Pusat Pengajian Sains Matematik - Tesis
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- PublicationTopological Data Analysis In Analyzing The Similarity Of Air Pollutants’ Behavior Across Air Quality Monitoring Stations In Malaysia(2025-07)Nwabuisi, Madukpe VineAir pollution is increasingly recognized as a major global issue resulting from industrial processes, urban development, transportation emissions, and a wide range of human activities. This study investigates air pollutant behavior through a qualitative approach, utilizing topological data analysis (TDA) techniques, the conventional Mapper (CM), and its variant Ball Mapper (BM). It analyzes six major air pollutants (NO2, PM10, PM2.5, O3, CO, and SO2) collected from 60 air quality monitoring stations across Malaysia. The topological graphs generated using the CM algorithm revealed clusters of regions and stations exhibiting similar pollutant behavior. The results showed similar patterns in PM10 behavior across the years 2013, 2015, and 2020.
- PublicationTrajectory Prediction And Near Miss Detection Using Social Distancing Monitoring And Distance Based Proximal Indicators(2025-07)Lim, Lek MingDespite efforts to improve road safety, accidents persist due to insufficient evidence from manual police reporting, non-optimized detection algorithms, and technical limitations in real-time video processing and modelling. This study focuses on detecting and tracking vehicles within a monitoring system and analysing near-miss incidents (black spot and blind spot), specifically examining the influence of video quality on detection performance using advanced model detectors (YOLOv3-tiny, YOLOv4-tiny, YOLOv5, YOLOv7, YOLOv7+G3HN, YOLOv7+CNeB, and Faster RCNN). The experiment employed methods for vehicle detection and trajectory prediction through the monitoring system.
- PublicationJ-Type Random 2,3 Satisfiability Reverse Analysis Topological-Based Method In Discrete Hopfield Neural Network(2025-07)Jiang, XiaofengThe development of satisfiability logical representation in Discrete Hopfield NeuralNetworks has evolved into a more flexible structure, allowing for both systematic and non-systematic logic. However, the main issue with the exiting flexible satisfiability representation is the appearance of first order clauses which will degrade the quality of the logical rule as a neuron representation and leads to overfitting issue. Therefore, this thesis proposes a hybrid higher order satisfiability logical rule named J-Type Random 2,3 Satisfiability. The proposed logical rule randomly generates structures based on either second order, third order, or a combination of both clauses. The behavior of the proposed logical rule will be evaluated using various performance metrics in terms of training error, retrieval error, energy analysis, and similarity analysis. Simulation results indicate that the proposed model achieves the highest global minimum ratio with an average value of 0.4674. The newly proposed model will be incorporated into the logic mining model known as topology based J-type random 2,3 satisfiability reverse analysis. The unsupervised attribute selection method called topological data analysis is employed in selecting most significant attributes. Meanwhile, permutation operation improves the ability of the logic mining model to retrieve the best induced logic that can extract patterns from the dataset. The proposed logic mining model demonstrates superior performance compared with existing state-of-the-art logic mining models with an average accuracy of 0.8375 in the selected various real-life datasets.
- PublicationNumerical Approximations Of Time-Fractional Partial Differential Equations Based On B-Splines Collocation Methods(2025-09)Anya, Okeke AnthonyRecently, there has been an upsurge in the study of fractional partial differential equations (FPDEs). This is because FPDEs have numerous applications in engineering and science owing to their non-local properties. For instance, FPDEs have been employed to solve problems in the fields of physics, chemistry, biology, biochemistry, medicine, electron transportation, financial data, groundwater flow, and geo-hydrology. FPDEs are the generalizations of traditional partial differential equations. Exact analytical solutions for FPDEs are generally undetermined owing to their complicated nature. Thus, there is intense motivation to explore possibilities for developing efficient and reliable approximate analytical and numerical methods for solving FPDEs. This study focused on the development of efficient approximate numerical methods.
- PublicationMulti-Stage Differential Transform Methodforsolving Classical And Fractional Differential Algebraic Systems(2025-09)Alahmad, Khalil IbrahimDifferential equations are known as a mathematical method to model a problem that exists in science, chemistry, physics and economics. Generally, systems of differential equations can be classified into systems of fractional differential algebraic equations and systems of differential algebraic equations. Fractional differential algebraic equations and differential algebraic equations have been used to model complex systems in various fields, but the traditional numerical solution methods used often struggle with their solution behavior. The objective of this research is to develop two techniques to solve a system of fractional differential algebraic equations as well as a system of differential algebraic equations based on initial value problems through the standard differential transformation method and the fractional differential transformation method.