arXiv subjects

Gregory A. Worrell

Publications and source records attributed to Gregory A. Worrell.

4 recordsLinked to original sources

arXiv2025

M${}^2$NuFFT: A Computationally Efficient Suboptimal Power Spectrum Estimator for Fast Exploration of Nonuniformly Sampled Time Series

Nonuniformly sampled signals are prevalent in real-world applications. However, estimating their power spectra from finite samples poses a significant challenge. The optimal solution-Bronez Generalized Prolate Spheroidal Sequence (GPSS) by solving the associated Generalized Eigenvalue Problem (GEP)-is computationally intensive and thus impractical for large datasets. This paper describes a fast, nonparametric method: Multiband-Multitaper Nonuniform Fast Fourier Transform (M${}^2$NuFFT), which substantially reduces computational burden while maintaining statistical efficiency. The algorithm partitions the signal frequency band into multiple sub-bands. Within each sub-band, optimal tapers are computed at a nominal analysis band and shifted to other analysis bands using the Nonuniform Fast Fourier Transform (NuFFT), avoiding repeated GEP computations. Spectral power within the analysis band is then estimated as the average power across the taper outputs. For the special case where the nominal band is centered at zero frequency, tapers can be approximated via cubic spline interpolation of Discrete Prolate Spheroidal Sequence (DPSS), eliminating GEP computation entirely. This reduces the complexity from $O(N^4)$ to $O(N \log N + N \log(1/ε))$. Statistical properties of the estimator, assessed using Bronez GPSS theory, reveal that the bias and variance bound of the M2NuFFT estimator are identical to those of the optimal estimator. Additionally, the degradation of bias bound indicates deviation from optimality. Finally, we propose an extension of Thomson F-test to test periodicity in nonuniform samples. The estimator's performance is validated through simulation and real-world data, demonstrating its practical applicability. The MATLAB code of the fast algorithm is available on GitHub (https://github.com/jiecui/mtnufft).

eess.SP↗

arXiv2023

CARLA: Adjusted common average referencing for cortico-cortical evoked potential data

Human brain connectivity can be mapped by single pulse electrical stimulation during intracranial EEG measurements. The raw cortico-cortical evoked potentials (CCEP) are often contaminated by noise. Common average referencing (CAR) removes common noise and preserves response shapes but can introduce bias from responsive channels. We address this issue with an adjusted, adaptive CAR algorithm termed "CAR by Least Anticorrelation (CARLA)". CARLA was tested on simulated CCEP data and real CCEP data collected from four human participants. In CARLA, the channels are ordered by increasing mean cross-trial covariance, and iteratively added to the common average until anticorrelation between any single channel and all re-referenced channels reaches a minimum, as a measure of shared noise. We simulated CCEP data with true responses in 0 to 45 of 50 total channels. We quantified CARLA's error and found that it erroneously included 0 (median) truly responsive channels in the common average with less than or equal to 42 responsive channels, and erroneously excluded less than or equal to 2.5 (median) unresponsive channels at all responsiveness levels. On real CCEP data, signal quality was quantified with the mean R-squared between all pairs of channels, which represents inter-channel dependency and is low for well-referenced data. CARLA re-referencing produced significantly lower mean R-squared than standard CAR, CAR using a fixed bottom quartile of channels by covariance, and no re-referencing. CARLA minimizes bias in re-referenced CCEP data by adaptively selecting the optimal subset of non-responsive channels. It showed high specificity and sensitivity on simulated CCEP data and lowered inter-channel dependency compared to CAR on real CCEP data.

q-bio.QM↗

arXiv2021

Reinforcement Learning based Disease Progression Model for Alzheimer's Disease

We model Alzheimer's disease (AD) progression by combining differential equations (DEs) and reinforcement learning (RL) with domain knowledge. DEs provide relationships between some, but not all, factors relevant to AD. We assume that the missing relationships must satisfy general criteria about the working of the brain, for e.g., maximizing cognition while minimizing the cost of supporting cognition. This allows us to extract the missing relationships by using RL to optimize an objective (reward) function that captures the above criteria. We use our model consisting of DEs (as a simulator) and the trained RL agent to predict individualized 10-year AD progression using baseline (year 0) features on synthetic and real data. The model was comparable or better at predicting 10-year cognition trajectories than state-of-the-art learning-based models. Our interpretable model demonstrated, and provided insights into, "recovery/compensatory" processes that mitigate the effect of AD, even though those processes were not explicitly encoded in the model. Our framework combines DEs with RL for modelling AD progression and has broad applicability for understanding other neurological disorders.

cs.LG↗

arXiv2013

Characterization of high frequency oscillations and EEG frequency spectra using the damped-oscillator oscillator detector (DOOD)

Objective: The surgical resection of brain areas with high rates of visually identified high frequency oscillations (HFOs) on EEG has been correlated with improved seizure control. However, it can be difficult to distinguish normal from pathological HFOs, and the visual detection of HFOs is very time-intensive. An automated algorithm for detecting HFOs and for wide-band spectral analysis is desirable. Methods: The damped-oscillator oscillator detector (DOOD) is adapted for HFO detection, and tested on recordings from one rat and one human. The rat data consist of recordings from the hippocampus just prior to induction of status epilepticus, and again 6 weeks after induction, after the rat is epileptic. The human data are temporal lobe depth electrode recordings from a patient who underwent pre-surgical evaluation. Results: Sensitivities and positive predictive values are presented which depend on specifying a threshold value for HFO detection. Wide-band time-frequency and HFO-associated frequency spectra are also presented. In the rat data, four high frequency bands are identified at 80-250 Hz, 250-500 Hz, 600-900 Hz and 1000-3000 Hz. The human data was low-passed filtered at 1000 Hz and showed HFO-associated bands at 15 Hz, 85 Hz, 400 Hz and 700 Hz. Conclusion: The DOOD algorithm is capable of high resolution time-frequency spectra, and it can be adapted to detect HFOs with high positive predictive value. HFO-associated wide-band data show intricate low-frequency structure. Significance: DOOD may ease the labor intensity of HFO detection. DOOD wide-band analysis may in future help distinguish normal from pathological HFOs.

q-bio.NC↗