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: BERTopic-Based Multi-Class Topic Classification on Indonesian Shopee E-commerce Reviews 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 Rings and It's Line Graph
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 Victims in West Java in 2024 Using Geographically Weighted Negative Binomial Regression
items: Numerical Pricing of European Stock Options Using Black-Scholes Interval Model
items: Stability Analysis of a Three-Trophic Rice Ecosystem with Holling Type 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
items: A Damped Hessian-Free Newton--Conjugate Gradient Method for Weighted Multiclass Neural Classification
items: Analysis of Color Space Transformations on MobileNetV2 Performance for Image Classification
items: Option Pricing Using Modification of Black Scholes Merton Model with GJR-GARCH
items: Haversine-Based Geographically Weighted Panel Regression of Human Development in Gorontalo (2016–2025)
items: ARIMA–GGJR–GARCH Modeling of Asymmetric Conditional Volatility in Wind Speed Time Series
items: A Simulation Study On The Robustness Of Bayesian Structural Equation Modeling Under Small Samples, Heavy Tails, and Collinearity
items: Modeling Airplane Passenger Volatility during the COVID-19 Crisis: a SARIMA and Intervention Analysis
items: Coronary Heart Disease Risk Prediction under Class Imbalance Using XGBoost with SHAP-Based Interpretation
items: Higher-Order Numerical Solution of the KdV-BBM Equation: A Comparative Analysis of Temporal Integration Schemes in the Method of Lines Framework
items: Total Edge Irregularity Strength of Cycle Snake Graphs
items: The Charactherization Criterion of g-quasi-Frobenius Lie Algebra Corresponding to Inner Derivation
items: Sentiment Analysis of Indonesia’s Free Nutritious Meal Program on X Using SVM and Random Forest
items: Spectral Analysis of a Cyclic Tank Mixing System
items: Local Stability and Bifurcation Analysis of a Mangrove Detritus Small-Fish Model with Dynamic Harvesting Effort under a Beddington-DeAngelis Functional Response
items: Spatial Regression Analysis using Queen Contiguity Weight Matrix and PCA Dimensionality Reduction
items: β-Duality of the Sequence Space ℓpL and a Geometric Realization via Wulff Shapes
items: The Triple Total Graph of The Ring Zn
items: Stability Analysis of a Predator-Prey Model with Disease in Prey, Predator Harvesting, and Internal Migration of Susceptible Prey in a Closed Ecosystem
items: Minor-Eigenvalue Spectral Analysis in Intuitionistic Fuzzy Soft Sets for Multicriteria Decision Making

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

BERTopic-Based Multi-Class Topic Classification on Indonesian Shopee E-commerce Reviews Using Ensemble Learning
type: item
description: The rapid growth of e-commerce platforms has resulted in a large volume of unstructured user reviews, creating challenges for scalable analysis. This study proposes a multi-class topic classification framework for Indonesian Shopee application reviews by integrating BERTopic-based embedding-driven topic modeling with ensemble learning. A total of 23,956 reviews are analyzed, with BERTopic applied exclusively to 19,167 training reviews to derive eight dominant topic labels, which serve as pseudo-labels for supervised classification using CatBoost and Extra Trees. Model performance is evaluated on a held-out test set under baseline and hybrid resampling settings to address severe class imbalance. The results show that hybrid resampling substantially improves balanced accuracy, particularly for CatBoost, while ROC–AUC remains consistently high, indicating robust class discrimination. Analysis of an unlabeled 2025 dataset, used solely in a deployment-style setting, reveals semantically consistent topic distributions on unseen data. Overall, the findings demonstrate that embedding-based topic modeling combined with ensemble learning provides an effective and scalable solution for multi-class topic classification in highly imbalanced e-commerce review data, with clear separation between training, evaluation, and post-deployment analysis.
creator: Kevin Alifviansyah
creator: Asep Saefuddin
creator: Septian Rahardiantoro
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 the risk of the Middle Income Trap (MIT), a condition in which economic growth stagnates after reaching middle-income status. This study aims to identify and model socio--economic factors affecting MIT at the provincial level in Indonesia during 2020--2023. The Generalized Additive Model (GAM) is employed to capture nonlinear and heterogeneous relationships between predictors and GRDP per capita with complex patterns that conventional linear or parametric models often fail to detect. The use of GAM in this context represents a methodological contribution, as studies applying GAM for MIT analysis in Indonesia remain very limited. This research therefore introduces a novel analytical approach by demonstrating how GAM can reveal flexible functional relationships and uncover nonlinear effects that are overlooked by traditional panel regression. GRDP per capita is modeled using six predictors: life expectancy, poverty rate, informal employment share, upper secondary education completion, food insecurity prevalence, and population density. The best model is obtained using the Gaussian family with an identity link, with five predictors showing nonlinear effects and food insecurity exhibiting a negative linear influence. The selected model demonstrates strong performance, indicated by an AIC value of 2743.279 and a R^2 of 98.6%, suggesting a very high explanatory power. In addition, the model achieves good predictive accuracy, with a MAPE of 8.04%. The findings support evidence-based policies aligned with Sustainable Development Goal (SDG) 8, promoting inclusive and sustainable 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 public health threat, with its transmission dynamics strongly influenced by vector control strategies and human behavior. This study constructs and analyzes a mathematical model based on a system of differential equations to investigate the transmission dynamics of DHF by integrating three control strategies: treatment, public awareness, and the release of Wolbachia-infected mosquitoes. The basic reproduction number (R0) is derived using the Next Generation Matrix (NGM) method and serves as a threshold parameter for disease spread. Numerical simulations show that when R0 < 1, the system converges to the disease-free equilibrium, indicating that the disease will eventually die out. Conversely, by adjusting the parameter δ such that R0 > 1, the system becomes stable at the endemic equilibrium, implying the persistence of the disease within the population. These findings highlight the importance of controlling key parameters through integrated intervention strategies to reduce R0 below unity.
creator: Rafika Nanda Agustina
creator: Budi Priyo Prawoto
rights: Copyright (c) 2026 Rafika Nanda Agustina, Budi Priyo Prawoto 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 increases morbidity, treatment failure, and healthcare costs. This study analyzes TB–DM transmission dynamics and identifies effective prevention strategies using a ten-compartment mathematical model that distinguishes non-diabetic and diabetic populations, each classified into susceptible, latent, active, treatment, and recovered classes. Numerical analysis verifies that the disease-free equilibrium is stable when the basic reproduction number is less than one, whereas an endemic equilibrium exists when it exceeds one. Using baseline parameter values, the reproduction number is estimated as 3.592, indicating persistent TB–DM transmission. An optimal control framework is formulated to evaluate two time-dependent interventions: reducing TB transmission through case detection and contact tracing, and preventing diabetes onset in non-diabetic individuals through metabolic monitoring. Numerical simulations demonstrate that the combined implementation of both control strategies significantly reduces TB–DM incidence while minimizing intervention costs. These findings support the importance of integrated, time-varying TB–DM control programs for public health.
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 bandwidth optimization using the corrected Akaike Information Criterion (AICc) as the objective function. For standard GWR, the bandwidth was selected using Cross-Validation (CV) to minimize prediction error, while for the GWR–FPA model, bandwidth optimization was performed using the Flower Pollination Algorithm (FPA) with the corrected Akaike Information Criterion (AICc) as the objective function. Three predictors were analyzed: population size (X1), literacy rate (X2), and mean years of schooling (X3). 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: X1 showed no significant local effect, whereas educational factors (X2 and X3) 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. The results highlight the dominant contribution of education-related components to the spatial decomposition of HDI variation across East Java. 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, 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 Rings and It's Line Graph
type: item
description: The prime graph of the ring R, P G(R), is a graph which set of vertices consists of elements of R and two different vertices are adjacent if their product in the ring is zero. We study the prime graph of cartesian product of the rings Zp1 × Zp2 for distinct prime numbers p1 and p2. We find that some properties of P G(Zp1 × Zp2 ) such as order, size, the number of triangles, and Wiener index. Further, we construct the line graph of P G(Zp1 × Zp2 ) and calculate the order, size, and Wiener index of L(P G(Zp1 × Zp2 )).
creator: Vira Hari Krisnawati
creator: Ayunda Faizatul Musyarrofah
creator: Noor Hidayat
creator: Farah Maulidya Fatimah
rights: Copyright (c) 2026 Vira Hari Krisnawati, Ayunda Faizatul Musyarrofah, Noor Hidayat, 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, up to four equilibrium points are obtained mathematically. Among these, three equilibria are biologically feasible under typical parameter values, corresponding to total extinction, predator extinction, and coexistence states. The total extinction equilibrium is always unstable, while the stability of the predator extinction and coexistence equilibria depends on the predator attack rate. Numerical simulations in the form of phase portraits were obtained by varying the parameters related to the predator attack rate. The simulation results show various dynamic behaviors, including predator extinction, asymptotically stable coexistence between prey and predators, and bistability. Numerical continuation analysis identifies a subcritical Hopf bifurcation at α=0.4595, confirmed by a positive first Lyapunov coefficient, as well as a saddle-node at α= 0.0478 and transcritical bifurcations α=3.0505 that alter equilibrium structure and stability. These findings demonstrate how prey group defense and predator cooperation can generate bistability and abrupt transitions between extinction and coexistence, accompanied by damped oscillatory dynamics near critical parameter values.
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 NPK fertilizers and chemical industries. Despite its importance, domestic production remains limited, and potential supply from by-product sources has not been utilized effectively. Consequently, Indonesia depends heavily on imports sourced mainly from a single country. This situation creates vulnerabilities in industrial supply chain and highlights the need for a clearer understanding of import volume and value dynamics. This study employs a Threshold Vector Autoregressive Integrated (TVARI) model to capture nonlinear and regime-dependent adjustments in the joint dynamics of import volume and value, with import volume growth as the threshold variable. The approach's novelty lies in its ability to accommodate structural changes that cannot be adequately represented by a single linear specification. Empirical results identify two statistically distinct regimes defined by whether import growth lies below or above an estimated threshold. In the first regime, where growth is below the threshold, short-run dynamics are primarily driven by changes in import value, indicating price-related adjustments. In the second regime, import volume exhibits stronger responses, reflecting quantity adjustments associated with supply-side conditions. These findings demonstrate that linear models are insufficient to capture asymmetric adjustment mechanisms in import behavior. By providing a formal mathematical description of regime-dependent dynamics, this study contributes to a deeper understanding of Indonesia’s industrial import structure and offers insights for data-informed supply chain planning. The results support policy discussions related to Sustainable Development Goals 8 (economic stability), 9 (industry resilience), and 12 (responsible consumption and production).
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 Ikbar Surya Andhika
creator: Sugiyarto Surono
creator: Aris Thobirin
rights: Copyright (c) 2026 Reynaldi Ikbar Surya 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 Victims in West Java in 2024 Using Geographically Weighted Negative Binomial Regression
type: item
description: Violence against children remains a critical issue in Indonesia, with West Java consistently reporting high numbers of reported child violence victims. This study examines socioeconomic factors associated with the count of reported child violence victims across 27 districts and cities in West Java in 2024, using secondary administrative data obtained from Open Data Jabar. The explanatory variables include poverty rate (X1), average years of schooling (X2), number of divorce cases (X3, Labor Force Participation Rate (X4), and Open Unemployment Rate (X5). Diagnostic tests indicate the presence of spatial heterogeneity and overdispersion, supporting the application of a Geographically Weighted Negative Binomial Regression (GWNBR) model with a child population offset. Model performance comparison based on in-sample fit criteria shows that the GWNBR model provides superior fit (deviance = 42.94, AICc = 99.87) compared to the global Negative Binomial Regression model (deviance = 48.27, AIC = 105.63). The GWNBR results reveal substantial spatial variation: average years of schooling (X2) is statistically significant across all 27 regions, while the number of divorce cases (X3) is significant in 23 regions. Poverty rate (X1) shows localized significance in 16 regions. Labor force participation rate (X4) and unemployment rate (X5) each exhibit significance in 6 regions, though with distinct spatial patterns. These findings highlight geographically varying risk structures that cannot be adequately captured by global models and underscore the importance of spatially adaptive modeling for informing region-specific child protection policies. Although the analysis relies on reported administrative data that may not fully represent the true underlying prevalence of child violence, the results provide valuable spatial insights relevant to policy development aligned with SDG 3, SDG 4, and 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 Type 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. 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. Parameter values are obtained from relevant literature where available, and the remaining parameters are considered reasonable biological assumptions for exploring the dynamics of the system qualitatively. 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 theoretical insights that may support the development of sustainable planthopper pest management 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 presents a Systematic Literature Review (SLR) and bibliometric analysis to identify the state of the art in green shortest path optimization. Using the PRISMA guideline, the study analyzes 20 articles selected from Scopus, ScienceDirect, and Dimensions databases published between 2021 and 2025. Results indicate that the field is dominated by metaheuristic and AI-based approaches, while deterministic methods with explicit objective prioritization remain underutilized. Bibliometric visualization identifies traffic congestion and carbon emission policies as major research clusters, yet few studies integrate these with real-time GPS data in developing countries. Based on these findings, this paper proposes a conceptual framework for a GPS-based Lexicographic Multi-Objective Optimization model. The proposed framework prioritizes carbon emission minimization as the primary objective, followed by travel time, offering a transparent decision-making tool for sustainable urban transportation.
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, and 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. This paper provides the approximation properties that hold to the equivalence and dominance relations using the concept of three types of approximations defined on a set. In addition, it identifies the properties that hold in the equivalence relations but do not necessarily hold in the dominance relations. Furthermore, this paper proves that the three types of approximations on a set w.r.t an equivalence relation are identical, but this result does not necessarily hold for a dominance relation, especially for the third type.
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 effects shape its flow conditions. These 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 -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, 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: This study investigates risk-sensitive reinforcement learning (RL) for portfolio decision-making under empirically heavy-tailed return distributions. We compare two policy-gradient architectures—REINFORCE with baseline (REINFORCE-BL) and batched Advantage Actor–Critic (A2C-B)—and examine how tail-based risk measures modify learning dynamics and robustness. Quantitative diagnostics confirm substantial excess kurtosis and strong rejection of normality in daily NASDAQ returns, motivating the integration of tail-sensitive objectives. Risk sensitivity is introduced at the episodic level through penalties based on Value at Risk (VaR), Conditional Value at Risk (CVaR), and Entropic Value at Risk (EVaR) at the 95% confidence level. Experiments are conducted in a multi-asset portfolio exposure-control environment, with performance evaluated across multiple random seeds using both training dynamics and out-of-sample financial metrics (CAGR, volatility, Sharpe ratio, drawdown, and realized tail risk). Results show that while both architectures perform comparably under the risk-neutral objective, actor–critic learning exhibits greater stability and lower dispersion under coherent tail penalties. In particular, CVaR and EVaR objectives lead to smoother convergence and reduced instability compared to VaR, especially for A2C-B. Statistical tests indicate that performance differences become more pronounced under coherent tail-risk objectives. These findings highlight the interaction between heavy-tailed environments, coherent risk measures, and algorithmic architecture, suggesting that actor–critic methods provide a more robust foundation for risk-sensitive RL in financial settings exposed to extreme events.
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 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 using a Fractal Interpolated Function constructed by the affine function that forms the Box Fractal shape. The developed method is 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 the interpolation results. For the n^{th} iteration, the number of boxes formed is 5^n, and the number of pairs of points is 4×5^n. Based on the rice demand data from one of the factories, the best MAPE was obtained at the $6^{th}$ iteration, with a value of 16.319%, which falls into the good category. Based on the data used, the affine function forming the Box Fractal as a Fractal Interpolated Function can be applied in fractal interpolation techniques.
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 (ICP) is highly volatile due to fluctuations in global demand, energy policies, and geopolitical tensions, making accurate forecasting challenging. This study compares three forecasting models: ARIMA, Random Forest, and Hybrid ARIMA–Random Forest. The models are evaluated using Time-Series Cross-Validation (TSCV) with MAPE, sMAPE, and RMSE as performance metrics. The results indicate that the Hybrid ARIMA–Random Forest model achieves the lowest MAPE and sMAPE, while Random Forest attains the lowest RMSE, and ARIMA exhibits the highest forecast errors. Diebold–Mariano (DM) tests confirm that ARIMA’s predictive accuracy is significantly lower than both machine-learning-based models, whereas no significant difference is found between Random Forest and the hybrid model. Out-of-sample forecasts for January–June 2026 show relatively stable price movements within 59–63 USD per barrel, with short-term fluctuations reflected in wide prediction intervals. These findings suggest that Indonesian crude oil prices contain both linear and non-linear components, which are effectively captured by the hybrid approach. Overall, the Hybrid ARIMA–Random Forest model provides the most accurate forecasts in percentage-based metrics, offering a robust and reliable tool 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: This applied quantitative study implements Simpson's 1/3 numerical integration to systematically evaluate the pricing of discrete-dividend-adjusted European options. Using an anonymized technology stock, XYZ Tech Corp., as an empirical case study, this research pursues two primary objectives: validating the computational convergence of the numerical algorithm against the exact Black-Scholes analytical benchmark using Relative Error, and analyzing the model's empirical pricing deviation against real market observations across various moneyness zones. Computational tests demonstrate that the Simpson's 1/3 method, which is theoretically bounded by a fourth-order truncation error, achieves optimal and rapid convergence. By establishing the grid partition at N = 200, the algorithm successfully suppresses the relative error strictly below a 0.001% threshold compared to the analytical solution, while executing efficiently in under 0.005 seconds. Empirically, while the theoretical model exhibits high accuracy for In-The-Money (ITM) options with minimal deviation, it consistently reveals a significant overvaluation bias for Out-Of-The-Money (OTM) Call contracts, whereas OTM Put valuations exhibit a structurally different deviation pattern. This valuation asymmetry suggests a potential limitation of the constant historical volatility assumption, which appears inadequate to fully capture the implied volatility skew and shifting risk perceptions prevalent in actual market microstructures.
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

A Damped Hessian-Free Newton--Conjugate Gradient Method for Weighted Multiclass Neural Classification
type: item
description: This study presents a deterministic damped Hessian-free Newton--CG method for weighted multiclass neural classification. The method is built from a weighted categorical cross-entropy objective, a damped local quadratic model, and a matrix-free curvature representation through Hessian--vector products. The search direction is computed by an inexact conjugate gradient solve, while Armijo backtracking and adaptive damping are used to improve stability. The method is implemented for the classification of academic predicate categories using preprocessed student data with mixed categorical and numerical features. Its numerical behavior is compared with SGD with momentum, RMSProp, and Adam under the same loss, initialization, and network architecture. The proposed method is computationally feasible, attains the best overall weighted test-set performance among the compared methods, and exhibits a distinct optimization trajectory driven by curvature-informed updates. These results show that a damped Hessian-free formulation provides a mathematically transparent, reproducible, and practically competitive framework for second-order optimization in multiclass neural classification.
creator: Andy Irawan
creator: Zainal Abidin
creator: Mohammad Jamhuri
rights: Copyright (c) 2026 Andy Irawan, Zainal Abidin, Mohammad Jamhuri 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: 820
ending page: 841
doi: 10.18860/cauchy.v11i1.40243

Analysis of Color Space Transformations on MobileNetV2 Performance for Image Classification
type: item
description: This study analyzes the effect of color space transformation on the performance of MobileNetV2 for rice leaf disease classification using RGB, HSV, CIELab, and their combinations. The RGB color space is used as the baseline representation, while HSV and CIELab are applied to provide alternative representations of color information. In addition, a dual-stream architecture is employed to combine different color spaces for feature extraction. The results show that the choice of color space influences classification performance. In the single color-space scenario, RGB achieves the highest accuracy of 91.42%, while in the combined scenario, the RGB+CIELab model achieves the best performance with an accuracy of 97.00%. These findings suggest that the use of multiple color spaces can provide richer feature representations and may improve classification performance. Furthermore, the results indicate that optimizing input representation plays an important role in improving model performance, particularly when using lightweight architectures such as MobileNetV2. This study shows that color space transformation can improve classification performance in the rice leaf disease dataset used in this study.
creator: Sherlyn Vironica
creator: Sugiyarto Surono
creator: Aris Thobirin
rights: Copyright (c) 2026 Sherlyn Vironica, Sugiyarto Surono, Aris Thobirin 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: 842
ending page: 856
doi: 10.18860/cauchy.v11i1.41353

Option Pricing Using Modification of Black Scholes Merton Model with GJR-GARCH
type: item
description: Option pricing is an important topic in modern finance as it plays a role in investment strategy and risk management. The Black-Scholes-Merton (BSM) model introduced in 1973 has become the standard in option pricing, but the assumption of constant volatility and symmetry makes this model often less suitable for volatile and asymmetric market conditions. This study aims to modify the BSM by incorporating volatility estimated through the Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) model, and compare its performance with the Fractional Black-Scholes-Merton (FBSM) model. The data used is the daily closing price of Apple Inc. shares for the period January 7, 2022 to March 7, 2025 obtained from Yahoo Finance. The research procedure includes stationarity test using Augmented Dickey-Fuller (ADF), ARIMA identification, heteroscedasticity testing, and volatility estimation with GJR-GARCH (1,1) model. European call option prices are estimated by BSM and FBSM using both historical volatility and GJR-GARCH volatility. The results show that the FBSM model with GJR-GARCH (1,1) volatility provides the most accurate estimation with a Mean Absolute Percentage Error (MAPE) of 4.08%. In contrast, the BSM with historical volatility yields a MAPE of 17.25%. These findings confirm that the integration of FBSM with GJR-GARCH volatility is more realistic and reliable in option pricing under dynamic and asymmetric market conditions.
creator: Fatimah Oktaviani
creator: Emy Siswanah
rights: Copyright (c) 2026 Fatimah Oktaviani, Emy Siswanah 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: 857
ending page: 869
doi: 10.18860/cauchy.v11i1.37426

Haversine-Based Geographically Weighted Panel Regression of Human Development in Gorontalo (2016–2025)
type: item
description: Spatial disparities in human development indicate that socioeconomic factors may influence development outcomes differently across locations. This study aims to analyze spatially varying relationships between the Human Development Index and its key determinants in districts and cities in Gorontalo Province, Indonesia, during the period 2016--2025. The analysis uses balanced panel data and models human development as a function of mean years of schooling, life expectancy at birth, and real per capita expenditure. A geographically weighted panel regression approach is applied, with spatial relationships modeled using great-circle distances and an adaptive kernel weighting scheme, while a fixed-effects panel model serves as the global reference. The results reveal a clear spatial heterogeneity in the effects of the explanatory variables, where education consistently shows the strongest positive influence on human development in all regions, followed by health conditions. Economic expenditure exhibits a weaker and spatially varying effect and is not influential in the provincial capital. These findings underscore the importance of accounting for spatial heterogeneity in regional development analyses and support the formulation of place-based human development policies tailored to local conditions.
creator: Debora Dwi Kurniawati
creator: Henny Pramoedyo
creator: Suci Astutik
creator: Friansyah Gani
rights: Copyright (c) 2026 Debora Dwi Kurniawati, Henny Pramoedyo, Suci Astutik, Friansyah Gani 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: 870
ending page: 886
doi: 10.18860/cauchy.v11i1.40886

ARIMA–GGJR–GARCH Modeling of Asymmetric Conditional Volatility in Wind Speed Time Series
type: item
description: Volatility modeling plays a crucial role in time-series forecasting, particularly for wind speed, where variability and asymmetric responses to shocks are commonly observed. Accurate wind speed forecasting can help mitigate potential risks associated with extreme or uncontrolled wind events. While the Autoregressive Integrated Moving Average (ARIMA) model is widely used to model the conditional mean of time series, it does not capture time-varying volatility or asymmetric effects. To address this limitation, we combine ARIMA with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and asymmetric extensions, including the Glosten–Jagannathan–Runkle GARCH (GJR-GARCH) and its generalized form (GGJR-GARCH). This framework allows simultaneous modeling of the conditional mean and conditional variance, accommodating heteroscedasticity and leverage effects in wind speed data. The empirical results indicate that negative shocks exert a stronger impact on conditional volatility than positive shocks, confirming the presence of asymmetry. Based on forecasting performance evaluation, the ARIMA(2,0,1)–GGJR-GARCH(1,1) specification provides the most accurate predictions among the competing models.
creator: Nurhayati Nurhayati
creator: Andi Fitriawati
rights: Copyright (c) 2026 Nurhayati Nurhayati, Andi Fitriawati 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: 887
ending page: 903
doi: 10.18860/cauchy.v11i1.41180

A Simulation Study On The Robustness Of Bayesian Structural Equation Modeling Under Small Samples, Heavy Tails, and Collinearity
type: item
description: Bayesian Structural Equation Modeling (BSEM) is increasingly used in health and social research, yet its operating characteristics under district-level constraints remain under-documented when three difficulties co-occur: small sample sizes, heavy-tailed errors, and strong correlations among exogenous constructs. We evaluate BSEM robustness using a Monte Carlo simulation with a fixed full-mediation SEM comprising four latent variables (two exogenous constructs, a mediator, and an outcome) and three reflective indicators per construct. A balanced 2×2×2 design varies sample size (n ∈ {22, 75}), error family (Normal vs. Student-t with ν = 5, variance-matched), and exogenous correlation (ρ ∈ {0.30, 0.80}). For each scenario, R = 50 independent datasets are generated and fitted using MCMC (Stan/NUTS via blavaan). We summarize global fit via posterior predictive p-values (PPP), sampling quality via \hat{R} and effective sample size (ESS), and sampler diagnostics including divergent transitions, alongside parameter recovery via Monte Carlo bias, RMSE, and 95% credible-interval coverage for structural paths, mediated effects, and ρ. Across conditions, increasing n improves both parameter recovery and sampling behavior. The most fragile settings occur when n = 22 and ρ is high, where the parallel paths X1→M and X2→M become weakly identified and heavy-tailed errors can further degrade precision. These results provide practical guidance for applying BSEM to district-level studies with limited sample sizes.
creator: Agustina Susi Susanti Parung
creator: Ani Budi Astuti
creator: Rahma Fitriani
rights: Copyright (c) 2026 Agustina Susi Susanti Parung, Ani Budi Astuti, Rahma Fitriani 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: 904
ending page: 920
doi: 10.18860/cauchy.v11i1.41328

Modeling Airplane Passenger Volatility during the COVID-19 Crisis: a SARIMA and Intervention Analysis
type: item
description: The COVID-19 pandemic in early 2020 had a severe impact on air traffic at Indonesia’s Soekarno-Hatta International Airport, which is among the busiest in the world. This caused a sharp decline in passenger numbers in April 2020, resulting in significant data fluctuations that required statistical intervention. Therefore, to forecast passenger numbers during these fluctuating trends, this study used the SARIMA and Step Function Intervention analysis. The results showed that the Step Function Intervention model was more accurate than SARIMA in predicting the number of passengers at the domestic departure terminal. Based on data for the period between January 2006 and June 2024, the step function intervention model produced MAD, MSE, RMSE, and MAPE values that are smaller than the SARIMA model. The best model, SARIMA Intervention (2,1,0)(1,1,1)12 b = 0, s = 3, r = 1, fulfilled the white noise and normality assumptions with a MAD accuracy value of 82381.85 and MAPE of 9.62%. In addition, the Step Function Intervention Method further reduced the MAPE value by up to 6.93%.
creator: Nur Faizin
creator: Achmad Fauzan
rights: Copyright (c) 2026 Nur Faizin, Achmad Fauzan 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: 921
ending page: 936
doi: 10.18860/cauchy.v11i1.40880

Coronary Heart Disease Risk Prediction under Class Imbalance Using XGBoost with SHAP-Based Interpretation
type: item
description: Coronary heart disease (CHD) risk prediction is challenging because clinical data are heterogeneous and the response variable is imbalanced. This study develops an interpretable predictive framework for CHD risk using Extreme Gradient Boosting (XGBoost), median imputation, IQR-based winsorization, standardization, the Synthetic Minority Over-sampling Technique (SMOTE), bootstrap-based uncertainty assessment, and Shapley Additive Explanations (SHAP). The learning problem is formulated within a regularized empirical risk minimization framework, so the model is viewed as a statistical estimator rather than merely an algorithmic classifier. To avoid information leakage, train–test splitting is performed before any resampling, and SMOTE is applied only to the training data. The primary analysis is fixed a priori at an 80:20 stratified split, whereas 60:40 and 70:30 splits are treated as sensitivity analyses rather than model-selection devices. In the primary analysis, the model attains accuracy of 79.36%, precision of 27.88%, recall of 22.48%, F1-score of 24.89%, and ROC–AUC of 0.6502. The 95% bootstrap confidence interval for ROC–AUC is [0.6017, 0.6981]. SHAP analysis in probability space identifies age , cigsPerDay , male , heartRate , and sysBP as the most influential predictors. These results show that the proposed framework is mathematically well-structured and interpretable, but that its out-of-sample discrimination on this dataset is moderate rather than high.
creator: Siti Amiroch
creator: Fitri Nur Laili
creator: Awawin Mustana Rohmah
creator: Dicka Yale Kardono
rights: Copyright (c) 2026 Siti Amiroch 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: 937
ending page: 955
doi: 10.18860/cauchy.v11i1.37938

Higher-Order Numerical Solution of the KdV-BBM Equation: A Comparative Analysis of Temporal Integration Schemes in the Method of Lines Framework
type: item
description: This study investigates the numerical simulation of solitary wave propagation governed by the KdV-BBM equation using a robust Method of Lines (MOL) framework. The governing nonlinear equation is transformed into a system of ordinary differential equations through spatial discretization, and the performance of three temporal integration schemes is evaluated: the first-order Euler method, the fourth-order Runge-Kutta (RK-4), and the fifth-order iRK-5 method. Quantitative analysis using Mean Absolute Error (MAE) for various time steps (Δt = 0.2, 0.1, 0.05, and 0.01) reveals that the iRK-5 scheme provides enhanced temporal precision, achieving error magnitudes as low as 10−6 and consistently aligning with the exact traveling-wave solution. Notably, the iRK-5 method demonstrates greater algorithmic efficiency, achieving an accuracy level of 4.55 × 10−6 at a coarser time step of Δt = 0.1, whereas the RK-4 scheme requires a finer time step of Δt = 0.05 to reach the same precision. Both high-order methods eventually reach a spatial error floor where further temporal refinement yields no significant reduction in MAE, emphasizing that high-order temporal integration, particularly the iRK-5 scheme, is essential for preserving the physical integrity of complex nonlinear wave phenomena while maintaining optimal computational effort.
creator: Dita Ardiana
creator: Ummu Habibah
creator: Trisilowati Trisilowati
creator: Rahifa Binti Ranom
rights: Copyright (c) 2026 Dita Ardiana, Ummu Habibah, Trisilowati -, Rahifa Binti Ranom 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: 956
ending page: 969
doi: 10.18860/cauchy.v11i1.41525

Total Edge Irregularity Strength of Cycle Snake Graphs
type: item
description: Let G be a simple undirected graph with vertex and edge sets. A total labeling that assigns integers from 1 to k to the union of the vertex and edge sets is called a k-total labeling. The weight of an edge uv, denoted by w(uv), is defined as the sum of the labels of the two vertices u, v, and the label of edge uv itself. A k-total labeling is called an edge irregular total k-labeling of G if the weights of all distinct edges are different. The minimum k for which every edge of G has a distinct weight is called the total edge irregularity strength of G, denoted by tes(G). A cycle snake graph CSm,n is obtained from the path graph Pn with n + 1 vertices and n edges by replacing each edge with a cycle graph Cm, where m ≥ 3 and n ≥ 2. In this paper, we study the graphs CS3,n and CSm,n and determine their total edge irregularity strength. The case m = 3 is considered separately because the structure of CS3,n gives a different representation of the vertex and edge sets than for m ≥ 4, requiring a different labeling construction.
creator: Stenly Pranata
creator: Vira Hari Krisnawati
creator: Darmajid Darmajid
rights: Copyright (c) 2026 Stenly Pranata 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: 970
ending page: 986
doi: 10.18860/cauchy.v11i1.41552

The Charactherization Criterion of g-quasi-Frobenius Lie Algebra Corresponding to Inner Derivation
type: item
description: The structure of a g-quasi-Frobenius Lie Algebra can be realized as a quasi-Frobenius Lie Algebra modules over a Lie Algebra g. This research discusses a special condition of the g-quasi-Frobenius Lie Algebra, namely when g acts on its self. This condition supports the construction of an inner derivation on g. The criterion investigated is the characterization of the g-quasi-Frobenius Lie Algebra in relation to the inner derivation. The result obtained is a criterion: a g-quasi-Frobenius Lie Algebra can be constructed on g itself if and only if the inner derivation is zero. Furthermore, several concrete examples are provided to test this criterion.
creator: Muhammad Arief Budiman
creator: Edi Kurniadi
creator: Sukono Sukono
rights: Copyright (c) 2026 Muhammad Arief Budiman, Edi Kurniadi, Sukono Sukono 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: 987
ending page: 1002
doi: 10.18860/cauchy.v11i1.41601

Sentiment Analysis of Indonesia’s Free Nutritious Meal Program on X Using SVM and Random Forest
type: item
description: The Free Nutritious Meal (Makan Bergizi Gratis/MBG) Program was introduced to address stunting in Indonesia, yet its implementation has sparked diverse public debate. This study aims to map public perception on social media X and compare the performance of Support Vector Machine (SVM) and Random Forest algorithms in sentiment classification. Utilizing a large-scale dataset of 7,452 tweets collected via stratified random sampling from January to October 2025, this research applies TF-IDF feature extraction and SMOTE data balancing. The analysis reveals that positive sentiment dominates at 47.62%, while negative sentiment accounts for 39.8\%, and neutral for 12.57%. In model comparison, SVM without SMOTE achieved the best performance with 80.66% accuracy and an F1-Score of 79.79%, outperforming Random Forest, which only reached a maximum accuracy of 72.23% after SMOTE application. These findings provide an objective overview of MBG policy acceptance and methodological insights into the effectiveness of SVM in handling high-dimensional text data.
creator: Ferdy Aliansyah Hasyim
creator: Talenta Parfaibya Mahenindra
creator: Lilis Sriwahyuni
creator: Alika Azka Shapira
creator: Wigawijayanti Wigawijayanti
creator: Nadhifa Zahra Ghaisani
creator: Mirlan Sujana
creator: Sri Nurdiati
creator: Mohamad Khoirun Najib
rights: Copyright (c) 2026 Ferdy Aliansyah Hasyim, Talenta Parfaibya Mahenindra, Lilis Sriwahyuni, Alika Azka Shapira, Wigawijayanti Wigawijayanti, Nadhifa Zahra Ghaisani, Mirlan Sujana, Sri Nurdiati, Mohamad Khoirun Najib 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: 1003
ending page: 1016
doi: 10.18860/cauchy.v11i1.40717

Spectral Analysis of a Cyclic Tank Mixing System
type: item
description: In this paper, we study a cyclic mixing tank system consisting of n identical tanks arranged in a closed-loop configuration, each operating under constant volume with equal inflow and outflow rates. The model is further generalized to an m-layer structure, where each layer comprises n circularly interconnected tanks. Based on mass balance principles, the concentration dynamics are formulated as a linear system of first-order ordinary differential equations. By exploiting the structured form of the system matrix, we derive an explicit analytical solution and obtain a closed-form characterization of its spectrum. We show that the eigenvalues of the system are explicitly given by λk,j = α(-2 + e2πi(k-1)/n), which inherently guarantees the decay of all modes. In particular, the solution exhibits a polynomial-exponential form associated with the multilayer cyclic tank. We also establish that the system is exponentially stable under conditions ensuring decay of all modes. Finally, we present numerical simulations to validate the analytical results and to illustrate the transient dynamics of the multilayer system.
creator: Pebrudal Zanu
creator: Sri Wahyu
creator: Mohammad Januar Ismail Burhan
rights: Copyright (c) 2026 Pebrudal Zanu, Sri Wahyu, Muhammad Januar Ismail Burhan 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: 1017
ending page: 1032
doi: 10.18860/cauchy.v11i1.41466

Local Stability and Bifurcation Analysis of a Mangrove Detritus Small-Fish Model with Dynamic Harvesting Effort under a Beddington-DeAngelis Functional Response
type: item
description: This study develops a three-dimensional mangrove detritus small fish model with a dynamics harvesting effort governed by a threshold rule and a Beddington DeAngelis functional response. The main objective is to understand how adaptive harvesting and consumer interference shape long-term dynamics and stability. Equilibrium points are derived and their local stability is examined using the Jacobian matrix and eigenvalue-based criteria, supported by numerical simulations. Bifurcation analysis with respect to the threshold parameter is performed using numerical continuation to detect qualitative transitions in system behavior. The results show the existence of biologically feasible coexistence equilibria with active harvesting, including a stable branch and an unstable branch. A Hopf bifurcation is detected at approximately a = 6.6159, confirming the emergence of sustained oscillations limit cycles in fish density and harvesting effort, while a fold limit point occurs near a = 22.001, indicating changes in equilibrium structure. Moreover, simulation scenarios demonstrate that reducing environmental capacity and increasing fish mortality can drive the system toward a no-effort equilibrium where harvesting collapses. These findings highlight the threshold parameter as a key control factor that can switch the system between stable harvesting, effort extinction, and oscillatory harvesting regimes.
creator: Donna Kurniasih
creator: Dian Savitri
rights: Copyright (c) 2026 Dian Savitri, Donna Kurniasih 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: 1033
ending page: 1048
doi: 10.18860/cauchy.v11i1.41486

Spatial Regression Analysis using Queen Contiguity Weight Matrix and PCA Dimensionality Reduction
type: item
description: Conventional linear regression often falls short in poverty analysis, as it fails to account for spatial interdependence between neighboring regions and frequently encounters multicollinearity among socioeconomic variables. This study investigates the presence and nature of spatial effects in poverty data across regencies and cities in Central Java Province, Indonesia, and assesses the performance of an enhanced spatial regression model. We employ a Spatial Autoregressive Model (SAR) integrated with a queen contiguity spatial weight matrix and apply Principal Component Analysis (PCA) to reduce dimensionality and mitigate multicollinearity. The results demonstrate a strong model fit, with a pseudo R2 of 0.94311, and reveal a statistically significant negative spatial lag coefficient (ρ = -0.2039, p-value = 0.04420), indicating that areas of lower poverty are often surrounded by higher poverty neighbors. This integrated approach provides a more accurate framework for spatial poverty mapping, offering actionable insights for designing regionally targeted development policies.
creator: Joko Purwadi
creator: Iliana Dewinta
rights: Copyright (c) 2026 Joko Purwadi, Iliana Dewinta 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: 1049
ending page: 1064
doi: 10.18860/cauchy.v11i1.40908

β-Duality of the Sequence Space ℓpL and a Geometric Realization via Wulff Shapes
type: item
description: In the present paper, we investigate the structural and geometric properties of the non-absolute type sequence space ℓpλ. Our primary novel contribution lies in demonstrating that the natural norm on its β-dual coincides with the dual norm of ℓpλ. We then investigate geometric properties of the space and prove that ℓpλ inherits uniform convexity and uniform smoothness from the classical space ℓp for 1 < p < ∞, while these properties fail in the case p = 1. Finally, by considering finite-dimensional truncations, we interpret the dual norm geometrically through the Wulff construction. This yields a visualization of the norm unit sphere as a Wulff shape and shows that geometric features of the resulting shape reflect the convexity and smoothness properties of the underlying sequence space.
creator: Adrian Taruna Barus
creator: Meisya Shekina
rights: Copyright (c) 2026 Adrian Taruna Barus 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: 1065
ending page: 1081
doi: 10.18860/cauchy.v11i1.40008

The Triple Total Graph of The Ring Zn
type: item
description: Let R be a commutative ring and let Z(R) denotes the set of zero-divisors of R. The triple total graph of R, denoted by TT(R), is a simple graph whose vertex set is R∖{0}. Two distinct vertices v1 and v2 are adjacent in TT(R) if and only if v1+v2∉Z(R) and there exists v3∈R∖{0}, with v3≠v1 and v3≠v2, such that v1+v3∉Z(R), v2+v3∉Z(R), and v1+v2+v3∈Z(R). In this paper, we investigate the structural properties of the graph TT(Zn). We show that if n is even with n > 2, then TT(Zn) is an empty graph. When n is prime with 2 < n < 11, the graph TT(Zn) is disconnected. In contrast, for prime integers n≥ 11, the graph becomes connected with diam(TT(Zn))=2 and gr(TT(Zn))=3. Moreover, each vertex has degree n−5, implying that the graph is (n−5)-regular and consequently both Eulerian and Hamiltonian. These results illustrate how the arithmetic nature of n determines the global structure of the triple total graph.
creator: Vika Yugi Kurniawan
creator: Syaifudin Zyuhri
creator: Santoso Budi Wiyono
rights: Copyright (c) 2026 Vika Yugi Kurniawan, Syaifudin Zyuhri, Santoso Budi Wiyono 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: 1082
ending page: 1094
doi: 10.18860/cauchy.v11i1.41488

Stability Analysis of a Predator-Prey Model with Disease in Prey, Predator Harvesting, and Internal Migration of Susceptible Prey in a Closed Ecosystem
type: item
description: This study develops and analyzes a mathematical model of a predator-prey system incorporating three simultaneous ecological factors: disease in the prey population, harvesting of the predator, and internal migration of healthy prey within a closed ecosystem. The prey population is divided into two compartments healthy prey and infected prey where disease transmission follows the law of mass action. The predator population is subject to a constant harvesting rate representing external pressure such as hunting or capture. Internal migration of healthy prey is modeled as a density-dependent flux governed by a migration parameter m, which drives the redistribution of healthy prey across spatial patches without allowing permanent emigration from the system. The model is formulated as a system of three autonomous ordinary differential equations. Six equilibrium points are identified, representing a range of ecological scenarios from total extinction to full coexistence of all populations. The local stability of each equilibrium point is analyzed by linearization via the Jacobian matrix, and stability conditions are derived in terms of the model parameters, including the application of the Routh–Hurwitz criterion for the coexistence equilibrium. A key finding is that the migration parameter m does not alter the location of equilibrium points but directly influences the eigenvalues of the Jacobian, thereby affecting the rate at which the system recovers from perturbations. Numerical simulations are conducted to verify and illustrate the analytical results. This work extends the model of Mansur et al. [1] by introducing an internal spatial dimension, offering a more ecologically realistic framework for understanding population dynamics in ecosystems where disease, harvesting, and migration co-occur
creator: Muhammad Thariq Firmansyah
creator: Dian Savitri
rights: Copyright (c) 2026 Dian Savitri, Muhammad Thariq Firmansyah 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: 1095
ending page: 1121
doi: 10.18860/cauchy.v11i1.41546

Minor-Eigenvalue Spectral Analysis in Intuitionistic Fuzzy Soft Sets for Multicriteria Decision Making
type: item
description: Multi-criteria decision making (MCDM) under uncertain data requires a framework capable of capturing ambiguity and non-linear interactions among criteria. This study develops an Intuitionistic Fuzzy Soft Set (IFSS)-based MCDM model using spectral analysis of aggregation matrices constructed with the Einstein operator. Unlike approaches that rely mainly on global eigenvalues, the proposed method utilizes dominant eigenvalues of principal minors to capture local structural variations among alternatives. The method is validated using subdistrict-level economic facility data from Lamongan Regency. The results produce spectral scores ranging from 0.0683 to 2.0000, with Bluluk obtaining the lowest score and Lamongan obtaining the highest score. Several alternatives with comparable global structural characteristics also exhibit distinct minor-eigenvalue responses, indicating that the proposed approach can reveal local structural variations that may not be reflected in global spectral analysis. These findings suggest that minor-eigenvalue-based spectral analysis provides an alternative local perspective for distinguishing alternatives within the IFSS framework. The proposed framework contributes theoretically to IFSS-based spectral modeling and practically supports decision-makers in prioritizing subdistrict development based on local structural characteristics.
creator: Silfiatis Sabila Azra Shofa
creator: Siti Amiroch
creator: Awawin Mustana Rohmah
rights: Copyright (c) 2026 Silfiatis Sabila Azra Shofa, Siti Amiroch, Awawin Mustana Rohmah 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: 1122
ending page: 1138
doi: 10.18860/cauchy.v11i1.41247

Qualitative and Numerical Analysis of an SVEIR Model for HIV-HBV Co-Infection
type: item
description: The dynamics of HIV-HBV co-infection present significant epidemiological challenges, particularly in resource-limited areas. This study employs the SVEIR mathematical model to explore the transmission and control of HIV-HBV co-infection in Kupang City, Indonesia. Using the Next Generation Matrix method, the basic reproduction number (R0) was estimated at 1.36, indicating persistent disease transmission without effective intervention. Sensitivity analyses identified HBV vaccination coverage and treatment accessibility as critical parameters significantly influencing infection dynamics. Numerical simulations validated the theoretical model, demonstrating that increased vaccination rates and enhanced antiviral therapy access substantially reduce co-infection prevalence. Furthermore, equilibrium analyses revealed that effective interventions capable of lowering R0 below unity could transition the system from persistent endemicity toward disease elimination. These results emphasize the necessity of integrated intervention strategies, including expanded HBV vaccination, improved antiviral therapy access, and comprehensive community education to mitigate HIV-HBV co-infection. Future research should address existing limitations, incorporating behavioral and socioeconomic determinants to enhance model accuracy and applicability.
creator: Maria Lobo
creator: Adelya Hanaya Mage
creator: Ariyanto Ariyanto
rights: Copyright (c) 2026 Maria Lobo 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: 1139
ending page: 1154
doi: 10.18860/cauchy.v11i1.40185

Comparison of Extreme Value Logistic and Copula Approaches for Bivariate Extreme Value in Pekanbaru
type: item
description: Global climate change has intensified extreme weather events in tropical regions, increasing heat-related risks in Pekanbaru City. This study aims to analyze the joint behavior of extreme maximum temperature and humidity using a multivariate extreme value framework. Daily data from 2014–2024 were processed using a seasonal block maxima approach, resulting in 24 seasonal extreme observations. The marginal distributions follow a Weibull-type Generalized Extreme Value (GEV) distribution, indicating bounded extreme values. Dependence analysis indicates a weak association, where the Joe copula converges to the independence case, while the Frank copula yields the lowest AIC value among the fitted copula models. However, the difference in AIC values is small and should be interpreted cautiously. Joint return period analysis indicates that joint exceedance of seasonal block maxima is relatively infrequent (approximately 100 years), whereas single-variable exceedances occur more frequently (approximately 5.2 years). These return period estimates are exploratory and subject to uncertainty due to the limited sample size. Overall, the results suggest a weak dependence structure between the variables, and the findings should be interpreted cautiously in the context of climate-related risk assessment.
creator: Fadilla Afsari
creator: A'yunin Sofro
rights: Copyright (c) 2026 Fadilla Afsari, 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: 1155
ending page: 1170
doi: 10.18860/cauchy.v11i1.41081

Risk Analysis of Shallot Farm Income Using D-vine Copula-Based Monte Carlo Simulation
type: item
description: Shallot farm income is highly uncertain due to fluctuations in yields, prices, and production costs, which are interdependent and significantly correlated. This study evaluates income risk by modeling the dependence structure among the variables that constitute income, while addressing data limitations. Two approaches are employed. First, a parametric approach models income as a univariate variable under the assumption of a normal distribution, ignoring dependence among its components. Second, a multivariate simulation approach utilizes a D-vine copula, combined with Monte Carlo simulation, to capture the dependence among income components and generate synthetic observations that better represent tail behavior. Risk is measured using Value-at-Risk (VaR) and Expected Shortfall (ES) based on 32 observations of average shallot farm income per harvest season over the period 2014–2024, and the results are compared with empirical estimates. Due to limited data, the empirical approach produces relatively coarse estimates, particularly in the tail region. The normal distribution approach yields higher and smoother estimates, indicating a higher level of risk. In contrast, the D-vine copula approach provides lower estimates than the normal distribution. These differences indicate that each method offers a distinct perspective on income risk.
creator: Fatimah Fuzzaroh
creator: Berlian Setiawaty
creator: I Gusti Putu Purnaba
rights: Copyright (c) 2026 Fatimah Fuzzaroh, Berlian Setiawaty, I Gusti Putu Purnaba 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: 1171
ending page: 1186
doi: 10.18860/cauchy.v11i1.41556

Application of Reich-Perov 𝛼-Contractive Mapping in Vector Valued Metric Space
type: item
description: This paper presents two new applications of a fixed point theorem for Reich–Perov α-contractive mappings in vector-valued metric spaces. As a new application, we first demon-strate the existence and uniqueness of a solution to the vector valued Volterra-Fredholm integral equation system. By constructing suitable integral operators, we show that they satisfy the α-contractive Reich-Perov condition. The second application concerns the determination of the fixed point for discrete recursive systems with coupled components, for which the existence of a unique solution is established.
creator: Sunarsini Sunarsini
creator: Mahmud Yunus
creator: Subiono Subiono
rights: Copyright (c) 2026 Sunarsini Sunarsini, Mahmud Yunus, Subiono Subiono 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: 1187
ending page: 1201
doi: 10.18860/cauchy.v11i1.41240

Dynamical Analysis of a Trophic Model on Guano, Invertebrates, and Fish in Cave Ecosystems
type: item
description: This study investigates the dynamical interaction between guano biomass density (x), invertebrate biomass density (y), and fish biomass density (z) through a three-compartment trophic model representing a nutrient-based cave ecosystem. The analysis identifies three equilibrium points: the consumer-free equilibrium E0, the predator-free equilibrium E1, and the coexistence equilibrium E2. Local stability analysis shows that the coexistence equilibrium is asymptotically stable, characterized by eigenvalues with negative real parts (λ1 = -0.519706 and λ2,3 = -0.085385 ± 0.188169i). Numerical simulations using the fourth–fifth order Runge–Kutta method (RK45) support these analytical results, showing trajectories that exhibit damped oscillations before converging to the steady state. Furthermore, a bifurcation analysis reveals a critical Branching Point (BP) at the predation rate b2 ≈ 0.043956. This threshold signifies a transcritical bifurcation where the system transitions from a predator-extinction regime to a stable coexistence regime, highlighting the sensitivity of the food web to energy transfer efficiency. These findings suggest that under the assumed parameter set, the interaction between guano nutrients, invertebrates, and fish can maintain a stable ecological balance through top-down control and nutrient-dependent dynamics.
creator: M Niko Axsella Ibrahim
creator: Dian Savitri
rights: Copyright (c) 2026 Dian Savitri, M Niko Axsella Ibrahim 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: 1202
ending page: 1217
doi: 10.18860/cauchy.v11i1.41524

A Two-Stage Kalman Filter and ARIMA Framework for High-Frequency Wind Speed Modeling in Equatorial Regions
type: item
description: High-frequency wind speed data collected via environmental monitoring systems often contain significant stochastic noise that can obscure underlying patterns and degrade the reliability of statistical models. A two-stage modeling framework (integrating a Kalman Filter (KF) for signal purification and Autoregressive Integrated Moving Average (ARIMA) for predictive modeling) was developed and applied to five-minute interval wind speed data in Pontianak, West Kalimantan. The dataset, comprising 3,742 observations recorded from December 11 to 24, 2024, was utilized to evaluate the effectiveness of the KF in enhancing model fitting. The model quality was further assessed using Individual Moving Range (IMR) control charts to monitor residual stability and detect localized anomalies. Results demonstrate that the KF-ARIMA approach significantly improves performance, reducing the Root Mean Square Error (RMSE) from 1.123 m/s to 0.145 m/s, representing an 87.1\% improvement in precision compared to the standalone ARIMA model. The I-MR charts confirmed that the KF-ARIMA residuals remained consistently within the $3\sigma$ control limits, effectively identifying transient variations that standard diagnostic tests might overlook. This integrated framework proves that combining state-space filtering with traditional time-series models provides a robust approach for characterizing high-frequency meteorological data in equatorial regions.
creator: Nurfitri Imro'ah
creator: Nur'ainul Miftahul Huda
creator: Kartika Sari
creator: Rahmi Hidayati
rights: Copyright (c) 2026 Nurfitri Imro'ah, Nur'ainul Miftahul Huda, Kartika Sari, Rahmi Hidayati 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: 1218
ending page: 1233
doi: 10.18860/cauchy.v11i1.41753

Design of Fuzzy Logic Controller Based on Gustafson-Kessel Clustering for Quadcopter Altitude Control
type: item
description: Quadcopter altitude control is a critical issue in unmanned aerial vehicle systems due to its nonlinear dynamics and impact on operating conditions. Various fuzzy logic-based approaches have been used to address these nonlinear characteristics. However, in many previous studies, the rule structure and membership function were determined heuristically or based on expert knowledge, resulting in a less systematic design process that did not fully represent the distribution of system dynamics data. This study proposes a data-driven fuzzy control approach using the Gustafson–Kessel clustering algorithm to automatically generate fuzzy rules from system data. This algorithm is used to identify an ellipsoidal cluster structure in the input space formed by the error variable (e) and the error change (Delta e). The cluster center parameters are used to construct Gaussian membership functions and a rule base for the fuzzy inference system that generates control signals for the quadcopter's vertical dynamics. Evaluation is conducted through quadcopter altitude control simulations using several error metrics. The simulation results show Integral Squared Error value of 0.363789, Integral Absolute Error of 0.554409, Root Mean Square Error of 0.190637, and Mean Absolute Error of 0.055386, with a maximum error of 0.999600 in the beginning of the system response.
creator: Belgis Ainatul Iza
creator: Heri Purnawan
creator: Moh. Khoridatul Huda
creator: Nurul Laili
rights: Copyright (c) 2026 Belgis Ainatul Iza, Heri Purnawan, Moh. Khoridatul Huda, Nurul Laili 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: 1234
ending page: 1250
doi: 10.18860/cauchy.v11i1.41543

A Mathematical Model of Human-to-Human Transmission of Monkeypox with Reinfection
type: item
description: Monkeypox is a zoonotic disease caused by the monkeypox virus and remains a public health concern due to its potential for sustained human-to-human transmission. This study analyzes the transmission dynamics of monkeypox by developing a deterministic compartmental model that explicitly incorporates reinfection arising from waning immunity. The model is analyzed by deriving the basic reproduction number and determining the disease-free and endemic equilibrium points, whose local and global stability properties are rigorously investigated. A sensitivity analysis is conducted to identify key parameters driving transmission dynamics. Motivated by these results, an optimal control problem is formulated in which vaccination is implemented as a time-dependent control, and the optimal strategy is characterized using Pontryagin’s Minimum Principle. Numerical simulations reveal that even low reinfection rates can sustain endemic transmission in the absence of control, while appropriately timed vaccination strategies significantly reduce infection levels and prevent long-term persistence.
creator: Eka Widia Rahayu
creator: Noorma Yulia Megawati
rights: Copyright (c) 2026 Eka Widia Rahayu, Noorma Yulia Megawati 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: 1251
ending page: 1269
doi: 10.18860/cauchy.v11i1.40140

Binary Logistic Regression Modeling using Bayesian method: Analysis and Simulation on the Poverty Percentage of Districts in East Java
type: item
description: In conducting logistic regression modeling, parameter estimation is considered an important stage. Determination of parameter estimates is often influenced by sample size and data characteristics. To cope with this issue, the Bayesian method is used as it is expected to be more robust, for instance to small sample size. In this method, MCMC is used to determine parameter values that are difficult to solve analytically. The study aims at determining the binary logistic regression model and its application to determine the factors that influence the percentage of city/district poverty rates in East Java in 2023. East Java was chosen because it has the highest percentage of poverty rates in Indonesia. This study uses informative and non-conjugate priors which is normal distribution in this case. Based on the results of the MCMC simulation with the Gibbs Sampling Algorithm, the random sample of study converged at the 266, 000th iteration with a burn-in of 60, 000 and a thin of 10. The results of this study indicate that the variables influencing the percentage of the poverty rate of cities/regencies in East Java are the Human Development Index (HDI), Life Expectancy (LE), and Gini Ratio (GR) which have significant effects. The residual deviance value shows a number that is smaller than the chi-square value. This means that the resulting model is appropriate. The model can predict data correctly by 84.2%. Simple simulations are carried out with different observed sample sizes. The simulation results show that the Bayesian method is somewhat better than likelihood estimation, particularly for data with small samples. Furthermore, we suggest the government of East Java would have more concern on HDI, LE, and GR as well as other factors related to them for poverty reduction policies.
creator: Achmad Efendi
creator: Restilia Anggita Sari
creator: Samingun Handoyo
creator: Nur Silviyah Rahmi
creator: Friansyah Gani
rights: Copyright (c) 2026 Friansyah Gani, Achmad Efendi, Restilia Anggita Sari, Samingun Handoyo, Nur Silviyah Rahmi 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: 1270
ending page: 1285
doi: 10.18860/cauchy.v11i1.41326

Maximizing MSMEs Profits via Simulated Annealing and Linear Programming
type: item
description: Maximizing profitability is a key objective for Micro, Small, and Medium Enterprises (MSMEs), particularly those in the patchwork fabric industry. This study develops a multi-constraint Linear Programming (LP) model integrated with Simulated Annealing (SA) to determine the optimal production plan that maximizes profits while considering resource constraints. The LP model provides an optimal solution by selecting the most profitable product mix, whereas the SA heuristic explores a broader solution space to find alternative production plans. The results indicate that the LP model achieves a maximum profit of 16,640,000, primarily by selecting Tote bag as the most profitable product, while the SA approach distributes production across multiple products, resulting in a lower total profit of 7,739,000. Sensitivity analysis of the LP model highlights high reduced costs for non-selected products, making their inclusion in the production plan economically unfeasible. The findings suggest that LP is superior for-profit maximization, while SA provides alternative solutions for production diversification. Future research should explore hybrid approaches that integrate LP’s precision with SA’s flexibility to optimize MSME production strategies under uncertain demand conditions.
creator: Afnaria Afnaria
creator: Rina Fillia Sari
creator: Isnaini Halimah Rambe
rights: Copyright (c) 2026 Afnaria Afnaria 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: 1286
ending page: 1297
doi: 10.18860/cauchy.v11i1.32585

An Integrated Circular Intuitionistic Fuzzy MCDM Framework with Radius Operators for Same-Day Delivery Service Selection
type: item
description: The rapid expansion of e-commerce has increased the demand for rapid, reliable, and efficient logistics services, particularly same-day delivery (SDD). Selecting SDD service providers is a multi-criteria decision-making (MCDM) problem because it involves multiple evaluation criteria and expert judgments under uncertainty. This study develops a decision-making framework based on circular intuitionistic fuzzy sets (CIFS) for SDD service selection and evaluates the effect of different CIFS radius operators on ranking outcomes. The proposed methodology is implemented in a case study of SDD service selection in Malang, involving 30 experts, four criteria, and three alternatives. Expert evaluations are aggregated and analyzed using three radius operators: maximum Euclidean distance, radius algebraic product, and radius algebraic sum. A sensitivity analysis is also conducted over the full range of the parameter lambda. The results show that the radius algebraic product operator provides the most stable ranking, consistently producing (AL3 > AL2 > AL1). These findings indicate that the choice of CIFS radius operator significantly affects decision stability and supports more reliable recommendations.
creator: Dwi Nurkarimah
creator: Noor Hidayat
creator: Abdul Rouf Alghofari
rights: Copyright (c) 2026 Dwi Nurkarimah, Noor Hidayat, Abdul Rouf Alghofari 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: 1298
ending page: 1317
doi: 10.18860/cauchy.v11i1.42211

Two-Parameter Exponential Estimation via EM Algorithm: Uterine Leiomyosarcoma Survival Risk Analysis
type: item
description: Accurate survival prognosis is critical for clinical decision-making, yet analyzing censored on cological data remains a statistical challenge. This study aims to implement the Expectation Maximization (EM) algorithm for the two-parameter exponential distribution to estimate parameters and forecast extreme survival risks in uterine leiomyosarcoma (uLMS). Using clinical data from 122 patients, the EM algorithm achieved rapid convergence after 19 it erations, yielding a scale parameter of 68.7037 months and a 2-month survival threshold. Statistical validity was confirmed by a Kolmogorov-Smirnov test (p = 0.2084) and a 94.5% coverage probability from Monte Carlo simulations. A key contribution of this research is the integration of Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) metrics, which identified a 95% survival threshold of 207.82 months. Sensitivity analysis further demonstrated the es timator’s structural stability across varying censoring proportions. These results signify that the proposed framework provides a robust and reliable tool for quantifying extreme survival probabilities, offering clinicians a sophisticated method for long-term risk management and personalized patient prognosis.
creator: Ardi Kurniawan
creator: Deby Victoria
creator: Christabel Lee Angie Sugianto
rights: Copyright (c) 2026 Ardi Kurniawan, Deby Victoria, Christabel Lee Angie Sugianto 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: 1318
ending page: 1333
doi: 10.18860/cauchy.v11i1.41855

On Temperature-Dependent and Spatially Structured Dengue Transmission Models: A Mathematical Review
type: item
description: Dengue fever remains a major public health concern in tropical and subtropical regions, where transmission dynamics are strongly influenced by environmental variability and human mobil ity. Mathematical modelling provides a rigorous framework for capturing these interactions and informing effective control strategies. This review presents recent advances in deterministic and spatially structured dengue transmission models that incorporate temperature-dependent parameters and human mo bility. Emphasis is placed on compartmental formulations, including multi-patch and meta population models, where movement between regions plays a key role in disease spread. The influence of temperature on key epidemiological parameters, such as mosquito biting rates, development rates, and survival probabilities, is examined through nonlinear functional relationships. In addition, common analytical approaches are discussed, including the derivation of the basic reproduction number, stability analysis of equilibria, and sensitivity analysis. The integration of control strategies within these frameworks is also reviewed, demonstrating how intervention policies can be evaluated under varying environmental and mobility conditions. Overall, the review highlights the importance of combining environmental and spatial effects to better understand dengue transmission and support adaptive control strategies.
creator: Abdullahi Abdu
creator: Admi Nazra
creator: Arrival Rince Putri
creator: Mahdhivan Syafwan
rights: Copyright (c) 2026 Abdullahi Abdu, Admi Nazra, Arrival Rince Putri, Mahdhivan Syafwan 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: 1334
ending page: 1358
doi: 10.18860/cauchy.v11i1.42040

Modeling the Dynamics of Cardiovascular Disease Using a SEICRD Framework
type: item
description: Cardiovascular disease remains a major public health challenge worldwide, often progressing silently toward chronic complications. Increasing awareness through media and individual behavioral responses plays an important role in preventing disease transmission and reducing long-term complications. Motivated by this, we formulate a deterministic compartmental model to investigate the dynamics of cardiovascular disease by incorporating media awareness and individual awareness as control-related parameters. The population is divided into susceptible, exposed, infected, chronic, recovered, and deceased compartments. A qualitative analysis of the linear dynamical system is carried out, including positivity of solutions, bound- edness, equilibrium points, and local stability analysis using eigenvalue criteria. Numerical simulations are performed to illustrate the effects of key epidemiological and awareness-related parameters on disease progression. The simulation results indicate that increased media and individual awareness significantly reduce the long-term burden of chronic cardiovascular complications. In contrast, higher incidence and disease progression rates lead to increased accumulation in the chronic compartment, even when the number of active infections declines more rapidly. Sensitivity analysis confirms that awareness parameters have a negative influ- ence on chronic disease prevalence, whereas core epidemiological parameters exert a strong positive effect. These findings highlight the critical role of awareness-based interventions in mitigating chronic cardiovascular disease and provide a quantitative framework to support effective prevention and control strategies.
creator: Arista Fitri Diana
creator: Mia Siti Khumaeroh
creator: Tarita Intan Soraya
rights: Copyright (c) 2026 Arista Fitri Diana, Mia Siti Khumaeroh, Tarita Intan Soraya 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: 1359
ending page: 1380
doi: 10.18860/cauchy.v11i1.41645

Rolling-Origin Evaluation of Lag-Based Regularized Regression Models for Indonesian Inflation Forecasting
type: item
description: Inflation forecasting studies often rely on external macroeconomic predictors or complex machine learning models, while the predictive value and limitations of the internal lag structure of Indonesian inflation remain less explicitly examined. This study evaluates Indonesian inflation forecasting within a univariate lag-based framework using monthly inflation data from January 2010 to December 2025. Lagged inflation values are used to construct regression predictors, and OLS, Ridge, LASSO, and Elastic Net are evaluated through rolling-origin forecasting with an expanding window. To strengthen the time-series basis of the analysis, this study also conducts stationarity diagnostics, ACF and PACF analysis, seasonal diagnostics, lag-specification robustness checks, and comparisons with standard forecasting benchmarks, including Naive, Seasonal Naive, AR selected by AIC, and ARIMA selected by AIC. The ADF test produces a p-value of 0.608360, indicating weak evidence of stationarity in level form. Among the regularised regression models, Ridge produces the lowest descriptive forecast errors, with RMSE of 0.405018 and MAE of 0.308967. However, Diebold–Mariano tests indicate that the differences among OLS, Ridge, LASSO, and Elastic Net are not statistically significant. Benchmark comparisons show that the Naive forecast achieves the lowest RMSE of 0.373819, while ARIMA selected by AIC achieves the lowest MAE of 0.279641 and MAPE of 16.560958. Robustness checks also show that the twelve-lag specification is competitive for OLS and Ridge, but it is not uniformly optimal across all models. These findings suggest that the main value of lag-based regularised regression lies in clarifying the limited but useful short-run predictive information contained in the internal temporal structure of Indonesian inflation, rather than in providing a statistically dominant or complete inflation forecasting model.
creator: Rehan Risqi Saputra
creator: Atik Wintarti
creator: Riska Wahyu Romadhonia
rights: Copyright (c) 2026 Rehan Risqi Saputra, Atik Wintarti, Riska Wahyu Romadhonia 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: 1381
ending page: 1397
doi: 10.18860/cauchy.v11i1.41964

Properties of Clear Graph of Ring ℤp
type: item
description: Let ℤp be the ring of integers modulo a prime p > 3. The clear graph of ℤp, denoted by Cr2(ℤp), is a graph whose vertices are ordered pairs (x,u), where x is a nonzero regular unit and u is a unit of ℤp, and two vertices (x,u) and (y,v) are adjacent if either xy = yx = 0 or uv = vu = 1. This work extends previous research on clear graphs, which established the basic structure of Cr2(R) for certain rings, including aspects of isomorphism, connectedness, and other structural properties. In this paper, we focus on the prime ring ℤp and analyze several fundamental graph-theoretic properties of Cr2(ℤp). Specifically, we show that this graph has order (p−1)2, size ½(p2−2p−1)(p−1), diameter ∞, radius at most 2, independence number ½(p2−4p+7), and clique, chromatic, and domination numbers each equal to p−1. The results provide a deeper understanding of how algebraic properties of ℤp influence the combinatorial structure of its associated clear graph.
creator: Mohammad Ilham Maulana
creator: Vira Hari Krisnawati
creator: Ratno Bagus Edy Wibowo
rights: Copyright (c) 2026 Mohammad Ilham Maulana, Vira Hari Krisnawati, Ratno Bagus Edy Wibowo 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: 1398
ending page: 1408
doi: 10.18860/cauchy.v11i1.41856

Toward Optimal Quantum Multipliers: Space–Time Efficiency and Asymptotic Bounds for Advanced Toom–Cook Methods
type: item
description: This paper studies the asymptotic bounds of quantum resources required for high-degree multiplication based on the Toom–Cook algorithm. This work extends prior investigations on high- and half-degree quantum multiplication and proposes an optimized Toom–Cook 25.5-way quantum multiplication architecture to establish optimal asymptotic bounds on quantum resource consumption for Toom–Cook-based multiplication schemes. We provide asymptotic expressions for qubit complexity, Toffoli gate count, and Toffoli depth. The proposed Toom–Cook 25.5-way architecture achieves improved asymptotic performance, requiring a qubit count of n1.176, approximately 648nlog2651 − 666n Toffoli count, and n1.03025 Toffoli depth. Compared with existing classical and quantum Toom–Cook-based methods, the proposed 25.5-way Toom–Cook algorithm achieves lower asymptotic complexity and reduced quantum resource costs, yielding tighter bounds for optimal quantum multiplication.
creator: Rini Wisnu Wardhani
creator: Dedy Septono Catur Putranto
rights: Copyright (c) 2026 Rini Wisnu Wardhani, Dedy Septono Catur Putranto https://creativecommons.org/licenses/by-sa/4.0
license: https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-31
publication date: 2026-05-31
volume: 11
number: 1
starting page: 1409
ending page: 1434
doi: 10.18860/cauchy.v11i1.41908