International Journal of Mathematical Sciences and Optimization: Theory and Applications

Penalized Cox Regression Models for High-Dimensional Survival Analysis: An Application to Breast Cancer Microarray Data

F. A. Okolie — 2026-03-15

Survival analysis provides a statistical framework for examining the relationship between time to event outcomes and explanatory variables. The Cox proportional hazards (Cox PH) model is widely used for this purpose, but its performance deteriorates in high-dimensional settings, where the number of predictors is large and strong collinearity is present. Penalized Cox regression methods have been developed to address these limitations by incorporating regularization into the estimation process. This study applies penalized Cox regression models to breast cancer microarray survival data obtained from the Gene Expression Omnibus dataset GSE20685, which contains gene expression measurements for 54,682 genes across 327 patients. The aim of this study is to fit and compare Ridge, LASSO, and Elastic Net Cox models with the classical Cox PH model. Model performance is evaluated using root mean square error (RMSE), with emphasis placed on test set results to assess predictive generalization. The results show that penalized Cox regression models consistently outperform the Cox PH model on the test set across all evaluated predictor dimensions. While the Cox PH model fails to produce reliable predictions when the number of predictors is large, the penalized models remain stable and effective. Among the penalized approaches, Ridge regression demonstrates the most robust performance in ultra-high-dimensional settings, whereas LASSO and Elastic Net provide competitive performance at lower and moderate dimensional levels through feature selection. These findings highlight the importance of regularization for survival modelling in high-dimensional genomic data and demonstrate that penalized Cox regression offers a more reliable alternative to the classical Cox PH model for microarray-based survival prediction.

A Mathematical Model of Folate Metabolism and DNA Methylation: Stability Analysis

Michael Aku — 2026-03-15

In the mammalian genome, DNA methylation could be used to deduce health conditions associated with ageing and many other pathological conditions. In addition, folate is nutritionally vital for improving human health and growth. Folate is also essential in the activity of mammalian epigenetics, through its transfer of methyl groups for the DNA methylation reaction. Furthermore, folate, as part of the B12 vitamins, not only plays a key role in our diet, but is involved in the mechanism of DNA synthesis, maintenance of DNA methylation, and metabolism of the amino acids required for growth and cell division, especially during pregnancy and infancy. Investigations have shown that vitamin deficiency B12 has effects in all age groups, although to a higher degree among older people, infants, and pregnant women. Over the years, many mathematical models have been constructed, but none explicitly captured the complexity of the interdependent biochemical and molecular mechanisms of folate metabolism and DNA methylation. In this paper, we develop and assembled an all-inclusive model that connects folate metabolism and DNA methylation, and we investigated the stability of the system. We were also able to show that the system is stable, which is a basis for further analysis like bifurcation analysis and its applications.

Combined Effects of Dufour, Soret, Dissipation and Thermal Radiation on Heat and Mass Transfer of Free Convective Flow Past an Impulsively Moving Vertical Plate in a Non-Darcy Porous Medium

T. M. Asiru — 2026-03-15

Combined effects of Dufour, Soret, dissipation, thermal radiation on heat and mass transfer of free convective flow of a viscous incompressible, chemically-reacting and electrically conducting fluid past an impulsively moving vertical plate adjacent to a non-Darcy porous regime in the presence of heat generation, variable surface temperature and concentration conditions have been investigated. The governing non-linear partial differential equations of the flow field were solved using the implicit Crank-Nicolson finite difference method. The velocity, temperature and concentration profiles were studied for different values of thermophysical parameters such as thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, Dufour number, Soret number, and chemical reacting parameter. Also, numerical values of Skin friction coefficient, local Nusselt number and Sherwood number were computed and analyzed.

Viscosity Approximation Method with Inertia for Attractive Points of Finite Families of Generalized Nonexpansive Mappings in Uniformly Convex Banach Spaces

Mamuda Buhari — 2026-03-31

In this research paper, an attractive point problem involving generalized non-expansive mapping is studied, using viscosity approximation method with inertia parameters. We established strong convergence theorem for an attractive point of finite families of generalized non-expansive mapping in a uniform convex Banach space, which is also a solution of some variational inequality problems in a Banach space. Finally, we give a numerical experiment to validate the performance of our algorithm. Our results improve and extend some recent results in the literature review.

Changepoint Detection in Multivariate Climate Time Series: Performance Assessment of Hybrid PELT+RF Against Baseline PELT

A. A. Ademuwagun — 2026-04-05

The research studied the performance of Hybrid Pruned Exact Linear Time and Random Forest Proximity Anomaly Scores (PELT+RF) against Baseline PELT in accurately detecting change points in Climate time series Data using simulation. The research adopts a Monte Carlo simulation framework to develop, implement and evaluate a hybrid change-point detection technique that combines the Pruned Exact Linear Time (PELT) algorithm with machine learning anomaly detection method (RF). The hybrid approach Pruned Exact Linear Time + Random Forest Proximity Anomaly Scores (PELT+RF) is compared against baseline PELT using simulated multivariate climate datasets. Across small, moderate, and large sample sizes, the same directional patterns persist- temperature and humidity increase while rainfall decreases with more breaks. However, larger samples make the regime shifts more distinct and less noisy. This finding underscores that robust detection methods must perform well not only in large datasets but also in small samples, where noisy signals make breaks harder to capture. Enhanced detection algorithms are therefore vital for early warning in short observational records or regional climate data with limited length. PELT+RF showed slightly stronger precision and F1-scores in small-sample, high-change scenarios, making it the better performer in noisy and data-limited environments. On balance, PELT+RF emerged as a strong hybrid in practical, small-sample climate contexts, where data scarcity and noise are common. Its incremental improvements in precision and F1 are particularly valuable for regional climate monitoring and early-warning systems. This Study carried out a Performance Assessment on the developed, implemented and evaluated Hybrid change-point detection framework which integrates the Pruned Exact Linear Time (PELT) algorithm with machine learning anomaly detection method (Random Forest proximity Based Anomaly Scores) for robust identification of structural breaks in multivariate climate time series against Baseline PELT Algorithm of which PELT+RF emerged a strong Hybrid. For instance, at four change points with $n = 70$ , PELT+RF achieves a precision of 0.1981 compared to 0.1919 for PELT, alongside a higher F1- score (0.3302 vs. 0.3217). Relative to all other alternatives for Change Point Detection, the Hybrid PELT+RF approach balanced computational efficiency, interpretability, and robustness. It retains PELT's exact segmentation while using ML scorers to capture multivariate, nonlinear anomalies.

Klein-4 Group of Constructing Distinct Sets of Mutually Orthogonal Latin Squares of Order

A. J. Saka — 2026-04-15

The concept of mutually orthogonal Latin squares (MOLS) have been studied extensively since Euler's pioneering work in 1782. The construction of MOLS of various orders have since been the subject of considerable research. Researchers have utilized different algebraic structures to construct MOLS, while some emphasized on matrices and maximal partial spreads in finite projective spaces. However, the basis of the aforementioned methods were the provision of systematic approach to ensure orthogonality. A new method of constructing distinct set of mutually orthogonal Latin squares (MOLS) of order 4 called Klein-4 Group is presented in this paper. Therein the symmetries of rectangle (isomorphic to Klein-4 group $C_{2} \times C_{2}$ ) is leveraged on to aid the construction of 4 distinct complete sets of MOLS. The design could open ways for its application in cryptography, generation of one time password (OPT) and in cyber environments such as Internet of Things (IoT) needing lightweight cybersecurity measures.

Dissipative Hydromagnetic Flow of an Arrhenius Fluid with Variable Properties under No-Slip Boundary Conditions

A. Adeniyan — 2026-04-15

This study focuses on investigating the non-slip hydromagnetic laminar dissipation flow with Arrhenius kinetics in binary reactions characterized by reaction order and variable properties within an unbounded isothermal device. In the absence of material distortion, the species mixture in the fluid is activated by factors such as internal heating, reaction order, and activation energy. This study focuses on investigating the non-slip hydromagnetic laminar dissipation flow with Arrhenius kinetics in binary reactions characterized by reaction order and variable properties within an unbounded isothermal device. In the absence of material distortion, the species mixture in the fluid is activated by factors such as internal heating, reaction order, and activation energy. The partial differentiation model is nondimensionalized to a thermofluidic dimensionless form. An invariant quasi-linear coupled ordinary differentiation model is obtained using appropriate similarity quantities. Computation solutions of the dimensionless invariant formulated derivative model are offered in plots and tabular formats to illustrate the sensitivity of critical terms. The analysis reveals that the species mixture leads to a reduction in flow velocity but an increase in binary species reaction by 0.734%. Furthermore, the activation energy and coefficient material enhance the thermic profile within the flow medium. Consequently, this study provides valuable insights for industrial development, aiding in the informed selection of working fluid properties.

Combined Effects of Anisotropic Permeability, Chemical Reaction, and Dual Stratifications on Unsteady Free Convection Around a Vertical Circular Cylinder

A. Adeniyan — 2026-04-15

The unsteady free convection boundary layer flow past a vertically translating circular cylinder embedded in a saturated anisotropic porous medium is investigated under simultaneous thermal and solutal stratifications with a first-order homogeneous chemical reaction. The porous resistance is modelled with a tensor-based Darcy-Brinkman formulation in which the permeability is represented by a symmetric positive-definite second-order tensor, and wall suction/injection is permitted. Using boundary-layer scaling and similarity transformations, the governing PDE system is reduced to a seventh-order nonlinear two-point boundary value problem. The reduced system is solved by an adaptive Lobatto IIIa collocation scheme, selected for its A-stability and reliable performance on stiff boundary-layer equations. The solver reproduces the Crane flat-plate exact solution to six decimal places and matches published stretching-cylinder data to within 2%. The results show that porous drag and transverse curvature govern wall shear and heat transfer, the Schmidt number and chemical reaction strength govern mass transfer, and thermal stratification enhances the Nusselt number through boundary layer thinning. Global sensitivity analysis using Latin Hypercube sampling identifies the Prandtl number as most influential for heat transfer, the Schmidt number for mass transfer, and the porous drag parameter for skin friction. The main contribution is the unified treatment of anisotropic tensor permeability, chemical reaction, and dual stratification for an unsteady translating cylinder, together with a quantitative ranking of parameter influence under a single consistent modelling framework. The results are relevant to geothermal energy extraction, contaminant transport in stratified aquifers, and catalytic processes in enhanced oil recovery.

Ratio Estimation of Population Proportion With Optimality in Presence of Non-Response

M. Cherotich — 2026-05-20

Studies on the estimation of population proportions have been around at improving the accuracy and efficiency of survey designs. A number of studies have been carried out on estimation of population proportion without non-response under optimality, however, non-response remains a significant challenge, often introducing bias and reducing reliability. This study examined the impact of non-response on sample size, bias, variance and relative efficiency using the ratio estimation. Simulations study has been performed using R-Software to compare empirical estimator of the population proportion. Results indicated that an increase in the non-response rate leads to a larger sample size, increased MSE and reduced bias and variance. Graphical analysis confirmed that the MSE increased the sample size, highlighting the limitations of large samples in the presence of non-response. From the results it was confirmed that the ratio estimators were reliable method for proportion estimation provided non-response adjustments and optimal sample allocation are implemented.

Fixed Point Results for Some Enriched Contractions in Convex B-Metric Spaces

S. Yakubu — 2026-05-20

In this study, we show the existence of fixed points for enriched contractions and enriched ϕ-contractions of Hardy-Rogers type using Krasnoselskii's iterative process. Furthermore, we show that our results imply related fixed- point results for enriched contractions and enriched - contractions of Banach, Kannan, Chatterjea and Reich types. Our results are novel for convex b- metric spaces and generalize several established results in convex metric spaces.