Modeling, Segmenting and Statistics of Transient Spindles via Two-Dimensional Ornstein-Uhlenbeck Dynamics
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912758524542976 |
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| author | Sun, C. Fettahoglu, D. Holcman, D. |
| author_facet | Sun, C. Fettahoglu, D. Holcman, D. |
| contents | We develop here a stochastic framework for modeling and segmenting transient spindle-like oscillatory bursts in electroencephalogram (EEG) signals. At the modeling level, individual spindles are represented as path realizations of a two-dimensional Ornstein{Uhlenbeck (OU) process with a stable focus, providing a low-dimensional stochastic dynamical system whose trajectories reproduce key morphological features of spindles, including their characteristic rise{decay amplitude envelopes. On the signal processing side, we propose a segmentation procedure based on Empirical Mode Decomposition (EMD) combined with the detection of a central extremum, which isolates single spindle events and yields a collection of oscillatory atoms. This construction enables a systematic statistical analysis of spindle features: we derive empirical laws for the distributions of amplitudes, inter-spindle intervals, and rise/decay durations, and show that these exhibit exponential tails consistent with the underlying OU dynamics. We further extend the model to a pair of weakly coupled OU processes with distinct natural frequencies, generating a stochastic mixture of slow, fast, and mixed spindles in random temporal order. The resulting framework provides a data-driven framework for the analysis of transient oscillations in EEG and, more generally, in nonstationary time series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10844 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modeling, Segmenting and Statistics of Transient Spindles via Two-Dimensional Ornstein-Uhlenbeck Dynamics Sun, C. Fettahoglu, D. Holcman, D. Neurons and Cognition Spectral Theory 92-08 We develop here a stochastic framework for modeling and segmenting transient spindle-like oscillatory bursts in electroencephalogram (EEG) signals. At the modeling level, individual spindles are represented as path realizations of a two-dimensional Ornstein{Uhlenbeck (OU) process with a stable focus, providing a low-dimensional stochastic dynamical system whose trajectories reproduce key morphological features of spindles, including their characteristic rise{decay amplitude envelopes. On the signal processing side, we propose a segmentation procedure based on Empirical Mode Decomposition (EMD) combined with the detection of a central extremum, which isolates single spindle events and yields a collection of oscillatory atoms. This construction enables a systematic statistical analysis of spindle features: we derive empirical laws for the distributions of amplitudes, inter-spindle intervals, and rise/decay durations, and show that these exhibit exponential tails consistent with the underlying OU dynamics. We further extend the model to a pair of weakly coupled OU processes with distinct natural frequencies, generating a stochastic mixture of slow, fast, and mixed spindles in random temporal order. The resulting framework provides a data-driven framework for the analysis of transient oscillations in EEG and, more generally, in nonstationary time series. |
| title | Modeling, Segmenting and Statistics of Transient Spindles via Two-Dimensional Ornstein-Uhlenbeck Dynamics |
| topic | Neurons and Cognition Spectral Theory 92-08 |
| url | https://arxiv.org/abs/2512.10844 |