Open Access Original Research Article

The 7 and 8 Families of Hybrid Block Methods for Numerical Solution of Initial Value Problems in Stiff Equations

Y. Skwame

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2017/34225

An independent hybrid block Simpson’s methods with a very closely accurate members of order p=q+2 as a block was formulated. This was obtained through increasing the number k in the multi-step collocation (MC). Maple software was used to facilitate the derivation of the k-step continuous formulae for k=6 and 7. In this paper, one off-grid collocation point was added in the MC in-between the last two step sizes, to get the desirable schemes. These schemes were evaluated for simultaneous application on stiff equations. The numerical results obtained signified the efficiency of the schemes.

Open Access Original Research Article

E-Bayesian and Hierarchical Bayesian Estimations Based on Dual Generalized Order Statistics from the Inverse Weibull Model

Hesham M. Reyad, Adil M. Younis, Soha A. Othman

Journal of Advances in Mathematics and Computer Science, Page 1-29
DOI: 10.9734/JAMCS/2017/34540

This paper is devoted to compare the E-Bayesian and hierarchical Bayesian estimations of the scale parameter corresponding to the inverse Weibull distribution based on dual generalized order statistics. The E-Bayesian and hierarchical Bayesian estimates are obtained under balanced squared error loss function (BSELF), precautionary loss function (PLF), entropy loss function (ELF) and Degroot loss function (DLF). The properties of the E-Bayesian and hierarchical Bayesian estimates are investigated. Comparisons among all estimates are performed in terms of absolute bias (ABias) and mean square error (MSE) via Monte Carlo simulation. Numerical computations showed that E-Bayesian estimates are more efficient than the hierarchical Bayesian estimates.

Open Access Original Research Article

Image-Based Identification of Cell Cultures by Machine Learning

Oluleye Babatunde, Ashley Baltes, John Yin

Journal of Advances in Mathematics and Computer Science, Page 1-25
DOI: 10.9734/JAMCS/2017/34357

Biomedical laboratories often use different cell types in the same assay or the same cell type in different assays. One cell type can become contaminated by another, or cells can be mis-identified, giving poor results. Addressing these issues by DNA analyses can be time-consuming, labor intensive or costly to implement. Here we uniquely employ Legendre moments (LM), Zernike moments (ZM), circularity and a genetic algorithm (GA) to advance a computer-based vision system, and we task it to identify four cell types used in virology: HeLa, Vero, BHK and PC3. By employing a k-nearest neighbor (kNN), multilayer perceptron (MLP), Convolutional Neural Networks (CNN) classifiers and a GA-selected 9-vector candidate comprising 4 ZMs, 4 LMs, and circularity, we provide adaptive system for deep machine learning. Our approach provides avenue to measure the performances of two of the conventional and popular classifiers (kNN and MLP) with a relatively recent classifier (CNN). We provide detailed mathematical treatments of the image signatures for accessibility and reproducibility in computer vision. Our methods are unique in biomedical applications. The performance of the kNN for k = 1, 2, and 3 using 10-fold cross-validationyielded accuracies of (83.59%, 82.03%, 81.25%) and (84.38%, 82.82%, 82.03%) for 8-class and 4-class training sets, respectively, drawn from the same data while those of the MLP and CNN were 86% and 87.25% respectively. These results establish the feasibility of reliable automated cell identification, with diverse applications in biological and biomedical research.

Open Access Original Research Article

On Generalized Douglas - Kropina Spaces

S. Ceyhan, G. Çivi

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/JAMCS/2017/34386

Sakaguchi proved that the class of Weyl metrics belong to the class of generalized Douglas–Weyl metric. Then, Matsumoto studied Weyl–Kropina metric. Recently, Yoshikawa and Okubo obtained the conditions for a Kropina space to be of constant curvature by improving the characterization given by M.Matsumoto. In this paper, we obtain the necessary and sufficient conditions for a Kropina metric to be scalar flag curvature or Weyl-Kropina metric. After that, we prove a necessary and sufficient condition that characterizes generalized Douglas-Kropina metrics of scalar flag curvature.

Open Access Original Research Article

On a Discrete Time Semi-Markov Risk Model with Dividends and Stochastic Premiums

Cui Wang

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2017/34678

A discrete semi-Markov risk model with dividends and stochastic premiums is investigated. We derive recursive equations for the expected penalty function by using the technique of probability generating function. Finally, a numerical example is given to illustrate the applicability of the results obtained.