CAUCHY: Jurnal Matematika Murni dan Aplikasi
CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI p-ISSN: 2086-0382 | e-ISSN: 2477-3344 (BRIN | ISSN Portal) CAUCHY: Jurnal Matematika Murni dan Aplikasi is an open-access, peer-reviewed journal published twice a year (May and November) by the Department of Mathematics, Faculty of Science and Technology, Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia. The journal is accredited at SINTA 2 by the Ministry of Research and Technology / National Agency for Research and Innovation, Republic of Indonesia (Decree No. 177/E/KPT/2024), valid from May 2023 to May 2028. CAUCHY welcomes high-quality submissions of original research articles, comprehensive literature reviews, and special-topic contributions in pure and applied mathematics. All manuscripts must be written in English and prepared using the official CAUCHY LaTeX template available on Overleaf. Aims and Scope CAUCHY publishes manuscripts that demonstrate clear mathematical novelty and methodological rigor. The journal prioritizes contributions that present new mathematical results, develop or analyze mathematical models with sound theoretical justification, or propose computational and algorithmic methods supported by rigorous mathematical analysis such as correctness, convergence, stability, complexity, or reproducibility. The scope of the journal covers, but is not limited to, the following areas: Analysis (real analysis, functional analysis, applied analysis) Algebra and number theory Geometry and topology Discrete mathematics and graph theory Optimization and operations research Probability and mathematical statistics Dynamical systems and control Mathematical modeling with rigorous formulation and validation Computational mathematics and scientific computing Fuzzy systems and uncertainty modeling Actuarial and financial mathematics Out of Scope CAUCHY maintains a strong mathematical emphasis. Manuscripts will be considered out of scope and may be desk-rejected if they primarily fall into one or more of the following categories: Application-only case studies or implementations that do not present a clear mathematical model, theoretical analysis, or mathematically justified methodology. Machine learning / data-driven papers that mainly report benchmark results or metric comparisons (e.g., accuracy, F1-score, AUC) without explicit mathematical novelty, analytical justification, or substantive methodological contribution. Routine use of standard techniques with minimal originality (e.g., applying commonly used models to a new dataset) and without a meaningful mathematical development, analysis, or insight. Software or system papers that focus on implementation details, engineering features, or interfaces without rigorous mathematical content (e.g., correctness proof, convergence/stability analysis, complexity analysis, or error bounds). Surveys or review manuscripts that are primarily narrative/tutorial, lack a systematic review protocol, provide limited critical synthesis, or do not clearly articulate research gaps and future directions. Manuscripts with insufficient rigor or transparency to support verification and reproducibility (e.g., incomplete method description, unclear assumptions, unverifiable claims). Manuscript Requirements Submitted manuscripts must be original, clearly written, and methodologically rigorous, with sufficient detail to support verification and reproducibility. All claims should be supported by logical reasoning and appropriate evidence. The recommended manuscript length is 10–16 pages, including figures, tables, and references. Literature review articles may extend up to 25 pages and should include at least 25 references, with a minimum of 80% drawn from peer-reviewed journals published within the last five years. Journal Updates 2009–2012: Cover changed from yellow to purple 2013–2015: Two-column layout adopted 2016–present: One-column layout; all submissions in English Vol. 4 No. 2 (2016): New article layout introduced Starting from Vol. 10 No. 2 (2025): New LaTeX template in use. See the template at Overleaf . Submission guidelines and detailed author instructions are available here.
Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang
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Cluster Analysis of Cities/Districts in West Kalimantan based on Stunting Response Indicators using the Calinski Harabasz Index
The stunting rate in West Kalimantan has reached 27% , mainly due to the government’s inability to prioritise regions for essential services and education, especially for adolescents and pregnant women. This study aims to explain the role of modified K-Means and CHI methods in forming optimal clusters and interpreting their conditions. Eight research variables, sourced from BPS and SIGA in 2023, were used: number of adolescents receiving counselling, informed consents, complication cases, aslokon expenditure, aslokon stock, population growth rate, population density, and life expectancy. Clustering was done by analysing the data for each variable and the characteristics of the objects using the Euclidean distance, determining the centroid values, and iterating until the results stabilised. The clusters were evaluated from one to seven to find the optimal amount using CHI. The results identified five clusters: cluster 1 (relatively poor, three objects), cluster 2 (inferior, four objects), cluster 3 (good, three objects), cluster 4 (exquisite, three objects) and cluster 5 (good, one object).
Copyright (c) 2026 Tegar Rama Priyatna, Yundari Yundari, Nur'ainul Miftahul Huda https://creativecommons.org/licenses/by-sa/4.0
Interpolation of Fire Radiative Power Based on GSTAR Model Predictions with Queen Contiguity Weights Using Ordinary Kriging
Forest fires are a persistent environmental issue in West Kalimantan, Indonesia, driven by both natural and human factors. Fire Radiative Power (FRP) serves as a vital indicator for assessing wildfire intensity and energy release. This study aims to model and predict the spatial temporal dynamics of FRP using the Generalized Space Time Autoregressive [GSTAR(1;1)] model combined with Ordinary Kriging interpolation. The dataset covers West Kalimantan from July 2024 to September 2025, comprising four attributes: observation date, longitude, latitude, and FRP value. Data filtering was applied from the national to provincial level, focusing on three regencies Sanggau, Sekadau, and Ketapang across 14 sub-districts represented by a 1.25×1.25 grid. The data consisted of 65 weekly observations, with 61 used for training and 4 for testing. The GSTAR(1;1) model with a spatial area-based framework achieved an optimal MAPE of 12.63% and satisfied the white noise assumption, indicating reliable performance. Predictions for October 2025 indicated relatively stable fire intensity, with a slight FRP decrease in Nanga Tayap and Sandai during the final week. Overall, the integrated GSTAR–Kriging framework effectively captured both temporal and spatial variations, supporting improved fire risk assessment and regional decision making for wildfire management in West Kalimantan.
Copyright (c) 2025 Gita Fitriyana, Nurfitri Imro'ah, Nur’ainul Miftahul Huda https://creativecommons.org/licenses/by-sa/4.0
Implementation of DBSCAN and K-MEANS++ Methods for Flood Vulnerability Cluster Mapping in East Java Province, 2024
Flood disasters remain one of the most frequent natural hazards in Indonesia, particularly in East Java Province, where variations in rainfall, population density, and land use contribute to differing levels of flood vulnerability. Although numerous studies have explored flood susceptibility using geospatial and statistical models, comparative analyses of clustering algorithms specifically designed for complex regional topographies remain limited. This study aims to implement and compare two clustering algorithms Density Based Spatial Clustering of Applications with Noise (DBSCAN) and K-Means++ to map flood vulnerability patterns across the region. The urgency of this study lies in the province’s increasing flood frequency and its impact on infrastructure and livelihoods, which demand an adaptive and data driven spatial analysis approach. DBSCAN was selected for its ability to detect irregular, non-linear cluster shapes, while K-Means++ offers efficiency and stability through improved centroid initialization. The dataset includes hydrometeorological and socio-environmental indicators such as rainfall, elevation, slope, land cover, and population density. Clustering performance was assessed using the Silhouette Index (SI) and Davies Bouldin Index (DBI). Results showed that DBSCAN achieved a higher SI (0.3266) compared to K-Means++ (0.2453), indicating better cohesion and separation. Spatially, DBSCAN generated four distinct clusters corresponding to actual flood prone areas, particularly in Jember, Lumajang, Pasuruan, and Sidoarjo. These findings suggest that density-based clustering provides a more reliable representation of heterogeneous spatial flood patterns, supporting local governments in targeted mitigation planning and regional disaster risk management.
Copyright (c) 2025 A'yunin Sofro https://creativecommons.org/licenses/by-sa/4.0
Triple-Mutation Bat Algorithm–Optimized Extreme Learning Machine for Fetal Health Classification
Fetal health assessment is crucial for preventing perinatal risks; however, the manual interpretation of cardiotocography (CTG) signals remains susceptible to variability and diagnostic delays. To address this challenge, this study aims to develop an accurate and computationally efficient model for automated fetal health classification. This study proposes a hybrid intelligent model named TMBA–ELM (Extreme Learning Machine parameters optimized with Triple Mutation Bat Algorithm) for accurate and efficient classification of fetal health conditions. The purpose of this research is to improve the diagnostic reliability of CTG data analysis while maintaining low computational complexity. The proposed TMBA–ELM integrates the adaptive exploration–exploitation mechanism of the Tuned Modified Bat Algorithm (BA) with the fast learning capability of the Extreme Learning Machine (ELM) to optimize both the hidden neuron size and the activation function. Three adaptive mutation strategies: Cauchy, Gaussian, and position modification—are applied to enhance convergence and population diversity. The model was evaluated using an imbalanced CTG dataset containing 2,126 samples classified as Normal, Suspect, or Pathological, and benchmarked against BA-ELM (ELM parameters tunned with BA), EMD-FA-ELM (ELM parameters tunned with firefly algorithm and the data decompositioned by empirical mode decomposition), and PSO-EM-ELM (error minimized ELM parameters tunned with particle swarm optimization) using five performance metrics: accuracy, precision, recall, F1-score, and computation time. Experimental results show that TMBA–ELM achieve high performance with 91.4% accuracy, 82.8% precision, 77.77% recall, and 79.93% F1-score, while maintaining the high computation time (164.23 second) with moderate stability (deviation = 12.76 second). The model also demonstrates improved recall for minority classes, confirming robustness in handling data imbalance. Although have bad computational efficiency, TMBA-ELM offers highest recall and F1-score, making it suitable for real-time fetal monitoring. The originality of this study lies in integrating triple adaptive mutation strategies within the Bat Algorithm to optimize ELM parameters.
Copyright (c) 2025 Prabowo Wisnumurti, Syaiful Anam, Mohammad Muslikh https://creativecommons.org/licenses/by-sa/4.0
University Scheduling Optimization Using Integer Programming: A Case Study
This paper presents an Integer Linear Programming (ILP) model to construct a weekly lecture timetable for the Mathematics Study Program at HKBP Nommensen University, Pematangsiantar. The case study comprises 25 courses, three rooms (RK~11, RK~12, and LAB~1), five teaching days (Monday--Friday), and 13 time periods per day. The model enforces hard constraints on room, lecturer, and cohort non-overlap; consecutive periods according to credit load; room-type compatibility between theory and practicum sessions; and an institutional worship-time restriction on Tuesday. Lecturers' availability is represented by a binary acceptance matrix collected at the course level, and rejected time periods are penalized in the objective. The ILP is implemented in Python using the PuLP (Python Linear Programming) library and solved with the CBC (Coin-or Branch and Cut) solver. For the real instance, the solver returns an optimal solution with objective value $Z^*=0$ (no scheduled period falls in a rejected slot) in approximately 94 seconds. The resulting timetable is conflict-free and operationally interpretable, with a weekly room-time utilization of about 31.3\%. To support verification and communication to stakeholders, the paper also provides a heatmap of the acceptance matrix and a graphical timetable by room and day.
Copyright (c) 2025 Gayus Simarmata, Rajainal Saragih, Anil Hakim Syofra https://creativecommons.org/licenses/by-sa/4.0
Nasdaq Inc. Stock Price (NDAQ) Prediction Due to Trump's Tariff Policy Using Pulse Function Intervention Analysis
Nasdaq Inc. (NDAQ) is one of the leading stock exchanges in the United States, ranking second globally after the New York Stock Exchange (NYSE) based on market capitalization. As a highly dynamic and information-sensitive market, Nasdaq Inc. stock prices respond quickly to internal corporate conditions and external macroeconomic or policy changes. One notable event affecting market stability was President Donald Trump's import tariff policy, aimed at protecting U.S. industries from foreign competition, particularly Chinese imports. The implementation of this policy triggered significant volatility, including a sharp decline in Nasdaq Inc. stock prices on March 2, 2025. This study examines the impact of this policy on Nasdaq Inc. stock movements using the ARIMA(0,2,1) model with an intervention of order b=0, r=1, and s=0. The results show that all model parameters are statistically significant and produce accurate forecasts, with a MAPE of 2.19%, an RMSE of 5.98766, and an MAE of 2.05232. These findings indicate that intervention analysis effectively captures the impact of import tariff policies on stock market dynamics and provides valuable insights for investors and policymakers in anticipating market fluctuations driven by global economic policy changes.
Copyright (c) 2026 Kimberly Maserati Siagian https://creativecommons.org/licenses/by-sa/4.0
Quadratic And Truncated Spline Structural Equation Modeling With Double Bootstrap In The Waste Management Economy
This study aims to develop and apply a semiparametric Structural Equation Modeling (SEM) approach that integrates quadratic and truncated spline estimation, enhanced with a double bootstrap resampling method. The semiparametric SEM is employed to overcome the limitations of conventional SEM, particularly when data complexity and social behavior do not fully satisfy linearity assumptions. The model was applied to analyze public mindset and participation in waste management based on the 3R (Reduce, Reuse, Recycle) principle, focusing on the role of waste banks in optimizing the economic value of waste. The truncated spline approach enables flexible modeling of non-linear relationships among latent variables, while the quadratic term captures global curvature effects. Furthermore, the double bootstrap improves estimation precision by reducing bias and refining confidence intervals. The simulation and empirical results demonstrate that the semiparametric SEM with double bootstrap produces higher model stability and more accurate parameter estimation compared to the single bootstrap approach. This method provides a robust analytical framework for modeling complex social phenomena such as community-based waste management.
Copyright (c) 2026 Anggun Fadhila Rizqia, Solimun Solimun, Nurjannah Nurjannah, Kamelia Hidayat, Fachira Haneinanda Junianto https://creativecommons.org/licenses/by-sa/4.0
Sensitivity Analysis of the SIRD Model for TB-Related Life Insurance Claims in Southeast Sulawesi
Tuberculosis (TB) remains a major public health challenge in Indonesia and generates significant mortality-related risk for the life insurance sector. This study develops an integrated Susceptible–Infected–Recovered–Deceased (SIRD) model to analyze TB transmission dynamics in Southeast Sulawesi and to estimate related life insurance claims. The model is calibrated using regional TB data from 2021–2023 and validated against 2024 observations. Analytical results include equilibrium analysis and the basic reproduction number, while long-term dynamics are examined through scenario-based simulations. Epidemiological outcomes are translated into actuarial projections by converting cumulative TB-related deaths into annual incremental deaths and expected insurance claims under optimistic, baseline, and pessimistic scenarios. Parameter sensitivity is assessed using Latin Hypercube Sampling and Partial Rank Correlation Coefficients. The results show that the transmission rate is the most influential determinant of the present value of TB-related insurance claims, followed by the recovery rate, whereas TB-induced mortality has a smaller but significant effect. These findings highlight that reducing transmission and improving treatment effectiveness can simultaneously mitigate public health impacts and lower long-term insurance liabilities, demonstrating the relevance of integrating epidemiological modeling with actuarial risk assessment.
Copyright (c) 2026 Asriani Arsita Asni, Fitriyani Fitriyani, Ira Puspita https://creativecommons.org/licenses/by-sa/4.0
b-Chromatic Number of Tree Graph Families
Tree graph is a connected graph and has no circuits. Tree graphs used in this study include: broom graph, firework graph, banana tree graph, centipede graph, E graph, and double star graph. Graph coloring is the process of giving color to graph elements with the rule that neighboring elements must not have the same color and the number of colors used must be as minimal as possible. b-Coloring of a graph G is a coloring of the vertices of G such that each color class has at least one vertex adjacent to all other color classes. The b-Chromatic number of a graph G is denoted by φ (G), is the largest integer k such that G has a b-coloring with k colors. The limit of b-coloring of graph G with maximum degree ∆(G) is as follows. χ(G)≤φ(G)≤∆(G)+1.χ(G) is the chromatic number of a graph G where χ(G) is the minimum value of the color required for proper coloring of graph G. While ∆(G) is the maximum degree of the vertices in graph G. This study uses an exploratory research type with axiomatic deductive method and pattern detection method. Based on the results of this study, the results of the b-coloring analysis on the tree graph family are known. The results of this study are expected to be used as study material and development of scientific knowledge related to b-coloring of other graphs
Copyright (c) 2026 Arika Indah Kristiana, Rafiantika Megahnia Prihandini, Lusita Risma Dana, Edy Wihardjo, Robiatul Adawiyah https://creativecommons.org/licenses/by-sa/4.0
Enhancing Spatio-Temporal PCA with FASTMCD for Climate Comfort Assessment
This study presents a robust formulation of the Spatio-Temporal Principal Component Analysis (STPCA) by integrating the Fast Minimum Covariance Determinant (FASTMCD) estimator into the spatio-temporal decomposition framework. Unlike classical STPCA—which constructs the spatio-temporal matrix from sample-based means and is therefore highly sensitive to extreme observations—the proposed STPCA–FASTMCD replaces the classical mean and scatter structure with robust estimates derived from FASTMCD. The method incorporates functional Fourier-based temporal smoothing and an inverse power–distance spatial weight matrix to better capture the underlying spatio-temporal patterns. Monthly climate data (thermal comfort, cloud cover, rainfall, and wind speed) from 24 monitoring locations in Bali during 2010–2019 are analyzed. Performance is evaluated using mean-shift analysis, eigenvalue-stability assessment, and eigenvector perturbation diagnostics. The classical STPCA produces inflated and unstable leading components, with the first eigenvalue reaching 63.36, whereas STPCA–FASTMCD reduces this value to 37.79 and yields smoother, more coherent spatial loading patterns. The robust STPC1 reveals a clear thermal–wind variability mode, enhancing the interpretability of spatial gradients relevant to climate comfort. Overall, the proposed formulation substantially improves the stability and climatic relevance of dominant spatio-temporal modes, providing a more reliable foundation for climate comfort assessment in Bali.
Copyright (c) 2026 Agus Yarcana, Henny Pramoedyo, Suci Astutik https://creativecommons.org/licenses/by-sa/4.0
Implementation of DenseNet121 Based on Convolutional Neural1 Network with Geometric Augmentation for Breast Cancer2 Histopathology Image Classification
The development of a robust deep learning architecture that is not easily affected by overfitting is an important factor in improving the performance of medical image classification systems. This study aims to assess the ability of the DenseNet121 architecture to classify histopathological images into two categories. The model utilizes pre-trained weights from ImageNet and is adjusted through fine-tuning, while geometric data augmentation techniques are performed to increase sample variation. The training process utilizes the AdamW optimizer and the Binary Cross-Entropy loss function, with performance assessment using binary classification metrics. The test results show that DenseNet121 achieved a training accuracy of 98.96%, a validation accuracy of 97.72%, and a testing accuracy of 97.09%, indicating consistent performance at each stage and no signs of overfitting. This finding indicates that DenseNet121 has great potential as an effective structure in histopathological image classification systems.
Copyright (c) 2026 Nabilah Evi Ariani https://creativecommons.org/licenses/by-sa/4.0
Management in Design-Build Projects by Construction Management Consultants: SEM-PLS And IPMA Approaches
This study investigates the factors influencing the potential audit findings in Design and Build (DB) construction projects in Indonesia, employing Structural Equation Modelling–Partial Least Squares (SEM-PLS) and Importance–Performance Map Analysis (IPMA). Data were collected from 100 respondents, including project owners, contractors, and construction management consultants. The SEM-PLS results reveal that Integrity & Compliance Culture (β = –0.169, p = 0.045) and Administrative & Financial Compliance (β = –0.193, p = 0.027) significantly reduce the probability of audit findings, while other technical factors such as planning, supervision, and team competence show no direct effect. IPMA highlights Integrity & Compliance Culture and Contract & Documentation Management as top improvement priorities. These findings demonstrate that governance and compliance dimensions are more critical than technical performance in shaping audit outcomes. Strengthening compliance culture, enhancing administrative transparency, and implementing robust contract management are therefore key strategies to minimize audit risks in DB projects. The study contributes to the applied statistics literature in construction management and offers practical insights for policymakers, contractors, and auditors aiming to achieve accountable and transparent infrastructure delivery in Indonesia.
Copyright (c) 2026 Al Dwi Kautzar, Mawardi Amin, Agus Suroso https://creativecommons.org/licenses/by-sa/4.0
A Study on Multi-Class Topic Prediction for E-commerce Review Data Using Ensemble Learning
The exponential growth of e-commerce platforms has generated massive volumes of unstruc tured user reviews, necessitating advanced automated analysis methodologies to extract actionable insights for strategic decision-making. This study addresses multi-class text classi f ication challenges by integrating BERTopic-based topic modeling with ensemble learning algorithms to analyze Indonesian e-commerce reviews. A dataset comprising 24,000 customer reviews from Google Play Store underwent systematic preprocessing and topic extraction using BERTopic, yielding eight distinct thematic clusters reflecting application performance, product quality, pricing, delivery logistics, and service reliability. The dataset exhibited severe class imbalance with an imbalance ratio of 65:1, where the dominant class represented 76.02% of instances while minority classes constituted less than 2.12%. Hybrid resampling techniques combining undersampling and oversampling successfully reduced the imbalance ratio to 1.4:1. TF-IDF vectorization transformed preprocessed text into numerical features, followed by supervised classification using CatBoost and Extra Trees classifiers optimized through randomized hyperparameter search with stratified k fold cross-validation. CatBoost demonstrated superior performance, achieving balanced accuracy of 0.829, recall of 0.829, and AUC of 0.965, attributed to its ordered boosting mechanism and capacity for handling categorical and imbalanced data. Independent validation of 2025 data confirmed robust gen eralization with prediction confidence exceeding 0.90, revealing significant temporal evolution in which product-related topics emerged dominant at 70.35%, pricing concerns increased from 6.58% to 16.57%, while application issues decreased from 76.02% to 2.51%. This research establishes a methodologically rigorous framework integrating unsupervised topic discovery with supervised ensemble classification, demonstrating computational efficiency while providing scalable solutions for automated review categorization.
Copyright (c) 2026 Kevin Alifviansyah https://creativecommons.org/licenses/by-sa/4.0
Modelling Factors Affecting the Middle Income Trap in Indonesia Using Generalized Additive Models (GAM)
Indonesia is currently facing a significant challenge known as the Middle Income Trap (MIT), a condition where economic growth stagnates after reaching middle-income status, hindering progress toward becoming a high-income country. This study aims to identify and model the socio-economic factors influencing MIT at the provincial level in Indonesia during the 2020–2023 period. The Generalized Additive Model (GAM) is employed to estimate nonlinear relationships between predictors and the response variable while capturing complex patterns in panel data. GRDP per capita is used as an indicator of MIT, with six predictor variables: life expectancy, poverty rate, informal employment share, secondary education completion rate, food insecurity prevalence, and population density. The results showed that the best model was obtained based on the minimum GCV and AIC values of the Gaussian family with an identity link function and 5 knot points with the highest correlation of 99,9%. Five variables show nonlinear effects, while food insecurity exhibits a significant negative linear impact. The findings provide a valuable reference for designing inclusive and adaptive eco nomic policies based on each region’s socio-economic characteristics to mitigate MIT risks and also supports the achievement of Sustainable Development Goal (SDG) 8, which promotes decent work and sustained economic growth.
Copyright (c) 2026 Dita Amelia, Suliyanto Suliyanto, Azizah Atsariyyah Zhafira, Aulia Ramadhanti, Billy Christandy Suyono, Firqa Aqila Hizbullah https://creativecommons.org/licenses/by-sa/4.0
Transmission Dynamics of Dengue Disease Incorporating Treatment, Mass Awareness, and Wolbachia Intervention
Dengue Hemorrhagic Fever (DHF) remains a serious global health threat, with transmission dynamics significantly influenced by vector control strategies and human behavior. This study constructs and analyzes a differential equation-based mathematical model to investigate dengue transmission dynamics by integrating three control strategies: medical treatment, mass awareness, and the release of Wolbachia-infected mosquitoes. The basic reproduction number (R0) is derived using the Next Generation Matrix (NGM) method as a threshold quantity for disease transmission. Simulation results demonstrate that when parameter values satisfy the condition R0 < 1, the system trajectories converge to the disease-free equilibrium, implying that the disease will be eliminated over time. Conversely, modifying parameters δ and p such that R0 > 1 results in system stability at the endemic equilibrium, indicating disease persistence within the population. This study concludes the importance of controlling these key parameters through integrated interventions to reduce the value of R0 to less than unity
Copyright (c) 2026 Budi Priyo Prawoto, Rafika Nanda Agustina https://creativecommons.org/licenses/by-sa/4.0
Modeling the Dynamics of Tuberculosis-Diabetes Mellitus Coinfection with an Optimal Control Approach
Tuberculosis–Diabetes Mellitus (TB-DM) coinfection poses a significant public health challenge, contributing to increased morbidity, treatment failure, and healthcare costs. This study develops a mathematical model that stratifies TB infection into latent and active classes to examine the dynamics of TB–DM coinfection. The model is analyzed to determine the disease-free and endemic equilibrium points, supported by numerical evaluation using established parameter values. Furthermore, prevention strategies are assessed through an optimal control framework, formulated using Pontryagin’s Minimum Principle and validated through numerical simulations. The findings are expected to provide effective strategies to reduce TB-DM transmission and minimize optimal control costs, thereby supporting the development of improved public health policies.
Copyright (c) 2026 MUNA AFDI MUNIROH https://creativecommons.org/licenses/by-sa/4.0
Spatial Variation of HDI in East Java: A Tricube-Based Geographically Weighted Regression–Flower Pollination Algorithm Modeling Approach
Understanding spatial disparities in human development is essential for designing equitable development policies. This study examines the spatial variation of the Human Development Index (HDI) in East Java Province using an integrated Geographically Weighted Regression–Flower Pollination Algorithm (GWR--FPA) optimized with a Tricube kernel. The integration of GWR and FPA enables simultaneous spatial weighting and metaheuristic-based bandwidth optimization. Three predictors were analyzed: population size ($X_1$), literacy rate ($X_2$), and mean years of schooling ($X_3$). Statistical diagnostics indicated significant spatial autocorrelation and heteroskedasticity in the OLS residuals, justifying the use of a spatial modeling framework. The GWR estimates revealed strong spatial non-stationarity: $X_1$ showed no significant local effect, whereas educational factors ($X_2$ and $X_3$) were significant in all 38 districts and cities. The FPA optimization enhanced bandwidth selection, resulting in improved model fit. Model comparison based on AIC and AICc showed that the GWR--FPA--Tricube model achieved the lowest values (AIC = 135.8821; AICc = 137.0045), outperforming both global OLS and standard GWR. These findings demonstrate that education-related variables are the primary drivers of HDI variation in East Java, while demographic size contributes minimally. The optimized model provides a more accurate spatial representation of local development disparities, supporting targeted policy interventions and illustrating the effectiveness of integrating metaheuristic optimization within spatial regression.
Copyright (c) 2026 Friansyah Gani, Henny Pramoedyo, Henny Pramoedyo, Achmad Efendi, Achmad Efendi https://creativecommons.org/licenses/by-sa/4.0
Some Properties of Prime Graph of Cartesian Product of the Ring
The prime graph of the ring R, (PG(R)) is a graph which set of vertices consists of elements of R and two different vertices are adjacent if their product in the ring is zero. We study the prime graph of cartesian product of the ring Z_(p_1 )×Z_(p_2 ) for distinct prime numbers p_1 and p_2. We find that some properties of PG(Z_(p_1 )×Z_(p_2 ) ) such as order, size, the number of triangles, and Wiener. Further, we construct the line graph of PG(Z_(p_1 )×Z_(p_2 ) ) and calculate the order, size, and Wiener index of L(PG(Z_(p_1 )×Z_(p_2 ) )).
Copyright (c) 2026 Vira Hari Krisnawati, Noor Hidayat, Ayunda Faizatul Musyarrofah, Farah Maulidya Fatimah https://creativecommons.org/licenses/by-sa/4.0
Dynamic Analysis of a Predator–Prey Model with Group Defense in Prey and Cooperative Hunting in Predators
This article discusses a single-prey and single-predator model by incorporating two behavioral mechanisms, namely group defense in prey modeled through a Holling type IV response function and cooperative hunting in predators represented by a predation rate dependent on predator density. Through system analysis, three critical points were obtained, namely the total extinction point, the predator extinction point, and the interior point that describes the coexistence of both species. The total extinction point is always unstable, while the other two critical points are conditionally stable depending on the predator attack rate parameter. Numerical simulations in the form of phase portraits were obtained by varying the parameters related to the predator attack rate. The simulation results show double stability (bistability) when α = 3, where the system can lead to predator extinction or stable coexistence depending on the initial population conditions. Furthermore, numerical continuation was performed to track changes in equilibrium point stability. The results show a Hopf bifurcation at α = 0.4595, marked by a change in the stability of the interior point, a limit point bifurcation (saddle-node) at α = 0.0478 due to the merging of two interior equilibrium points, and a transcritical bifurcation at α = 3.0505, which shows an exchange of stability between equilibrium points.
Copyright (c) 2026 Dian Savitri https://creativecommons.org/licenses/by-sa/4.0
Sensitivity Analysis of a Tuberculosis Transmission Model with Incomplete Treatment
Tuberculosis (TB) remains a major global health concern due to its complex transmission dynamics and frequent treatment interruptions. This study utilizes a SEITR compartmental model to quantitatively analyze the spread and control of TB. The model calculates the basic reproduction number, disease-free equilibrium, and endemic equilibrium to evaluate system stability. Sensitivity analysis identifies key parameters influencing the infected population: effective contact rate, natural mortality rate, population recruitment rate, and treatment rate. Among these, the effective contact rate and natural mortality rate significantly impact disease persistence. The findings suggest that effective TB control can be achieved through early detection and isolation of infectious individuals, timely and proper treatment, improved indoor ventilation, and the consistent use of masks by active TB patients. This model-based approach offers empirical evidence to inform public health policies, highlighting critical intervention points to interrupt TB transmission and improve treatment outcomes.
Copyright (c) 2026 Joko Harianto, Diki Fernandi https://creativecommons.org/licenses/by-sa/4.0
Mathematical Modeling and Regime Dynamics of Ammonium Chloride Imports in Indonesia Using Threshold Vector Autoregressive Integrated (TVARI) Approach
Ammonium chloride plays an important role in Indonesia as a key raw material for Nitrogen, phosphorus, and potassium (NPK) fertilizers and various chemical industries. Despite its importance, domestic production remains limited, and the potential supply from by-product sources has not been utilized in a meaningful way. As a result, Indonesia depends heavily on imports that come mainly from a single country. This situation creates vulnerabilities in the industrial supply chain and highlights the need for a clearer understanding of how import volume and import value behave over time. This study offers a mathematical model that examines the joint movement of these two variables by using the Threshold Vector Autoregressive Integrated approach, commonly known as TVARI. The novelty of the study lies in its use of a nonlinear threshold structure to show how the system shifts between different market conditions. The model reveals that import behavior changes across regimes. When import growth is low, movements are shaped mostly by changes in import value. When growth becomes higher, the pattern reflects the stronger influence of supply conditions. A single linear model cannot fully explain these shifts. By presenting a mathematical description of these regime movements, the study enhances the understanding of the underlying dynamics of Indonesia’s industrial imports. The insights support data informed decisions in supply chain planning and relate to Sustainable Development Goal 9 (industry resilience) and Sustainable Development Goal 12 (efficient and responsible use of raw materials). Goal 8 of the Sustainable Development Agenda, which is to encourage stable and sustainable economic activity, is likewise aligned with the enhanced comprehension of market behavior.
Copyright (c) 2026 Carissa Egytia Widiantoro, Restu Arisanti, Gumgum Darmawan https://creativecommons.org/licenses/by-sa/4.0
ResNet-50 and ResNeXt-50 for Multiclass Classification of Chronic Wound Images under Gaussian Blur
Chronic wound image classification is important for supporting the assessment of conditions such as diabetic foot ulcers (DFU) and pressure ulcers (PU). While convolutional neural network (CNN)–based approaches have shown promising results, most previous studies focus on binary classification and rarely evaluate robustness in multiclass chronic wound scenarios. This study investigates multiclass classification of chronic wound images, distinguishing DFU, PU, and Normal Skin, using ResNet-50 and ResNeXt-50 architectures. A total of 2,146 publicly available images were stratified at the image level into training (70%), validation (15%), and test (15%) sets. Both models were trained under an identical configuration using data augmentation and class-weighted loss. On clean test images, ResNet-50 and ResNeXt-50 achieved strong and comparable performance, with accuracies of 0.9877 and 0.9938 and macro-averaged F1-scores of 0.9866 and 0.9928, respectively. Robustness was evaluated by applying Gaussian blur at the inference stage to simulate image defocus. Under stronger blur (σ = 2.0), ResNeXt-50 maintained higher performance (accuracy 0.9723, macro-F1 0.9679) than ResNet-50 (accuracy 0.9200, macro-F1 0.9123). These results highlight the contribution of this study in evaluating robustness to blur in multiclass chronic wound image classification, while emphasizing that robustness is limited to resistance against image blur or defocus.
Copyright (c) 2026 Reynaldi Ikbar Andhika https://creativecommons.org/licenses/by-sa/4.0
Spatial Analysis of Child Violence in West Java Using a Geographically Weighted Negative Binomial Regression Approach
Kekerasan terhadap anak tetap menjadi isu kritis di Indonesia, dengan Jawa Barat secara konsisten melaporkan jumlah kasus yang tinggi. Studi ini meneliti faktor-faktor sosioekonomi yang memengaruhi jumlah kasus kekerasan terhadap anak di 27 kabupaten dan kota, dengan fokus pada tingkat kemiskinan, rata-rata tahun sekolah, tingkat perceraian, Tingkat Partisipasi Angkatan Kerja (PFPR), dan Tingkat Pengangguran Terbuka (OUR). Tes diagnostik mengidentifikasi heterogenitas spasial dan overdispersi, yang mendukung penggunaan model Regresi Binomial Negatif Berbobot Geografis (GWNBR). Model GWNBR mengungguli model Poisson dan Binomial Negatif global, yang ditunjukkan oleh nilai Akaike Information Criterion (AIC) terendah sebesar 193,23, yang menunjukkan kemampuannya untuk menangani data hitungan spasial yang overdispersi. Hasil penelitian mengungkapkan variasi spasial yang substansial dalam pengaruh faktor-faktor sosioekonomi. Rata-rata tahun sekolah dan tingkat perceraian signifikan di sebagian besar wilayah, sementara Kota Bandung adalah satu-satunya wilayah di mana kelima prediktor tersebut signifikan. Temuan ini menunjukkan struktur risiko yang bervariasi secara geografis yang tidak dapat ditangkap oleh model global. Studi ini menyoroti pentingnya pemodelan adaptif spasial dalam analisis sosial dan demografis serta menyarankan agar karakteristik spesifik wilayah dipertimbangkan dalam perumusan kebijakan. Temuan ini mendukung strategi perlindungan anak yang terarah dan selaras dengan SDG 3, SDG 4, dan SDG 16.
Copyright (c) 2026 Suliyanto Suliyanto, Dita Amelia, Lisa Amanda Putri, Aurellia Calista Anggakusuma https://creativecommons.org/licenses/by-sa/4.0
Numerical Pricing of European Stock Options Using Black-Scholes Interval Model
This study presents the numerical implementation of the Black-Scholes interval model for determining the price of European call options under parameter uncertainty. Unlike the classic Black-Scholes model, which assumes fixed volatility and risk-free interest rates, this study represents both parameters as limited intervals constructed based on historical data. Daily stock closing prices obtained from Yahoo Finance and risk-free interest rate data from the Federal Reserve Bank of St. Louis were used to define the parameter ranges. The interval Black-Scholes model was discretized in the asset price and time domains and solved numerically by formulating an optimization problem that minimizes the residual error of the interval partial differential equation with terminal payoff constraints. The numerical solution produces lower and upper bounds for option prices in the specified domain. Simulation results show that classic Black-Scholes option prices lie within the calculated interval price bounds, demonstrating numerical consistency between the deterministic and interval formulations.This study provides a structured numerical case study showing how the Black-Scholes interval model can be implemented to generate option price bounds under bounded parameter uncertainty
Copyright (c) 2026 Muhammad Iqbal Aditama, Rudianto Artiono https://creativecommons.org/licenses/by-sa/4.0
Stability Analysis of a Three-Trophic Rice Ecosystem with Holling II and Crowley–Martin Responses
This study examines three-trophic-level ecological dynamics in rice field ecosystems involving rice as the producer, brown planthoppers (Nilaparvata lugens) as herbivores, and Pardosa sp. spiders as top predators. Population interactions were modeled using logistic growth for rice and two response functions: the Holling type II response for planthopper predation on rice, and the Crowley–Martin response for Pardosa sp. predation on planthoppers to capture predator interference. The resulting model was formulated as a system of nonlinear differential equations. Analytically, four equilibrium points were obtained: total population extinction, extinction of planthoppers and Pardosa sp., extinction of Pardosa sp., and coexistence of all three species. Local stability analysis at each equilibrium point was conducted using the Jacobian matrix and the Routh–Hurwitz criterion. Numerical simulations were performed for several parameter combinations by varying planthopper growth efficiency and Pardosa sp. predation intensity. The simulation results were consistent with the theoretical analysis and showed that small changes in biological parameters could shift the system from stable coexistence to near extinction of the planthopper population. Ecologically, the model demonstrates that rice field ecosystem balance is strongly influenced by the interaction between planthopper reproductive capacity and the predatory strength of Pardosa sp., providing a theoretical basis for sustainable planthopper pest control strategies.
Systematic Literature Review of GPS-based Multi-Objective Environmentally Friendly Shortest Path with a Proposed Lexicographic Framework
Environmentally friendly path planning has become an important topic in transportation research as concerns about carbon emissions continue to grow. This study aims to review existing research on environmentally friendly shortest path problems and to identify the current state of the art in green shortest path optimization. A Systematic Literature Review is conducted using the PRISMA guideline and supported by bibliometric analysis to examine research trends and optimization methods discussed in the literature. The review indicates that most studies focus on metaheuristic and artificial intelligence–based approaches, while deterministic methods with explicit objective prioritization receive less attention. Based on the synthesis of previous studies, this paper discusses emerging research directions and outlines a conceptual framework for priority-based multi-objective shortest path optimization. The results of this review provide a clear overview of current methods and can support future research on eco-friendly shortest path models.
Copyright (c) 2026 Thania Nur Salsabila, Diah Chaerani, Herlina Napitupulu https://creativecommons.org/licenses/by-sa/4.0
Hybrid Otsu Morphological Pre-processing for EfficientNetB4 Based Acute Lymphoblastic Leukemia Classification
Image quality plays a crucial role in improving the performance of image-based classification models, particularly when raw images exhibit noise, uneven illumination, and unclear object boundaries. This study proposes a hybrid segmentation approach to enhance object separation by reducing background interference and refining object contours. The method combines Otsu thresholding for initial object–background separation with elliptical morphological operations to improve region consistency and boundary definition. The segmented grayscale images are replicated into three channels and resized to 224×224 pixels before being used as input to an EfficientNetB4-based classification model optimized with the AdamW optimizer and fine-tuning. Experimental results under identical data splits, training settings, and fine-tuning protocols show that the proposed segmentation-based method achieves a final test accuracy of 97%, outperforming the baseline model trained on raw images (95% test accuracy) using the same EfficientNetB4-AdamW configuration. These results demonstrate that incorporating segmentation in the preprocessing stage effectively enhances discriminative feature learning and improves overall classification performance.
Copyright (c) 2026 MARETTA MIA AUDINA, SUGIYARTO SURONO, ARIS THOBIRIN, GOH KHANG WEN https://creativecommons.org/licenses/by-sa/4.0
Approximation Properties on a Set Based on Equivalence Relations and Dominance Relations
An equivalence relation on a set forms equivalence classes so that the concept of approximation is formed on that set (rough set). The concept of approximation on a set is developing very rapidly. Some papers replace the equivalence relation with other relations, one of which is the dominance relation. The symmetry property of the equivalence relation is replaced by the anti-symmetry property so that a dominance relation is formed. This paper reviews several papers related to approximation on a set $w.r.t$ equivalence and dominance relations by describing the approximation properties that hold in both relations in terms of the concept of 3 types of approximation on a set. This paper also provides the approximation properties that hold in the equivalence relation but do not hold in the dominance relations in terms of the concept of 3 types of approximation on a set. The main contribution of this paper is showing that the relationship between the concept of 3 types of approximation on a set $w.r.t$ the equivalence relation and the dominance relation.
Copyright (c) 2026 Dian Winda Setyawati, Soleha Soleha, Rinurwati Rinurwati https://creativecommons.org/licenses/by-sa/4.0
Application of the Saint-Venant Model for Simulation of the Kapuas River Flow Using the Finite Difference Method
The Kapuas River plays an essential role in transportation, fisheries, tourism, and natural drainage in Pontianak, where river geometry and downstream tidal effects shape its flow conditions. These tidal forces produce variations in discharge and water level over space and time, which can exceed the river’s capacity and cause flooding. This study simulates the dynamics of discharge and water level along the Kapuas Kecil River segment. Researchers developed a mathematical flow model using the Saint-Venant framework, based on mass and momentum conservation principles. This study numerically solved the equations using a finite difference approach with a forward-time and central-space scheme. Researchers collected river width and depth data along a 5 km stretch from Pontianak Utara to Jungkat. The study presents simulation results as spatial and temporal profiles of water level and discharge. The results of this study show that water discharge increases along the channel, while water levels generally decrease over time in the direction of flow. These results provide insights into tidal-influenced river flows in urban environments and can support flood-related analysis and management efforts.
Copyright (c) 2026 Dian Eka Ratnasari, Meliana Pasaribu, Meliana Pasaribu, Yudhi Yudhi, Yudhi Yudhi https://creativecommons.org/licenses/by-sa/4.0
From Risk-Neutral to Risk-Sensitive Reinforcement Learning: Actor–Critic vs REINFORCE with Tail-Based Risk Measures
his study investigates the application of \emph{risk-sensitive reinforcement learning} on heavy-tailed return series by comparing two primary algorithms: REINFORCE with baseline (REINFORCE-BL) and episodic batched actor--critic (A2C-B). Initial exploratory analysis reveals an asymmetric return distribution with numerous extreme \emph{outliers}, rendering variance-based risk measures inadequate and motivating the integration of tail-based risk measures—specifically Value at Risk (VaR), Conditional Value at Risk (CVaR), and Entropic Value at Risk (EVaR)—into the RL objective function. This study constructs a simple portfolio environment with discrete actions (market entry, market exit, and \emph{hold}) and trains both algorithms under four scenarios: risk-neutral, VaR, CVaR, and EVaR. Experimental results demonstrate that A2C-B consistently outperforms REINFORCE-BL across all scenarios, exhibiting higher average long-term rewards, faster convergence rates, and more stable \emph{learning curves}. While VaR and CVaR penalties significantly reduce rewards and increase learning volatility for REINFORCE-BL, A2C-B experiences only moderate reward reductions while maintaining stability. In the EVaR scenario, both algorithms yield high rewards, yet A2C-B retains a slight advantage in terms of stability. These findings indicate that in environments with heavy-tailed returns, employing coherent risk measures (particularly CVaR and EVaR) within an actor--critic framework offers a more compelling trade-off between tail risk control and average performance, serving as a viable \emph{baseline} for the development of risk-sensitive RL in finance and actuarial science.
Copyright (c) 2026 Adhitya Ronnie Effendie https://creativecommons.org/licenses/by-sa/4.0
Stage-Structured Predator Model with Prey Protection: Application to Rice Plants–Leptocorisa oratorius
This study investigates a stage-structured predator–prey model consisting of prey, juvenile predators, and adult predators. The prey population follows logistic growth, while predation is described using a Holling type I functional response. Prey protection is incorporated through a protection parameter (1-m), representing the proportion of prey that successfully avoid predation by reducing the predation rate of adult predators. The model is analyzed by determining equilibrium points and examining their existence and stability. The results show four equilibrium points: total population extinction, prey-only equilibrium, juvenile predator extinction, and coexistence equilibrium. Predator extinction occurs when predation efficiency and predator reproduction are insufficient to compensate for predator mortality, whereas coexistence occurs when predation and conversion rates exceed mortality thresholds. Numerical simulations support the analytical results and demonstrate that increasing prey protection reduces predation pressure and may lead to predator decline, while appropriate predation efficiency promotes stable coexistence. These findings highlight the ecological importance of prey defense mechanisms in predator–prey interactions, particularly in rice–Leptocorisa oratorius.
Copyright (c) 2026 Dian Savitri, Safirah Rahmah https://creativecommons.org/licenses/by-sa/4.0
Box Fractal as an Iterated Function System in Fractal Interpolation for Determining the Approximate Value of Demand Data
A common problem in inventory planning is the uncertainty of the demand. One technique for determining the demand approximation value is the fractal interpolation. The aim of this study is to develop a fractal interpolation technique with an Fractal Interpolated Function constructed by the affine function that forms the Box Fractal shape. The development results are applied to interpolate rice demand data based on prices at a rice milling factory. Mean Absolute Percentage Error (MAPE) is used to measure the accuracy of interpolation results. For the nth iteration, the number of boxes formed are 5n and 4×5n pairs of points. Based on the rice demand data at one of the factories, the best MAPE was obtained at the 6th Iteration, which is 7.1596% within very good category. Based on the data used, the affine function that forms the Box Fractal as an Fractal Interpolated Function can be used in the fractal interpolation technique.
Copyright (c) 2026 Eka Susanti, Oki Dwipurwani, Dian Cahyawati Sukanda, Novi Rustiana Dewi, Husnul Khotimah, Wahyuni Apria Ningsih https://creativecommons.org/licenses/by-sa/4.0
Stability Analysis and Invasion Thresholds in a Rosenzweig--MacArthur Model with Prey Immigration and Cooperative Hunting
Predator--prey systems with multiple interacting ecological mechanisms require integrated modeling approaches for realistic analysis. This study develops a unified Rosenzweig--MacArthur model incorporating both continuous prey immigration and cooperative hunting among predators to analyze how these combined mechanisms affect equilibrium existence, stability, and transient dynamics. Analytical methods derive explicit invasion thresholds and local stability conditions through eigenvalue analysis, while numerical simulations with biologically plausible parameters compare two dynamical regimes: baseline conditions produce stable-node convergence, whereas high-efficiency conditions yield stable-spiral oscillations. Results show that immigration elevates prey density above invasion thresholds, enabling predator persistence, while increased cooperation intensity transitions the system from monotonic to oscillatory convergence. The integrated framework demonstrates how bottom-up (immigration) and top-down (cooperation) processes interact to shape predator--prey dynamics, providing testable predictions for ecosystems where both mechanisms operate simultaneously and establishing a foundation for more complex ecological modeling.
Copyright (c) 2026 Dian Savitri, Naufal Daffa Faustin https://creativecommons.org/licenses/by-sa/4.0
Sentiment Analysis of the 2022 Fuel Price Hike Using the Naïve Bayes Classifier
This study examines public opinion towards Indonesia’s 2022 fuel price hike using social media analytics and assesses the pace of a supervised machine learning classifier for policy-oriented sentiment analysis. The research aimed to answer the following two questions (1) What was the prevailing public sentiment articulated on Twitter after fuel pricing announcement? and (2) How well is a Naïve Bayes classifier able to classify sentiment polarity in this domain? We employed a quantitative cross-sectional design utilizing Twitter data obtained from 3–4 September 2022 via the hashtags #hargabbm and #bbmnaik. Ultimately, after preprocessing, there were 1,867 unique tweets out of the 2,003 retrieved ones. Training data consisted of a total of 489 manually labeled tweets, and 1,378 for testing. Tokenization and TF–IDF weighting were performed on text data, while the sentiment classification was done using Gaussian Naïve Bayes model and evaluated through confusion matrix metrics. The results suggest that public sentiment was overwhelmingly negative during the analysis period and that the classifier reached an accuracy of 94.89% with a precision of 73.40%, recall of 100%, and F1-score of 84.66. These findings show that probabilistic text classification offers newsworthy evidence about whether the public unanimously supports economically sensitive policies (or not), with voltage and salience meaningfully specified.
Copyright (c) 2026 Alia Lestari, Muhammad Hajarul Aswad, Subekti Masri https://creativecommons.org/licenses/by-sa/4.0
Complex-Valued Neural Networks with Adaptive Frequency Attention for Image Denoising
Image denoising encompasses various noise types; in this work, we focus specifically on periodic interference, which introduces coherent frequency-domain artifacts that are challenging to remove using conventional real-valued convolutional neural networks (CNNs). This paper introduces a Complex-Valued Neural Network with Adaptive Frequency Attention (CVNN-AFA) tailored to periodic noise removal, integrating complex-domain feature propagation with explicit radial frequency-band modulation. The proposed architecture employs complex convolutions, complex batch normalization, and ModReLU activations to jointly model amplitude and phase information. An Adaptive Frequency Attention (AFA) module operates in the Fourier domain and partitions the spectrum into low-, mid-, and high-frequency radial bands using distance-based masks, enabling adaptive band-wise reweighting aligned with interference characteristics. Experiments on the BSDS500 dataset augmented with synthetic periodic noise evaluate both low-noise and moderate-to-high noise regimes under matched training budgets and strong real-valued frequency-aware baselines. Results indicate that CVNN-AFA achieves competitive performance overall and provides consistent, moderate improvements in low-amplitude settings, while the real-valued frequency-aware baseline remains more robust under extreme corruption levels. Qualitative and spectral analyses suggest that the proposed approach offers incremental attenuation of periodic components while maintaining comparable detail preservation. These findings are specific to the controlled periodic noise scenarios evaluated in this study.
Copyright (c) 2026 Marjono Marjono, Avin Maulana, Anggi Gustiningsih Hapsani https://creativecommons.org/licenses/by-sa/4.0