BS Mathematics Research Outputs

SY. 2022-2023


Mathematical Model of Aquaculture Fisheries Production in Pampanga, Philippines

Micah L. Abrasaldo and Jocell D. Calma

The aquaculture industry in the province of Pampanga continues to be one of the leading producers of fish in the Philippines which provides the livelihood of many Kapampangan. The study aimed to develop a mathematical model for aquaculture fisheries production in the province. Results revealed that the highest volume of aquaculture fisheries production was recorded in 2021, with tilapia being the most produced species and catfish being the least. In addition, aquaculture production has been consistently increasing between 2016 and 2021, compared to other years. Moreover, analytical, and numerical methods were employed to analyze the production of aquaculture in the province. Polynomial regression models were developed with orders of five for catfish, seven for tilapia and milkfish, and nine for tiger prawn and mud crab, resulting in high r-squared values. The aquaculture production model of order five closely matched the actual production data. Based on the developed models, tilapia, mud crab, and catfish productions are projected to increase in the coming years, while tiger prawn and milkfish productions are expected to decline in the next nine years. The overall prediction model indicates that aquaculture fisheries production will continue to increase until 2030. To conduct further analysis, it is highly recommended to consider the existing factors that affect fish production, such as water quality, land availability, consumption changes, diseases, and climate variability.


An Analysis of the Spatial and Temporal Patterns of Avian Influenza Occurrence in Pampanga

Liezel M. Aquino and Lenie G. Magat

The Avian influenza (AI) is a severe infectious disease that can cause illness in domestic poultry, other birds, and animals. Understanding how AI spreads requires analyzing its spatiotemporal aspects. The AI in Pampanga commence in July 2017. Spatiotemporal statistical methods were employed to uncover how AI’s spatial direction and spatiotemporal aggregation characteristics behaved in Pampanga. These methods included direction analysis, spatial autocorrelation analysis, and spatiotemporal scan statistics. The ceasing of the epidemic was classified into three phases: phase 1 from July 2019 to March 2020, phase 2 from June 2020 to January 2021, and July 2021 to September 2022 in phase 3. The AI direction analysis showed statistically directional trends (p<0.05) in phases 1 and 3. Furthermore, the angular concentration in all phases is near 0, indicating random spread lines. The occurrence rate of the AI was aggregated spatially in phase 1 which has a positive spatial autocorrelation and a significant p-value (p<0.05) and became random in phases 2 and 3. The areas with high-high AI clusters, wherein the municipality and its neighboring areas are high, were classified in phases 1 and 3. A total of six high-risk AI clusters were detected, covering an average distance of 5.19 km. Overall, outbreaks were significantly directional, aggregated, and concentrated in the initial and final phase, however, they become scattered randomly in the second phase. The results obtained can potentially enhance comprehension regarding the spatiotemporal diffusion of AI in Pampanga.

Development of Mathematically Inspired Jewelry Wires

Jan Rinel A. Bagsic and Alvin M. Supan

Jewelry wires are known to be one of the ancient types of jewelries. They were created using wire wrapping which is an old way on making accessories. This research aimed to know the mathematical concepts like polar functions, dihedral group, and equation of a circle applied in creating the designs. Using descriptive-exploratory research method, ten jewelry designs were created, seven of which were polar functions inspired. The function used were of the form r = a cos 2θ , r = a sin 2θ , r = sin 3θ , r = − sin 3θ , r = asec  θ,   r = asec θ , 𝑟 = 𝑎 , r = a sin(2𝜃)2 + a cos(2𝜃)4 , r2 = 𝑎cos2θ, r2 = 𝑎2 sin(2𝜃) , 𝑟 = 𝜃, r = 2asinθ + acos4θ , r = a sin(𝜃)2 + a cos(𝜃)4, r = cos(2θ) +  and r = sin(2𝜃) + . Meanwhile, two designs used the equation of the circle (𝑥 − 𝑘)2 + (𝑦 − ℎ)2 = 𝑟2, while one design has a combination of a polar function and follows a geometrical pattern of the dihedral group D 4 = { e , a 1 , a 2 , a 3 , b , a 1 b , a 2 b , a 3 b }. The study recommended that other jewelry wire samples will be investigated to look for other mathematical concepts like group and coloring patterns.


Development and Simulation of Fractal Rangoli Design

Shaina C. Balisi and Ivy Gay O. Salvador

Rangoli is a visual art used by people in India during their festivals and occasions to welcome their guests. The design usually comes with patterns of geometrical shapes. The main objective of the study is to develop Rangoli designs through the applications of finite cyclic and dihedral groups and iterations of fractals. The researcher used both qualitative and descriptive research methods and was able to produce three different Rangoli designs. Six different fractals namely, swastika (iteration 3),anti-snowflake (iteration 2), hexaflake (iteration 3), vicsek (iteration 2), diamond (iteration 2), and octaflake (iteration 2) were used in designing the Rangoli. Moreover, rosette patterns involving groups of order C4, D3, D4, D6, D8 were also applied. The developed Rangolis were evaluated relevant and significant in Indian culture by a pool of experts.

Hamiltonian Path of the Most Visited Places in Pampanga: Applications of Greedy Algorithm and Ant Colony Optimization Algorithm

Jenifer N. Briones and Kathleen Shy Ann C. Castro

A path that visits each vertex once in a connected graph is called the Hamiltonian. The greedy algorithm takes the best optimal option at the moment. On the other hand, the ant colony optimization algorithm is a technique that finds the optimal path by mimicking the way ants find food. The objective of the study is to provide the shortest path of the most visited places in Pampanga using the Hamiltonian path identified by the greedy algorithm and ant colony optimization algorithm. This study used the descriptive design. The researcher used Google Maps to identify the distance of the most visited places in Pampanga. The Hamiltonian path was solved manually using the greedy algorithm and by Python programming using the ant colony optimization algorithm. The ten most visited places were identified by different websites found on Google. The researcher identified the shortest path of the most visited places in Pampanga with the use of the Hamiltonian path solved by the greedy algorithm and ant colony optimization algorithm. The shortest path will provide convenience to travelers.


Application of Floyd’s Algorithm: Development of Magalang Restaurants Website

John Rey R. De Jesus and Alvin M. Supan

The study’s major goal was to find the quickest route and least travel distance between any beginning point (restaurant or boundary arch) and any destination point (restaurant or boundary arch) in Magalang, Pampanga. Out of the twenty-two (22) registered restaurants in Magalang, Pampanga, fifteen (15) were found using Google Maps and described using the descriptive approach. In this study, Floyd’s algorithm-based network model optimization was used. Version 3.81 of Python additionally enabled the creation and execution of a computer program. The created restaurant locator application indicated the generated computer programming output. Finally, Wix.com was used to create the “Magalang Restaurants” website.

Profit Optimization of Pampanga State Agricultural University Bamboo Propagules

Jenny Rose P. Del Mundo, Ivy Gay O. Salvador and Allain James T. Aquino

PSAU Bamboo and Rattan RDE Center was established to meet the needs of various customers interested in bamboo-finished products. Through the production and sales of seedlings or propagules of various bamboo species, this center seeks to increase bamboo production and its ability to generate income. The study aims to determine the number of produced bamboo propagules per variety to obtain the optimum (maximum) profit to help the PSAU Bamboo and Rattan RDE Center solve problems and maximize revenues. The study used a descriptive-exploratory method of research wherein traditional solving, Excel solver, and Computer Proram were used in solving the optimum solution. The researcher used five (5) classified varieties of bamboo propagules for the objective function’s variables, selling price, and cost while the number of operating days and daily demand were used for the constraints. The study obtained an optimum profit of ₱14,497,448 and further revealed that Kawayan Tinik and Kawayan Bayog are the top two most profitable species while Japanese bamboo propagules are the least profitable. The study recommends that other programs in solving the optimum solution, such as AMPL software, Sci lab software, CPLEX, MATLAB, integer programming, and Maple, may be used, profit optimization model of this research may be implemented in PSAU Bamboo and Rattan RDE Center to assess its effectiveness, and future research on the other field of businesses using profit optimization may also be considered.


Climate Trend Analysis Using Mann-Kendall and Sen’s Slope Estimator Tests in Central Luzon, Philippines

Shiella Mae H. Fajardo and Jocell D. Calma

The climatological factors of rainfall, temperature, relative humidity, and wind speed were analyzed to determine the climate trend over the last 41 years in Central Luzon, Philippines. The non-parametric Mann-Kendall (MK) and Sen’s Slope Estimator (SSE) tests were utilized to the annual and monthly datasets from 1980 to 2021 in the seven synoptic weather stations across the region. The annual temperature exhibited a highly increasing trend in all the synoptic stations. The temperature significantly increased in the months of May, November, and December throughout the region. This trend suggests that Central Luzon will become warmer in the coming years. The relative humidity decreased annually in Central Luzon and in all months in Casiguran. The Baler Radar, Cabanatuan, and Iba stations experienced a downward trend in wind speed, while Casiguran exhibited an upward trend. The annual rainfall showed no significant increase or decrease, but an increasing trend in December in Casiguran and a decreasing trend in May in Cubi Point were observed. The climate trend analysis indicates that the region is facing climate change. These significant trends may lead to severe weather events such as droughts and heatwaves, which can negatively impact the agricultural sector. Further studies are necessary to investigate the causes of the increasing temperature trend and the decreasing relative humidity trend and their potential effects on the local and regional climate.

Visualization Dashboard: https://bit.ly/Climate-Central-Luzon

Rice and Corn Productions Model in Relation to Climate Variability in Central Luzon, Philippines

Ma. Esperanza M. Garcia and Aiza D. Villavicencio

Rice and corn are known as a staple food in the Philippines and are considered the key source of income for millions of Filipino farmers. Its production, on the other hand, can be driven by various factors and one of which is the climate variability. The main objective of the study was to describe and analyze the rice and corn production in relation to climate variability in Central Luzon, Philippines. A descriptive-correlational research method was utilized. Results have shown that the spatiotemporal visualization of rainfall, temperature, relative humidity, and wind speed using heatmaps appear to show fluctuating trends in the four quarters within the span of 25 years from 1997 to 2021. In addition, an increase in rice and corn production was observed. Multiple linear regression analyses were applied to describe rice and corn production in relation to climate variability. Results revealed that temperature was a significant predictor of rice production, while relative humidity was found to be a significant predictor of corn production, in which temperature is positively related and relative humidity is negatively related. This means that a rise in temperature in the following years can increase rice production while a rise in relative humidity can cause hindrance to corn production in Central Luzon. In addition, it was found that the developed spatiotemporal visualization and the formulated mathematical model of rice and corn production in Central Luzon based on climate variables were comparable annually.


Temporal and Spatial Evolution of African Swine Fever Epidemic in Pampanga

Kaye Kathlene M. Juanta and Lenie G. Magat

ASF is a viral disease that is extremely infectious and significantly affects the health of pigs. To better understand how the disease is transmitted, researchers conducted thorough analysis of the spatiotemporal dynamics of ASF. This involved using advanced statistical methods such as directional analysis of spreading rate, spatial autocorrelation, and retrospective scan analysis. ASF was first reported in September 2019 in Pampanga. Determining the direction in which African Swine Fever is spreading and analyzing how it’s spreading over time and space can aid in the development of efficient control measures and limit the disease’s further dissemination. The epidemic categorized into three distinct phases based on its cessation: Phase 1, which spanned from September 2019 to February 2020; Phase 2, which occurred from June 2020 to September 2020; and Phase 3, which took place between July 2022 and October 2022. ASF exhibited a significant level of dissemination during Phase 1 and Phase 2 of the epidemic, indicating a high degree of transmission. Moreover, the occurrence rate of ASF showed perfect randomness throughout Phase 1 to Phase 3. In Phase 2 of the epidemic, Mabalacat had the highest density of HH ASF clusters, which suggests that the disease had spread widely in this area. Two high-risk ASF clusters with a mean radius of 5.215km were identified. There was a significant to directional spread of ASF during the initial stages, followed by frequent and random outbreaks, which provided valuable insights into the temporal and spatial spread of the disease in Pampanga.

Route and Schedule Optimization of Garbage Collection in Magalang Using Hamiltonian Path

Crystel Joy M. Punzalan and Kathleen Shy Ann M. Canlas

The Hamiltonian path is a path that passes through the vertex exactly once. The objectives of this study were to optimize the route and schedule of garbage collection in Magalang, Pampanga using the Hamiltonian path. Descriptive exploratory research is used in this study and the researcher used Google Maps to identify the direction of the route and used a questionnaire for interview purposes. The study is conducted at Magalang, Pampanga, as the research locale, and the respondent are garbage drivers in Magalang, Pampanga. This study optimized the route and Schedule of garbage collection in Magalang, Pampanga using the Hamiltonian path to get the shortest path and reduce the time in collecting garbage. As the interview is conducted, all the information is gathered and analyzed. As for the results, all barangay in Magalang, Pampanga will be visited daily and the optimized route was determined by using the Hamiltonian path, and a new garbage collection schedule was developed based on the optimized route and the shortest distance possible. As a result, the researcher recommends this study to other researchers who are interested in using the Hamiltonian path in applying this to other places that they may want to explore. The researcher recommends this study to the Municipality of Magalang, so that the garbage collectors can use the proposed schedule in collecting garbage.


Factors Affecting Dengue Cases in Magalang, Pampanga: A Spatial and Path Analyses

Lilybeth A. Santiago and Aiza D. Villavicencio

According to the Department of Health (DOH), dengue cases are spreading rapidly in the country. As a result, a study was conducted to determine the areas in Magalang, Pampanga, with the highest incidence of dengue and the factors that contributed to this increase. The study utilized spatial and path analysis to visualize the data and identify the impact of both the independent variables, whether direct or indirect, on the dependent variable. Data from 2016 to 2021 was collected through a descriptive method, and the results indicated that Santa Lucia had the highest number of cases. The study also found that male in the age group of 11 to 20, male, and the probable case classification had the highest number of cases. Furthermore, it was discovered that agriculture is the primary land use in Magalang, Pampanga. As seen on the map, Santa Lucia is centered around agriculture and rivers, which are potential risk factors for dengue. The shaded areas with dark colors on the map indicate the regions having the greatest frequency of instances, indicating that Santa Lucia has the highest. Based on the trend analysis, it can be concluded that Santa Lucia had the highest number of dengue cases, while Navaling had the least. The trend shows fluctuations in different barangays each year. The path model revealed that only population density had a positive and significant effect on the case classification, while sex and age have an indirect effect on dengue cases.

Geometrical, Sequential, and Spatial Patterns of Aglibut Sweet Tamarind (Tamarindus Indica) Epidermal Cells Under the Lens of Scanning Electron Microscope Imaging

Joseph Martin S. Tayag, Jessie H. Licup, and Nathaniel B. Supan

Pampanga State Agricultural University is renowned for its institute-based type of tamarind (Tamarindus indica) branded as Aglibut Sweet. This tamarind type has become a relevant subject of various studies with reference to its economic potential and its possible impacts to the ecosystem. Anatomical and morphological profiling of its cellular arrangement – epidermal cells (Stomatal apparatus, Neighboring and Subsidiary Cells) of its leaves in particular are necessitated. This could unveil its environmental advantage, specifically on its ability in carbon sequestration process. Thus, this study has evaluated the cellular configuration of Aglibut Sweet’s epidermis under the lens of scanning electron microscope (SEM) using mathematical pattern concepts such as geometry, sequence, as well as spatial aspects. SEM images were subjected and described through a descriptive-exploratory assessment and present patterns, respectively. Aglibut sweet epidermal cells revealed an estimated three to seven edged polygons tessellated together and clumped in pairs and occasionally triads. Some are observed to be sequenced in streaks of consecutive pairs and often branch off these streaks. The epidermal cells exhibit a similar behavior to Voronoi cells and use up the maximum number of colors of the four-color theorem. Subsidiary cells that surround the guard cells (Stomata) occur in two to three cells. Around three stomatal apparatus were remarked for every two square millimeters of leaf. Results from these mathematical interpretations are deemed useful data as an essential reference for further studies concerning its carbon sequestration potential.