Siddhant Sood | Searcharxiv

arXiv2026

Predicting the occurrence of Braess paradox in the synchronization threshold of coupled oscillator systems

We study Braess-type paradoxes in coupled oscillator networks where the addition of an edge to the network leads to an increase in the critical coupling required for the existence of a stable phase-locked synchronized solution. By introducing a continuous edge-weight parameter and constructing an augmented system that allows application of the Implicit Function Theorem, we derive an explicit first-order formula for the sensitivity of the critical coupling, $K'_c(0)$, to small changes in the network structure. This formula reveals that an edge is locally Braess if the ordering of the oscillators being coupled is opposite the ordering of their components in the critical eigenvector at the saddle-node bifurcation, providing a simple criterion for Braess paradox to occur. We then employ this local approximation as a predictor for the occurrence of Braess paradox when the edge is fully incorporated in the network. This prediction is tested numerically in several classes of random networks, demonstrating both high predictive fidelity and the nonlinear limitations of the local approximation. We also examine several explicit examples, highlighting possible motifs by which Braess-type paradoxes occur. Together, these results establish a predictive framework for understanding how incremental changes in network topology can produce counterintuitive synchronization outcomes.

math.DS↗

arXiv2023

EchoVest: Real-Time Sound Classification and Depth Perception Expressed through Transcutaneous Electrical Nerve Stimulation

Over 1.5 billion people worldwide live with hearing impairment. Despite various technologies that have been created for individuals with such disabilities, most of these technologies are either extremely expensive or inaccessible for everyday use in low-medium income countries. In order to combat this issue, we have developed a new assistive device, EchoVest, for blind/deaf people to intuitively become more aware of their environment. EchoVest transmits vibrations to the user's body by utilizing transcutaneous electric nerve stimulation (TENS) based on the source of the sounds. EchoVest also provides various features, including sound localization, sound classification, noise reduction, and depth perception. We aimed to outperform CNN-based machine-learning models, the most commonly used machine learning model for classification tasks, in accuracy and computational costs. To do so, we developed and employed a novel audio pipeline that adapts the Audio Spectrogram Transformer (AST) model, an attention-based model, for our sound classification purposes, and Fast Fourier Transforms for noise reduction. The application of Otsu's Method helped us find the optimal thresholds for background noise sound filtering and gave us much greater accuracy. In order to calculate direction and depth accurately, we applied Complex Time Difference of Arrival algorithms and SOTA localization. Our last improvement was to use blind source separation to make our algorithms applicable to multiple microphone inputs. The final algorithm achieved state-of-the-art results on numerous checkpoints, including a 95.7\% accuracy on the ESC-50 dataset for environmental sound classification.

cs.SD↗