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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Agrokreatif Jurnal Ilmiah Pengabdian kepada Masyarakat Publication Library and Information Science International Journal of Computing Science and Applied Mathematics Jurnal Riset Mahasiswa Matematika Journal of Research on Community Engagement
Ari Kusumastuti
Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Maulana Malik Ibrahim Malang
Agriculture, Biological Sciences & Forestry Humanities Computer Science & IT Education Library & Information Science Mathematics Social Sciences

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Penyelesaian Sistem Persamaan Hukum Laju Reaksi dengan Metode Transformasi Differensial Maftuhah, Siti; Widayani, Heni; Kusumastuti, Ari
Jurnal Riset Mahasiswa Matematika Vol 2, No 4 (2023): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v2i4.16805

Abstract

This research is focused on solving the rate law equation by using the differential transformation method. The rate law equation describes the chemical reaction problem from the concentration of a reactant that produces a product. The differential transformation method is a semi-analytic numerical method that can provide approximate solutions in the form of a series because the method is obtained from the expansion of the Taylor series expansion. With the help of Maple software, a comparison of the solution plots of y_1 (t),y_2  (t) and y_3 (t), can be observed that the difference in computational results between the Runge-kutta method and the differential transformation depends on the order of k. The curve of the differential transformation method is getting closer to the curve of the Runge-Kutta method at a certain value of k for each y_1 (t),y_2  (t) and y_3 (t). The conclusion of this research is that the application of the differential transformation method has been successfully carried out in the case of a system of ordinary differential equations. For further research, the researcher suggests that the next research applies the method of differential transformation in cases and initial values that are more varied.
Analisis Dinamik Model Infeksi Mikrobakterium Tuberkulosis Dengan Dua Lokasi Pengobatan KT, Ummul Aulia; Widayani, Heni; Kusumastuti, Ari
Jurnal Riset Mahasiswa Matematika Vol 2, No 3 (2023): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v2i3.16753

Abstract

Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. The disease is considered dangerous because it infects the lungs and other organs of the body and can lead to death. This study discusses a mathematical model for the spread of tuberculosis with two treatment sites as an effort to reduce the transmission rate of TB cases. Treatment for TB patients can be done at home and in hospitals. The purpose of this study was to construct a mathematical model and analyze the qualitative behavior of the TB spread model. The construction of the model uses the SEIR epidemic model which is divided into five subpopulations, namely susceptible subpopulations, latent subpopulations, infected subpopulations receiving treatment at home, and infected subpopulations receiving treatment at the hospital, and cured subpopulations. The analysis of qualitative behavior in the model includes determining the local and global equilibrium and stability points. The results of the analysis shows that the model has two equilibrium points, namely a disease-free equilibrium point and the endemic equilibrium point. The existence of endemic equilibrium point and the local and global stability of the two equilibrium points depend on the basic reproduction number denoted by . If ,  there is only disease-free equilibrium point. If , there are two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. Stability analysis shows that the disease-free equilibrium point is locally and globally asymptotically stable if . While, if , the endemic equilibrium point will be asymptotically stable locally and globally.
Metode Backward Time Central Space dalam Penyelesaian Model Matematika Vibrasi Dawai pada Alat Musik Petik Damayanti, Atik; Kusumastuti, Ari; Hidayati, Nurul A.
Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v1i4.14454

Abstract

This research was conducted to obtain a numerical solution of the mathematical model of string vibration on stringed instruments. This mathematical model is a representation of the phenomenon of string vibration on a stringed instrument subject to deviation. The model was constructed by Kusumastuti, et al (2017) and is in the form of a second-order partial differential equation. The method used in completing this research is the BTCS (Backward Time Central Space) method. The numerical solution is obtained by the following steps, 1). Discretize mathematical models, as well as discretize initial conditions and boundary conditions. 2). Performing stability analysis of numerical solutions to determine the terms of solution stability and conducting consistency analysis as a condition of the convergence of the obtained numerical solutions. 3). Simulate numerical solutions and perform graph interpretations. The results show that the numerical solution of the mathematical model of string vibration on stringed instruments is unconditionally stable and has an error order (〖∆x〗^2,〖∆t〗^3).
Analisis Dinamik Model Matematika Penyebaran COVID-19 Pada Populasi SEIR Meyliana, Ester; Kusumastuti, Ari; Juhari, Juhari
Jurnal Riset Mahasiswa Matematika Vol 1, No 4 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v1i4.14458

Abstract

This study discusses the dynamic analysis of the mathematical model of the spread of COVID-19 using daily cases in Indonesia which are classified into four variables, namely, Susceptible (S), Exposed (E), Infected (I), and Recovered (R) which are then analyzed dynamically by calculate the equilibrium point and look for stability properties. The two equilibrium points of this model are the disease-free equilibrium point  and the endemic equilibrium point . Then, it is linearized around the equilibrium point using the given parameters. Linearization around the equilibrium point  produces four eigenvalues, one of which is positive. Linearization around the equilibrium point  yields two negative real eigenvalues and a pair of complex eigenvalues with negative real parts. Phase portraits and numerical simulations have shown that all variables S, E, I, and R will be asymptotically stable locally towards the equilibrium point, namely the endemic equilibrium point . Thus, based on the dynamic analysis obtained, it is shown that the disease-free equilibrium point  is unstable and the endemic equilibrium point is locally asymptotically stable.
Simulasi Numerik Model Matematika Vibrasi Dawai Flying Fox Menggunakan Metode Adams-Bashforth-Moulton Utami, Febry Noorfitriana; Kusumastuti, Ari; Juhari, Juhari
Jurnal Riset Mahasiswa Matematika Vol 2, No 1 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v2i1.14512

Abstract

This study discusses numerical simulation using the Adams-Bashforth-Moulton (ABM) method of order 4 in the flying fox string mathematical model which is in the form of ordinary differential equations depending on time, consisting of two equations, namely the equation of the flying fox string y(t) and the angular equation of the flying fox string θ(t). This mathematical model is a model that has been constructed by Kusumastuti, et al (2017) and has been validated by comparing analytical solutions to its numerical solutions by Sari (2018). The analysis of the behavior of the Kusumastuti 2017 model conducted by Makfiroh (2020) shows that the phase portrait graph is in the form of a spiral with eigenvectors pointing towards the equilibrium point so that the mathematical model of the flying fox string vibration can be concluded as a valid mathematical model that is close to the actual situation. This study attempts to determine the numerical simulation of the deflection of the flying fox string y(t) and the numerical simulation of the angle of the flying fox string θ(t). The Runge-Kutta method of order 4 was used to generate 3 initial values for order 4 ABM. Next, a comparison of the y(t) and θ(t) solution graphs of order 4 ABM with the solution graph with Runge-Kutta of order 4 was performed in Sari 2018. The first simulation was carried out when h=1, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 fluctuated in the range of [0,0.09] with almost the same graphic profile, and the difference in the value of θ(t) ABM of order 4, and Runge-Kuta order 4 which is quite large with different graphic profiles. The second simulation was carried out when h=0.01, the difference in the value of y(t) of order 4 ABM and Runge-Kutta order 4 was fluctuating which also ranged from [0.0.09] with the same graphic profile, and the difference in the values of θ(t) ABM of order 4 and Runge -Kutta order 4 fluctuates in the range of [0,1] with the same graphic profile. So concluded that when h=0.01 comparison of ABM of order 4 and Runge-Kutta of order 4 is the best for displaying the graph profiles of y(t) and θ(t). Further research can explore numerical solutions using other methods.
Implementasi Jaringan Syaraf Tiruan Backpropagation untuk Menentukan Prediksi Jumlah Permintaan Produksi Dodol Apel Sari, Farrah Nurmalia; Kusumastuti, Ari; Fahmi, hisyam
Jurnal Riset Mahasiswa Matematika Vol 2, No 2 (2022): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v2i2.14899

Abstract

Forecasting is importantly in accordance with the planning strategy; therefore it will affect the way of decision making. One of the forecasting methods is Artificial Neural Network with Backpropagation as the algorithm. This research aims to measure the accuracy of the network architecture which is being applied in order to calculate the prediction of the future’s apple paste product monthly demand which was obtained from CV. Bagus Agriseta Mandiri. The data which are being used are 36 monthly data from the year 2017, 2018 and 2019. Furthermore, the data obtained are normalized and divided into two, 66,66% as the data for training process and 33,33% as the data for testing process. Network architecture that is applied in this research is 12 : 10 :1, where 12 are neurons for input layer, 10 are neurons for one hidden layer and 1 is neuron for output layer. The Network with that framework obtained a result 20.161% for MAPE and 79.839% for the accuracy. That model is categorized as good enough for its forecasting ability. Moreover, the network was entirely validated using k-fold cross validation method with . The result obtained as follows: the average of MAPE is 47.079% and the average accuracy is 52.921%. According to it, the entire model can be categorized as good enough in order to run a forecast. As a comparison, another testing has been done with the same fold but different in the network architecture (model 6 – 8 – 1). The second model obtained results as follows: the average of MAPE is 26.74% and the average accuracy is 73.18%, so that the two prediction models’ ability are in the same category, it is good enough to run a forecast.
Pemberdayaan Masyarakat Sekitar Masjid Al-Birr Desa Purwodadi Donomulyo Melalui Pengolahan Bahan Pangan Berbasis Ketela Pohon Maharani, Dian; Kusumastuti, Ari; Zahroh, Fatmawati; Anggraeni, Nurul; Sukron, Muhammad
JRCE (Journal of Research on Community Engagement) Vol 6, No 2 (2025): Journal of Research on Community Engagement
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrce.v6i2.26718

Abstract

The mosque, which has often been used primarily as a place of worship, was also utilized as a gathering and consultation space in this research to discover new breakthroughs in launching a new agricultural processing business. In this study, the community around Masjid Al-Birr in Purwodadi Village, Donomulyo District, was trained to create cassava-based brownies and noodles. The aim of this training was to expand the community's thinking to generate new business ideas while providing innovation in cassava processing. The training took place from May to June 2023. As a result, the community showed enthusiasm and was capable of producing brownies and noodles using cassava as the main ingredient.
Cross-Dataset Evaluation of Support Vector Machines: A Reproducible, Calibration-Aware Baseline for Tabular Classification Syafi'ah, Nurus; Jamhuri, Mohammad; Pranata, Farahnas Imaniyah; Kusumastuti, Ari; Juhari, Juhari; Pagalay, Usman; Khudzaifah, Muhammad
Jurnal Riset Mahasiswa Matematika Vol 4, No 6 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i6.33438

Abstract

Support Vector Machines (SVMs) remain competitive for small and medium-sized tabular classification problems, yet reported results on benchmark datasets vary widely due to inconsistent preprocessing, validation, and probability calibration. This paper presents a calibration-aware, cross-dataset benchmark that evaluates SVMs against classical baselines—Logistic Regression, Decision Tree, and Random Forest—under leakage-safe pipelines and statistically principled protocols. Using three representative binary datasets (Titanic survival, Pima Indians Diabetes, and UCI Heart Disease), we standardize imputation, encoding, scaling, and nested cross-validation to ensure comparability. Performance is assessed not only on discrimination metrics (accuracy, precision, recall, F1, PR--AUC) but also on probability reliability (Brier score, Expected Calibration Error) and threshold optimization. Results show that tuned RBF--SVMs consistently outperform Logistic Regression and Decision Trees, and perform comparably to Random Forests. Calibration (Platt scaling, isotonic regression) substantially reduces error and improves decision quality, while domain-specific features enhance Titanic prediction. By embedding all steps in a transparent, reproducible protocol and validating across multiple datasets, this study establishes a rigorous methodological baseline for SVMs in tabular binary classification, providing a reference point for future machine learning research.
Understanding The Mechanism of GLUT4 Translocation Involving Non-Conserved Complexes from A Modeling and Simulation T2DM Perspective Kusumastuti, Ari; Irawan, Mohammad Isa; Fahim, Kistosil
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.29292

Abstract

Understanding the mechanism of Glucose Transporter 4 (GLUT4) translocation to the cell membrane is essential for describing daily glucose uptake. A normal mechanism maintains glucose homeostasis and reduces the occurrence of Type 2 Diabetes Mellitus (T2DM) and its complications. Kinetic reactions are crucial for revealing the interactions involving proteins, enzymes, and complexes within the system. We propose a system of ordinary differential equations (ODEs) to elucidate the underlying mechanism under the assumption of non-conservative complexes . The insulin signaling pathway, which includes the GLUT4 mechanism, serves as the basis for reconstructing the necessary kinetic reactions. Investigating the behaviour of the model through numerical simulations and dynamics within parameters and initial conditions from relevant researchs .
On the Approximation Capabilities of Deep Neural Networks for Multivariate Time Series Modeling Jamhuri, Mohammad; Irawan, Mohammad Isa; Kusumastuti, Ari; Mondal, Kartick Chandra; Juhari, Juhari
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.32760

Abstract

Multivariate time series forecasting plays a crucial role in various domains, including finance, where accurate stock price prediction supports strategic decision-making. Traditional methods such as Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing (ETS), and Vector Autoregression (VAR) often fall short when dealing with complex, non-linear data—particularly those exhibiting long-term temporal dependencies. This study evaluates deep learning approaches, namely Multilayer Perceptron (MLP), Convolutional Neural Networks (CNN), and Long Short-Term Memory (LSTM), using daily AAPL stock price data from January 2020 to November 2024. The results show that the MLP model with a 10-day time window achieves the best accuracy, yielding lower values in Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) compared to CNN, LSTM, and VAR. The findings suggest that MLP is particularly effective in capturing complex patterns in multivariate time series forecasting.
Co-Authors Afidah Karimatul Laili, Afidah Karimatul Angga Dwi Mulyanto Anggraeni, Nurul Atik Damayanti Damayanti, Atik Dewi Firdaus Dian Maharani, Dian Ester Meyliana Fahim, Kistosil Farrah Nurmalia Sari Fatmawati Zahroh Febry Noorfitriana Utami Hairur Rahman Heni Widayani Hidayati, Nurul A. Hisyam Fahmi Hisyam Fahmi Imam Mufid, Imam Janah, Miftakul Juhari Juhari Juhari Juhari Juhari Juhari, Juhari Junik Rahayu KT, Ummul Aulia Lukman Hakim Meyliana, Ester Miftakul Janah Mohammad Isa Irawan Mohammad Jamhuri Mondal, Kartick Chandra Muhammad Khudzaifah Muhammad Sukron, Muhammad Nisa, Khoirotun Nurul A. Hidayati Nurul Anggraeni Hidayati Permata, Hendrik Widya Pranata, Farahnas Imaniyah Rahmadhani, Anis Putri Rizqyah, Ilfa Wardatul Sari, Farrah Nurmalia siti maftuhah Siti Maftuhah Syafi'ah, Nurus Ummul Aulia KT Usman Pagalay Utami, Febry Noorfitriana Wina Permana Sari