Jurnal Matematika, Statistika dan Komputasi
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Skin Brightening Effects of Ascorbic Acid with ACTISOLV™ Integration: A Longitudinal Analysis Using Repeated Measures ANOVA
Full text linkAscorbic Acid is a well-established active ingredient recognized for its efficacy in skin brightening and its antioxidant properties. However, its low chemical stability in cosmetic formulations remains a significant limitation. In response to this challenge, the patent-pending ACTISOLV™ formulation technology has been developed to enhance the stability of Ascorbic Acid, improving its resistance to oxidation and effectiveness in inhibiting melanin production. This study contributes to the advancement of sustainable cosmetic science through the development of more stable, eco-friendly, and sustainable skincare products. This study aimed to evaluate the longitudinal effects of a cream containing 20% Ascorbic Acid formulated with ACTISOLV™ on skin brightness. This study used longitudinal experimental data analyzed by Repeated Measures ANOVA. The results demonstrated a statistically significant increase in skin brightness over time (p-value = 0.000 < 0.05). Posthoc analysis revealed that skin brightness at weeks 6 and 12 differed significantly from baseline. However, no significant difference was found between the control and treatment groups and no significant interaction was observed between time and treatment group. These findings suggest that the observed improvement in skin brightness occurred similarly in both groups, indicating no additional effect attributable to the test formulation
Random Forest vs Elastic-Net Penalized Logistic Regression for Patient Discharge Classification in BPJS Primary Care
Full text linkThis study analyzes and compares Random Forest and Penalized Logistic Regression (Elastic Net, SAGA solver) for classifying patient discharge status at BPJS Kesehatan primary care facilities (FKTP). The large-scale dataset consists entirely of nominal predictors with class imbalance (~64.9% majority). The experimental design applies an 80/20 train–test split, one-hot encoding, and class_weight = balanced for both models. Hyperparameters are tuned via a staged coarse→fine randomized search with a local-optimum convergence rule (improvement threshold ε = 1e−6, patience = 10), followed by 10-fold cross-validation for internal validation and final testing on the hold-out set. We evaluate three primary metrics: F1-Score, Precision–Recall AUC (PR-AUC), and Brier Score. On the test set, Random Forest attains F1 = 0.996679, PR-AUC = 0.999933, and Brier = 0.002646; Penalized Logistic Regression attains F1 = 0.996676, PR-AUC = 0.999928, and Brier = 0.002017. The near-identical F1 and PR-AUC indicate comparable discrimination between methods, while the lower Brier Score for Penalized Logistic Regression demonstrates superior probability calibration. Overall, both approaches lie on the same performance plateau for discrimination, with a consistent calibration advantage for Penalized Logistic Regression; method choice can thus be guided by whether operational needs prioritize calibrated probabilities or flexible non-linear decision boundaries
Mathematics Model SAHTR for the Number of Drug Abusers with Economic and Educational Factors
Full text linkThis study develops a mathematical model of drug abuse involving susceptible (S), light users (A), heavy users (H), treatment (T), and recovered (R) compartments, incorporating economic and educational factors. The analysis includes determining equilibrium points, assessing their stability, calculating the basic reproduction number, and performing numerical simulations using the Runge–Kutta Fehlberg method. Results show that the model yields two equilibrium points: drug-free and endemic. Both are stable when the inflow rate into the light-user compartment—affected by effective contact rate, anti-drug campaign effectiveness, and economic conditions—exceeds the outflow rate. Numerical simulations confirm the analytical findings and illustrate that reducing interactions between vulnerable individuals and drug users, strengthening anti-drug campaigns, and improving economic conditions can diminish the potential spread of drug abuse
Forecasting The Number of ASEAN Tourists in Indonesia: The Impact of The COVID-19 Pandemic Using Intervention Analysis
Full text linkThe COVID-19 pandemic has had a significant impact on Indonesia’s tourism sector, particularly on the number of tourist arrivals from ASEAN countries. International travel restrictions led to a drastic decline in visitor numbers. This study aims to forecast the number of ASEAN tourists visiting Indonesia using an intervention analysis based on the Autoregressive Integrated Moving Average (ARIMA) model to capture both the pandemic shock and the subsequent recovery phase. The data used are secondary data from Statistics Indonesia (BPS) covering the period January 2017–November 2024, with the training data divided into three phases: the pre-pandemic period (January 2017–January 2020), Intervention I or the pandemic period (February 2020–April 2022), and Intervention II or the recovery period (May 2022–December 2023). Testing data are used to evaluate forecasting performance for the period January 2024–November 2024. The results show that the ARIMA(2,1,0) model with a step-type intervention successfully captures significant changes in the data pattern, yielding a Mean Absolute Percentage Error (MAPE) of 14.91% on the training data—an improvement over both the non-intervention model (MAPE 86.31%) and the first intervention model (MAPE 56.68%). On the testing data, the model achieves even higher accuracy with a MAPE of 8.21%, indicating that the intervention model effectively represents the dynamics of the pandemic impact and the subsequent recovery
A Study of (R,S)-Bimodules Homomorphisms
No full textThis paper discusses the generalization of the fundamental theorems of -module homomorphisms to the structure of -bimodules, where and are rings with identity. The study begins with a review of the definitions, properties, and types of -bimodule homomorphisms. Subsequently, three fundamental theorems of -module homomorphisms are generalized to the -bimodule setting. The results show that the fundamental structures and relationships in module theory can be naturally extended to bimodules by considering the actions of two rings that are compatible with the bimodule operations. This generalization provides a broader framework for studying algebraic structures involving two interacting ring actions.This paper discusses the generalization of the fundamental theorems of -module homomorphisms to the structure of -bimodules, where and are rings with identity. The study begins with a review of the definitions, properties, and types of -bimodule homomorphisms. Subsequently, three fundamental theorems of -module homomorphisms are generalized to the -bimodule setting. The results show that the fundamental structures and relationships in module theory can be naturally extended to bimodules by considering the actions of two rings that are compatible with the bimodule operations. This generalization provides a broader framework for studying algebraic structures involving two interacting ring actions
Small Area Estimation for Gross Enrollment Rate at the College Level Using a Hierarchical Bayes Approach
Full text linkQuality education is one of the goals of the Sustainable Development Goals (SDGs) aimed at improving human resources. According to the March 2023 Susenas, participation at the college level has the lowest Gross Enrollment Rate (GER), and Kepulauan Bangka Belitung Province has the lowest GER at the college level in Indonesia. The March 2023 Susenas data indicates that four of the seven districts and cities in Kepulauan Bangka Belitung Province still have estimated GER values at the college level with insufficient precision. Therefore, to increase precision, indirect small area estimation (SAE) methods are required using auxiliary variables derived from Podes 2021. The research results show that SAE Hierarchical Bayes (HB) estimation using the beta distribution approach produces the best estimates compared to other methods for estimating GER at the college level
Poisson-Exponential Distribution Approach to Survival Analysis of Right-Censored Data of Lung Cancer Patients
Full text linkSurvival analysis of lung cancer patients is essential for understanding the dynamics of their survival probabilities over time. The Poisson–Exponential (PE) distribution is particularly relevant for data involving complementary risks and right-censoring, and it provides a framework for comparing different parameter estimation approaches. This study aims to estimate the parameters of the PE distribution for the survival times of lung cancer patients treated at Dr. Wahidin Sudirohusodo Hospital, Makassar, in 2015, and to compare the performance of two estimation methods: Maximum Likelihood Estimation (MLE) and Maximum Product Spacing (MPS). Parameter estimation was conducted numerically using the Newton–Raphson algorithm, resulting in and . The survival probabilities decline as survival time increases, and both the PE–MLE and PE–MPS curves closely follow the Kaplan–Meier estimator. All information criteria indicate that MPS outperforms MLE, as reflected by a higher log-likelihood and lower AIC, AICc, and CAIC values. These findings demonstrate that the PE distribution is suitable for modeling the survival dynamics of lung cancer patients, with MPS identified as the most appropriate parameter estimation method for the analyzed dataset
Application of Small Area Estimation for Global Hunger Index at Regency/Municipality Level in Papua Island
Full text linkReducing hunger is one of the primary targets of the Sustainable Development Goals (SDGs), particularly Goal 2: Zero Hunger. The Global Hunger Index (GHI) is a key indicator used to measure hunger, comprising four components: the prevalence of undernourishment (PoU), child mortality rate, child stunting, and wasting. While PoU and child mortality data are available at the district/city level across Indonesia, limited data on stunting and wasting in several makes it difficult to calculate the GHI at the local level. Data limitations hinder the formulation of locally targeted policies. This study aims GHI in Papua Province using the Small Area Estimation (SAE) approach. Data sources include the 2023 Indonesia Health Survey and Podes 2021. , while wasting is estimated using the Hierarchical Bayes Beta approach. that SAE improves estimation precision compared to direct estimation, as reflec by . Estimates reveal GHI may vary in category between serious to extremely alarming, with Jayapura City having the lowest and Dogiyai as the highest GHI in Papua.
Geometric Anisotropic Semivariogram Modelling of Hotspot Confidence Levels in South Matan Hilir Subdistrict
Full text linkThe purpose of this research is to apply geometric anisotropic semivariogram modelling to confidence level of hotspots in South Matan Hilir Subdistrict, Ketapang Regency. The confidence level of hotspot can be used as an indicator of the likelihood of forest and land fires. A higher confidence level indicates a greater certainty that a fire has actually occurred at the hotspot location. The hotspot confidence level is spatial data because it is a random variable with an index location; therefore, the relationships among locations can be represented using a semivariogram model. A geometric anisotropic semivariogram model was employed in this study since the influence of direction exists in the distribution of hotspots. The results present that the exponential semivariogram model is the most suitable to represent the data, with the strongest spatial influence occurring in the north-south direction. Moreover, spatial dependence remains significant at a distance of 0.02027
Rainfall Forecasting Using Gaussian Process Regression with Brownian Motion Prior (Case Study: Special Region of Yogyakarta Province)
Full text linkClimate variability significantly impacts the agricultural sector, necessitating accurate forecasting methods to support agricultural planning. This study aims to develop a rainfall forecasting model using the Gaussian Process Regression (GPR) method with Brownian motion prior. Monthly climate data from the Yogyakarta Geophysics Station for the period January 2015 to December 2024 were utilized, comprising predictor variables (air humidity and wind speed) and response variable (rainfall). The posterior GPR model was developed for parameter estimation using the marginal log-likelihood approach, with missing data handled through seasonal mean imputation that preserves temporal patterns. The results demonstrate that the GPR model achieves reasonable forecasting performance with a Mean Absolute Percentage Error (MAPE) of 36.84% and strong correlation (r = 0.94) between predicted and actual values. The highest predicted rainfall occurred in March 2024 (20.148 mm) and the lowest in June 2024 (0.022 mm), consistent with the seasonal patterns of Indonesia\u27s tropical climate