The purpose of this study is to develop a robust methodology for the automated detection and quantitative analysis of tandem repeats in genomic sequences, taking into account mismatches and distances, to enhance primer design and improve the accuracy of genomic research. The approach combines an efficient algorithm for identifying complementary DNA fragments, focusing on the 3' end of primers, and integrates two independent similarity metrics: the Hardy–Weinberg χ² test and cosine similarity. The methodology involves generating similarity matrices, heat maps, 3D surface visualizations, and scatter plots for comprehensive evaluation of sequences. Experimental validation of the complete genome of Lactobacillus brevis ATCC 367 identified 586 tandem repeats, demonstrating high consistency between the two metrics and revealing high similarity among most repeats, while highlighting specific cases with discrepancies that require further investigation. The developed methodology effectively combines statistical and vector analyses, enhancing the reliability of genomic studies and enabling the identification of biologically significant variations. The proposed tool can be widely applied in molecular biology, especially for primer design, genome annotation, and biomarker discovery. It is scalable and adaptable to large genomic datasets, making it suitable for high-throughput bioinformatics analyses.

This study presents PAGER-Life, an adaptive hybrid framework for the early prediction of lithium-ion battery service life under heterogeneous operating conditions. The system integrates physically interpretable degradation features and standardized charge–discharge curves using linear regression, decision tree-based models, and neural networks. An error-aware routing mechanism combines expert predictions based on out-of-fold errors, while conformal prediction enables uncertainty quantification. The framework was evaluated using the MATR and HUST datasets with observation horizons of 20, 50, and 100 cycles, following a protocol that accounts for the grouped data structure and prevents information leakage. A comparative analysis involving 114 physical cells and 14 alternative methods demonstrated the following performance metrics for PAGER-Life: Mean Absolute Percentage Error (MAPE) of 12.827%, Mean Absolute Error (MAE) of 166.766 cycles, Root Mean Square Error (RMSE) of 210.715 cycles, and a macro-averaged coefficient of determination (R²) of 0.495. Ablation studies indicated that removing the physically grounded degradation features substantially degraded predictive performance. The results indicate that the adaptive integration of complementary prognostic models offers a promising approach for the early estimation of battery service life under heterogeneous operating conditions.