliptic Element(Uoem, 2021-08-19) Kimani, Patrick Mwangi; Adicka, DanielMost researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroups. In this paper, we consider the action of PGL(2,q) centralizer of an elliptic element which is a non maximal subgroup c(q+1). In particular, we determine the subdegrees, rank and properties of the suborbital graphs of the action. We achieve this through the application of the action of a group by conjugation. We have proved that the rank is q and the subdegrees are [1][2] and [q+ 1][q-2].Item Action ofPGL (2 ,q ) on the Cosets of the Centralizer of an Eliptic Element(UoEm, 2021) Kimani, patrick; Adicka, DanielMost researchers consider the action of projective general group on the cosets of its maximal subgroups leaving out non-maximal subgroupsCq+1. In this paper, we consider the action ofPGL (2, ) centralizer of an elliptic element which is a non maximal subgroup . In particular, we determine the subdegrees, rank and properties of the suborbital graphs of the action. We achieve this through the application of the action of a group by conjugation. We have proved that the rank is and the subdegrees are [1][ ] and [ + 1][ ] .Item Analysis of Static Code Techniques for Vulnerability Detection: A reviewed Literature(2017-10) Musyoka, Faith M.Web applications have become an integral part of the daily lives of trillions of users. These systems are usually complex and are developed by different programmers. Regularly programmers make mistakes in the code which could generate critical software vulnerabilities. Despite the knowledge about vulnerabilities nowadays there is still a growing tendency in the number of reported vulnerabilities, reason why software security has become an important field of research. Due to the presence of vulnerabilities it has been necessary to have tools that can help programmers detect them in code development stage. This paper has analysed pattern matching and taints analysis techniques that are currently used in development of static tools to in detection of vulnerabilities.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 Aperture Maximization with Half-Wavelength Spacing, via a 2-Circle Concentric Array Geometry that is Uniform but Sparse(Journal of Advances in Mathematics and Computer Science, 2019-05-25) Kinyili, Musyoka; Kitavi, Dominic Makaa; Ngari, Cyrus GitongaThis paper proposes a new sensor-array geometry (the 2-circle concentric array geometry), that maximizes the array’s spatial aperture mainly for bivariate azimuth-polar resolution of direction-of-arrival estimation problem. The proposed geometry provides almost invariant azimuth angle coverage and offers the advantage of full rotational symmetry (circular invariance) while maintaining an inter-sensor spacing of only an half wavelength (for non-ambiguity with respect to the Cartesian direction cosines). A better-accurate performance in direction finding of the proposed array grid over a single ring array geometry termed as uniform circular array (UCA) is hereby analytically verified via Cram´er-Rao bound analysis. Further, the authors demonstrate that the proposed sensor-array geometry has better estimation accuracy than a single ring array.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 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 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 Application Of Multiple Circular-Linear Regression Models To Animal Movement Data With Covariates(2016-04) Mutwiri, Robert M.In a many biological and physical sciences studies, a set of techniques have been developed to analyse the relationship between the circular and linear data derived from the geographical positioning system (GPS) telemetry to describe animal movement. Yet, many of the models used by ecologists do not provide a link between the circular and linear variables. This chapter demonstrates the application of the circular-linear regression in describing such a relationship. We describe numerical methods of obtaining maximum likelihood model parameter estimates. We discuss the technical limitations of the model through simulation and application to real elephant movement data with covariates collected from Kruger national park, South Africa. These results provide a new statistical paradigm for understanding the need to landscape features in elephant and similar animal models and evolutionary forces driving unpredictable.Item Approaches for Testing Uniformity Hypothesis in Angular Data of Mega-Herbivores(2016-03) Mutwiri, Robert M.; Mwambi, Henry; Slotow, RobCircularstatistics is an area not used verymuch by ecologists to describe animal movement patterns.Nevertheless,the connection betweenthe evaluation of temporalrecurring events and theanalysis of directional data haveconverged in several papers, and showcircularstatistics to be an outstandingtoolforunderstanding animal movementbetter. Theaim of thischapter is to evaluate the applications of circularstatisticaltests to check uniformityhypothesis in animal movement and its potential interpretationwithin the general framework of movementecology. Four methods of circularstatistics: Rayleigh’s,Watson’s,Rao’s spacing and Kuiper’s test based on the mean resultantlengthare applied to examine theuniformityhypothesis of GPS derived telemetry data of elephant movementcollected fromKrugerNationalPark(KNP) South Africa.Overall,circularstatisticaluniformitytests methods represent a usefultoolfor evaluation of directionalityelephant movement with applications including(i) assessment of animal foragingstrategies; (ii)determination of orientation in response to landscape features and (iii)determination of therelativestrengths of landscape features present binacomplex environment.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 An Assessment of Suitable and Affordable Smart armband for preeclampsia Management in Antenatal Care(2019-06) Musyoka, Faith M.; Thiga, Moses M.; Muketha, Geoffrey M.Blood pressure is one of the measurements that is taken during antenatal care visits. Though motherhood is a fulfilling experience in the society, it is connected to ill-health and even death in some women leading to maternal morbidity and mortality due to preeclampsia syndromes. United Nations’ Sustainable Development Goal 3 aims to reduce global maternal mortality ratio to less than 70 per 100,000 live births. Therefore, this study sought to assess the suitability and affordability of smart armbands for preeclampsia management in antenatal care. An exploratory design was adopted in the study to assess the suitability and affordability of the device in antenatal care to ensure real time monitoring. Twelve categories were used in assessment to select the most suitable smart armband. It was found out that F1 smart armband was suitable and affordable. The study has shown great potential for actual adoption in health care systems in developing countries.Item A Classification Model for Water Quality analysis Using Decision Tree(2019-06) Gakii, Consolata; Jepkoech, JenniferA classification algorithm is used to assign predefined classes to test instances for evaluation) or future instances to an application). This study presents a Classification model using decision tree for the purpose of analyzing water quality data from different counties in Kenya. The water quality is very important in ensuring citizens get to drink clean water. Application of decision tree as a data mining method to predict clean water based on the water quality parameters can ease the work of the laboratory technologist by predicting which water samples should proceed to the next step of analysis. The secondary data from Kenya Water institute was used for creation of this model. The data model was implemented in WEKA software. Classification using decision tree was applied to classify /predict the clean and not clean water. The analysis of water Alkalinity,pH level and conductivity can play a major role in assessing water quality. Five decision tree classifiers which are J48, LMT, Random forest, Hoeffding tree and Decision Stump were used to build the model and the accuracy compared. J48 decision tree had the highest accuracy of 94% with Decision Stump having the lowest accuracy of 83%.Item Cramer-Rao Bound of Direction Finding Using a Uniform Hexagonal Array(2019-06) Ndiritu, Grace Wakarima; Kitavi, Dominic M.; Ngari, Cyrus G.Direction-of-arrival (DOA) estimation is a key area of sensor array processing which is encountered in many important engineering applications. Although various studies have focused on the uniform hexagonal array for direction nding, there is a scanty use of the uniform hexagonal array in conjunction with Cram er-Rao bound for direction nding estimation. The advantage of Cram er- Rao bound based on the uniform hexagonal array: overcome the problem of unwanted radiation in undesired directions. In this paper, the direction-of-arrival estimation of Cram er-Rao bound based on the uniform hexagonal array was studied. The proposed approach concentrated on deriving the array manifold vector for the uniform hexagonal array and Cram er-Rao bound of the uniform hexagonal array. The Cram er-Rao bound based on the uniform hexagonal array was compared with Cram er-Rao bound based on the uniform circular array. The conclusions are as follows. The Cram er-Rao bound of uniform hexagonal array decreases with an increase in the number of sensors. The comparison between the uniform hexagonal array and uniform circular array shows that the Cram er-Rao bound of the uniform hexagonal array was slightly higher as compared to the Cram er-Rao bound of the uniform circular array. The analytical results are supported by graphical representation.Item Cramer-Rao Bound of Direction Finding Using Uniform Arc Arrays(2019) Nyokabi, Veronicah; Kitavi, Dominic M.; Ngari, Cyrus G.Direction-of-Arrival estimation accuracy using arc array geometry is considered in this paper. There is a scanty use of Uniform Arc Array (UAA) in conjunction with Cram er-Rao bound (CRB) for Direction-of-Arrival estimation. This paper proposed to use Uniform Arc Array formed from a considered Uniform Circular Array (UCA) in conjunction with CRB for Direction-of-Arrival estimation. This Uniform Arc Array is obtained by squeezing all sensors on the Uniform Circular Array circumference uniformly onto the Arc Array. Cram er-Rao bounds for the Uniform Arc Array and that of the Uniform Circular Array are derived. Comparison of performance of the Uniform Circular Array and Uniform Arc Array is done. It was observed that Uniform Arc Array has better estimation accuracy as compared to Uniform Circular Array when number of sensors equals four and ve and azimuth angle ranging between π 9 7 and π and also 18 10 9 π and 25 18π. However, UCA and UAA have equal performance when the number of sensors equals three and the azimuth angle ranging between 0 and 2π. UCA has better estimation accuracy as compared to UAA when the number of sensors equals four and ve and the azimuth angle ranging between π 2 and π and also 32 π and 2πItem Crame´R-Rao Bound of Direction Finding using Uniform Circular Array And 2-Circle Concentric Uniform Array(2019-09) Musyoka, DavidSource direction-of-arrival estimation problem has received much attention in recent years following its significant role in array-signal processing and wide range of applications such as radar, wireless communication, sonar, seismology among others. Direction finding has been solved by several techniques such as Maximum likelihood estimator, MUltiple Signal Classification, Estimation of Parameters via Rotational Invariance Technique and Cram´er- Rao bound using array of sensors in both uniformly-spaced and non-uniformly-spaced. The sensors have further been arranged in different geometric patterns ranging from onedimension to three-dimensional. However, little effort has been made in direction finding using concentric planar arrays with fixed centers at the Cartesian origin. In this study, a new planar sensor-array geometry (the 2-circle concentric uniform array geometry) centered at the Cartesian origin, that maximizes the array’s spatial aperture mainly for bivariate azimuth-polar resolution of direction-of-arrival estimation problem was proposed. The proposed geometry provides almost invariant azimuth angle coverage and offers the advantage of full rotational symmetry (circular invariance) while maintaining an inter-sensor spacing not exceeding half wavelength (for non-ambiguity with respect to the Cartesian direction cosines) among other advantages. The study adopted Cram´er-Rao bound technique of direction finding via a uniform circular array (single ring array) and the proposed geometry to estimate the bivariate azimuth-polar angles-of-arrival. Both the array manifolds and the Cram´er-Rao bounds for the uniform circular array and that of the proposed array grid were derived. Further, a better-accurate performance in direction finding of the proposed array grid over that of the single ring array grid was analytically verified under different constraints of investigation. It was found that the proposed sensor-array geometry has better estimation accuracy than a single ring array and the 2-circle concentric uniform array geometry would have the best estimation accuracy for minimal number of sensors hence reducing the hardware cost. The study therefore recommends that the 2-circle concentric uniform array geometry should be used for direction finding with minimal number of sensors and with an inter-sensor spacing not exceeding half a wavelength as opposed to a uniform circular array geometry. xItem 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 Ordered pairs(UoEm, 2016-04) Muthoka, Geoffrey; Kamuti, Ireri; Kimani, Patrick; Hussein, LaoThe cycle index of dihedral group Dn acting on the set of the vertices of a regular n-gon was studied by Harary and Palmer in 1973 [1]. Since then a number of researchers have studied the cycle indices dihedral group acting on different sets X={1,2,...,n} and the resulting formulas Dn have found applications in enumeration of a number of items. Muthoka (2015) [2] studied the cycle index formula of the –the n vertices of a regular -gon. In this paper we study the dihedral group acting on unordered pairs from the set X={1,2,..,n} cycle index formulas of acting on ordered 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 n .