Research Papers/Topics in Mathematics And Statistics

Asap: A Stochastic Adaptive PCA Method For Increasing Block Size Setting

AbstractWe propose Asap, an adaptive stochastic optimization algorithm for principal component analysis (PCA), in the increasing block size setting. Asap is a novel generalized variant of the classical Oja’s algorithm (Oja, 1982), but can compute top-k principal components without the necessity of tuning the step size. Asap performs PCA by first-order gradient-based optimization based on adaptive estimates of lower-order moments as with Adagrad and Adam. We provide a theoretical guaran...

Finding The Distribution Of A Random Variable From Its Moment Function

ABSTRACT Consider the problem of r t / randomly distributed points in a unit n-ball and the convex hull created by these points. Let ~ 11 be r.t times the r-content of an rsimplex whose p vertices are in the interior and r + /- p vertices on the boundary of a unit n-ball. Explicit expressions for the exact distribution functions of ~,, are given when r 1 / points are independently, and identically distributed according to the Uniform distribution. The exact distributions are obtained usi...

New Models For Quark Stars With Charge And Anisotropy

Abstract We find new classes of exact solutions for the Einstein-Maxwell field equations. The solutions are obtained by considering charged anisotropic matter with a linear equation of state consistent with quark stars. The field equations are integrated by specifying forms for the measure of anisotropy and one of the gravitational potentials which are physically reasonable. A general feature of our models is that isotropic pressures are regained when certain parameters vanish; this beh...

Relating Mathematics To Machine Learning Through Algorithm Development For Big Data Analysis

ABSTRACTData has increased at an exponential rate and has outpaced our capability to analyze it. However, new ways of data analysis, which thrive in big data such as Machine Learning (ML) have emerged. This study explores Machine Learning by creating a Machine Learning algorithm based on Support Vectors. This was done by converting mathematical formulations into a computer algorithm that was then used for data classification. The algorithm was evaluated and compared to other algorithms. The r...

Modelling Volatility Of Kes/Usd Exchange Rates Using Time Series Models (A Case Study Of The Kenyan Exchange Rates)

ABSTRACTResearch work examines the accuracy and forecasting performance of volatility models forthe KES/USD exchange rate return in Kenya using the EGARCH and TARCH. In fittingthese models to the daily and monthly exchange rate returns data collected from CBK whichextended from the period January 2008 to December 2015, In this study, performance ofTime series models ( asymmetric EGARCH and TARCH models) in forecasting thevolatility behavior of Kenya FOREX market was examined. Daily FOREX rate...

Application Of Markov Chain Model In Transition Of Girls In Public Secondary Schools; A Case Study Of Kisumu West Sub-County, Kenya

ABSTRACTTransition is a very important factor in determining success of a student in secondaryschool. It forms a basis for implementing poverty reduction strategy by the governmentthrough acquisition of basic literal skills to increase opportunities for employment. Girlshave not had an efficient transition from form one to the next form in secondary schoolsbecause of choices of secondary school types they enroll in. This research uses a Markovchain model to compare and predict the percentage ...

Application Of Markov Chain Model In Career Progression Of University Academic Staff:A Case Study Of The Moi University - Eldoret, Kenya.

ABSTRACTThe use of Mathematical models for manpower planning has increased in recent times forbetter manpower planning quantitatively both in public and private sectors. In respectof organizational management, numerous previous studies have applied Markov chainmodels in describing title or level promotions, demotions, recruitment, withdrawals, orchanges of different career development paths to confirm the actual manpower needs ofan organization or predict the future manpower needs. The moveme...

A Delayed Vaccination Model For Rotavirus.

ABSTRACTRotavirus is the most common cause of severe gastroenteritis infection in infants andyoung children, occurring even with very high standard of hygiene. The disease spreads bycontact with infected faeces and might also be transmitted through faecally-contaminated:food, water and respiratory droplets. Rota teq and Rotarix are the two licensed oralvaccine intervention for rotavirus. However, it takes time for the development of vaccineinducedimmunity to complete, hence the need to invest...

Mathematical Modelling Of Hiv/Aids Co-Infection With Tuberculosis And Pneumonia Incorporating Protection

ABSTRACTThe synergistic relationship between HIV/AIDS and respiratory infections, such as tu-berculosis(TB) and pneumonia not only results in high mortality rates but is also a sourceof economic burden borne by many nations in the sub-saharan Africa. The search for acure or vaccine for HIV/AIDS has yielded no conclusive results so far. Treatment fail-ure and lack of adherence to treatment schedule which results in the evolution of drugresistant strains of diseases are challenges to grapple wi...

Analysis Of Young People’s Career By Use Of Markov Chains: Case Study Of Kisumu City

ABSTRACTIt is the desire of every person to have a career. Not much thought has been takenby young people on how they can arrive at their future careers. The reason is mainlybecause they are not aware. As much as many people have attained their careers througheducation, not much consideration has been given to the other factors within educationthat leads one to his or her career. The study traced one’s career from primary to presentposition. There are stages one follows to reach the career,...

Optimal Investment Strategies Of A Defined Contribution Pension Fund

ABSTRACTThe issue that a pension fund manager faces is how to optimize his or her investmentstrategies. The question we resolved is the optimal design of the minimum guaranteein a defined contribution pension Fund Scheme. We study the optimal asset allocationstrategy a given fund manager can adopt to maximize surplus (the difference between thetotal wealth and the Guarantee) and the payback ratio (ratio between total wealth andGuarantee). Finally, We analyze the impact of the main parameter w...

Constraints Faced By Small And Medium Entreprise In Accessing Bank Finance In Eldoret Town Kenya

ABSTRACTSmall and Medium Enterprises (SMEs) play an important role in the economies of developed and developing countries, through creation of new jobs. Access to bank financial resources seems to be a major constraint to the growth of SMEs in the developing context. This study thus, aimed at finding out the constraints faced by SMEs in particular accessing bank financing. The study adopted the adverse selection theory of credit markets. This study adopted an explanatory and descriptive surve...

Difference In Difference Method To Impact Evaluation: A Case Study Of Fruiting Africa Project

ABSTRACTDevelopment programs designed to address particular global challenges are facingincreasing pressure to demonstrate their impact on the targeted com munities.The method mostly used to measure impact of development programs isby comparing the changes in outcomes of the program participants over timecommonly know as before-and-after comparison. However, in some cases, thetreatment and control groups are usually heterogeneous at baseline, making thedifference in difference (DiD) method th...

Application Of Logistic Regression Model To Determine Factors Causing Maternal Mortality: A Case Study Of Migori County Referral Hospital (2007-2015)

AbstractKenya is one of the major contributors to the poor maternal healthstatus in Africa with maternal mortality ratio of 488 maternal deathsper 100,000 live births translating to 7,700 maternal deaths annually [23].There are regional disparities in maternal mortality among the 47 countieswith county with the highest maternal mortality has almost 20 timesmaternal deaths of that with the lowest. Migori County is one of thecounties with the highest burden of maternal mortality in the country ...

The Analysis Of Gamma Strategies For A Nonlinear Black-Scholes Equation

ABSTRACTThere has been a significant growth in research in the field of financial mathematicssince the derivation of the standard Black-Scholes-Merton PartialDifferential Equation by Black and Scholes, and Merton in 1973. The derivationwas done under the assumption that the market is liquid and frictionless(no restrictions on trade and no transaction costs). The nonlinear equationut + 12σ2S2uSS(1 + 2ρSuSS) = 0 for modeling illiquid markets has only beensolved analytically using a positive g...


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