Block Spots Identification and Predictive Modeling of Road Accidents in Magalang, Pampanga

Hiddy Trisha M. Santos and Aldrin P. Mendoza

The unforeseeable nature of road accidents poses an immense dilemma, causing approximately 1.19 million yearly fatalities worldwide. As per the World Health Organization (WHO), this global issue is projected to ascend to the seventh leading cause of death by the end of 2030 if no preventive measures are implemented. In light of this, extensive black spot identification and the establishment of predictive modeling for road accidents were executed in Magalang. The Kernel Density Estimation (KDE) heatmap unveiled that the weighted accidents spanning 2019 to 2022 are highly concentrated along Magalang-Concepcion Rd and Magalang-Arayat Rd, covering 1.15 km from San Nicolas 1 Barangay Hall to Alasas Bridge in Santa Cruz. Meanwhile, heatmaps using the partitioned datasets attributed to year, month, day, and time period revealed that the black spots were mostly scattered along the major roads.
Furthermore, Global and Local Moran’s I analyses were performed to evaluate the spatial statistical correlation of accidents. The unpartitioned accidents and datasets containing accidents per year, May, November, Monday, Wednesday, Saturday, morning, and night, exhibiting cluster patterns, primarily comprised of low-low, high-low, and insignificant accidents in the identified black spots. Meanwhile, the prediction model showed that types of vehicles, such as passenger cars, heavy vehicles, multiple modes, and time, including morning and afternoon, were found to significantly decrease the expected number of casualties per accident by a certain percentage. The selection of Poisson regression in modeling the count data is well-suited based on its remarkable goodness-of-fit test and prediction performance with 2023 data.

Spatiotemporal Trend Analysis of Agricultural Crops Production in the Philippines

Mark Angelo L. Razon and Jocell D. Calma

The study investigated the production trends of agricultural crops from 1992 to 2022, employing a descriptive-correlational research design. Utilizing non-parametric tests, including the Mann-Kendal (MK) and Sen’s Slope Estimator (SSE), the study assessed fluctuations in crop production. Results indicate varying production levels across crops such as rice, corn, sugarcane, banana, cassava, mango, cacao, coconut, pineapple, camote, coffee, onion, and oil palm. Notably, coconut and pineapple demonstrate consistent production, while camote exhibits increasing production and coffee and onion show declines. Rice, corn, cassava, camote, and cacao display significant positive production trends, whereas sugarcane, coffee, and onion exhibit significant negative trends. Conversely, coconut, banana, pineapple, and mango present non-significant trends. The study recommends further investigation into the decreasing trends observed across various agricultural crops in different provinces. This analysis offers valuable insights into the dynamics of agricultural crop production, informing future research and policy interventions to address fluctuating trends and enhance crop sustainability.

Visualization Dashboard: https://bit.ly/Agri-Crops-Trend-Philippines

On Irregular Reuleaux Triangle

Arieztotle P. Buccat and Jocell D. Calma

This paper rigorously examines an irregular Reuleaux triangle, a geometric figure of constant width comprising six circular arcs derived from extending the sides of an irregular triangle. We thoroughly discuss its components and construction steps. Six properties, including constant width, three construction properties, and two measurements, are presented and mathematically proven through propositions.

Influenza-Like Illness (ILI) Incidence in the Philippines: A Systems of Differential Equation Model

Lyza Mirah I. Villapaña and Alvin M. Supan

The study’s main objective was to create and demonstrate a differential equation system that would simulate the dynamics of Influenza-like illness (ILI) in the Philippines using a descriptive research method. Data sourced from the Department of Health’s surveillance report were described and modeled. The SIR-based compartmental model was used, with adjustments for regions with and without deaths. It was derived from the traditional SIR model by Kermack and McKendrick. Results have shown fluctuating ILI cases, with Region XI exhibiting the highest incidence. The basic SIR model was employed for the cases with no deaths, while an SIR-D model for the regions that had death cases. Additionally, analytical and numerical methods were utilized in analyzing the model. After solving I(t) analytically, the models’ parameters were solved using Excel solver’s optimization. The Runge-Kutta method was applied to obtain the numerical solutions for dS/dt, dR/dt, and dD/dt (which was used for the regions with death cases) using Scilab version 6.1.1. The findings have indicated the model per region that somehow closely fitted the observed data.

Probability Distribution Fitting of Agricultural Crops Production in the Philippines

Makyla Ann M. Bolos and Alvin M. Supan

Agricultural crops in the Philippines are the lifeline of millions, fuelling agricultural incomes and generating economic resilience. The main goal of this research was to better understand Normal, Lognormal, and Weibull distribution’s in fitting the agricultural crops production in the Philippines. This study delved into the production of agricultural products in the Philippines, with an emphasis on high-value crops like sugarcane, coconut, bananas, sweet potatoes, pineapples, cassava, mangoes, and oil palms, as well as staples like rice and corn. Data spanning from 1987 to 2022, to find the best fitting probability distribution for each crop. The goodness-of-fit of the distributions was assessed using statistical tests, such as the Anderson-Darling test (AD), Kolmogorov-Smirnov test (KS), supplemented by the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The findings show that most of the agricultural crop production in the Philippines, Normal distribution provides the best fit to the observed data based on the statistical tests. Specifically, Region XI (Davao Region) in rice production shows that it provides the best fit based on the statistical tests and provides the most accurate representation under Normal distribution. One of the conclusions after conducting this study is not rely entirely on visual inspection of histograms or Q-Q plots, instead, the outcomes of goodness-of-fit tests and model selection criteria should be prioritized too. Suggestions are also provided for future study, investigate different probability distributions, use other statistical tests, and expand the analysis to a more precise geographic scale, like the province level.

Exploring Growth Patterns of Kawayan Tinik (Bambusa blumeana J.A and J.H Schultes), Giant Bamboo (Dendrocalamus asper Schultes et. Backer ex Heyne), and Giant Bolo (Gigantochloa levis Blanco) Merrill): A Mathematical Modeling Approach

Shiela Mhay M. Lapuz, Jocell D. Calma and Allain James T. Aquino

Bamboo stands as a pivotal resource for sustainable development, renowned for its rapid growth and diverse applications in construction, furniture, and textiles, alongside its capacity for carbon sequestration and ecological restoration. This study endeavours to comprehensively model the growth patterns of three exemplary bamboo species – Kawayan Tinik, Giant Bamboo, and Giant Bolo. The experimentation period spanned for 147 days, from October 2023 to March 2024 where meticulous observation and data collection was facilitated across 450 bamboo branches which were partitioned into three blocks per species. Applying the principles of natural growth, an exponential model was employed to articulate the growth dynamics, yielding a general formula of H(t)=H_0 e^rt, where H represents height, t denotes time, and r symbolizes the growth rate. Notably, new branch emergence predominantly occurred on days three, eleven, and seven, with corresponding counts of 151, 139, and 260, while instances of branch mortality numbered 91, 82, and 176, respectively. The constructed growth pattern models exhibit commendable predictive accuracy, as evidenced by R-squared values of 92.82%, 95.43%, and 96.11%. These findings underscore the potential for significant expansion in bamboo biomass over the six-month horizon, emphasizing the importance of environmental considerations, such as soil moisture and water quality, for optimized cultivation management. This study provides valuable insights into harnessing bamboo’s sustainable attributes for ecosystem restoration and resource utilization, informing future strategies for enhancing its ecological and economic benefits.

Campus-Wide Local Area Network Topology Design at Pampanga State Agricultural University Using Prim’s Algorithm

Ronald B. Pacampara, Aldrin P. Mendoza and Rodel R. Pentecostes

The main objective of this study was to determine the minimum spanning tree for the campus-wide local area network topology design of all the buildings and infrastructures at Pampanga State Agricultural University. A descriptive-exploratory method was utilized and the existing network topology design provided by the Main Internet Server Office of PSAU served as the baseline. An optimization method in the network model using Prim’s algorithm to find the minimum spanning tree was utilized in the study. The minimum spanning tree was also solved analytically, and a computer program was created and executed in Python. The Ekahau Site Survey was used to determine the number of access points needed in a building and infrastructure. A Cisco Packet Tracer was utilized to enhance the visualization of the proposed campus-local area network topology design. Cost analysis was done based on the proposed campus-wide local area network design layout.

Modeling Growth of Oyster Mushroom at Pampanga State Agricultural University Mushroom Center

Missy S. Catacutan, Aiza D. Villavicencio, and Rudy M. Gonzales

This study aimed to develop a mathematical model to accurately describe the growth performance of oyster mushrooms at the PSAU Mushroom Center. Using a combined descriptive-experimental approach, the data were gathered through observations in three experimental blocks, analyzing hourly cap diameter measurements. The collected data were organized and analyzed using Microsoft Excel, followed by validation and graphical representation using SciLab 6.1.1. The 48-hour cultivation cycle showed cap diameters ranging from 2.69 cm to nearly 9 cm, revealing natural growth variation. The one-way ANOVA analysis revealed no statistically significant differences in growth patterns among blocks. Meanwhile, the logistic growth model identified differences between modeled and observed data, aligning closely with uniform growth patterns but highlighting areas for refinement in irregular patterns. The evaluation through independent t-test indicated no significant difference between observed and predicted data, emphasizing the model’s accuracy. This study offers insights into oyster mushroom growth dynamics and underscores the importance of accurate modeling for optimizing cultivation practices and increasing growth efficiency.

Probability Distribution Fitting of Infectious Diseases Cases in the Philippines

Blessel May C. Mercado and Erwin B. Maniago

Global population health is directly tied to national interests. Infectious diseases thus have a negative impact on the Western Pacific region’s social and economic growth. Accordingly, the study’s primary goal is to determine which probability distribution best fits the cases of infectious diseases in the Philippine region. With the maximum likelihood estimation, the normal, lognormal, weibull, gamma, and exponential parameters were utilized. Various goodness of fit tests and criteria were used to assess the model’s accuracy in each region, including the Anderson-Darling, Kolmogorov-Smirnov, Akaike, and Bayesian information criteria. In a given location, the characteristics of the available data on infectious diseases determine which probability model is most appropriate to estimate. Based on the data, it concluded that, out of the sixteen infectious diseases, the lognormal distribution best describes the majority of the regions. The other best fitted probability distributions that fit perfectly in the infectious diseases in the Philippines are followed by the weibull, gamma, exponential, and normal distributions.

A System of Differential Equations Modeling HIV/AIDS Cases in the Philippines

Jasmin Rhea G. Dulay and Aldrin P. Mendoza

The study’s main objective was to formulate a system of differential equations that would represent the dynamics of HIV/AIDS transmission in the Philippines. Results have shown that the number of HIV-infected cases in the first quarter of 2020 was three to four times higher than in 2012. The COVID-19 pandemic caused a drop in cases in the second quarter of 2020 but continued to rise in 2021–2023. An extended SIAD (susceptible (S), HIV-infected (I), AIDS-infected (A), and deceased (D)) model was developed using the basic SIR model to simulate the development of HIV/AIDS in the Philippines. The developed model was solved using both analytical and numerical solutions. The analytical solution for I(t) was fitted in Excel, and the remaining three differential equations were numerically solved using the Runge-Kutta method in Scilab version 6.1.1. The model’s performance was evaluated by comparing the predicted values and observed cases for 2018–2023 using an independent sample t-test. The result appeared to indicate that there is no significant difference at 5% alpha level of significance between the predicted cases and observed cases, indicating that the generated model can be used to predict HIV/AIDS cases in the future, and this was validated by predicting susceptible, HIV-infected, AIDS-infected, and deceased cases from 2018–2023. As a result, the predicted cases were closely fitted to the actual cases.

Spatial Analysis of Carbon Storage and Sequestration of Selected Timber Trees at Pampanga State Agricultural University

Joshua D. Maninang, Aiza D. Villavicencio, and Luisito B. Terbio

Carbon dioxide storage and sequestration are the most effective approaches, and they have emerged as powerful weapons against rising carbon emissions. The role of trees in the sequestration and storage of carbon is to lessen the excessive amount of carbon released by vehicles, electricity, etc. The main objective of this study was to determine the spatial analysis of carbon storage and sequestration of trees at Pampanga State Agricultural University. A descriptive method of research was used to show the different distribution and composition of tree species, namely: banaba, lanete, mahogany, narra, teak, and yemane. The allometric equation was used to calculate the total above-ground biomass (AGB), carbon storage (C), and carbon sequestration (CO2) of trees. Mahogany was found to have outstanding performance with a total carbon storage of 454,701.12 kg and carbon sequestration of 1,667,073.54 kg, which can absorb a vast amount of carbon in the atmosphere. Quantum Geographic Information was applied to estimate and visualize the C and CO2 of trees in each area within the vicinity of PSAU. Additionally, a heat map (kernel density estimation) was applied to show the concentration and spatial distribution of C and CO2. PSAU-Area 10 have significantly performed in carbon storage and carbon sequestration with >13,188.3697 kg/m^2 and > 48,352.5457 kg/m^2, respectively. A linear combination was utilized in order to solve the exact solution; 1882 teak and 1,164 yemane were generated for population density. 1 mahogany, 1 narra, 8 teak, and 2 yemane were generated for vehicles.

Profit Optimization Model of Tamarind RDE Center Production at Pampanga State Agricultural University*

Lianne Nhalie R. Paruli and Aiza D. Villavicencio

Tamarind RDE Center’s main goal was to conduct research and development activities aimed at enhancing the cultivation, processing, and utilization of tamarind, ultimately contributing to the advancement and sustainability of the agricultural sector. The objective of the study is to find the number of product per product to be invested in obtaining the optimum (maximum) profit to support the Tamarind RDE Center at PSAU in solving problems and maximizing revenues. The researcher used three (3) different kinds of products with, selling prices and production costs for the objective function. The study obtained an optimum profit of PHP 128,642.11 from the resulting optimization model. The study further revealed the following quantities of the products to be produced: 2,666 bottles of tamarind wine and 4,079 bottles of tamarind juice. On the other hand, the least number of products to be produced is the tamarind vinegar. Based on the acquired results, the researcher recommends the following: first, prioritize investments in tamarind wine juice production lines to capitalize on their high-profit potential. Second, focus on the research and development efforts aimed at improving Tamarind Vinegar production processes. Next, other software programs for solving the optimal solution, including AMPL software, MATLAB, Integer Programming, and Maple, offer alternative approaches. Then the profit optimization model of this research may be implemented in the PSAU-Tamarind RDE Center to assess its effectiveness. Lastly, future research on the other field of businesses using production and profit optimization may be considered.

Crystallography and Interlacement Pattern of Sitio Cananaoan Basketry*

Berlin L. Benosa and Ivy Gay O. Salvador

Ethnomathematics education is a research program that examines how various groups of indigenous people communicate, comprehend, and apply mathematical concepts or ideas in their daily lives. Indigenous handicrafts had drawn curiosity among numerous researchers who wants to study and discover the mathematics behind the culture and arts of our ethnic groups. The main objective of this study was to describe the basketry of an indigenous group residing at Sitio Cananaoan, San Agustin, Magalang, Pampanga. Descriptive research method was used to show the crystallography and interlacement patterns of their hand-made baskets which they commonly call bangkat. These bangkat was categorized into two; imata and sinawali. On the interlacement pattern, imata is a plain weave while sinawali is a twill. Both of the basket pattern belongs to the crystallographic group pl. The researcher was able to recreate 18 new coloring designs out of the original interlacement base pattern of these bangkat. The new designs belong to the crystallographic group pg, pmm, and p4. Among the 18 designs, only 10 of them can be straightly woven in accordance with the proper positioning of the colored warp and weft threads and only one design possesses the original weaving patterns of the imata bangkat basket.

A System of Differential Equations Modeling Dengue Incidence in the Philippines*

Aubrey Kaye T. Castro and Aldrin P. Mendoza

This study investigates the epidemiological dynamics of Dengue fever in the Philippines from 2021 to 2023, focusing on infected, recovered, and mortality cases. Analyzing data across regions, the research reveals a significant increase in Dengue infections over time, with varying patterns in different areas. Employing a Basic SIR model, derived from Kermack and McKendrick’s compartmentalized framework, the study predicts disease transmission dynamics accurately within the population. The model was solved using both analytical and numerical solutions. The analytical solution for I(t) was fitted in Excel, while S(t) and R(t) were numerically solved using the Runge-Kutta method in Scilab version 6.1.1. By utilizing an independent t-test and comparing modeled values and observed cases of 2023, the results showed a significant difference between modeled cases and observed cases in most regions in the Philippines except NCR. Upon evaluation of the model, the National Capital Region (NCR) is the only region exhibiting a strong fit between modeled and observed cases. However, in most other regions, significant disparities were observed, indicating that the model’s accuracy may be affected by assumptions and parameter estimation.

Probability Distribution Fitting of Climatic Factors in Central Luzon, Philippines*

Gerwin R. Mallari and Erwin B. Maniago

This study delves into the fitting of probability distributions for climatic factors in Central Luzon, Philippines, aiming to characterize the statistical properties of key variables and determine suitable distributions for modelling. Historical data on temperature, rainfall, humidity, and wind speed from meteorological stations across the region undergo meticulous exploratory analysis. Various distributions, such as normal, log-normal, gamma, Weibull, and Gumbel Type I, are rigorously fitted to the data using maximum likelihood estimation. The goodness-of-fit is thoroughly assessed through visual inspection and statistical tests like the Kolmogorov-Smirnov and Anderson-Darling tests, complemented by model selection criteria like AIC and BIC. Insights derived from this comprehensive analysis deepen our understanding of climatic distribution characteristics in Central Luzon, informing the development of more accurate climate models. These findings hold significant implications for climate monitoring, impact assessment, and adaptation planning efforts not only in Central Luzon but also in similar regions globally.

Application of Depth-First Search (DFS) Algorithm in Solving Hidato Puzzles*

Noel Stephen S. Lagmay and Ivy Gay O. Salvador

Hidato (Hida approach riddle in Hebrew) is a common sense puzzle recreation much like the extremely famous Sudoku. The Hidato puzzle consists of n grid cells in which the player has to fill in the cells with natural numbers from 1 to n in such a way that the following numbers remain in the adjacent cells. With this, the study investigates the application of the Depth-First Search (DFS) algorithm in solving Hidato puzzles. The primary objective is to explore how DFS can be utilized, be developed into a program, and be applied to solve these puzzles. The study found that the Depth-First Search (DFS) algorithm is applicable in solving Hidato puzzles by going through potential paths and methodically examining the puzzle until it finds one or more solutions. The study demonstrates the effectiveness of DFS in solving Hidato puzzles, provides a methodology for developing a DES-based program, and illustrates the practical application of such a program.

Graphical Illustrations of Morphological Characteristics of Selected Genus of Butterflies*

Maria Lhizette T. Guina and Ivy Gay O. Salvador

This study will concentrate on the polar curves that can be seen in the morphological characteristics of a butterfly. The researcher used the descriptive type of research. The polar curves that used to graph butterflies specifically Eurema hecabe, Eurema blanda, Catopsilia pomona, Catopsilia scylla, Appias nero and Appias paulina were described. The researcher used Desmos Graphing Calculator to graph the equation of the butterfly, the formulation of the equation for the butterflies starts by using the Fay Butterfly equation as a reference. The results shows that species Catopsilia pomona and Catopsilia scylla has the most similar equation followed by species Eurema hecabe and Eurema blanda and the least similar equation, the Appias pomona and Appias nero and for genus the Eurema and Catopsilia have many similar in equations while the similar equation for the genus Eurema and Appias is the same with Catopsilia and Appias genus they have the least similar in equation. All the similarities of the three genus of butterflies in their equation is r = W1 (Equation 9.1) and for the genus Eurema and Catopsilia is r = W1 + W2 (Equstion 9.3). For the species Eurema hecabe and Eurema blanda is r = W1 + W2 + X1 (Equation 10.2) while for the species Catopsilia pomona and Catopsilia Scylla is r = W1 + W2 + X2 (Equation 11.2) lastly, the species Appias paulina and Appias nero is r = W1 + X3 (Equation 12.2).

Food and Water-Borne Diseases Cases in the Philippines: A System of Differential Equations Model*

Maria Lourdes A. Guevarra and Alvin M. Supan

The study aimed to generate a mathematical model for the food and waterborne diseases cases in the Philippines per region using the systems differential equations model. The data revealed that the highest infected cases were recorded in Region XIII, with cholera being the most at risk and Hepatitis A being the least. In addition, the infected cases have been consistently increasing in 2021 compared to other years. Moreover, an analytical and numerical method was used to analyze the instances of food and water-borne diseases in the Philippines. SIR model were employed which was developed by Kermack and McKendrik in 1927. I(t) was solved analytically by integrating with the particular solution I = I0 e(Ba)t followed by solving the unknown parameters with the used of Excel solver by optimizing the SSR. The numerical solution for the susceptible and recovered was utilized in Scilab 6.1.1 using Runge-Kutta method. The modeled cases of the food and waterborne diseases closely matched the observed cases. Based on the evaluation of the models, the rotavirus is projected to increase over time, while acute bloody diarrhea, acute viral hepatitis, cholera, and typhoid fever will increase and decrease in the future. To conduct further analysis, it is highly recommended to consider the factors that affecting the food and water-borne diseases, such as climate change variability in terms of food and water safety.

A Systems of Differential Equation Modeling the Vaccine Preventable Diseases Incidences in the Philippines*

Carla D. Francisco and Erwin B. Maniago

The primary goal of the research was to model the incidence of vaccine preventable diseases in each region of the Philippines. It ascertained the cases of vaccine-preventable diseases in the Philippines according to regions in terms of infected and recovered individuals. The vaccine preventable diseases cases were started from January 2021 to December 2023. The number of recovered cases is increasing in direct proportion to the number of infected cases. Through an adaptation of the traditional SIR model created by McKendrick and Kermack, this method offers a precise framework for examining the dynamics of disease throughout time. In this model analysis, an analytical and numerical approach was adopted. After solving I(t) analytically, the model’s parameter was solved using the Excel solver’s optimization procedure. Scilab 6.1.1 Runge-Kutta method was used to solve the numerical solutions for dS/dt and dR/dt. Using independent samples t-tests for evaluating the observed and predicted cases of vaccine preventable diseases in the Philippines per region, the study effectively evaluated changes in illness prevalence over time.