Thanks to the ongoing expansion of internet access and, most recently, the movement restrictions ... more Thanks to the ongoing expansion of internet access and, most recently, the movement restrictions that were put in place globally to stop COVID-19 spread, many small and medium enterprises (SMEs) are prepared to use social media platforms to market their products as a way to improve their business performance in emerging economies. Businesses at all levels that use social media marketing (SMM) see a considerable increase in their output. This study’s objective is to identify the factors that significantly help Ugandan SMEs implement SMM techniques to enhance their commercial performance. Here, statistical models are utilized to analyze how the age and gender of SMEs owners as moderating variables affect the adoption and performance of SMEs in Uganda. A theoretical model that is based on the Technology Acceptance Model (TAM) and Innovation Diffusion Theory (IDT) theories has been put out as part of a specific conceptual framework. The following indicators are used to evaluate the perf...
In this work, a reduced model proposed by Lubuma and Gumel for transmission dynamics of Mycobacte... more In this work, a reduced model proposed by Lubuma and Gumel for transmission dynamics of Mycobacterium tuberculosis and Bovine tuberculosis in a community consisting of humans andAfrican buffaloes is considered. The buffalo-only component of the model is however, examined for parameter estimation. The problem is to propose an analytical approach for restoring the state variables, EB1 and EB2 which are the early and advanced-exposed buffaloes to Bovine tuberculosis respectively. These model variables are the assumed missing information about the population of susceptible Buffaloes. The discussed method is then used to restore this missing information in the susceptibles. The approach uses differential equations that are linearized through new parameters to form an objective function that is minimized using the least-squares methods in order to compute the required model coefficients. The Results show that the approach is efficient given the relatively small absolute errors of order 10...
In this paper, we present two unfamiliar novel estimation techniques (UNET) for the constrained r... more In this paper, we present two unfamiliar novel estimation techniques (UNET) for the constrained regression coefficients in the frame-work of a standard multiple linear regression model. Estimation of a linear regression problem with constraints on the regression coefficients are firstly derived by minimising a formulated goal function that minimises the total sum of the squared errors, plus the sum of the linear constraints multiplied by a Lagrangian. We also show that the solution to the system of equations can be obtained without differentiating the goal function, rather expressed interms of the known matrices. This is achieved by employing properties of a blocked linear system. The UNET is justified by a numerical simulated system of linear equations in 3-dimensions. The UNET yields estimates that are comparable to those generated by the Schur complement principle.
Business intelligence (BI) technologies have attracted attention from academics and entrepreneurs... more Business intelligence (BI) technologies have attracted attention from academics and entrepreneurs, enterprise mangers are starting to employ them to make informed decisions for proper management. While several studies have been conducted on the need for BI in small and medium enterprises (SMEs), they have concentrated on performance and adoption and give insights and approaches, suitable for large-scaled enterprises, but insufficient for SMEs. In this study, BI acceptance is examined within South Africa’s SMEs in the City of Tshwane (n= 161). Perceived benefits and challenges are analysed in their efforts to adopt BI. By classifying BI acceptance into three categories, multinomial logistic regression is used. We build a refined model on the considerations of the supported hypotheses within, technological, organizational, environmental and behavioural factors. Supported hypotheses are aligned to a respective BI characteristic. Application of the refined model will contribute towards...
In this paper, based on the model proposed by Gumel, Moghadas and Mickens, which monitors the imp... more In this paper, based on the model proposed by Gumel, Moghadas and Mickens, which monitors the impact of live attenuated HIV vaccines, a new method for restoring the unknown data is proposed. Missing data in both epidemiological and ecological surveys and experiments can be due to a number of causes, like, unprovided domains of required data, complete refusal by respondents etc. Differential methods are used to linearize the non-linear equations for the model as the parameter space of the original models is increased. Least squares methods are employed to estimate the unknown model coefficients. Results show that the proposed method is able to restore the missing data with an acceptable accuracy. The efficiency of the proposed method is verified by comparing the restored and observed data using the absolute percentage error. The proposed method can be used in practical research 1Corresponding author. and studies to provide a clue on which data to analytically restore in case of missi...
This article presents a novel approach for generating time series data by bootstrapping the resid... more This article presents a novel approach for generating time series data by bootstrapping the residuals and compares the method with that proposed by Efron and Tibishirani in 1993. Two real datasets, one for the luteinizing hormone levels, and the other for the highest mean monthly levels of Lake Michigan, , are bootstrapped using the proposed data generating process (Prop DGP) and the Efron-Tibishirani method (Efron DGP). The accuracy of the methods is assessed by both graphical and the conventional methods, that is, root mean squared error (RMSE), mean absolute error (MAE) and standard error (SE). Bootstraps from Prop DGP are generated as while those from Efron DGP as . In both methods, the bootstrapped residuals on each run are added to the independent variables as defined in the two models. The new method produces better bootstrap samples than the Efron-Tibishirani method, hence it is recommended for both practical and theoretical applications.
Understanding the population dynamics at the human-livestock-wildlife interface is key to managin... more Understanding the population dynamics at the human-livestock-wildlife interface is key to managing zoonotic and cross-species diseases as well as maintaining ecosystem biodiversity at this interface. This necessitates elucidation of the effects of within and between species interactions and human activities such as farming and animal harvesting among others.
British Journal of Mathematics & Computer Science, 2016
Two approaches to parameter estimation for a mixture of two univariate Gaussian distributions are... more Two approaches to parameter estimation for a mixture of two univariate Gaussian distributions are numerically compared. The proposed method (PM) is based on decomposing a continuous function into its odd and even components and estimating them as polynomials, the other is the usual maximum likelihood (ML) method via the expected maximisation (EM) algorithm. An overlapped mixture of two univariate Gaussian distributions is simulated. The PM and ML are used to re-estimate the known mixture model parameters and the measure of performance is the absolute percentage error. The PM produces comparable results to those of to the ML approach. Given that the PM produces good estimates, and knowing that the ML always converges given good initial guess values (IGVs), it is thus recommended that the PM be used symbiotically with the ML to provide IGVs for the EM algorithm.
Abstract Two new approaches (method I and II) for estimating parameters of a univariate normal pr... more Abstract Two new approaches (method I and II) for estimating parameters of a univariate normal probability density function are proposed. We evaluate their performance using two simulated normally distributed univariate datasets and their results compared with those obtained from the maximum likelihood (ML) and the method of moments (MM) approaches on the same samples, small n = 24 and large n = 1200 datasets. The proposed methods, I and II have shown to give significantly good results that are comparable to those from the standard methods in a real practical setting. The proposed methods have performed equally well as the ML method on large samples. The major advantage of the proposed methods over the ML method is that they do not require initial approximations for the unknown parameters. We therefore propose that in the practical setting, the proposed methods be used symbiotically with the standard methods to estimate initial approximations at the appropriate step of their algorit...
Synthetic antioxidants such as butylated hydroxyanisole (BHA) and butylated hydroxytoluene (BHT) ... more Synthetic antioxidants such as butylated hydroxyanisole (BHA) and butylated hydroxytoluene (BHT) are toxic and carcinogenic, thus they induce DNA damage. This calls for the need to find alternative antioxidants from natural products. Tagetes minuta (Asteraceae) is an annual herb that belongs to the Asteraceae family. It is used in common medicine and grows in temperate regions of South America, some parts of Africa and Asia. Essential oil from T. minuta was obtained by hydrodistillation while solvent extracts were obtained using ethyl acetate and methanol. Antioxidative compounds of T. minuta were isolated both from the Ethyl acetate extract and the essential oil. It was done by determining the scavenging activity using 2,2-diphenyl-1-picrylhaydrazyl free radical (DPPH) using thin layer chromatography (TLC). The active compounds were tested quantitatively for their radical scavenging activity using the U-1100 UV-VIS Spectrophotometer. The active fractions were isolated using TLC and...
A statistical study has been made on the isothermal treatments of A356.0-type Al-Si-Mg alloy. The... more A statistical study has been made on the isothermal treatments of A356.0-type Al-Si-Mg alloy. The reprocessed alloy was subjected to hardness evaluation. The values obtained were processed using statistical package for social scientists (SPSS) software to compare all tempers and multiple-step thermal ageing treatment (MSTAT) values by analysis of variance (ANOVA) and Pearson Correlation Index. Equally, a non-parametric and parametric statistics consisting of sign test and t- test respectively were employed for further evaluation of results. This indicate that up to 47% (obtained from the adjusted R square) of the variation in hardness is explained by ageing time. From the statistical analysis of the reprocessed alloy, it was evidenced using one-way ANOVA that all the temper conditions and MSTAT showed six hardness values that have been computed with their corresponding mean and standard error bars. Most of the treatments conducted indicate a significant improvement in the hardness v...
Journal of Computational and Theoretical Nanoscience, 2016
Methods like the maximum likelihood and Newton's iterative techniques are usually employe... more Methods like the maximum likelihood and Newton's iterative techniques are usually employed to estimate the parameters of the classical Rydberg interatomic potential function. However, such approaches require initial guess values (IGV) to compute the optimal solutions of the unknowns. In this work, a multiple objective function approach that is used to compute the parameter estimates via the least-squares method is presented. The new approach does not necessitate the uniqueness and existence of the initial guess values to compute the required estimates. The classical Rydberg interactomic potential is firstly considered as a general solution of a second order linear differential equation with constant coefficients. Secondly, the characteristic equation of the general solution of the potential function is formulated and it's constraints derived. Two objective functions are constructed from the assumed ordinary differential equation. The first objective function is constrained and selected parameters are estimated using the least-squares method and the second objective function is directly minimised by formulating normal equations that can be solved for exact solutions of the unknowns. The new method and the computer algebraic system (CAS) are tested using experimental datasets of copper, silver ions and silver-copper alloy. Estimates from both approaches are compared and used to construct potential energy curves of the atoms considered. Three potential surfaces, that is, for experimental data, new method and the CAS for each atom are plotted on the same axis for better comparison. It is observed that estimates from the new method are greater in absolute terms than those from the CAS. However, all the estimates have the same direction. The potential curves from the experimental data, the new method and the CAS all have the same shape and close to each other, especially at the minimum of the potential well and at that point they are all indistinguishable. Estimates from the new method can be trusted as they produce a potential curve that is close to that of the experimental data and the CAS. As the present iterative methods usually converge to the required solutions given " good " IGVs, it is proposed that the new method be used symbiotically with the present methods to systematically compute the necessary IGVs. Hence the new method can be used in both theoretical and practical applications to estimate parameters of the Rydberg potential function since it does not require provision of IGVs to the unknown parameters.
Exact solutions for the generalized Morse potential parameters are obtained using the ordinary le... more Exact solutions for the generalized Morse potential parameters are obtained using the ordinary leastsquares (OLS) method. The function is linearized by reducing the dimensionality of its parameter space through integral techniques. Experimental data sets of 3-diatomic molecules, that is, HBr, HI and HCl are used to evaluate the performance of the computed estimates using the proposed method (PM). Potential energy curves (PECs) of the diatomic molecules are reconstructed using estimates from the PM. It is shown that PECs reconstructed using the estimates compare well with those from the randomized experimental dataset. In a departure from previous studies that developed methods of PEC fitting, their accuracy was only considered at the minimum of the potential well, the current work proposes a method that accounts for the experimental data points at a wider range of interatomic compression and stretching. Another advantage of the PM over the existing regular methods is that, it does n...
Background Uganda has a unique set up comprised of resource-constrained economy, social-economic ... more Background Uganda has a unique set up comprised of resource-constrained economy, social-economic challenges, politically diverse regional neighborhood and home to long-standing refuge crisis that comes from long and protracted conflicts of the great lakes. The devastation of the on-going global pandemic outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is likely to be escalated by these circumstances with expectations of the impact of the disease being severe. Materials and methods In this study, we formulate a mathematical model that incorporates the currently known disease characteristics and tracks various intervention measures that the government of Uganda has implemented since the reporting of the first case in March 2020. We then evaluate these measures to understand levels of responsiveness and adherence to standard operating procedures and quantify their impact on the disease burden. Novel in this model was the unique aspect of modeling the trace-and-i...
Thanks to the ongoing expansion of internet access and, most recently, the movement restrictions ... more Thanks to the ongoing expansion of internet access and, most recently, the movement restrictions that were put in place globally to stop COVID-19 spread, many small and medium enterprises (SMEs) are prepared to use social media platforms to market their products as a way to improve their business performance in emerging economies. Businesses at all levels that use social media marketing (SMM) see a considerable increase in their output. This study’s objective is to identify the factors that significantly help Ugandan SMEs implement SMM techniques to enhance their commercial performance. Here, statistical models are utilized to analyze how the age and gender of SMEs owners as moderating variables affect the adoption and performance of SMEs in Uganda. A theoretical model that is based on the Technology Acceptance Model (TAM) and Innovation Diffusion Theory (IDT) theories has been put out as part of a specific conceptual framework. The following indicators are used to evaluate the perf...
In this work, a reduced model proposed by Lubuma and Gumel for transmission dynamics of Mycobacte... more In this work, a reduced model proposed by Lubuma and Gumel for transmission dynamics of Mycobacterium tuberculosis and Bovine tuberculosis in a community consisting of humans andAfrican buffaloes is considered. The buffalo-only component of the model is however, examined for parameter estimation. The problem is to propose an analytical approach for restoring the state variables, EB1 and EB2 which are the early and advanced-exposed buffaloes to Bovine tuberculosis respectively. These model variables are the assumed missing information about the population of susceptible Buffaloes. The discussed method is then used to restore this missing information in the susceptibles. The approach uses differential equations that are linearized through new parameters to form an objective function that is minimized using the least-squares methods in order to compute the required model coefficients. The Results show that the approach is efficient given the relatively small absolute errors of order 10...
In this paper, we present two unfamiliar novel estimation techniques (UNET) for the constrained r... more In this paper, we present two unfamiliar novel estimation techniques (UNET) for the constrained regression coefficients in the frame-work of a standard multiple linear regression model. Estimation of a linear regression problem with constraints on the regression coefficients are firstly derived by minimising a formulated goal function that minimises the total sum of the squared errors, plus the sum of the linear constraints multiplied by a Lagrangian. We also show that the solution to the system of equations can be obtained without differentiating the goal function, rather expressed interms of the known matrices. This is achieved by employing properties of a blocked linear system. The UNET is justified by a numerical simulated system of linear equations in 3-dimensions. The UNET yields estimates that are comparable to those generated by the Schur complement principle.
Business intelligence (BI) technologies have attracted attention from academics and entrepreneurs... more Business intelligence (BI) technologies have attracted attention from academics and entrepreneurs, enterprise mangers are starting to employ them to make informed decisions for proper management. While several studies have been conducted on the need for BI in small and medium enterprises (SMEs), they have concentrated on performance and adoption and give insights and approaches, suitable for large-scaled enterprises, but insufficient for SMEs. In this study, BI acceptance is examined within South Africa’s SMEs in the City of Tshwane (n= 161). Perceived benefits and challenges are analysed in their efforts to adopt BI. By classifying BI acceptance into three categories, multinomial logistic regression is used. We build a refined model on the considerations of the supported hypotheses within, technological, organizational, environmental and behavioural factors. Supported hypotheses are aligned to a respective BI characteristic. Application of the refined model will contribute towards...
In this paper, based on the model proposed by Gumel, Moghadas and Mickens, which monitors the imp... more In this paper, based on the model proposed by Gumel, Moghadas and Mickens, which monitors the impact of live attenuated HIV vaccines, a new method for restoring the unknown data is proposed. Missing data in both epidemiological and ecological surveys and experiments can be due to a number of causes, like, unprovided domains of required data, complete refusal by respondents etc. Differential methods are used to linearize the non-linear equations for the model as the parameter space of the original models is increased. Least squares methods are employed to estimate the unknown model coefficients. Results show that the proposed method is able to restore the missing data with an acceptable accuracy. The efficiency of the proposed method is verified by comparing the restored and observed data using the absolute percentage error. The proposed method can be used in practical research 1Corresponding author. and studies to provide a clue on which data to analytically restore in case of missi...
This article presents a novel approach for generating time series data by bootstrapping the resid... more This article presents a novel approach for generating time series data by bootstrapping the residuals and compares the method with that proposed by Efron and Tibishirani in 1993. Two real datasets, one for the luteinizing hormone levels, and the other for the highest mean monthly levels of Lake Michigan, , are bootstrapped using the proposed data generating process (Prop DGP) and the Efron-Tibishirani method (Efron DGP). The accuracy of the methods is assessed by both graphical and the conventional methods, that is, root mean squared error (RMSE), mean absolute error (MAE) and standard error (SE). Bootstraps from Prop DGP are generated as while those from Efron DGP as . In both methods, the bootstrapped residuals on each run are added to the independent variables as defined in the two models. The new method produces better bootstrap samples than the Efron-Tibishirani method, hence it is recommended for both practical and theoretical applications.
Understanding the population dynamics at the human-livestock-wildlife interface is key to managin... more Understanding the population dynamics at the human-livestock-wildlife interface is key to managing zoonotic and cross-species diseases as well as maintaining ecosystem biodiversity at this interface. This necessitates elucidation of the effects of within and between species interactions and human activities such as farming and animal harvesting among others.
British Journal of Mathematics & Computer Science, 2016
Two approaches to parameter estimation for a mixture of two univariate Gaussian distributions are... more Two approaches to parameter estimation for a mixture of two univariate Gaussian distributions are numerically compared. The proposed method (PM) is based on decomposing a continuous function into its odd and even components and estimating them as polynomials, the other is the usual maximum likelihood (ML) method via the expected maximisation (EM) algorithm. An overlapped mixture of two univariate Gaussian distributions is simulated. The PM and ML are used to re-estimate the known mixture model parameters and the measure of performance is the absolute percentage error. The PM produces comparable results to those of to the ML approach. Given that the PM produces good estimates, and knowing that the ML always converges given good initial guess values (IGVs), it is thus recommended that the PM be used symbiotically with the ML to provide IGVs for the EM algorithm.
Abstract Two new approaches (method I and II) for estimating parameters of a univariate normal pr... more Abstract Two new approaches (method I and II) for estimating parameters of a univariate normal probability density function are proposed. We evaluate their performance using two simulated normally distributed univariate datasets and their results compared with those obtained from the maximum likelihood (ML) and the method of moments (MM) approaches on the same samples, small n = 24 and large n = 1200 datasets. The proposed methods, I and II have shown to give significantly good results that are comparable to those from the standard methods in a real practical setting. The proposed methods have performed equally well as the ML method on large samples. The major advantage of the proposed methods over the ML method is that they do not require initial approximations for the unknown parameters. We therefore propose that in the practical setting, the proposed methods be used symbiotically with the standard methods to estimate initial approximations at the appropriate step of their algorit...
Synthetic antioxidants such as butylated hydroxyanisole (BHA) and butylated hydroxytoluene (BHT) ... more Synthetic antioxidants such as butylated hydroxyanisole (BHA) and butylated hydroxytoluene (BHT) are toxic and carcinogenic, thus they induce DNA damage. This calls for the need to find alternative antioxidants from natural products. Tagetes minuta (Asteraceae) is an annual herb that belongs to the Asteraceae family. It is used in common medicine and grows in temperate regions of South America, some parts of Africa and Asia. Essential oil from T. minuta was obtained by hydrodistillation while solvent extracts were obtained using ethyl acetate and methanol. Antioxidative compounds of T. minuta were isolated both from the Ethyl acetate extract and the essential oil. It was done by determining the scavenging activity using 2,2-diphenyl-1-picrylhaydrazyl free radical (DPPH) using thin layer chromatography (TLC). The active compounds were tested quantitatively for their radical scavenging activity using the U-1100 UV-VIS Spectrophotometer. The active fractions were isolated using TLC and...
A statistical study has been made on the isothermal treatments of A356.0-type Al-Si-Mg alloy. The... more A statistical study has been made on the isothermal treatments of A356.0-type Al-Si-Mg alloy. The reprocessed alloy was subjected to hardness evaluation. The values obtained were processed using statistical package for social scientists (SPSS) software to compare all tempers and multiple-step thermal ageing treatment (MSTAT) values by analysis of variance (ANOVA) and Pearson Correlation Index. Equally, a non-parametric and parametric statistics consisting of sign test and t- test respectively were employed for further evaluation of results. This indicate that up to 47% (obtained from the adjusted R square) of the variation in hardness is explained by ageing time. From the statistical analysis of the reprocessed alloy, it was evidenced using one-way ANOVA that all the temper conditions and MSTAT showed six hardness values that have been computed with their corresponding mean and standard error bars. Most of the treatments conducted indicate a significant improvement in the hardness v...
Journal of Computational and Theoretical Nanoscience, 2016
Methods like the maximum likelihood and Newton's iterative techniques are usually employe... more Methods like the maximum likelihood and Newton's iterative techniques are usually employed to estimate the parameters of the classical Rydberg interatomic potential function. However, such approaches require initial guess values (IGV) to compute the optimal solutions of the unknowns. In this work, a multiple objective function approach that is used to compute the parameter estimates via the least-squares method is presented. The new approach does not necessitate the uniqueness and existence of the initial guess values to compute the required estimates. The classical Rydberg interactomic potential is firstly considered as a general solution of a second order linear differential equation with constant coefficients. Secondly, the characteristic equation of the general solution of the potential function is formulated and it's constraints derived. Two objective functions are constructed from the assumed ordinary differential equation. The first objective function is constrained and selected parameters are estimated using the least-squares method and the second objective function is directly minimised by formulating normal equations that can be solved for exact solutions of the unknowns. The new method and the computer algebraic system (CAS) are tested using experimental datasets of copper, silver ions and silver-copper alloy. Estimates from both approaches are compared and used to construct potential energy curves of the atoms considered. Three potential surfaces, that is, for experimental data, new method and the CAS for each atom are plotted on the same axis for better comparison. It is observed that estimates from the new method are greater in absolute terms than those from the CAS. However, all the estimates have the same direction. The potential curves from the experimental data, the new method and the CAS all have the same shape and close to each other, especially at the minimum of the potential well and at that point they are all indistinguishable. Estimates from the new method can be trusted as they produce a potential curve that is close to that of the experimental data and the CAS. As the present iterative methods usually converge to the required solutions given " good " IGVs, it is proposed that the new method be used symbiotically with the present methods to systematically compute the necessary IGVs. Hence the new method can be used in both theoretical and practical applications to estimate parameters of the Rydberg potential function since it does not require provision of IGVs to the unknown parameters.
Exact solutions for the generalized Morse potential parameters are obtained using the ordinary le... more Exact solutions for the generalized Morse potential parameters are obtained using the ordinary leastsquares (OLS) method. The function is linearized by reducing the dimensionality of its parameter space through integral techniques. Experimental data sets of 3-diatomic molecules, that is, HBr, HI and HCl are used to evaluate the performance of the computed estimates using the proposed method (PM). Potential energy curves (PECs) of the diatomic molecules are reconstructed using estimates from the PM. It is shown that PECs reconstructed using the estimates compare well with those from the randomized experimental dataset. In a departure from previous studies that developed methods of PEC fitting, their accuracy was only considered at the minimum of the potential well, the current work proposes a method that accounts for the experimental data points at a wider range of interatomic compression and stretching. Another advantage of the PM over the existing regular methods is that, it does n...
Background Uganda has a unique set up comprised of resource-constrained economy, social-economic ... more Background Uganda has a unique set up comprised of resource-constrained economy, social-economic challenges, politically diverse regional neighborhood and home to long-standing refuge crisis that comes from long and protracted conflicts of the great lakes. The devastation of the on-going global pandemic outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is likely to be escalated by these circumstances with expectations of the impact of the disease being severe. Materials and methods In this study, we formulate a mathematical model that incorporates the currently known disease characteristics and tracks various intervention measures that the government of Uganda has implemented since the reporting of the first case in March 2020. We then evaluate these measures to understand levels of responsiveness and adherence to standard operating procedures and quantify their impact on the disease burden. Novel in this model was the unique aspect of modeling the trace-and-i...
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