International Journal Of Mathematics And Computer Research

Development of a Chaotic Tent Map-Enhanced Pelican Optimization Algorithm for Artificial Neural Network-Based Intrusion Detection in Mobile Ad Hoc Networks

Olanrewaju S. S. — 2026-09-03

Mobile Ad hoc Networks are self-organising, infrastructure-less networks with dynamic topologies. These characteristics provide flexibility in network deployment but also make the network highly susceptible to serious security threats such as blackhole, sybil and wormhole attacks that can affect network performance. Standard ANN has been identified as a strong intrusion detection technique once the best hyperparameters were selected also standard optimization algorithms often suffer from premature convergence during optimization process, this study introduces a Chaotic Tent Map-Enhanced Pelican Optimization Algorithm-Artificial Neural Network (CTM-POA-ANN) framework to improve intrusion detection performance through efficient ANN hyperparameter optimization. The proposed methodology intends to improve population diversity, global exploration and effective fine-tuning of ANN hyperparameters using enhanced pelican optimization algorithm, the CTM-POA-ANN technique is tested using network traffic generated in the NS-3 simulation under normal communication and multiple attack scenarios. The experimental results depict that the proposed CTM-POA-ANN framework achieved 95.93% precision, 95.84% recall, accuracy of 95.85% and F1-score of 95.77% which outperforms traditional ANN and POA-ANN paradigms significantly. The findings indicate that the integration of Chaotic Tent Map with the Pelican Optimization Algorithm significantly enhances ANN hyperparameter optimization, resulting in a robust, efficient, and intelligent intrusion detection framework capable of improving the security and reliability of MANETs under dynamic routing attack scenarios.

Development of an Explainable Ai-Driven Early Warning System for Predicting Postpartum Haemorrhage in Low-Resource Environments

Bamikole Joseph OLOJIDO — 2026-09-03

Postpartum haemorrhage (PPH) is a leading cause of maternal morbidity and mortality worldwide, with a disproportionate burden in low-resource settings where timely diagnosis is often difficult. This study presents an interpretable AI-based early warning framework for predicting PPH using machine learning. A retrospective dataset of 223 anonymized obstetric records from Mpilo Central Hospital, Zimbabwe, was used for model development. Preprocessing involved missing-value imputation, outlier capping, feature engineering, and normalization, generating clinically relevant features such as labour duration in minutes, binary obstetric risk indicators, and a composite maternal risk score. Random Forest and Multilayer Perceptron (MLP) models were trained and evaluated on an 80:20 split. Random Forest achieved superior performance, with 86.67% accuracy, 89.47% precision, 80.95% recall, an F1-score of 85.00%, and ROC-AUC of 0.8730 for the PPH class. Labour duration and delivery method were the most influential predictors. SHAP (Shapley Additive Explanations) was used to enhance interpretability and clinical transparency. The findings show that interpretable machine learning can deliver reliable predictive performance even on small clinical datasets from resource-constrained settings, supporting proactive obstetric intervention and improved decision-making.

Deep Learning and Ensemble Learning Techniques for Breast Cancer Detection: A Review of Recent Advances

Abraham Temilade Olumide — 2026-09-07

Breast cancer remains the most frequently diagnosed cancer and a leading cause of cancer death among women worldwide, so tools that support early and accurate detection are urgently needed. This review synthesizes a pool of one hundred studies, largely published between 2023 and 2026, on deep learning, ensemble learning, and optimization algorithms for breast cancer detection across mammography, ultrasound, magnetic resonance imaging, and histopathology. Relevant studies were identified from major scientific databases using search terms combining breast cancer, deep learning, convolutional neural networks, ensemble learning, metaheuristic optimization, and adversarial robustness, then organized by architecture, ensemble strategy, and outcome. Convolutional Neural Networks such as VGG16/19, ResNet50, DenseNet121, EfficientNet, Xception, and MobileNet, typically adapted through transfer learning, consistently exceed 90% classification accuracy on benchmark datasets, while bagging, boosting, voting, and stacking ensembles yield further, consistent gains by exploiting complementary feature representations. Metaheuristic algorithms, including Particle Swarm, Genetic, Ant Colony, Grey Wolf, and Bayesian Optimization, are increasingly used to tune hyperparameters and ensemble weights, reducing computational overhead while preserving accuracy. Attention-augmented and hybrid CNN-transformer models, federated learning, and explainability tools such as Grad-CAM and SHAP are emerging as important extensions. Nevertheless, high computational cost, limited dataset diversity, restricted multimodal integration, susceptibility to adversarial perturbation, and weak interpretability continue to restrict clinical translation. The review concludes that optimized, explainable, and adversarially robust ensemble frameworks, validated through multi-center clinical trials, represent the most promising direction for translating deep learning research into dependable and deployable breast cancer detection systems.

The Application of Group Theory on Planetary Motion

Ifan Setiawan Yuntoro — 2026-09-08

Group theory studies the algebraic structure known as groups. A group is a non-empty set with a binary operation that satisfies some axioms. These axioms include associativity, the existence of an identity element, and the existence of an inverse element. An Abelian group is a group that satisfies the commutative law. One of the most well-known examples of a group is the cyclic group , whose elements repeat periodically after steps under modular addition. On the other hand, planetary rotation and revolution are continuous dynamical processes that repeat periodically and are governed by gravitational mechanics. In this research, we construct a discrete mathematical model of planetary periodic motion. Since physical planetary motion is continuous, we discretize each planet's rotation and revolution period to the nearest positive integer in an appropriate time unit, yielding a finite set of positional states , where represents the planet's position at time step . We define the binary operation , which represents the composition of two successive time progressions modulo the period. We then verify that satisfies the group axioms, forming an Abelian group isomorphic to . Our purpose here is to show some applications of algebra outside the classroom.

Hybrid deterministic-stochastic modeling of typhoid fever using jump diffusion for epidemic control and decision support

Bukola O. Akin-Awoniran — 2026-09-11

A hybrid deterministic-stochastic (jump-diffusion) model for typhoid fever dynamics, addressing the limitations of classical deterministic models in capturing random environmental fluctuations and sudden outbreak events is pre sented. The model extends a deterministic seven-compartment framework by introducing both Brownian motion and discrete (Poisson jump) stochastic perturbations in the infected, treated, and recovered compartments. Ana lytical results establish the positivity and well-posedness of solutions, derive explicit expressions for disease-free and endemic equilibria, conditions for reducible nonlinear jump-endemic model. The basic reproduction numbers for both deterministic (R0) and stochastic (Rjp) systems were established. Sensitivity analysis using normalized indices and Partial Rank Correlation Coefficient (PRCC) methods identifies the symptomatic transmission rate (β1), vacci nation rate (ν), and recovery/treatment rates (γ1,δ) as the most influential parameters affecting R0. PRCC results show β1 and α have the strongest positive impact on R0, while γ1 and ν have strong negative effects, highlighting the importance of vaccination and treatment in disease control. Numerical simulations demonstrate that increasing ν or γ1 can reduce R0 below unity, leading to disease eradication, while higher β1 or positive jump intensities can sustain outbreaks even under control measures. The stochastic reproduction number Rjp is shown to decrease with stronger diffusion but increase with higher jump intensity, emphasizing the need for adaptive, non-constant inter ventions. The jump-diffusion framework thus provides a robust tool for epidemic decision support under uncertainty.

A Study on Cubic Fuzzy Competition Graph Labeling

M. Ragavi — 2026-09-18

In this work, we study the notion of cubic fuzzy competition graphs as a hybrid framework for modeling competitive interactions under uncertainty. The proposed model combines the structure of competition graphs with cubic fuzzy information, where each arc or induced competition relation is described by a point membership and an interval-valued membership. This dual representation provides greater flexibility and precision than ordinary fuzzy competition graphs in capturing ambiguous relations. We define the cubic fuzzy competition graph associated with a cubic fuzzy digraph and discuss with example.

Group Acceptance Sampling Plans for Life Tests Based on New Rayleigh Pareto Distribution

P. Jyothi — 2026-09-19

In this paper, we present the development of a Group Acceptance Sampling Plans (GASPs) for the lifetime of an item follow the new Rayleigh-Pareto distribution. We determine the plan parameters, including the minimum group size, g and the acceptance number, c required under specified test termination conditions and consumer's risk. Our analysis demonstrates that the proposed GASP performs existing plans by achieving comparable decisions with smaller sample sizes. The operating characteristic values of the sampling plans and producer’s risk are also deliberated. The findings are explained with the help of real data set.

Equivelar Maps on Non-Orientable Surfaces

Hardeep Singh — 2026-09-22

In this article we construct {p, q}-equivelar maps for the pairs (p, q) satisfying the equation p + q = 10 on all non-orientable surfaces, wherever such maps exist. We further believe that the method can be generalized to construct {p, q}-equivelar maps for arbitrary p, q ≥ 3.

Source Term Estimation for Atmospheric Pollutant Releases from Sparse Sensor Networks: A Methodological Review and Comparative Assessment

T.R. Shafiyev — 2026-09-22

Determining the location, release strength and temporal profile of an unknown atmospheric pollutant source from concentration measurements recorded by a small number of ground-based sensors is a core problem of environmental monitoring, industrial safety and emergency response. Because the number of independent observations is typically far smaller than the number of unknown source parameters, source term estimation (STE) from sparse networks is an ill-posed inverse problem in the sense of Hadamard, and its solution has developed along three largely independent methodological lines: deterministic approaches built on adjoint transport equations and Tikhonov-type regularization; Bayesian approaches relying on Markov chain Monte Carlo (MCMC) sampling; and, over the last five years, machine-learning surrogate and physics-informed neural network (PINN) approaches that accelerate the repeated forward-model evaluations required inside an iterative inversion loop. This paper reviews the primary literature across all three streams, classifies it by the degree of information deficiency a method was designed to tolerate — the ratio of independent sensor readings to unknown source parameters — and identifies a specific, still largely open regime: reconstruction from 5–15 non-uniformly placed sensors under weak-wind, near-neutral atmospheric stability, conditions characteristic of arid inland regions such as Central Asia. Unlike a literature-only survey, the comparative claim is tested directly: four representative methods (unregularized least squares, adjoint-equivalent Tikhonov regularization, Bayesian MCMC, and a quadratic-surrogate-accelerated inversion) are implemented and run on a common closed-form advection–diffusion test problem across 5–20 sensors and 1–20% observation noise (192 independent trials). The experiment confirms the expected degradation of all methods as the network sparsifies, shows that a fixed regularization parameter introduces an avoidable bias relative to the unregularized estimate under low noise while stabilizing it under high noise, and shows that a naively chosen low-order polynomial surrogate fails outright on this nonlinear, compactly-supported forward map — a cautionary result that supports, rather than merely asserts, the recent shift toward neural-network and physics-informed surrogates in the reviewed literature. Two open problems follow directly from the combined review and experiment: automatic, data-driven regularization-parameter selection under sparse, noisy data, and a principled criterion for detecting when a machine-learning surrogate is operating outside its training domain.

Generalized Hyers–Ulam Stability for Quadratic Functional Equations of Several Variables in Banach Algebras

M. Settu — 2026-09-25

In this paper, we obtain the general solution and Generalized Hyers-Ulam-Rassias stability of the n-dimensional quadratic functional equation in Random Normed Space, where n is a positive integer with using direct and fixed-point methods.