Mathematical Sciences and Informatics Journal

COMPARATIVE ANALYSIS OF EULER AND RUNGE-KUTTA FEHLBERG METHODS IN SOLVING THE LOTKA-VOLTERRA COMPETITIVE MODEL

NURIZATUL SYARFINAS AHMAD BAKHTIAR — 2024-11-27

Problem:

Based on articles written by Razali and Abdullah (2013), exclusion often occurs at a slow rate. Therefore, it was difficult to determine if equilibrium and stability exist. Equilibrium is the state of an ecosystem in which all components are in balance with one another. In addition, equilibrium species supposedly survive through a competitive survival strategy rather than through reproduction or dispersal to survive in harsh conditions where food resources are scarce. Unfortunately, based on the principle of competitive exclusion proposed by Gause (1934) which states that two species competing for the same resources cannot coexist, one will drive out.

Aims/Objectives:

1) To analyse the competitive interactions between lions (Panthera leo) and leopards (Panthera pardus) in the Sabi Sand Game Reserve, South Africa by comparing among exact solutions using Euler and RKF methods on the Lotka–Volterra Competitive model.

2) To discuss the impact of carrying capacity (capability survival) of dynamic behaviors in competition between two different species.

3) To analyze equilibrium and stability of the competition between two species depending on the initial conditions.

Methodology/approach:

This study used data from Balme et al. (2017) to examine competitive interactions between two top predators, lions (Panthera leo) and leopards (Panthera pardus) from 2010 to 2015 in the Sabi Sand Game Reserve, South Africa. This study will test whether lions, as the dominant competitor, will limit the distribution and abundance of leopards by using dietary data collected concurrently on the 2 species. Dietary overlap between lions and leopards was initially limited, with lions targeting large- to very large-sized prey and leopards small- to medium-sized prey. The Euler and Runge-Kutta Fehlberg (RKF) methods will be applied for solving this model and subsequently compare the simulation results with their exact solutions. It is anticipated that these numerical approximations will undertake to find out approximate solutions to nonlinear problems. Numerical approximation tests the reliability and precision of both methods applied to the logistic equation. This result is supported by computations carried out using the Mathematica 13.2 software.

Results/finding:

The findings indicate that the RKF method provides an accurate approximation, outperforming the Euler method. The results demonstrate that a larger carrying capacity is associated with a greater ability for a species to thrive and survive in competitive environments. Carrying capacity refers to the maximum population size a species can sustain indefinitely, considering factors like food, habitat, water, and others. During the curve-fitting procedure, it was observed that leopards have a higher carrying capacity compared to lions. Therefore, it can be inferred that the population of leopards is not significantly affected by the presence of lions.

Implication/impact:

The study will be beneficial to future researchers who engage with nonlinear differential equations, mathematical biology, and numerical techniques. By utilizing data stimulation to mimic real-world problems. As suggestion, this study can provide insights and solutions for related issues faced by the Department of Wildlife and National Malaysia. For example, it can aid in the restoration of large carnivores to support struggling ecosystems in Malaysia (Ripple, 2014). Furthermore, this study will contribute to the verification of the theory of exclusion and its applicability in various competitive scenarios. It will help determine whether both predator species, lions, and leopards, can coexist while undergoing competition. Additionally, the study will demonstrate the practical application of numerical approximation as a predictive tool, enabling researchers to determine the outcome of interspecific competition without the need for extended experimental periods. Moreover, these findings will enhance our understanding and provide illustrations of how numerical approximation can be utilized to predict competition outcomes, aiding researchers in determining which species may prevail in different interspecific competition scenarios.

Forecasting the Air Pollution Index: A Case Study in Shah Alam, Selangor

Isnewati Ab Malek — 2024-11-27

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E-Learning Application based on Gagne’s Instructional Design Model (E-DBLEARN)

Nor Azila Awang Abu Bakar — 2024-11-27

Learners often struggle with the complex and interconnected terminology in database environments and data modeling, leading to difficulties in understanding and applying key concepts effectively. In addition, a preliminary study has revealed that inadequate classroom facilities, varying learning styles, and the use of external resources that are not tailored to the syllabus have negatively impacted the understanding of theory-based topics. This study aims to achieve several objectives: identifying requirements of an e-learning application for Introduction to Database, design and develop the e-learning application and evaluating the e-learning application’s functionality and usability. This research has been initiated by preliminary analysis on the application requirements based on literature review and surveys. The design phase followed, producing essential diagrams which are navigation map and storyboards. The development was done utilizing Adobe Animate, Adobe Premiere Pro, Adobe Audition and Adobe Photoshop for producing the application for learning database. Lastly, the functionality and usability of the application was verified through testing. Usability testing involved expert evaluation with input from three experts. The results acquired give a positive indicator for further implementation. Further evaluation with 30 respondents from the target users has produced results indicated high satisfaction with the application’s overall usability, particularly in visual design and self-assessment and learnability constructs, which achieved the highest mean scores of 4.80 with standard deviations of 0.41 and 0.48, respectively. In conclusion, E-DBLEARN offers university students studying database courses an interactive, multimedia-rich platform expected to boost engagement, understanding, and self-directed learning, while equipping lecturers with an effective tool to teach theoretical concepts in the database courses. Gagne’s Instructional Design Model was incorporated to ensure that learning is effective, efficient, and structured by guiding the instructional process through a systematic approach.

Total Variation-based Active Contour Model for Medical Images

ABDUL KADIR JUMAAT — 2024-11-27

The Active Contour Model (ACM) is a mathematical model in image processing that is commonly utilized to partition or segment an image into specific objects. The segmentation method in region-based ACM can be categorized into two classes: global ACM and selective ACM Selective ACM isolates a specific target item from an input image, which is more advantageous than the global ACM due to its proven use, particularly in medical image analysis. However, the selective ACM appears to produce poor outcomes when segmenting an image with uneven (inhomogeneous) intensity. Additionally, the current selective ACM that uses the Gaussian function as a regularizer generates a non-smooth segmentation curve, especially for images containing noise. This study introduces a new selective ACM that is designed to segment medical images with inhomogeneous intensity levels. The model incorporates a Total Variation term as a regularizer, distance function, and local image fitting concepts. The Euler-Lagrange (EL) equation was given to solve the suggested model, which is approximately 5% more accurate with a processing time that is around three times faster than the existing model, as shown by numerical testing. The suggested mathematical model can be advantageous for the image analysis community, particularly in the medical industry, to automatically segment a specific object in a medical image.

Predicting Default and Non-Default Firms using Discriminant Analysis: Adaptation of KMV-Merton's Default Probabilities and Financial Ratios

Norliza Muhamad Yusof — 2024-11-27

The KMV-Merton model provides conceptual determinants for predicting firms' default risk, but its accuracy was tested long ago, and it contains insufficient statistics for default prediction. Therefore, previous literature adapted the KMV-Merton model into a statistical model involving financial ratios to improve its predictive capabilities. Discriminant Analysis (DA) is a widely used statistical model for predicting financial distress. The objectives of this study are to identify financial ratios significant to KMV-Merton's default probabilities using DA, to predict default and non-default firms using the DA model obtained, and to compare the performance of the KMV-Merton and DA models in predicting default risk. The study uses 11 years of data from Malaysian publicly listed firms, applying the KMV-Merton model and stepwise DA in SPSS. DA identifies the significance of selected financial ratios to firm default, with KMV-Merton's default probabilities as the dependent variable, forming a discrimination function to predict default and non-default firms. Credit ratings and Type 1 and Type II errors are used to compare model performance. The DA using SPSS reveals a discriminant function with net profit margin and return on assets significantly related to KMV-Merton's default probabilities. The DA model is more biased in predicting non-default firms due to the need for more information on default firms, yet it slightly outperforms the KMV-Merton model. This study offers guidance on adapting KMV-Merton's default probability estimates with financial ratios in the DA model and highlights the significant financial ratios related to KMV-Merton's default probabilities.

Reliability and Construct Validity Assessment of the Student Competency Questionnaire among Final Year Diploma Students: A Statistical Analysis Approach

Nor Faezah Mohamad Razi — 2024-11-27

The university strives to provide students a curriculum that is pertinent and taught by educators with exceptional delivery methods, in a stimulating and dynamic learning setting. The objective is for students to graduate from the institution as individuals who can positively impact society, establish businesses, and assume leadership roles in the professional realm. The objectives of this research are to develop the Student Competency Questionnaire (SCQ) and evaluate its reliability and validity. The evaluation followed classical test theory, focusing on reliability, construct validity, and content validity. A postal questionnaire containing 49 items was sent in October 2022 to a sample of 59 final-year diploma students from various programs. Three experts in education, statistical modeling, and decision-making evaluated the content validity of the scale. The Content Validity Index (CVI) for all constructs ranged from 0.96 to 1, exceeding the threshold of 0.70, indicating that the items are 'content valid.' Cronbach's alpha values showed a high level of internal consistency, all exceeding 0.90. Additionally, all items within each construct were highly related to one another, with correlations exceeding 0.30. This research demonstrates that the Pillar 1 education 5.0 @ UiTM frameworks effectively capture essential skills for students' academic and professional development, enhancing their employability. The focus on Personal, Adaptive, Digital, 21st Century, and Social competencies, along with student satisfaction, ensures students are equipped with diverse skills needed to thrive in dynamic environments. Overall, UiTM's approach prepares students for success in their future careers and personal lives.

Assessing Flood Risk through Frequency Analysis at Sayong River Station

Nur Diana Zamani — 2024-11-27

This research investigates extreme flood events at Sayong River Station using two statistical distributions: the Generalized Logistic (GLO) and Generalized Extreme Value (GEV) distributions. The study employs the L-moment method for parameter estimation and evaluates quantile estimates for return periods of 10, 50, and 100 years. The primary objective is to determine which distribution provides a more accurate representation of extreme flood behavior. Quantile estimates derived from the GLO distribution are 197.3153 m³/s for the 10-year return period, 363.8308 m³/s for the 50-year return period, and 469.9711 m³/s for the 100-year return period show better alignment with observed data compared to the GEV distribution. The GLO distribution's superior performance indicates its enhanced ability to capture the tail behavior of extreme floods, providing more reliable estimates for flood risk management. The findings emphasize the importance of selecting an appropriate distribution model for accurate flood risk assessment. The efficacy of the GLO distribution in representing extreme values underscores its appropriateness for forecasting extreme flood magnitudes and providing guidance for infrastructure design and flood mitigation measures.

Operational Cost Optimization on Solid Waste Collection Using Goal Programming

Diana Sirmayunie Mohd Nasir — 2024-11-27

Waste collection is the Waste management, comprising storage, collection, transportation, and disposal, is the most expensive aspect of waste management, involving resources in strategy, execution, and oversight. Even in Perlis, the smallest state in Malaysia, waste management has become a concern due to population growth and increased industrial activities. This study aims to identify the most cost-effective approach for a private company's monthly waste collection in Perlis, utilizing goal programming to determine the optimal cost. Data from E-Idaman Kangar Sdn. Bhd, a private company managing solid waste in Perlis, was utilized. The goal is to achieve optimization by formulating an objective function and utilizing Lingo software version 18.0. The study targets five goals: minimizing labor, collection, vehicle, and consumable costs, as well as minimizing the financial statement of operation for each route. The research results indicate that E-Idaman Kangar's collection expenses are already at an optimal state. The analysis reveals that the cost of each vehicle involved in the collection is optimized. The objective value indicates that the total expenditure can still be reduced by RM3, representing a 0.01% decrease. In conclusion, the organization demonstrates efficient waste collection practices.

Application Of Cubic Trigonometric Hermite Interpolation curve With Shape Parameters In 2 Dimensional Objects

NURSYAZNI MOHAMAD SUKRI — 2024-11-27

Problem: Achieving accurate mathematical representations of an object's geometry for computer-aided design and manufacturing is complex. Designing both objects demands a method that provides the necessary flexibility and smoothness in curves, which traditional methods lack of flexibility and smoothness in curves needed for precise and efficient design.

Aims/Objectives: The main objective is to explore and implement cubic trigonometric Hermite interpolation as a method for constructing two-dimensional objects. Next, to discussed the properties of this interpolation method and to determine the best value of the shape parameter that produces smooth curves

Methodology/approach: Cubic trigonometric Hermite interpolation is used for constructing two-dimensional objects. This process is conducted using Mathematica. The different values of the shape parameter are used to achieve the desired curve characteristics in the geometric models.

Results/finding: The correct images of the two dimensional objects are also located and the suitable shape parameters can be obtained after studying the behavior of the curve using free parameters. Two dimensional object can be formed using cubic trigonometric Hermite interpolation without making any easy blunders or errors.

Implication/impact: The impact of this project lies in its potential to improve geometric modelling by providing the best value of shape parameter that enhances the precision and efficiency of creating two-dimensional geometric models. This can significantly benefit technical drawing, computer-aided design, and manufacturing by offering a more flexible and accurate way to represent objects' geometry.

Complex Network Analysis on NASDAQ Stock Market around COVID-19

Jia Hou Chin — 2024-11-27

Problem: The United States plays an important role in the global economy, and the COVID-19 pandemic significantly affected the U.S. stock market. Over the two decades, numerous studies have incorporated complex network analysis to analyze the stock market, but there is a lack of study in identifying anomalies in network structures during financial crises.

Aims/Objectives: The main objective of this research is to implement complex network analysis in examining the changes in the network structures and centralities of the NASDAQ stock networks at periods around the COVID-19 pandemic.

Methodology/approach: The opening prices of the stocks under NASDAQ index in the last two quartile of 2019 and the first quartile of 2020 were collected from Yahoo Finance. The collected data was parsed into edges lists which was then used to construct multiple stock networks. The structures of the stock networks were analyzed using topological metrics such as network density, average clustering coefficient, average path length, network centralizations, and modularity of community structure. The centrality scores of the stocks in the networks were calculated and they were ranked according to the scores.

Results/finding: The results show abnormal values in the number of edges, network density, betweenness centralization, and modularity of the community structure in the initial stages of the COVID-19 pandemic. However, no significant anomalies are observed in the average clustering coefficient, average path length, degree centralization, and closeness centralization. Meanwhile, degree centrality proves effective in identifying influential stocks, while closeness and betweenness centralities are found to be less suitable for this particular purpose in the networks used in this study.

Implication/impact: This paper provides insights on the changes within the stock market at both micro and macro levels around financial crisis, where the anomalies serve as indicators of an impending financial crisis.