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.