The Mindanawan Journal of Mathematics

Performance Analysis of Classical Algorithms for the Traveling Salesman Problem

2024-12-20T09:11:16+08:00

The Traveling Salesman Problem (TSP) is a fundamental optimization problem with wide-ranging applications in logistics, routing, and network design. This paper presents a comprehensive performance analysis of classical algorithms applied to solve the TSP, including exact methods like Brute Force and Dynamic Programming, and heuristic approaches such as Particle Swarm Optimization (PSO), Simulated Annealing (SA), Genetic Algorithms (GA), and k-Nearest Neighbors (KNN). The study evaluates these algorithms across multiple problem instances, varying in scale and complexity, to compare their solution quality, computational efficiency, and scalability.

Enhancing Density-Based Spatial Clustering of Applications with Noise (DBSCAN) with Kernel Density Estimation

2024-04-29T15:36:30+08:00

Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is one of the prominent methods that are efficient at uncovering clusters of various shapes. However, it faces limitations when dealing with datasets containing clusters of varying densities, to address this limitation this study integrates kernel density estimation into the DBSCAN algorithm to enhance its capacity to capture density variations and handle irregularly shaped clusters. Specifically, we employ Kernel Density Estimation (KDE) using Epanechnikov as the kernel function and the grid search method with cross-validation for the bandwidth selection, along with the added density threshold. The simulation study shows that the proposed procedures were able to correctly specify the number of clusters even for varying densities. Moreover, empirical results show that the proposed clustering procedure was able to enhance the DBSCAN algorithm and give meaningful results.

Analysis of an Epidemic Model Incorporating Anxiety Dynamics

2024-12-31T21:54:17+08:00

This study formulates and analyzes a COVID-19 disease contagion model, incorporating a psychological variable over a population considering that infected cases can be confirmed or unreported. Using a system of ordinary differential equations, the model describes the impact of anxiety on the disease progression where the contact parameter is defined as a function of anxiety level. We derive the basic reproduction number $\mathcal{R}_0$ and numerical simulations validate our theoretical results. Our findings provide a qualitative understanding of the interplay between psychological states and epidemiological outcomes, offering a novel framework for future research and potential policymaking applications in epidemic response.

Principal component and multiple regression analysis in modelling of grade and factors affecting the students' performance in Pre-Calculus

2025-01-23T11:15:01+08:00

Predicting students' academic performance is helpful for educational institutions striving to improve students' success and provide support to those at risk of getting a failing grade. This paper presents an empirical study that uses students' academic performance and demographic data to predict the Pre-Calculus grades of Senior High School students in the STEM track during the first quarter of the 2023-2024 academic year, employing both multiple linear regression and principal component regression methods. Multiple regression analysis was used to fit the Pre-Calculus grade using forty-three (43) school-related variables
as predictors. A variable selection method based on high loadings of varimax rotated principal components was used to obtain subsets of the predictor variables to be included in the regression model of the Pre-Calculus grade. Result shows that while MLR exhibits slightly higher R2, lower MSE, and lower MAE compared to MLR-PCA, the differences are negligible. Attending a private school, achieving high grades in core subjects such as Mathematics, Science, English, and Filipino and performing well on assessments such as pre-test, post-tests, and entrance exams play a significant role in the grade of the student in Pre- Calculus. Moreover, the variable regular attendance, fewer past class failures, and shorter commute times seems to contribute improvement of the student's grade in Pre-Calculus.