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CAUCHY: Jurnal Matematika Murni dan Aplikasi
Published by Universitas Islam Negeri Maulana Malik Ibrahim Malang
ISSN : 20860382     EISSN : 24773344     DOI : 10.18860
Core Subject : Education,
Mathematics
Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh Mitra Bestari (reviewer) untuk dinilai substansi kelayakan naskah. Redaksi berhak mengedit naskah sejauh tidak mengubah substansi inti, hal ini dimaksudkan untuk keseragaman format dan gaya penulisan.
Arjuna Subject : -
Articles 438 Documents
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Groundwater Pollution Concentration Estimation with Modified Kalman Filter Method Estuningsih, Nenik; Fatmawati, Fatmawati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.28467

Abstract

Groundwater quality is very important for human health. Estimation of groundwater pollution concentration to determine groundwater quality is necessary. The concentration of groundwater pollution is estimated using the modified Kalman filter method. The modified Kalman filter method is a method that collaborates the Kalman filter estimation algorithm with the model order reduction method. The model order reduction method used in this research is the LMI (Linear Matrix Inequality) method because the model reduction error using the LMI method is the smallest error compared to the reduction error using the Balanced Truncation method or the Singular Pertrubation Approximation method. The modified Kalman filter method is used in order to obtain accurate estimation results with a short computation time. It is found that the implementation of the Kalman filter algorithm in the original system as well as the implementation of the modified Kalman filter method of the reduced system with the LMI method produces very good estimates, close to the real state variable. The estimation of the original system takes longer time than the reduced system.
Pricing Modified Barrier Options Using the Bino-Trinomial Tree Model: A Strategy for Loss Minimization Rahayu, Rima Aulia; Agustina, Fitriani; Sidarto, Kuntjoro Adji
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33239

Abstract

A particular exotic option that is widely traded in the global financial market is the barrier option. Barrier options are attractive because they have a limit that must be reached to activate the option. These limits may be utilized by investors as a point of reference to minimize potential losses. Accordingly, the researcher attempts to use the bino-trinomial tree model as a new approach to minimize losses. The purpose of this study is to analyze the bino-trinomial tree model to provide investors with more flexible hedging experience. The bino-trinomial tree model is obtained by combining the trinomial tree model at the first stage, then the binomial tree model at a further stage. This analysis was conducted by calculating the type of knock-out european call options. The results demonstrate that this model can effectively, accurately and flexibly manage the complex options required by modern investors, including multi-step single moving barrier options and single window barrier options.
Geographically Weighted Random Forest Model for Addressing Spatial Heterogeneity of Monthly Rainfall with Small Sample Size Damayanti, Rismania Hartanti Putri Yulianing; Astutik, Suci; Astuti, Ani Budi
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.32161

Abstract

Rainfall modeling often involves complex spatial patterns that vary across locations. Traditional spatial models such as Geographically Weighted Regression (GWR) assume linear relationships and may fall short in capturing nonlinear interactions among predictors and the small sample size is more challenging to fix the assumptions. To address this limitation, this study applies the Geographically Weighted Random Forest (GWRF) method is a hybrid approach that integrates Random Forest (RF), a non-parametric machine learning algorithm with geographically weighted modeling. GWRF is advantageous as it accommodates both spatial heterogeneity and nonlinear relationships, making it suitable for modeling monthly rainfall, which is inherently spatially varied and influenced by complex factors. This study aims to implement and evaluate the performance of the GWRF model in monthly rainfall prediction across East Java. The model is tested using various numbers of trees to determine the optimal structure, and its performance is assessed using Root Mean Square Error (RMSE), Akaike Information Criterion (AIC), and corrected AIC (AICc). Results indicate that the model tends to overestimate the Out-of-Bag (OOB) Error at all tree variations, with the smallest RMSE (85.68) achieved at 750 trees. Humidity emerges as the most influential variable in predicting monthly rainfall in the region, based on variable importance analysis
Bias Correction of Lake Toba Rainfall Data Using Quantile Delta Mapping Rafhida, Syukri Arif; Nurdiati, Sri; Budiarti, Retno; Najib, Mohamad Khoirun
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.29124

Abstract

Lake Toba, located in North Sumatra, is the largest tectonic and volcanic lake in Indonesia. Lake Toba has an equatorial climate characterized by abundant rainfall throughout the year. High rainfall, coupled with annual increases due to climate change, results in a vulnerability to the unpredictable extreme weather, causing harm to the surrounding communities. Consequently, a rainfall prediction model is needed to anticipate the impacts of such extreme rainfall. One of the rainfall prediction models used is ERA5-Land. However, this prediction model has biases that can be avoided. A method that can be used is the statistical bias correction using the quantile delta mappings (QDM) by correcting ERA5-Land model data against BMKG observation data. The QDM method used in this study employs two types of methods: monthly and full distribution. The results shows that both methods can improve biases at Silaen, Laguboti, and Doloksanggul stations, as well as improve the model during the equatorial dry seasons in May, June, July, and August. However, the first method improves the model distribution more in Silaen and Laguboti, while the second method improves the model distribution more in Doloksanggul.
Generalized Space Time Autoregressive (GSTAR) Modeling in Predicting the Price of Bird’s Eye Chili in East Java, West Java, and Central Java Pusporani, Elly; Yuniar, Muhammad Alvito Dzaky Putra; Fajrina, Sofia Andika Nur; Alexandra, Victoria Anggia; Mardianto, Muhammad Fariz Fadillah
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.25730

Abstract

Bird’s eye chili (Capsicum frutescens L.) is a major agricultural commodity in Indonesia that contributes to the economy through high market demand and its impact on inflation. In 2022, production reached 1,544,441 tons, with East Java, Central Java, and West Java being the top producing provinces. However, price fluctuations due to production and market mismatches are a concern for farmers and policy makers. The objective of this study was to model the price dynamics of bird’s eye chili in the provinces of East Java, Central Java, and West Java, given their substantial contribution to national production. To address this, the Generalized Space Time Autoregressive (GSTAR) method was applied to model the price of bird’s eye chili from February to November 2023 using data from the National Food Agency with 8:2 ratio between training and testing data. By utilizing different weighting schemes-uniform weight, inverse distance, and cross-correlation normalization, the GSTAR(2_1 )I(1) with uniform location weights performed best, showing high predictive accuracy with MAPE values of 2.021% for training data and 2.045% for test data. The model is recommended to stabilize the price of bird’s eye chili, with further validation recommended to improve reliability
Identification and Modelling Tuberculosis Incidence Risk Factors in West Java with Negative Binomial Mixed Model Random Forest Arisanti, Restu; Pontoh, Resa Septiani; Winarni, Sri; Putri, Nisa Akbarilah; Maurin, Stefany
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.29750

Abstract

Tuberculosis (TB) remains a major public health problem in many parts of the world, including in West Java Province, Indonesia. By guiding targeted medication, an accurate assessment of TB risk factors can enhance overall efforts to control tuberculosis. This study introduces modelling by integrating Negative Binomial Mixed Models (NBMM) and Random Forest (RF) called the Negative binomial mixed model random forest (NBMMRF) model.  This model is used to identify and assess risk factors associated with the incidence of tuberculosis. First, utilized NBMM to add fixed effects and random effects in the model and compensate for overdispersion. Modelling count data with overdispersion is a crucial problem in epidemiological studies, and the NBMM component in this model provides a flexible. Afterward, we include a Random Forest component in the model, which helps us detect relevant predictive features and change model weights accordingly. The resulting Negative Binomial Mixed Model Random Forest (NBMMRF) has a high accuracy value of up to 0.915. In contrast to simpler models, the NBMMRF model can capture complex and nonlinear interactions between predictors and outcomes.
Hyperparameter Optimization Approach in GRU Model: A Case Study of Rainfall Prediction in DKI Jakarta Mashfia, Fidia Raaihatul; Astutik, Suci; Sumarminingsih, Eni
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.32277

Abstract

Rainfall is a crucial factor in water resource management and disaster mitigation. This study develops a rainfall prediction model for DKI Jakarta using a Gated Recurrent Unit (GRU) with hyperparameter optimization to enhance prediction accuracy. Daily rainfall data is processed using a sliding window technique, where 30 days of historical data serve as input to predict rainfall on the 31st day. The model is trained with various configurations of batch sizes and the number of neurons in hidden layers to determine the optimal performance. The results of hyperparameter tuning show that the batch size configuration of 64, hidden layer 1 with 32 neurons, and hidden layer 2 with 128 neurons produces an MAE of 6.66 and an RMSE of 13.94. The model is quite good at capturing daily rainfall patterns but still has difficulty in predicting extreme rainfall spikes
Enhancing Binary Classification Performance in Biomedical Datasets: Regularized ELM with SMOTE and Quantile Transforms Focused on Breast Cancer Analysis Aina, Brilliant Friezka; Kallista, Meta; Wibawa, Ig. Prasetya Dwi; Nugroho, Ginaldi Ari; Meiska, Ivana; Naf’an, Syifa Melinda
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.28785

Abstract

Using microarray datasets, this research investigation addresses the problem of unbalanced data in binary classification tasks. The objective is to increase classification performance by adding Extreme Learning Machine (ELM) regularization, as well as Synthetic Minority Over-sampling Technique (SMOTE) for data over-sampling and Quantile Transformer for data scaling. The study began with gathering important biological datasets from reputable sources such as UCI and Kaggle, including Pima Indian Diabetes, Heart Disease, and Wisconsin Breast Cancer. SMOTE was employed to solve the difficulty of data imbalance in the preparation of the dataset. The data was then separated into training (80%) and testing (20%) sets before being scaled using Quantile Transformation. To boost accuracy, ELMs were employed with an emphasis on introducing regularization techniques. Quantile Transforms are used to generate a Gaussian or uniform probability distribution from numerical input variables. Regularized ELM (R-ELM) surpasses ELM in terms of AUC, despite ELM's faster calculation time. The final selection of the regularization parameter (C) in R-ELM influences the model's performance and calculation time. Overall, R-ELM with SMOTE produces encouraging results when it comes to effectively categorizing biological dataset properties. A subsequent investigation and validation of additional datasets, however, are necessary to establish its generalizability and robustness.
Modeling Risk Factors of Acute Respiratory Infections using Logistic Regression and Multivariate Adaptive Regression Splines Kurniawan, Ardi; Fauziah, Nathania; Mahadesyawardani, Arinda; Gunawan, Syifa’ Azizah Putri; Anggakusuma, Aurellia Calista
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33833

Abstract

Acute Respiratory Infections (ARI) remain a leading cause of morbidity among toddlers, partic ularly in regions with limited healthcare access. This study aimed to model the risk factors of ARI in toddlers using Binary Logistic Regression and Multivariate Adaptive Regression Splines (MARS). Using secondary data from Southeast Aceh, seven predictor variables were analyzed, including ma ternal characteristics, breastfeeding status, and household conditions. Both models were statisti cally significant in identifying key predictors. Logistic regression showed superior performance with 86.96% accuracy, 85.00% precision, 91.89% recall, 81.25% specificity, and 88.30% F1-score. In contrast, MARS achieved a higher recall (97.30%) but lower specificity (62.50%), indicating higher sensitivity but a greater likelihood of false positives. Exclusive breastfeeding, home ventilation, and housing density were significant predictors in both models. Overall, logistic regression was found to be the more reliable and interpretable method, offering better balance in classification metrics. These f indings support the use of logistic regression for identifying ARI risk factors in similar contexts and contribute to improved data-driven public health strategies aimed at reducing ARI incidence among vulnerable populations.
Zero Inflated Negative Binomial (ZINB) Regression: Application to the Pneumonia Study and Simulation under Several Scenarios Salsabila, Santi Wahyu; Efendi, Achmad; Nurjannah, Nurjannah
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.32499

Abstract

This study aims at evaluating the performance of Zero Inflated Negative Binomial (ZINB) regression analysis using the Maximum Likelihood Estimation (MLE) approach through simulation study. The research data used are secondary data and simulations. Secondary data was obtained from the Ministry of Health of the Republic of Indonesia in 2023 regarding cases of under-five deaths due to pneumonia with a total of 38 samples. The simulation study is conducted to analyze the performance of ZINB regression based on various sample sizes and proportions of zero values. The results show that the ZINB regression model with the MLE approach produces parameter estimates that tend to be more sensitive to sample size, with improved performance at large sample sizes. Data with a large proportion of zeros reflects high variability as well as the presence of excess zeros, so the ZINB regression model can provide more stable and precise parameter estimates than those with a lower proportion of zeros. Therefore, the ZINB regression model is effective for data with a high proportion of zeros as it fits the characteristics of the data distribution, especially in cases of under-five deaths due to pneumonia.

Page 36 of 44 | Total Record : 438

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