Searcharxiv⌕ Search

arXiv subjects

Sergei Voronin

Publications and source records attributed to Sergei Voronin.

3 recordsLinked to original sources
arXiv2026

Curves of tangencies of foliation pairs and normalizing transformations

In this work we give a complete description of the collection of curves of tangencies induced by germs of foliation pairs -- non dicritical and dicritical -- given by analytic differential equations with degenerated non dicritical and dicritical singularities, satisfying some genericity assumptions. To this purpose we use local models and analytic normalizing transformations. Moreover, for each natural number $k$ we obtain $k$-normal forms for the normalizing transformations. These normal forms are used to give parametrizations, up to a finite jet, of the branches of the curves of tangencies. We also prove that under natural genericity assumptions any germ of analytic curve having pairwise transversal smooth branches is realized as curve of tangencies of a -- non dicritical and dicritical -- foliation pair.

math.DS↗
arXiv2024

Enhancing Object Detection Accuracy in Autonomous Vehicles Using Synthetic Data

The rapid progress in machine learning models has significantly boosted the potential for real-world applications such as autonomous vehicles, disease diagnoses, and recognition of emergencies. The performance of many machine learning models depends on the nature and size of the training data sets. These models often face challenges due to the scarcity, noise, and imbalance in real-world data, limiting their performance. Nonetheless, high-quality, diverse, relevant and representative training data is essential to build accurate and reliable machine learning models that adapt well to real-world scenarios. It is hypothesised that well-designed synthetic data can improve the performance of a machine learning algorithm. This work aims to create a synthetic dataset and evaluate its effectiveness to improve the prediction accuracy of object detection systems. This work considers autonomous vehicle scenarios as an illustrative example to show the efficacy of synthetic data. The effectiveness of these synthetic datasets in improving the performance of state-of-the-art object detection models is explored. The findings demonstrate that incorporating synthetic data improves model performance across all performance matrices. Two deep learning systems, System-1 (trained on real-world data) and System-2 (trained on a combination of real and synthetic data), are evaluated using the state-of-the-art YOLO model across multiple metrics, including accuracy, precision, recall, and mean average precision. Experimental results revealed that System-2 outperformed System-1, showing a 3% improvement in accuracy, along with superior performance in all other metrics.

cs.CV↗