CAUCHY: Jurnal Matematika Murni dan Aplikasi
type: channel
description: 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…
publisher: Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang
language: en-US
publication name: CAUCHY: Jurnal Matematika Murni dan Aplikasi
issn: 2086-0382
copyright: Authors who publish with this journal agree to the following terms: Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-ShareAlike 4.0 International License (CC-BY-SA 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
items: Cluster Analysis of Cities/Districts in West Kalimantan based on Stunting Response Indicators using the Calinski Harabasz Index
items: Interpolation of Fire Radiative Power Based on GSTAR Model Predictions with Queen Contiguity Weights Using Ordinary Kriging
items: Implementation of DBSCAN and K-MEANS++ Methods for Flood Vulnerability Cluster Mapping in East Java Province, 2024
items: Triple-Mutation Bat Algorithm–Optimized Extreme Learning Machine for Fetal Health Classification
items: University Scheduling Optimization Using Integer Programming: A Case Study
items: Nasdaq Inc. Stock Price (NDAQ) Prediction Due to Trump’s Tariff Policy Using Pulse Function Intervention Analysis
items: Quadratic and Truncated Spline Structural Equation Modeling With Double Bootstrap in The Waste Management Economy
items: Sensitivity Analysis of the SIRD Model for TB-Related Life Insurance Claims in Southeast Sulawesi
items: b-coloring Analysis on Tree Graph Families
items: Enhancing Spatio-Temporal PCA with FASTMCD for Climate Comfort Assessment
items: Implementation of DenseNet121 Based on Convolutional Neural Network with Geometric Augmentation for Breast Cancer Histopathology Image Classification
items: Management in Design-Build Projects by Construction Management Consultants: SEM-PLS and IPMA Approaches
items: A Study on Multi-Class Topic Prediction for E-commerce Review Data Using Ensemble Learning
items: Modelling Factors Affecting the Middle Income Trap in Indonesia Using Generalized Additive Models (GAM)
items: Transmission Dynamics of Dengue Disease Incorporating Treatment, Mass Awareness, and Wolbachia Intervention
items: Modeling the Dynamics of Tuberculosis-Diabetes Mellitus Coinfection with an Optimal Control Approach
items: Spatial Variation of HDI in East Java: A Tricube-Based Geographically Weighted Regression–Flower Pollination Algorithm Modeling Approach
items: Some Properties of Prime Graph of Cartesian Product of the Ring
items: Dynamic Analysis of a Predator–Prey Model with Group Defense in Prey and Cooperative Hunting in Predators
items: Sensitivity Analysis of a Tuberculosis Transmission Model with Incomplete Treatment
items: Mathematical Modeling and Regime Dynamics of Ammonium Chloride Imports in Indonesia Using Threshold Vector Autoregressive Integrated (TVARI) Approach
items: ResNet-50 and ResNeXt-50 for Multiclass Classification of Chronic Wound Images under Gaussian Blur
items: Spatial Analysis of Child Violence in West Java Using a Geographically Weighted Negative Binomial Regression Approach
items: Numerical Pricing of European Stock Options Using Black-Scholes Interval Model
items: Stability Analysis of a Three-Trophic Rice Ecosystem with Holling II and Crowley–Martin Responses
items: Systematic Literature Review of GPS-based Multi-Objective Environmentally Friendly Shortest Path with a Proposed Lexicographic Framework
items: Hybrid Otsu Morphological Pre-processing for EfficientNetB4 Based Acute Lymphoblastic Leukemia Classification
items: Approximation Properties on a Set Based on Equivalence Relations and Dominance Relations
items: Application of the Saint-Venant Model for Simulation of the Kapuas River Flow Using the Finite Difference Method
items: From Risk-Neutral to Risk-Sensitive Reinforcement Learning: Actor–Critic vs REINFORCE with Tail-Based Risk Measures
items: Stage-Structured Predator Model with Prey Protection: Application to Rice Plants–Leptocorisa oratorius
items: Box Fractal as an Iterated Function System in Fractal Interpolation for Determining the Approximate Value of Demand Data
items: Stability Analysis and Invasion Thresholds in a Rosenzweig--MacArthur Model with Prey Immigration and Cooperative Hunting
items: Sentiment Analysis of the 2022 Fuel Price Hike Using the Naïve Bayes Classifier
items: Complex-Valued Neural Networks with Adaptive Frequency Attention for Image Denoising
items: Evaluating Hierarchical Pathfinding A* (HPA*) for Multi‑Order Routing in a Small Warehouse Layout
items: Stability and Bifurcation of a 3D Eco Epidemiological Predator Prey Model with Pesticide
items: Temporary Immunity in a Fractional-Order SEIR Model: Stability Analysis
items: Stability Analysis of Conventional and E-Cigarette Smokers Behavior Model with Saturation Effects
items: Comparison of ARIMA, Random Forest, and Hybrid ARIMA-Random Forest Models in Forecasting Indonesian Crude Oil Prices
items: Clustering for Mapping Food Insecurity in the Land of Papua: A Five-Year Multiyear Analysis with Spatial Interpretation (2020-2024)
items: Deterministic Modeling of HIV–Malaria Co-Infection and Sensitivity Analysis in Papua
items: Compare Bede-Gal Between dH Differentiability of Set Valued Functions
items: Dynamics of Predator-Prey Model with Holling Type II Involving Predator Stage-Structured and Cannibalism
items: Comparison Of Methods For Handling Imbalanced Datasets In Improving Classification Algorithm Performance
items: A Review of Pompeiu-Hausdorff Metric Differentiability and Its Relation to Generalized Hukuhara Differentiability
items: Step-Stress Accelerated Life Testing with Type II Censoring and Exponential Distribution for Solar-Powered Lighting Systems
items: Numerical Pricing of Discrete-Dividend European Options: An Empirical Case Study
items: Latent Household Food Security in Raja Ampat Marine Protected Areas: A Binary CFA Approach
items: Short- and Long-Run Relationships Between Observed and Model 1 Output Rainfall Data in Majalengka Regency
items: Modification of Norms on the Sequence Space ℓp
items: On A-Distance (Anti)magic Labeling of Prime Graph over the Ring Zn
items: Comparison Of Vector Autoregressive and Multiresponse Fourier Series for Cryptocurrency Prediction Post-Bitcoin Halving 2024

Cluster Analysis of Cities/Districts in West Kalimantan based on Stunting Response Indicators using the Calinski Harabasz Index
type: item
description: 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).
creator: Tegar Rama Priyatna
creator: Yundari Yundari
creator: Nur'ainul Miftahul Huda
rights: Copyright (c) 2026 Tegar Rama Priyatna, Yundari Yundari, Nur'ainul Miftahul Huda https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2025-12-02
publication date: 2025-12-02
volume: 11
number: 1
starting page: 1
ending page: 15
doi: 10.18860/cauchy.v11i1.34510

Interpolation of Fire Radiative Power Based on GSTAR Model Predictions with Queen Contiguity Weights Using Ordinary Kriging
type: item
description: 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 RMSE of 7.42 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.
creator: Gita Fitriyana
creator: Nurfitri Imro'ah
creator: Nur’ainul Miftahul Huda
rights: Copyright (c) 2026 Gita Fitriyana, Nurfitri Imro'ah, Nur’ainul Miftahul Huda https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 16
ending page: 31
doi: 10.18860/cauchy.v11i1.37462

Implementation of DBSCAN and K-MEANS++ Methods for Flood Vulnerability Cluster Mapping in East Java Province, 2024
type: item
description: Flood vulnerability in East Java varies across districts due to differences in hydrometeorological pressure and exposure levels. This study compares two clustering algorithms—DBSCAN and K-Means++—for identifying patterns in eleven flood-impact indicators. DBSCAN parameter selection was conducted using a k-distance graph, resulting in ε = 0.8 and MinPts = 3, which produced five clusters and three noise points. The Silhouette Index for DBSCAN was 0.3266, calculated including noise points to ensure fair evaluation against K-Means++, which obtained a Silhouette Index of 0.2453 for five clusters. The findings indicate that DBSCAN produced higher internal cohesion under the given dataset. However, the resulting clusters are not interpreted as validated flood risk zones or as physically causal patterns, due to the absence of external validation layers such as historical flood maps, hydrological data, or topographic information. The results therefore provide a methodological comparison between density-based and centroid-based clustering for flood-impact variables without making geographical or causal inferences.
creator: Zalfa Zaliana Nugrahanto
creator: A'yunin Sofro
rights: Copyright (c) 2026 Zalfa Zaliana Nugrahanto, A’yunin Sofro https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 32
ending page: 44
doi: 10.18860/cauchy.v11i1.37410

Triple-Mutation Bat Algorithm–Optimized Extreme Learning Machine for Fetal Health Classification
type: item
description: Fetal health assessment is essential for preventing perinatal complications, yet manual interpretation of cardiotocography (CTG) signals is prone to variability and diagnostic delays. This study introduces TMBA–ELM, a hybrid intelligent model that optimizes Extreme Learning Machine (ELM) parameters using the Triple Mutation Bat Algorithm (TMBA). The novelty of this work lies in extending TMBA—originally designed for continuous optimization—into a mixed-variable optimization framework that simultaneously tunes the hidden-node size and the activation function. This is achieved through the integrated use of Cauchy, Gaussian, and time-based mutation strategies, representing the first adaptation of TMBA for ELM parameter optimization and its first application to CTG-based fetal health classification. The model was evaluated on an imbalanced CTG dataset comprising 2,126 samples and benchmarked against BA-ELM, EMD-FA-ELM, and PSO-EM-ELM. TMBA-ELM achieved 89.23% ± 0.44% accuracy, outperforming BA-ELM (ELM models with parameters tunned by ELM) with accuracy 87.37%±0.63%, PSO-EM-ELM (Error-minimizaed-ELM parameters tunned with particle swarm optimization) with accuracy 82.76% ± 1.83%, and EMD-FA-ELM (ELM parameters tunned with firefly algorithm and data decompositioned by empirical decomposition) with accuracy 87.76% ± 1.95%. However, TMBA-ELM required 164.23 ± 12.76 seconds of computation time, which is substantially higher than BA-ELM and PSO-EM-ELM with computing time 60.9 ± 10.24 seconds and 59.69 ± 5 seconds, respectively. Overall, TMBA-ELM provides improved accuracy compared with existing ELM-based models, while its increased computational cost represents a limitation for time-constrained applications.
creator: Prabowo Wisnumurti
creator: Syaiful Anam
creator: Mohammad Muslikh
rights: Copyright (c) 2026 Prabowo Wisnumurti, Syaiful Anam, Mohammad Muslikh https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 45
ending page: 60
doi: 10.18860/cauchy.v11i1.37525

University Scheduling Optimization Using Integer Programming: A Case Study
type: item
description: 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.
creator: Gayus Simarmata
creator: Rajainal Saragih
creator: Anil Hakim Syofra
rights: Copyright (c) 2026 Gayus Simarmata, Rajainal Saragih, Anil Hakim Syofra https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 61
ending page: 74
doi: 10.18860/cauchy.v11i1.37815

Nasdaq Inc. Stock Price (NDAQ) Prediction Due to Trump’s Tariff Policy Using Pulse Function Intervention Analysis
type: item
description: 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.
creator: Sediono Sediono
creator: Kimberly Maserati Siagian
creator: Josephin Viona Aditya
rights: Copyright (c) 2026 Kimberly Maserati Siagian https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-01-02
publication date: 2026-01-02
volume: 11
number: 1
starting page: 75
ending page: 90
doi: 10.18860/cauchy.v11i1.37168

Quadratic and Truncated Spline Structural Equation Modeling With Double Bootstrap in The Waste Management Economy
type: item
description: 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. Semiparametric SEM is used to overcome the limitations of conventional SEM, particularly when data complexity and social behavior do not fully satisfy the linearity assumptions. The model was applied to analyze the 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 approach yields smaller standard errors and higher relative efficiency in parameter estimation. 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.
creator: Anggun Fadhila Rizqia
creator: Solimun Solimun
creator: Nurjannah Nurjannah
creator: Kamelia Hidayat
creator: Fachira Haneinanda Junianto
rights: Copyright (c) 2026 Anggun Fadhila Rizqia, Solimun Solimun, Nurjannah Nurjannah, Kamelia Hidayat, Fachira Haneinanda Junianto https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 91
ending page: 105
doi: 10.18860/cauchy.v11i1.37591

Sensitivity Analysis of the SIRD Model for TB-Related Life Insurance Claims in Southeast Sulawesi
type: item
description: 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.
creator: Asriani Arsita Asni
creator: Fitriyani Fitriyani
creator: Ira Puspita
rights: Copyright (c) 2026 Asriani Arsita Asni, Fitriyani Fitriyani, Ira Puspita https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 106
ending page: 122
doi: 10.18860/cauchy.v11i1.36490

b-coloring Analysis on Tree Graph Families
type: item
description: A tree graph is a connected graph and has no circuits. Tree graphs used in this study include: broom graph, centipede graph, and Banana Tree 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 an axiomatic deductive method and a pattern detection method. Based on 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 the development of scientific knowledge related to b-coloring analysis on other graphs.
creator: Rafiantika Megahnia Prihandini
creator: Arika Indah Kristiana
creator: Lusita Risma Dana
creator: Edy Wihardjo
creator: Robiatul Adawiyah
creator: Hutkemri Zulnaidi
rights: Copyright (c) 2026 Arika Indah Kristiana, Rafiantika Megahnia Prihandini, Lusita Risma Dana, Edy Wihardjo, Robiatul Adawiyah https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 123
ending page: 134
doi: 10.18860/cauchy.v11i1.32328

Enhancing Spatio-Temporal PCA with FASTMCD for Climate Comfort Assessment
type: item
description: 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.
creator: Agus Yarcana
creator: Henny Pramoedyo
creator: Suci Astutik
rights: Copyright (c) 2026 Agus Yarcana, Henny Pramoedyo, Suci Astutik https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 135
ending page: 151
doi: 10.18860/cauchy.v11i1.37866

Implementation of DenseNet121 Based on Convolutional Neural Network with Geometric Augmentation for Breast Cancer Histopathology Image Classification
type: item
description: This study evaluates the performance of the DenseNet121 architecture for binary classification of breast cancer histopathological images using the BreakHis dataset. The model employs ImageNet pre-trained weights, fine-tuning, and geometric data augmentation to improve feature learning and generalization. To obtain more reliable results, three optimization algorithms (Adam, AdamW, and RMSprop) were evaluated through repeated experiments, and performance was reported using mean and standard deviation of test metrics. The experimental results demonstrate that DenseNet121 achieves consistently high classification performance across different optimizers, with the Adam optimizer showing the most stable results. These findings indicate that DenseNet121 combined with data augmentation provides an effective and robust approach for histopathological image classification while emphasizing the importance of repeated evaluation for reliable performance assessment.
creator: Nabilah Evi Ariani
creator: Sugiyarto Surono
creator: Aris Thobirin
rights: Copyright (c) 2026 Nabilah Evi Ariani https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 152
ending page: 165
doi: 10.18860/cauchy.v11i1.37896

Management in Design-Build Projects by Construction Management Consultants: SEM-PLS and IPMA Approaches
type: item
description: 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.
creator: Al Kautzar
creator: Mawardi Amin
creator: Agus Suroso
rights: Copyright (c) 2026 Al Kautzar, Mawardi Amin, Agus Suroso https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 166
ending page: 180
doi: 10.18860/cauchy.v11i1.37117

A Study on Multi-Class Topic Prediction for E-commerce Review Data Using Ensemble Learning
type: item
description: 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 …
creator: Kevin Alifviansyah
rights: Copyright (c) 2026 Kevin Alifviansyah https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 181
ending page: 193
doi: 10.18860/cauchy.v11i1.37941

Modelling Factors Affecting the Middle Income Trap in Indonesia Using Generalized Additive Models (GAM)
type: item
description: 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.
creator: Dita Amelia
creator: Suliyanto Suliyanto
creator: Azizah Atsariyyah Zhafira
creator: Aulia Ramadhanti
creator: Billy Christandy Suyono
creator: Firqa Aqila Hizbullah
rights: 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
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 194
ending page: 207
doi: 10.18860/cauchy.v11i1.35119

Transmission Dynamics of Dengue Disease Incorporating Treatment, Mass Awareness, and Wolbachia Intervention
type: item
description: 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
creator: Rafika Nanda Agustina
creator: Budi Priyo Prawoto
rights: Copyright (c) 2026 Budi Priyo Prawoto, Rafika Nanda Agustina https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 208
ending page: 223
doi: 10.18860/cauchy.v11i1.39026

Modeling the Dynamics of Tuberculosis-Diabetes Mellitus Coinfection with an Optimal Control Approach
type: item
description: 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.
creator: Muna Afdi Muniroh
creator: Kresna Oktafianto
creator: Eriska Fitri Kurniawati
rights: Copyright (c) 2026 MUNA AFDI MUNIROH https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 224
ending page: 238
doi: 10.18860/cauchy.v11i1.37539

Spatial Variation of HDI in East Java: A Tricube-Based Geographically Weighted Regression–Flower Pollination Algorithm Modeling Approach
type: item
description: 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.
creator: Friansyah Gani
creator: Henny Pramoedyo
creator: Achmad Efendi
rights: Copyright (c) 2026 Friansyah Gani, Henny Pramoedyo, Henny Pramoedyo, Achmad Efendi, Achmad Efendi https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 239
ending page: 254
doi: 10.18860/cauchy.v11i1.38007

Some Properties of Prime Graph of Cartesian Product of the Ring
type: item
description: The prime graph of the ring R, PG(R), is a graph whose set of vertices consists of elements of R, and two distinct vertices are adjacent if their product in the ring is zero. In this paper, we study the prime graph of the Cartesian product of rings Zp1 × Zp2, where p1 and p2 are distinct prime numbers. We determine several properties of PG(Zp1 × Zp2), including its order, size, number of triangles, and Wiener index. Furthermore, we construct the line graph of PG(Zp1 × Zp2) and compute the order, size, and Wiener index of L(PG(Zp1 × Zp2)).
creator: Vira Hari Krisnawati
creator: Ayunda Faizatul Musyarrofah
creator: Noor Hidayat
creator: Farah Maulidya Fatimah
rights: Copyright (c) 2026 Vira Hari Krisnawati, Noor Hidayat, Ayunda Faizatul Musyarrofah, Farah Maulidya Fatimah https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 255
ending page: 265
doi: 10.18860/cauchy.v11i1.32154

Dynamic Analysis of a Predator–Prey Model with Group Defense in Prey and Cooperative Hunting in Predators
type: item
description: 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.
creator: Nabilah Meladelvia
creator: Dian Savitri
rights: Copyright (c) 2026 Dian Savitri https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 266
ending page: 278
doi: 10.18860/cauchy.v11i1.40210

Sensitivity Analysis of a Tuberculosis Transmission Model with Incomplete Treatment
type: item
description: 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.
creator: Joko Harianto
creator: Diki Fernandi
rights: Copyright (c) 2026 Joko Harianto, Diki Fernandi https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 279
ending page: 289
doi: 10.18860/cauchy.v11i1.36325

Mathematical Modeling and Regime Dynamics of Ammonium Chloride Imports in Indonesia Using Threshold Vector Autoregressive Integrated (TVARI) Approach
type: item
description: 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.
creator: Carissa Egytia Widiantoro
creator: Restu Arisanti
creator: Gumgum Darmawan
rights: Copyright (c) 2026 Carissa Egytia Widiantoro, Restu Arisanti, Gumgum Darmawan https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 290
ending page: 309
doi: 10.18860/cauchy.v11i1.40052

ResNet-50 and ResNeXt-50 for Multiclass Classification of Chronic Wound Images under Gaussian Blur
type: item
description: 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.
creator: Reynaldi Andhika
creator: Sugiyarto Surono
creator: Aris Thobirin
rights: Copyright (c) 2026 Reynaldi Ikbar Andhika https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 310
ending page: 324
doi: 10.18860/cauchy.v11i1.40323

Spatial Analysis of Child Violence in West Java Using a Geographically Weighted Negative Binomial Regression Approach
type: item
description: 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.
creator: Suliyanto Suliyanto
creator: Dita Amelia
creator: Lisa Amanda Putri
creator: Aurellia Calista Anggakusuma
rights: Copyright (c) 2026 Suliyanto Suliyanto, Dita Amelia, Lisa Amanda Putri, Aurellia Calista Anggakusuma https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 325
ending page: 339
doi: 10.18860/cauchy.v11i1.40390

Numerical Pricing of European Stock Options Using Black-Scholes Interval Model
type: item
description: 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
creator: Muhammad Iqbal Aditama
creator: Rudianto Artiono
rights: Copyright (c) 2026 Muhammad Iqbal Aditama, Rudianto Artiono https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 340
ending page: 349
doi: 10.18860/cauchy.v11i1.40272

Stability Analysis of a Three-Trophic Rice Ecosystem with Holling II and Crowley–Martin Responses
type: item
description: 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.
creator: Anastasya Choirun Nisa'
creator: Dian Savitri
rights: Copyright (c) 2026 Dian Savitri https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 350
ending page: 363
doi: 10.18860/cauchy.v11i1.40204

Systematic Literature Review of GPS-based Multi-Objective Environmentally Friendly Shortest Path with a Proposed Lexicographic Framework
type: item
description: 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.
creator: Thania Nur Salsabila
creator: Diah Chaerani
creator: Herlina Napitupulu
rights: Copyright (c) 2026 Thania Nur Salsabila, Diah Chaerani, Herlina Napitupulu https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 364
ending page: 381
doi: 10.18860/cauchy.v11i1.40489

Hybrid Otsu Morphological Pre-processing for EfficientNetB4 Based Acute Lymphoblastic Leukemia Classification
type: item
description: 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.
creator: Maretta Mia Audina
creator: Sugiyarto Surono
creator: Aris Thobirin
creator: Goh Khang Wen
rights: Copyright (c) 2026 MARETTA MIA AUDINA, SUGIYARTO SURONO, ARIS THOBIRIN, GOH KHANG WEN https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 382
ending page: 400
doi: 10.18860/cauchy.v11i1.40730

Approximation Properties on a Set Based on Equivalence Relations and Dominance Relations
type: item
description: 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.
creator: Dian Winda Setyawati
creator: Soleha Soleha
creator: Rinurwati Rinurwati
rights: Copyright (c) 2026 Dian Winda Setyawati, Soleha Soleha, Rinurwati Rinurwati https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 401
ending page: 412
doi: 10.18860/cauchy.v11i1.40603

Application of the Saint-Venant Model for Simulation of the Kapuas River Flow Using the Finite Difference Method
type: item
description: 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.
creator: Dian Eka Ratnasari
creator: Meliana Pasaribu
creator: Yudhi Yudhi
rights: Copyright (c) 2026 Dian Eka Ratnasari, Meliana Pasaribu, Meliana Pasaribu, Yudhi Yudhi, Yudhi Yudhi https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 413
ending page: 425
doi: 10.18860/cauchy.v11i1.38622

From Risk-Neutral to Risk-Sensitive Reinforcement Learning: Actor–Critic vs REINFORCE with Tail-Based Risk Measures
type: item
description: 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.
creator: Aprida Siska Lestia
creator: Adhitya Ronnie Effendie
creator: Made Tantrawan
creator: Muhammad Rafli Azrarsyah
rights: Copyright (c) 2026 Adhitya Ronnie Effendie https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 426
ending page: 446
doi: 10.18860/cauchy.v11i1.40309

Stage-Structured Predator Model with Prey Protection: Application to Rice Plants–Leptocorisa oratorius
type: item
description: 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.
creator: Safira Rahmah
creator: Dian Savitri
rights: Copyright (c) 2026 Dian Savitri, Safirah Rahmah https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 447
ending page: 460
doi: 10.18860/cauchy.v11i1.40733

Box Fractal as an Iterated Function System in Fractal Interpolation for Determining the Approximate Value of Demand Data
type: item
description: 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.
creator: Eka Susanti
creator: Oki Dwipurwani
creator: Dian Cahyawati
creator: Novi Rustiana Dewi
creator: Husnul Khotimah
creator: Wahyuni Apria Ningsih
rights: 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
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 461
ending page: 472
doi: 10.18860/cauchy.v11i1.38905

Stability Analysis and Invasion Thresholds in a Rosenzweig--MacArthur Model with Prey Immigration and Cooperative Hunting
type: item
description: 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.
creator: Naufal Daffa Faustin
creator: Dian Savitri
rights: Copyright (c) 2026 Dian Savitri, Naufal Daffa Faustin https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 473
ending page: 488
doi: 10.18860/cauchy.v11i1.40677

Sentiment Analysis of the 2022 Fuel Price Hike Using the Naïve Bayes Classifier
type: item
description: 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.
creator: Alia Lestari
creator: Muhammad Hajarul Aswad
creator: Subekti Masri
rights: Copyright (c) 2026 Alia Lestari, Muhammad Hajarul Aswad, Subekti Masri https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 489
ending page: 504
doi: 10.18860/cauchy.v11i1.36473

Complex-Valued Neural Networks with Adaptive Frequency Attention for Image Denoising
type: item
description: 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.
creator: Marjono Marjono
creator: Avin Maulana
creator: Anggi Gustiningsih Hapsani
rights: Copyright (c) 2026 Marjono Marjono, Avin Maulana, Anggi Gustiningsih Hapsani https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 505
ending page: 523
doi: 10.18860/cauchy.v11i1.36851

Evaluating Hierarchical Pathfinding A* (HPA*) for Multi‑Order Routing in a Small Warehouse Layout
type: item
description: Hierarchical Pathfinding A* (HPA*) is a hierarchical search framework that partitions grid‑based environments into clusters to reduce computational time while preserving a near-optimal path. The warehouse layout features cross-aisle connectivity, and multi-order optimization is performed using the HPA* algorithm, which integrates travel times with multi-rack picking times to the objective cost function. We simulate by assigning 30 random orders, with a total of 10641 items stored in the warehouse and 10 item types. The travel time is calculated assuming a picker has a constant speed of 1.2 m/s along edges, the picking time is proportional to the number of items picked per rack, and a small warehouse layout. Estimated cycle times of the orders (travel plus picking time) range from 114.4 to 349.9 seconds using the HPA* optimization, with a mean of 232.0 seconds. From the optimization results, orders require an average of 5.2 rack visits, ensuring that the picker travels more than two racks per order. The HPA* reduces the original low‑level graph (50 nodes and 61 edges, including base and stage station) to a graph with 22 nodes and 17 edges, enabling faster route computation while preserving observed cycle‑time patterns when combined with picking-time durations. Compared to A*, given the layout and orders, HPA* demonstrates an efficient warehouse path‑planning method that reduces search computation while maintaining near‑optimal routing performance.
creator: Ig. Prasetya Dwi Wibawa
creator: Meta Kallista
creator: Ramdhan Nugraha
creator: Heni Widayani
creator: Harish Chandra Bhandari
creator: Angga Rusdinar
rights: Copyright (c) 2026 Ig. Prasetya Dwi Wibawa, Meta Kallista, Ramdhan Nugraha, Heni Widayani, Harish Chandra Bhandari, Angga Rusdinar https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 524
ending page: 539
doi: 10.18860/cauchy.v11i1.39659

Stability and Bifurcation of a 3D Eco Epidemiological Predator Prey Model with Pesticide
type: item
description: Eco--epidemiological predator--prey models provide an important mathematical framework for understanding the interaction between disease transmission, predation, and human intervention in ecological systems. This study investigates a three--dimensional deterministic model incorporating saturated disease incidence, Holling type II predation, and pesticide application. Analytical techniques are employed to determine the existence and local stability of biologically feasible equilibrium points, while numerical simulations using a fourth--order Runge--Kutta method illustrate the dynamical behavior of the system under different parameter regimes. The analysis reveals the possibility of disease--free, predator--free, and interior coexistence equilibria, as well as bistability depending on parameter values and initial conditions. Bifurcation analysis identifies critical thresholds in disease transmission and predator conversion efficiency that govern transitions between predator persistence and extinction. These findings provide theoretical insights for integrated pest management strategies by emphasizing the balance between chemical control and ecological stability.
creator: Aqiila Ollyana Savitri
creator: Dian Savitri
rights: Copyright (c) 2026 Dian Savitri https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 540
ending page: 555
doi: 10.18860/cauchy.v11i1.40676

Temporary Immunity in a Fractional-Order SEIR Model: Stability Analysis
type: item
description: Infectious disease has become a serious problem over the past few years. At the same time, research on disease dynamics keeps advancing, especially on diseases caused by viruses. One concept that has been used in epidemic models is fractional calculus, or more specifically, fractional differential equations. This paper discusses the analytical properties of a fractional-order SEIR model, which are then verified by numerical simulations. Analytical results have shown that the global asymptotic stability of disease-free equilibrium is achieved when the basic reproduction number is equal to or less than 1, while endemic equilibrium is globally asymptotically stable when the value is greater than 1. Simulation results from Explicit Fractional Order Runge-Kutta (EFORK) method are confirmed to be in agreement with the basic properties provided by the analysis. The results also illustrate the impact of fractional-order and recovery rate on temporary immunity, which indicates that smaller fractional-orders converge faster compared to larger orders.
creator: Muhammad Iqbal
creator: Mohammad Januar Ismail Burhan
creator: Adam Adam
rights: Copyright (c) 2026 Muhammad Iqbal, Mohammad Januar Ismail Burhan, Adam Adam https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 556
ending page: 570
doi: 10.18860/cauchy.v11i1.40849

Stability Analysis of Conventional and E-Cigarette Smokers Behavior Model with Saturation Effects
type: item
description: Smoking behavior is a harmful habit that poses serious health risks and has been regarded as a lifestyle by certain segments of society, regardless of age, gender, or social status. This study develops and analyzes a mathematical model of smoking behavior that classifies between conventional smokers and e-cigarette smokers, incorporates interaction with lung cancer patients, and considers the saturation effect on potential smokers as the number of smokers in the population increases. The method is determining assumptions to create a compartment diagram and construct the model. This model has four equilibrium points. The results show that when R01 < 1, R02 < 1, the smoker-free equilibrium point is asymptotically stable. When R01 < 1, R02 > 1, the endemic equilibrium point of e-cigarette smokers becomes stable. When R01 > 1 and R02 < 1, the endemic equilibrium point of conventional smokers becomes stable. Meanwhile, when R01 > 1 and R02 > 1, the endemic equilibrium point of coexistence of conventional and e-cigarette smokers becomes stable. Numerical simulations show that the intensity of smoking transmission affects the dynamics of the system. The lower the transmission rate by conventional and e-cigarette smokers, the faster the transition to a smoker-free population. The saturation effect plays a role in limiting excessive contact between potential smokers and smokers.
creator: Binti Mu'alafi Suryantini
creator: Budi Priyo Prawoto
rights: Copyright (c) 2026 Budi Priyo Prawoto, Binti Mu'alafi Suryantini https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 571
ending page: 592
doi: 10.18860/cauchy.v11i1.40109

Comparison of ARIMA, Random Forest, and Hybrid ARIMA-Random Forest Models in Forecasting Indonesian Crude Oil Prices
type: item
description: The price of Indonesian crude oil is highly volatile due to global demand fluctuations, energy policies, and geopolitical tensions, making accurate forecasting challenging. This study compares three forecasting models: ARIMA, Random Forest, and Hybrid ARIMA--Random Forest, to identify the most accurate approach. Model performance was evaluated using Time-Series Cross-Validation (TSCV) and metrics including Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE). The results indicate that the Random Forest model, tuned with \texttt{mtry = 1} and \texttt{ntree = 200}, outperformed both ARIMA and Hybrid ARIMA--Random Forest, achieving the lowest MAPE, MAE, and RMSE values. This suggests that Indonesian crude oil prices during the study period are predominantly non-linear, and Random Forest alone effectively captures these dynamics. Forecasts based on this model indicate a short-term increase in prices from 61.10 USD/Barrel in December 2025 to 64.29 USD/Barrel in March 2026, followed by a slight decline and modest recovery by June 2026. Overall, Random Forest provides a reliable and accurate tool for forecasting Indonesian crude oil prices, offering valuable insights for policymakers, investors, and market participants navigating volatile oil markets.
creator: Yeni Rahkmawati
creator: Selvi Annisa
creator: Hardianti Hafid
creator: Nuramaliyah Nuramaliyah
creator: Emeylia Safitri
rights: Copyright (c) 2026 Yeni Rahkmawati, Selvi Annisa, Hardianti Hafid, Nuramaliyah Nuramaliyah https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 593
ending page: 612
doi: 10.18860/cauchy.v11i1.36540

Clustering for Mapping Food Insecurity in the Land of Papua: A Five-Year Multiyear Analysis with Spatial Interpretation (2020-2024)
type: item
description: Food insecurity in the Land of Papua remains a critical issue due to extreme geographical conditions, limited infrastructure, and unstable food distribution systems. This study aims to map food vulnerability across 42 districts/cities in Papua using insufficient food consumption data from 2020 to 2024. Clustering was performed using five methods—Single Linkage, Complete Linkage, Ward, K-Means, and Gaussian Mixture Model (GMM)—and evaluated using three validation indices: Silhouette, Davies–Bouldin Index (DBI), and Calinski–Harabasz Index (CHI). To obtain a balanced and comprehensive model selection, a Performance-Based Weighting (PBW) framework was applied. In this framework, the DBI was first transformed to ensure a consistent higher-is-better orientation, and all validation indices were normalized to the [0,1] range prior to computing variance-based weights. This normalization step mitigates potential scale dominance, particularly from the unbounded CHI metric, ensuring proportional contribution from each validation criterion in the aggregated score. Although individual validation indices exhibited varying optimal values of k, the integrated PBW evaluation consistently identifies the two-cluster configuration as the most stable and interpretable overall structure. Specifically, Complete Linkage with k = 2 achieved the highest combined PBW score (0.8658), reflecting strong cluster separation and consistency across validation measures. Spatial interpretation of the resulting clusters reveals that the first cluster predominantly consists of high-risk mountainous districts with persistently elevated levels of food consumption inadequacy, particularly during 2021–2022, while the second cluster represents coastal and urban regions with comparatively lower and improving prevalence in 2023–2024. These findings provide a multiyear clustering perspective with geographic insight into regional disparities in food insecurity across Papua. Overall, this study presents a data-dr…
creator: Ishak Semuel Beno
creator: Alvian M Sroyer
creator: Felix Reba
creator: Remuz M. B. Kmurawak
creator: Antonius A. P. Tama
rights: Copyright (c) 2026 Ishak Semuel Beno https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 613
ending page: 627
doi: 10.18860/cauchy.v11i1.40366

Deterministic Modeling of HIV–Malaria Co-Infection and Sensitivity Analysis in Papua
type: item
description: HIV and malaria co-infection poses a significant public health challenge in Papua, Indonesia, where high HIV prevalence overlaps with persistent malaria endemicity. Their biological interaction worsens clinical outcomes and complicates transmission. This study develops a deterministic mathematical model using nonlinear differential equations to describe HIV--malaria co-infection dynamics, tailored to Papua's epidemiology. The model includes coupled human and vector compartments and is analyzed through disease-free and endemic equilibria. The basic reproduction number $R_0$ is derived using the next-generation matrix method and its sensitivity is assessed using normalized forward sensitivity indices to identify key parameters affecting transmission. The results show that the HIV transmission rate ($\beta_H$), the mosquito bite rate ($b_M$), and the malaria transmission from humans to mosquitoes ($\beta_V$) increase the most strongly $R_0$, while the progression of HIV to AIDS ($\alpha_1$), malaria-induced mortality ($\delta_M$), and vector mortality ($\mu_V$) reduce it. Numerical simulations based on realistic initial conditions for Papua indicate that the system reaches a stable equilibrium when interventions target the most sensitive parameters. These findings provide a mathematical foundation for integrated control strategies, emphasizing reduced human--vector contact, suppression of HIV transmission, and effective vector control. The model enriches biomathematics research on co-infection dynamics and supports evidence-based policymaking for managing dual epidemics in regions like Papua.
creator: Vina Lusiana
creator: Diva Hardiestya Fanny
creator: Muhammad Syazali
rights: Copyright (c) 2026 Vina Lusiana https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 628
ending page: 647
doi: 10.18860/cauchy.v11i1.40964

Compare Bede-Gal Between dH Differentiability of Set Valued Functions
type: item
description: This paper presents a comparative study between the Bede--Gal differentiability and the dH-differentiability for set-valued functions whose values belong to the family of nonempty compact convex subsets of $\mathbb{R}^n$. The Bede--Gal derivative, originally introduced for fuzzy and interval-valued functions, is redefined for the set-valued framework and analyzed through its metric properties. Meanwhile, the dH-derivative is formulated in terms of the Pompeiu-Hausdorff metric, allowing differentiability without requiring the existence of the Hukuhara or generalized Hukuhara difference. We establish several results clarifying the relationship between these two concepts, including sufficient conditions under which a function that is Bede-Gal differentiable is also dH-differentiable, and conversely. Illustrative examples are provided to demonstrate cases where one type of differentiability exists while the other fails. The comparison emphasizes that dH-differentiability provides a broader and more flexible framework, extending the applicability of the differential calculus in set-valued analysis.
creator: Wildan Bagus Wicaksono
creator: Mohamad Muslikh
rights: Copyright (c) 2026 Wildan Bagus Wicaksono https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 648
ending page: 666
doi: 10.18860/cauchy.v11i1.38181

Dynamics of Predator-Prey Model with Holling Type II Involving Predator Stage-Structured and Cannibalism
type: item
description: Predator–prey models with nonlinear functional responses provide a robust framework for understanding population regulation and oscillatory dynamics. This study analyzes a three-dimensional predator–prey model incorporating Holling type II functional responses, explicit predator stage structure, and cannibalism. The primary objective is to investigate how adult predation, maturation, and cannibalism parameters influence equilibrium stability and the emergence of oscillations through Hopf bifurcation. Analytical results establish the existence and local stability of a positive coexistence equilibrium. For a biologically relevant parameter set, numerical simulations demonstrate that trajectories converge to the coexistence equilibrium (59.9078, 23.9092, 56.0552). This state is locally asymptotically stable, as the real parts of all Jacobian eigenvalues are negative. Numerical continuation methods are employed to detect Hopf bifurcations induced by key parameters. Two Hopf points are identified for the adult predation rate at 0.4211 and 8.7725, while the maturation rate induces bifurcations at 0.2661 and 0.5271. Additionally, the cannibalism parameter triggers a Hopf bifurcation at 0.1835, initiating periodic population oscillations. These results demonstrate that maturation and cannibalism define distinct instability thresholds, jointly governing the transition from stable coexistence to sustained oscillatory dynamics in stage-structured systems
creator: Sela Tri Indah Sari
creator: Dian Savitri
rights: Copyright (c) 2026 Dian Savitri, Sela Tri Indah Sari https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 667
ending page: 682
doi: 10.18860/cauchy.v11i1.41044

Comparison Of Methods For Handling Imbalanced Datasets In Improving Classification Algorithm Performance
type: item
description: Data availability in large observations and dimensions is known as big data. There are several problems in processing big data, such as imbalanced datasets. In classification modeling, an imbalanced dataset is a common challenge. Data class predictions are more likely to be accurate in the majority class data and inaccurate in the minority class, resulting from the problem of imbalanced data. The data-level, the algorithm-level, and the ensemble method approach are the solutions that have been extensively researched. Some methods with a data-level approach are SMOTE, Undersampling, and Oversampling. The algorithm-level method is NWKNN. And then, the ensemble approach is UnderBagging, RUSBoosting, SMOTEBoost, and SMOTEBagging. The goal of this study is to determine the best method for handling each case of the imbalanced dataset. There are three cases of imbalance, namely mild, moderate, and extreme. A simulation study was conducted for each imbalanced case to evaluate the accuracy of each method. Based on the AUC value, the SMOTEBagging method is the best for mild imbalance cases with an AUC value of 0.9581. For moderate imbalance cases, the SMOTEBagging method is the best method, with an AUC value of 0.9033. Meanwhile, for extreme imbalance cases, the UnderBagging method provides the best performance.
creator: Dyah Setyo Rini
creator: Winalia Agwil
creator: Dian Agustina
creator: Ahmad Famuji
rights: Copyright (c) 2026 Winalia Agwil, Dyah Setyo Rini, Dian Agustina, Ahmad Famuji https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 683
ending page: 695
doi: 10.18860/cauchy.v11i1.35780

A Review of Pompeiu-Hausdorff Metric Differentiability and Its Relation to Generalized Hukuhara Differentiability
type: item
description: The Pompeiu-Hausdorff distance/Pompeiu-Hausdorff metric is a concept in analysis that measures the distance between two subsets of a metric space, one of its important applications being the Hausdorff metric differentiability of set-valued functions . This article reviews the definition and properties of Pompeiu-Hausdorff distance differentiability on the space of compact and convex subsets of the Euclidean space with dimension n. We also present concepts about the generalized Hukuhara difference and its differentiability. By studying both topics, we discuss the established relationship between Pompeiu-Hausdorff metric differentiability and generalized Hukuhara differentiability
creator: William Surya Putra
creator: Mohamad Muslikh
rights: Copyright (c) 2026 William Surya Putra https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 696
ending page: 711
doi: 10.18860/cauchy.v11i1.37820

Step-Stress Accelerated Life Testing with Type II Censoring and Exponential Distribution for Solar-Powered Lighting Systems
type: item
description: This study addresses the reliability assessment of solar-powered lighting systems using a partial step-stress accelerated life testing (ALT) model with Type-II censoring. The research aims to estimate the mean failure time and quantify the acceleration effect due to elevated stress. Secondary data from an experiment involving 31 lighting devices were analyzed. Initially, devices were tested at a normal temperature (293 K) until 16 failures occurred. Subsequently, the stress was increased to 353 K, and testing continued until all units failed or were censored. Under the assumption of an exponential lifetime distribution and a linear accelerated failure-time model, the maximum likelihood estimation (MLE) method was applied for parameter inference. The results show that the estimated mean failure time under normal conditions is approximately 711.6 hours, which reduces to about 38.7 hours under accelerated stress, yielding an acceleration factor of 18.354. Furthermore, a 95% confidence interval for the mean failure time under normal conditions is between 460.2 and 1245 hours. The reliability and percentile life at various stress levels were also derived. This research provides a practical statistical framework for evaluating the reliability of solar-powered lighting devices, offering a more efficient alternative to conventional life testing methods.
creator: Ardi Kurniawan
creator: Vanisia Suci Ananda
creator: Yovita Karin Kalista
rights: Copyright (c) 2026 ardi kurniawan, Vanisia Suci Ananda, Yovita Karin Kalista https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 712
ending page: 723
doi: 10.18860/cauchy.v11i1.41076

Numerical Pricing of Discrete-Dividend European Options: An Empirical Case Study
type: item
description: Studi kuantitatif terapan ini menerapkan integrasi numerik Simpson 1/3 untuk secara sistematis menerbitkan penetapan harga opsi Eropa yang disesuaikan dengan diskrit dividen. Menggunakan saham teknologi anonim (XYZ Tech Corp.) sebagai studi kasus empiris, penelitian ini mencapai dua tujuan utama: memvalidasi konvergensi komputasi algoritma numerik terhadap tolok ukur analitik Black-Scholes yang tepat menggunakan Kesalahan Relatif, dan menganalisis penyimpangan harga empiris model terhadap pengamatan pasar nyata di berbagai zona uang. Pengujian komputasi menunjukkan bahwa metode Simpson 1/3, yang secara inheren dibatasi oleh kesalahan pemotongan orde keempat, mencapai konvergensi optimal dan cepat. Dengan mengatur partisi grid pada N=200, algoritma berhasil menekan kesalahan relatif secara ketat di bawah ambang batas 0,001% dibandingkan dengan solusi analitik, dan dieksekusi secara efisien dalam waktu kurang dari 0,005 detik. Secara empiris, meskipun model teoritis menunjukkan akurasi tinggi untuk opsi In-The-Money (ITM) dengan deviasi minimal, model ini secara konsisten mengungkapkan bias valuasi yang signifikan untuk kontrak Call Out-Of-The-Money (OTM), sedangkan valuasi Put OTM menunjukkan pola deviasi yang berbeda secara struktural. Valuasi asimetri ini menunjukkan potensi batasan volatilitas historis konstan, yang tampaknya tidak mampu untuk sepenuhnya menangkap kemiringan volatilitas tersirat dan pergeseran persepsi risiko yang lazim terjadi dalam mikrostruktur pasar aktual.
creator: Muhammad Gibran Elgiffary
creator: Rudianto Artiono
rights: Copyright (c) 2026 Muhammad Gibran Elgiffary https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 724
ending page: 735
doi: 10.18860/cauchy.v11i1.40995

Latent Household Food Security in Raja Ampat Marine Protected Areas: A Binary CFA Approach
type: item
description: This study examines household food security in four marine protected areas in Raja Ampat using repeated cross-sectional household survey data. Data were collected between 2010 to 2024, grouped into five monitoring periods. This study aims to provide a measurement framework for household food security as a latent construct based on binary indicators representing dimensions of food access and to estimate latent household food security scores in the four analyzed areas. In addition to applying confirmatory factor analysis to new empirical data, this study also presents a systematic estimation framework for measuring the latent construct using binary household indicators in repeated cross-sectoral survey data. The framework includes indicator threshold estimation, tetrachoric correlation estimation, parameter estimation using the robust diagonally weighted least squares method, and derivation of latent scores based on posterior expectations using the Gauss–Hermite quadrature approach. The analysis results indicate that the one-factor model provides acceptable fit and adequate construct reliability across the analyzed area-period groups. Estimates of factor loadings and thresholds provide information on the relative contribution and severity of each indicator in representing variations in household food access conditions. Overall, the goodness-of-fit indices indicate that the one-factor structure provides a reasonable representation of the relationships among the observed indicators under the fitted measurement model.
creator: Indah Ratih Anggriyani
creator: I Made Sumertajaya
creator: Khairil Anwar Notodiputro
creator: Yenni Angraini
rights: Copyright (c) 2026 indah ratih anggriyani https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 736
ending page: 753
doi: 10.18860/cauchy.v11i1.40979

Short- and Long-Run Relationships Between Observed and Model 1 Output Rainfall Data in Majalengka Regency
type: item
description: This study examines the short-run and long-run relationships between observed monthly rainfall and CMIP6 climate model projections in Majalengka Regency, Indonesia. Monthly rainfall observations from the BMKG Kertajati Meteorological Station are analyzed using the Autoregressive Distributed Lag (ARDL) framework, which enables simultaneous assessment of short-term dynamics and long-term equilibrium relationships. Stationarity and cointegration are evaluated using the Augmented Dickey–Fuller test and ARDL bounds testing, respectively, while model performance is assessed through out-of-sample validation for the period 2015–2017 under three CMIP6 emission scenarios: SSP1-2.6, SSP2-4.5, and SSP5-8.5. The results indicate a positive and statistically significant short-run relationship between observed rainfall and CMIP6 projections across all scenarios, suggesting that climate models capture local scale monthly rainfall variability reasonably well. In contrast, the long-run relationship is weak and negative, highlighting limitations in representing long-term local rainfall dynamics. Model performance is highest under the low-emission SSP1-2.6 scenario and decreases under higher-emission scenarios. These findings suggest that CMIP6 outputs are more reliable for short-term rainfall analysis than for long-term local assessments without bias correction or downscaling.
creator: Sri Nurdiati
creator: Mohamad Khoirun Najib
creator: Fathia Rahmaisty
rights: Copyright (c) 2026 Sri Nurdiati, Mohamad Khoirun Najib, Fathia Rahmaisty https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 754
ending page: 771
doi: 10.18860/cauchy.v11i1.40902

Modification of Norms on the Sequence Space ℓp
type: item
description: In this article, we explore sequence spaces by introducing a newly defined norm. We construct the Orlicz sequence space and demonstrate that the norm in this space is equivalent to the norm in the ℓp space. As a result, the fundamental properties of the ℓp space are carried over to the Orlicz sequence space through the equivalence of norms. One significant implication of this result is that Hölder's inequality, which holds in ℓp spaces, can also be applied to the Orlicz sequence space with different positive constants.
creator: Rikha Syahda Salsabilla
creator: Mochammad Idris
rights: Copyright (c) 2026 Rikha Syahda Salsabilla, mochammad Idris https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 772
ending page: 786
doi: 10.18860/cauchy.v11i1.37178

On A-Distance (Anti)magic Labeling of Prime Graph over the Ring Zn
type: item
description: Let G = (V, E) be a simple graph with n vertices, and let A be an abelian group of order n. Let f: V(G) → A be a bijection, and define the weight of a vertex x by w(x) = Σy ∈ N(x) f(y), where N(x) denotes the open neighborhood of x. We call f an A-distance magic labeling if all vertex weights are equal, and an A-distance antimagic labeling if the weights of distinct vertices are pairwise different. The prime graph of a commutative ring R is the simple graph with vertex set R in which two vertices x and y are adjacent if and only if xRy = {0}. In this paper, we investigate the existence of A-distance magic and A-distance antimagic labelings of the prime graph over the ring Zn for several values of n.
creator: Muhammad Husnul Khuluq
rights: Copyright (c) 2026 Muhammad Husnul Khuluq https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 787
ending page: 800
doi: 10.18860/cauchy.v11i1.41237

Comparison Of Vector Autoregressive and Multiresponse Fourier Series for Cryptocurrency Prediction Post-Bitcoin Halving 2024
type: item
description: This study examines cryptocurrency price modeling after the 2024 Bitcoin halving by comparing two multivariate forecasting methods: the Vector Autoregressive (VAR) model and the cosine-based Multiresponse Fourier Series Estimator. The research aligns with SDGs 8 on Decent Work and Economic Growth, as accurate forecasting in digital asset markets can support financial stability and informed investment decisions. The novelty of this study lies in applying a Fourier-based multiresponse model for post-halving cryptocurrency prediction, an approach that remains limited in existing literature. The dataset consists of daily prices of Bitcoin, Ethereum, and Litecoin from April 2024 to August 2025 (t=480), obtained from investing.com, with 90% for data training and 10% for data testing. Prior to modeling, the Bartlett test produced p-value 0.000<α, indicating significant correlations among cryptocurrencies, thereby validating the use of simultaneous multivariate analysis. The results show that the Fourier Series Estimator with five oscillation parameters (k=5) provides superior predictive accuracy, achieving a MAPE of 3.768%, compared to the VAR model’s MAPE of 8.503%. These findings demonstrate that the Fourier estimator more effectively captures cyclical and nonlinear patterns in digital assets and offers valuable contributions to financial statistics, providing practical insights for investors and policymakers in the highly volatile cryptocurrency market.
creator: Dita Amelia
creator: Rizky Dwi Kurnia Rahayu
creator: Bimo Okta Syahputra
rights: Copyright (c) 2026 Dita Amelia, Rizky Dwi Kurnia Rahayu, Bimo Okta Syahputra https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-30
publication date: 2026-05-30
volume: 11
number: 1
starting page: 801
ending page: 819
doi: 10.18860/cauchy.v11i1.37720