{"ID":2825284,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.21768","arxiv_id":"2512.21768","title":"Numerical Twin with Two Dimensional Ornstein--Uhlenbeck Processes of Transient Oscillations in EEG signal","abstract":"Stochastic burst-like oscillations are common in physiological signals, yet there are few compact generative models that capture their transient structure. We propose a numerical-twin framework that represents transient narrowband activity as a two-dimensional Ornstein-Uhlenbeck (OU) process with three interpretable parameters: decay rate, mean frequency, and noise amplitude. We develop two complementary estimation strategies. The first fits the power spectral density, amplitude distribution, and autocorrelation to recover OU-parameters. The second segments burst events and performs a statistical match between empirical spindle statistics (duration, amplitude, inter-event interval) and simulated OU output via grid search, resolving parameter degeneracies by including event counts. We extend the framework to multiple frequency bands and piecewise-stationary dynamics to track slow parameter drifts. Applied to electroencephalography (EEG) recorded during general anesthesia, the method identifies OU models that reproduce alpha-spindle (8-12 Hz) morphology and band-limited spectra with low residual error, enabling real-time tracking of state changes that are not apparent from band power alone. This decomposition yields a sparse, interpretable representation of transient oscillations and provides interpretable metrics for brain monitoring.","short_abstract":"Stochastic burst-like oscillations are common in physiological signals, yet there are few compact generative models that capture their transient structure. We propose a numerical-twin framework that represents transient narrowband activity as a two-dimensional Ornstein-Uhlenbeck (OU) process with three interpretable pa...","url_abs":"https://arxiv.org/abs/2512.21768","url_pdf":"https://arxiv.org/pdf/2512.21768v2","authors":"[\"P. O. Michel\",\"C. Sun\",\"S. Jaffard\",\"D. Longrois\",\"D. Holcman\"]","published":"2025-12-25T19:26:40Z","proceeding":"q-bio.NC","tasks":"[\"q-bio.NC\"]","methods":"[]","has_code":false}