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BAREKENG: Jurnal Ilmu Matematika dan Terapan
Published by Universitas Pattimura
ISSN : 19787227     EISSN : 26153017     DOI : https://search.crossref.org/?q=barekeng
Core Subject : Economy, Science, Education, Engineering,
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation
BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure Mathematics (analysis, algebra & number theory), - Applied Mathematics (Fuzzy, Artificial Neural Network, Mathematics Modeling & Simulation, Control & Optimization, Ethno-mathematics, etc.), - Statistics, - Actuarial Science, - Logic, - Geometry & Topology, - Numerical Analysis, - Mathematic Computation and - Mathematics Education. The meaning word of "BAREKENG" is one of the words from Moluccas language which means "Counting" or "Calculating". Counting is one of the main and fundamental activities in the field of Mathematics. Therefore we tried to promote the word "Barekeng" as the name of our scientific journal also to promote the culture of the Maluku Area. BAREKENG: Jurnal ilmu Matematika dan Terapan is published four (4) times a year in March, June, September and December, since 2020 and each issue consists of 15 articles. The first published since 2007 in printed version (p-ISSN: 1978-7227) and then in 2018 BAREKENG journal has published in online version (e-ISSN: 2615-3017) on website: (https://ojs3.unpatti.ac.id/index.php/barekeng/). This journal system is currently using OJS3.1.1.4 from PKP. BAREKENG: Jurnal ilmu Matematika dan Terapan has been nationally accredited at Level 3 (SINTA 3) since December 2018, based on the Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia, with Decree No. : 34 / E / KPT / 2018. In 2019, BAREKENG: Jurnal ilmu Matematika dan Terapan has been re-accredited by Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia and accredited in level 3 (SINTA 3), with Decree No.: 29 / E / KPT / 2019. BAREKENG: Jurnal ilmu Matematika dan Terapan was published by: Mathematics Department Faculty of Mathematics and Natural Sciences University of Pattimura Website: http://matematika.fmipa.unpatti.ac.id
Arjuna Subject : Matematika - Matematika Terapan
Articles 1,248 Documents
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PREDICTION INTERVALS IN MACHINE LEARNING: RESIDUAL BOOTSTRAP AND QUANTILE REGRESSION FOR CASH FLOW ANALYSIS Safitri, Wa Ode Rahmalia; Mochamad Afendi, Farit; Susetyo, Budi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1625-1636

Abstract

Time series forecasting often faces challenges in producing reliable predictions due to inherent uncertainty in dynamic systems. While point predictions are commonly used, they may not adequately capture this uncertainty, especially in financial systems where forecasting accuracy directly impacts decision-making. Prediction intervals offer a solution by providing a range of likely outcomes rather than single-point estimates. This study implements multivariate time series forecasting using gradient boosting algorithms (XGBoost, CatBoost, and LightGBM) to predict cash flow patterns in banking transactions, focusing on constructing reliable prediction intervals. Using transaction data from Bank Rakyat Indonesia (BRI), the research analyzes both office and e-channel transactions with different lag structures based on Granger Causality tests. Model performance was evaluated using RMSLE, MAE, and MAPE metrics, with RMSLE chosen as primary due to its ability to handle skewed distributions. LightGBM achieved best performance for office cash-in transactions (RMSLE: 0.2395), while CatBoost outperformed others for office cash-out (RMSLE: 0.2848), e-channel cash-in (RMSLE: 0.3946), and e-channel cash-out (RMSLE: 0.4221). For prediction intervals, two methods were compared: Residual Bootstrap with 500 samples and Quantile Regression. Residual Bootstrap generally produced coverage probabilities closer to the 80% level (i.e., 10–90% prediction interval), especially for office transactions, while maintaining narrower interval widths. In contrast, Quantile Regression tended to generate wider intervals and often overestimated uncertainty, resulting in overly high coverage in some cases. However, both methods showed clear limitations when applied to e-channel transactions, particularly for cash-in e-channel, where coverage probabilities fell below 50% due to high volatility and irregular transaction patterns. Unlike previous work focused only on point forecasts, this study offers insights into forecast uncertainty by evaluating how well each method quantifies, providing practical guidance for financial institutions aiming to improve risk management through interval-based forecasting.
A MODEL ON MARKET EQUILIBRIUM USING A DIFFERENTIAL EQUATION WITH TIME DELAYS Widjaja, Jalina; Putra Irawan, Naufal Zidan; Soeharyadi, Yudi; Tampubolon, Dumaria R.
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1893-1904

Abstract

In this paper, a model on market equilibrium is proposed using a delay differential equation with discrete delays as a modified version of the one proposed by Kobayashi (1996). The price of a commodity is determined using the equation involving weighted supply and demand functions. Both supply and demand functions are considered at the current time and sometimes in the past. The delays are chosen by considering the seasonal behavior of the market. We use data on some main commodities in Indonesia from 2018 to 2024 to validate the model. We found that the implementation of our modified Kobayashi model improves the estimation given by the original one. The implementation of the method also shows some characteristics of delay equations, that is longer delay time may include more dynamics, and more fluctuation, although that means it is more prone to instabilities. However, the problem of optimal delay time is yet to be resolved.
FUZZY GEOGRAPHICALLY WEIGHTED CLUSTERING WITH OPTIMIZATION ALGORITHMS FOR SOCIAL VULNERABILITY ANALYSIS IN JAVA ISLAND Fadlurohman, Alwan; Utami, Tiani Wahyu; Amrullah, Setiawan; Roosyidah, Nila Ayu Nur; Dhani, Oktaviana Rahma
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1841-1852

Abstract

The Social Vulnerability Index (SoVI) measurement assesses social vulnerability. However, the measurement of SoVI can only describe the general conditions without being able to show which factors dominate. Therefore, a clustering approach has been proposed to characterise the dominant social vulnerability factors. Fuzzy Geographically Weighted Clustering (FGWC) is a method that works for this purpose. FGWC is an extension of the Fuzzy C-Means algorithm, which involves geographical influences in calculating membership values. However, the FGWC method is sensitive because the initial initialisation to determine the centroid is randomised, and it will affect the cluster quality. This research uses a metaheuristic approach to overcome the weakness of FGWC by using Particle Swarm Optimisation (PSO) and Artificial Bee Colony (ABC). This study aims to cluster districts/cities in Java Island using the PSO-FGWC and ABC-FGWC methods based on social vulnerability variables and determine the dominant factors of social vulnerability in each region. Optimum cluster selection uses the index of the largest Partition Coefficient (PC) and the smallest Classification Entropy (CE). Clustering social vulnerability in Java Island resulted in the best clustering using the ABC-FGWC method with 5 optimum clusters based on the PC and CE index values of 0.343 and 1.298, respectively. This research found that social vulnerability exists in each region of Java Island. Cluster 1, consisting of 19 districts/cities, is characterized by vulnerabilities in demography and education. Cluster 2, consisting of 33 districts/cities, is characterized by demographic and health vulnerabilities. Cluster 3, which consists of 24 districts/cities, is dominated by education and economic vulnerability factors. Cluster 4, consisting of 14 districts/cities, has the highest social vulnerability characteristics on the unemployment rate and the proportion of house rent. The last one, cluster 5, consists of 29 districts/cities and has a vulnerability problem in the population growth variable.
PERFORMANCE LOSS QUANTIFICATION IN KERNEL DENSITY ESTIMATION FOR ACTUARIAL AND FINANCIAL ANALYSIS Untsa, Shafira Fauzia; Susyanto, Nanang; Qoiyyimi, Danang Teguh; Ertiningsih, Dwi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp2029-2038

Abstract

Accurately estimating aggregate loss distributions is critical in actuarial and financial risk assessment, as it underpins effective risk analysis and the development of mitigation strategies. However, incorrect parametric assumptions can lead to biased risk estimates and underestimated losses. Non-parametric methods, such as Kernel Density Estimation (KDE), offer a flexible alternative by generating smooth empirical probability density functions (PDFs) directly from sample data without assuming a specific distributional form. This study examines the impact of dependence structures on risk measures by applying KDE with a Gaussian kernel to estimate aggregate loss distributions. To quantify the effects of ignoring dependence, we introduce the concept of performance loss, focusing on variance, Value at Risk (VaR), and Tail Value at Risk (TVaR). The results show that performance loss increases with the correlation coefficient, indicating that higher dependency leads to greater underestimation of risk. Additionally, higher confidence levels amplify performance loss for VaR and TVaR, underscoring the sensitivity of these measures to tail behavior. These findings highlight the importance of incorporating dependence structures in risk modeling to avoid misleading evaluations. The implications are particularly relevant for disaster risk management in Central Asia, where overlooking interdependencies in seismic losses could result in inadequate financial and actuarial strategies.
FETAL HEALTH RISK STATUS IDENTIFICATION SYSTEM BASED ON CARDIOTOCOGRAPHY DATA USING EXTREME GRADIENT BOOSTING WITH ISOLATION FOREST AS OUTLIER DETECTION Sari, Firda Yunita; Rini Novitasari, Dian Candra; Hamid, Abdulloh; Haq, Dina Zatusiva
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1711-1724

Abstract

Premature birth and birth defects contribute significantly to infant mortality, highlighting the need for early identification of fetal health risks. This study uses XGBoost for fetal health classification, integrating IForest for outlier detection to improve model performance. By varying the contamination percentage, learning rate (η), maximum depth, and n_estimator, the best results were achieved at CP = 8%, η = 0.01, max_depth = 7, and n_estimator = 100, which resulted in 100% accuracy, sensitivity, and specificity with a calculation time of 0.36 seconds. IForest effectively reduced the dataset from 2126 to 1956 samples by removing outliers, improving accuracy by 3.76%, and reducing computation time by 0.51 seconds. These findings suggest that IForest improves classification efficiency while maintaining high predictive performance, supporting early identification of fetal health risks to aid timely medical intervention.
DETERMINING TEACHING SCHEDULE AT STATE SENIOR HIGH SCHOOL 1 DEPOK USING ASSIGNMENT THEORY WITH HUNGARIAN METHOD AND NEW IMPROVED ONES ASSIGNMENT METHOD ASSISTED BY PYTHON Hindarto, Catherine Richelle; Sanjaya, Febi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1765-1778

Abstract

Every school has a lesson schedule that describes the allocation of teacher assignments to certain lesson hours in each class. The teaching schedule at State Senior High School 1 Depok is still made manually. Therefore, assignment theory using the Hungarian method and the New Improved Ones Assignment (NIOA) method assisted by Python is an alternative for automating the schedule creation process. The purpose of this research is to determine (1) the assignment model, (2) the application of the Hungarian method, (3) the application of the NIOA method, and (4) a comparison of the process and results using both methods from the teaching schedule at State Senior High School 1 Depok. The following research results were obtained. The assignment model can be arranged into assignment tables, which contain teacher codes in the rows, day and lesson hour codes in the columns, and the availability of teacher’s teaching hours, which is filled in with entry 1 if the teacher can teach and 0 if the teacher cannot teach in the corresponding cells. Those tables are processed using Python according to Hungarian and NIOA assignment algorithms. The difference in the application of the two methods is only in the algorithm for finding the initial basic feasible solution. Overall, the two methods applied produce the same schedule results. Differences in results are obtained if two teachers can only teach at the same time.
GRID SEARCH AND RANDOM SEARCH HYPERPARAMETER TUNING OPTIMIZATION IN XGBOOST ALGORITHM FOR PARKINSON’S DISEASE CLASSIFICATION Aqilah Khansa, Shafa Fitria; Ulinnuha, Nurissaidah; Utami, Wika Dianita
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1609-1624

Abstract

Parkinson's disease is a neurodegenerative disorder affecting motor abilities, with a prevalence of 329 cases per 100,000 individuals. Early diagnosis is crucial to prevent complications. This study classifies Parkinson's disease using the Extreme Gradient Boosting (XGBoost) algorithm with hyperparameter tuning via Grid Search and Random Search. The dataset from Kaggle consists of 2105 records from 2024 and includes 32 clinical and demographic features such as age, gender, BMI, medical history, and Parkinson's symptoms. The XGBoost method effectively manages large and complex data and reduces. Tuning was performed with 5-fold cross-validation for result validity. After tuning with Grid Search, the model achieved 93.35% accuracy in 44 minutes 51 seconds, with optimal parameters gamma=5, max depth=3, learning rate=0.3, n estimators=100, and subsample=0.7. Meanwhile, Random Search with 50 iterations achieved 93.97% accuracy in 3 minutes 4 seconds with optimal parameters gamma=5, max depth=3, learning rate=0.262, n estimators=58, and subsample=0.631. Random Search also shows better time efficiency than Grid Search, although with relatively similar accuracy. The results of this study confirm that hyperparameter tuning using Random Search not only produces competitive accuracy performance but also minimizes computation time, making it a more optimal choice for Parkinson's disease classification.
NONLINEAR TRACKING CONTROL FOR PREY STABILIZATION IN PREDATOR-PREY MODEL USING BACKSTEPPING Mu`tamar, Khozin; Naiborhu, Janson; Saragih, Roberd; Handayani, Dewi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1825-1840

Abstract

The common method used in population dynamics is optimal control, which employs Pontryagin’s minimum principle. This method minimizes costs, with the constraint function being the model dynamics. Unfortunately, if the main objective of the control function is to modify the population’s behavior to follow a specific pattern, this method is challenging to apply. This article introduces a control function to the predator-prey model for the tracking problem using the backstepping method. The control function drives the population from the initial value towards the given trajectory. The goal is to maintain the balance between predator and prey populations in the habitat, with the chosen trajectory being the equilibrium point. The application of backstepping to the predator-prey model is combined with input-output feedback linearization to obtain a normal form, enabling the implementation of backstepping. Simulation results show that the controller successfully drives the predator-prey populations toward the equilibrium point with a relatively small control function and excellent performance.
TRANSFORMER-BASED OPTICAL CHARACTER RECOGNITION APPROACH FOR IDENTIFYING MOTOR VEHICLES WITH OVERDUE TAXES Fazira, Nabila Dwi; Fauzan, Achmad
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1597-1608

Abstract

The high growth in the number of motorized vehicles in Indonesia has given rise to special attention in managing traffic administration, especially in relation to vehicle taxes. To present innovative solutions in vehicle tax administration, this research was conducted to detect the five-year tax status of motor vehicles in Indonesia using the Transformer Optical Character Recognition (TrOCR) model. The aim of this research is to evaluate the performance of the TrOCR model in recognizing text on motor vehicle number plates in Indonesia and classifying number plates that have and have not paid tax. The data used is primary data in the form of images of motor vehicle number plates taken around the Faculty of Mathematics and Natural Sciences, Universitas Islam Indonesia, using a purposive sampling with constraints on the representation of each class. Although the data collection was limited to this location, Indonesian vehicle plates follow a standardized format, with regional differences primarily in the prefix letters. Additionally, the university attracts students from various regions who often use vehicles registered in their home provinces. Consequently, the collected dataset reflects a diverse range of number plates, making it a reasonable representation of motor vehicle plates across Indonesia. The research results show that the TrOCR model succeeded in achieving a Character Error Rate (CER) value of 2.9% with a data configuration of 90% for training and 10% for testing, and using 8 epochs. Evaluation of model performance indicates that overall text detection is very effective in classifying the five-year tax status of motor vehicles. Although there are some prediction errors, the overall performance of the model can be considered good and is able to provide reliable information regarding the five-yearly vehicle tax status
IMPLEMENTATION OF PLS-PM IN KNOWING THE FACTORS THAT INFLUENCE THE INCIDENCE OF TYPHOID FEVER IN PATIENTS IN ANUTAPURA PALU HOSPITAL Damayanti, Virga; Fadjryani, Fadjryani; Setiawan, Iman
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1667-1680

Abstract

Typhoid fever is a multifactorial disease that has factors that can have an impact, including individual characteristics, maternal knowledge, hygiene, and nutritional status. Data on the incidence of typhoid fever involves many variables that cannot be examined directly (latent variables). This study used secondary data obtained from the medical records of typhoid fever patients at Anutapura Palu Hospital in 2023. One of the statistical methods that can be used to explain the relationship between indicators and latent variables is Partial Least Squares-Path Modeling (PLS-PM). Therefore, this study aims to model the influence of individual characteristics, maternal knowledge, hygiene, and nutritional status on the incidence of typhoid fever in patients at Anutapura Palu Hospital using PLS-PM analysis. The results of the PLS-PM analysis show that individual characteristics and nutritional status have a direct effect on the clinical images, while maternal knowledge and hygiene indirectly affect the clinical images through nutritional status, with a coefficient of determination of 0.828. So, it can be said that nutritional status is able to mediate between individual characteristics, maternal knowledge, and hygiene with the clinical images of typhoid fever.

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