EIGEN MATHEMATICS JOURNAL

Hyper-Wiener and Szeged Indices of non-Coprime Graphs of Modulo Integer Groups

Lalu Hasan Ghoffari — 2025-03-10

The non-coprime graph of the integer modulo group is a graph whose vertices represent the elements of the integer modulo group, excluding the identity element. Two distinct vertices are adjacent if and only if their orders are not relatively prime. This study explores two topological indices, the Hyper-Wiener index and the Szeged index, in the non-coprime graph of the integer modulo-n group. The results reveal that these indices are equal when the order is a prime power but differ when the order is the product of two distinct prime numbers. This research provides new insights into the patterns and characteristics of these indices, contributing to a broader understanding of the application of graph theory to abstract group structures.

The Extended Metric Space on Max-Plus Algebra

Lalu Riski Wirendra Putra — 2025-03-12

Max-Plus Algebra is the newly emerged mathematical object as one of the algebraic structures. Max Plus Algebra is a semi-ring with the maximum operation as its addition and the plus operation as its multiplication. In 2012, Carl et.al. established a novel notion about metric in max-plus geometry which is the semi-module over the semi-ring with maximum and addition biner operations. The writer researched to discover the distance function or metric, especially for the extended real-valued metric of Max-Plus Algebra and its properties with maximum and addition biner operations. By using both direct and indirect proof methods, the distance function of Max Plus Algebra and its topological properties were obtained.

Integrative Bioinformatics and Statistical Approaches for Identifying Prognostic Biomarkers and Therapeutic Targets in Breast Cancer

Gangga Anuraga — 2025-03-13

Breast cancer is a leading cause of cancer-related mortality worldwide, necessitating the identification of reliable biomarkers for prognosis and targeted therapy. This study employed an integrative bioinformatics and statistical approach to analyze differentially expressed genes (DEGs) in breast cancer using datasets GSE70947 and GSE22820 from the gene expression omnibus (GEO). A protein-protein interaction (PPI) network was constructed to identify hub genes, followed by functional enrichment analysis to determine their biological significance. Survival analysis using the KMplot database revealed that CDC45, KIF2C, CCNB1, KIF4A, CENPE, CHEK1, KIF15, AURKB, NCAPG, and HJURP were significantly associated with poor prognosis. These genes were primarily enriched in cell cycle regulation, mitotic spindle organization, and DNA damage response, highlighting their role in tumor progression. Among them, CCNB1, CHEK1, and AURKB were strongly linked to cell cycle progression and checkpoint regulation, while KIF2C and CENPE played essential roles in mitotic division. High expression levels of these genes correlated with reduced overall survival, suggesting their potential as prognostic biomarkers and therapeutic targets in breast cancer.These discoveries help us better understand how breast cancer develops and point to potential targets for tailored treatments.

Implementation of Random Forest Algorithm to Classify Earthquake in Indonesia

Alda Putri Pratiwi — 2025-04-10

Earthquakes are shocks that occur on the surface of the earth due to shifts in the earth's plates. Geographically, Indonesia is located in the Pacific Ring of Fire (King of Fire) region, this makes Indonesia prone to earthquakes. Earthquakes can cause environmental damage and tsunami disasters, but not all earthquakes can cause tsunamis. Classifying earthquakes that have the potential for a tsunami is very important to mitigate the damage caused. One classification method that has a high level of accuracy is random forest. The advantage of random forest is that this algorithm tends to be resistant to overfitting and can handle large data. This research uses real-time earthquake data from July to August 2023, sourced from the website of the Meteorology Climatology and Geophysics Agency (BMKG). The training data and test data used in this research are 70% and 30%. Confution Matrix is used as model evaluation, to measure the accuracy of the classification model. The results of this research obtained a high accuracy, equal 0.97 or 97%.

Implementation of Fuzzy Logic Using The Tsukamoto Method to Forecast Gold Price in Indonesia

Irfaliani Alviari — 2025-04-10

In the economy, gold is a commodity that has an important role. This indicates that gold is often used as an investment for investors and people involved in the business world. This research aims to determine how accurate gold price forecasting is using the Tsukamoto fuzzy method in Indonesia. Gold prices are influenced by several factors. These factors include exchange rates, interest rates, inflation, etc. Based on research results, fuzzy Tsukamoto determined the price of gold with a forecasting truth value of 99.91611654% and a MAPE value of 0.083883458%. The conclusion of this research is forecasting gold prices using the Tsukamoto fuzzy method is considered very good.

Analysis of Factors that Influence Poverty in West Nusa Tenggara Using Principal Component Regression

Lisa Harsyiah — 2025-06-11

West Nusa Tenggara (NTB) is one of the provinces in Indonesia with a percentage of poor people according to the March-September period in 2019, namely 14.56% -13.88%, while in 2020 it was 13.97% -14.23% and in 2021 the percentage was 14.14% -13.83%. The factors suspected of influencing poverty in each province have different conditions each year, so repeated observations are needed on poverty data and the factors that influence it. If the data contains multicollinearity, then one of the classic assumptions of multiple linear regression is not met so that the problem of multicollinearity needs to be addressed. The Principal Component Regression (PCR) method is the most consistent compared to the ridge and least square regression methods in solving multicollinearity problems. This study aims to analyze poverty in NTB using the PCR method. The data used in this study are the number of poor people and factors influencing poverty based on districts in NTB in 2020-2022. Based on the calculation results, it was obtained that Component 1 with an eigenvalue of 4.008 explained 57.2% of the variance, while Component 2 with an eigenvalue of 1.740 explained 82.1% of the variance. Both components significantly affect poverty according to the results of simultaneous and partial tests. This model has an R^2 value of 0.302 or 30.2% and the remaining 69.8% is influenced by external factors (error). The R^2 value is classified as a weak category and it is recommended to add other factors that affect poverty including access to electricity, access to sanitation, access to clean drinking water, and government spending.

Properties of Amalgamated Algebras Along an Ideal and Their Applications

Rintang Utami — 2025-06-12

If given rings A and B, a ring homomorphism f : A --> B, and an ideal J of B, then a new ring can be constructed called amalgamated algebras along an ideal which is denoted by $A \bowtie^f J := {(a, f(a)+j) \mid a \in A, j \in J}$ with component-wise addition and multiplication. This paper discusses the construction, definition, properties such as isomporhisms, and characterization of amalgamated algebras along an ideal that is a prime ring and a Noetherian ring with detailed explanations. We also discuss its characterization as a reduced ring, which is a continuation from the previous paper. Furthermore, we investigate its characterization as an Artinian ring by adding an additional condition that every ideal of J has unity.

Implementation of Fast Fourier Transform and Least Mean Square Algorithms in The Denoising Process of Audio Signal

Putri Rahmasari Rayes — 2025-06-13

Audio signals play an important role as a medium for storing information, such as lecture materials, interview results, and other archives. However, audio signals are often contaminated by noise, which is unwanted interference that can affect their quality. Therefore, a denoising process is needed to reduce or eliminate noise components in the signal. The Fast Fourier Transform (FFT) and Least Mean Square (LMS) algorithms are frequently used in the denoising process due to their simple and easy-to-implement steps. This research uses primary data, specifically audio signals recorded under two noise conditions: rain noise as Audio Signal 1 and guitar instrument noise as Audio Signal 2, both stored in WAV format. The denoising process was performed using MATLAB software and evaluated based on Signal-to-Noise Ratio (SNR) and Mean Squared Error (MSE) metrics. Higher SNR values and lower MSE values indicate the success of the denoising process in improving audio signal quality. The results of this study demonstrate the effectiveness of the applied algorithms, where the SNR value reached 38.2596 dB with an MSE of 0.0000028211 for Audio Signal 1, and an SNR value of 38.6881 dB with an MSE of 0.0000014988 for Audio Signal 2. An SNR value between 25 dB and 40 dB is categorized as a very good signal, indicating that the quality of the processed audio signals falls into the very good signal category.

Analysis Time Series (ARIMA): To determine the Development of Oil Exports in Indonesia

Isma Muthahharah — 2025-06-25

Oil exports are the largest export in Indonesia. Indonesia's oil exports from year to year tend to fluctuate and in the end continue to decline, however in the last three years exports of oil products have continued to increase from the previous year. This research aims to analyze the development of oil exports in Indonesia. The data used in this research is doil export data from 1996 to 2023 obtained from data Indonesian Central Statistics Agency (BPS). The method used to analyze development of oil exports in Indonesia is Autoregressive Integrated Moving Average (ARIMA). The research results show that Indonesia's oil exports have experienced significant fluctuations from year to year, with a quite striking decline in export volume in recent years. The ARIMA model (2,2,2) was identified as the best model for predicting future behavior from oil export data. This model succeeds in describing the intrinsic patterns in the export data well. Using the ARIMA (2,2,2) model it is known that forecasting results development of oil exports in Indonesia (2024-2035) will experience an increase from the previous year.