Delay differential analysis for dynamical sleep spindle detection

Decoding imagined speech with delay differential analysis

Speech decoding from non-invasive EEG signals can achieve relatively high accuracy (70-80%) for strictly delimited classification tasks, but for more complex tasks non-invasive speech decoding typically yields a 20-50% classification accuracy. However, decoder generalization, or how well algorithms perform objectively across datasets, is complicated by the small size and heterogeneity of existing EEG datasets. Furthermore, the limited availability of open access code hampers a comparison between methods. This study explores the application of a novel non-linear method for signal processing, delay differential analysis (DDA), to speech decoding. We provide a systematic evaluation of its performance on two public imagined speech decoding datasets relative to all publicly available deep learning methods. The results support DDA as a compelling alternative or complementary approach to deep learning methods for speech decoding. DDA is a fast and efficient time-domain open-source method that fits data using only few strong features and does not require extensive preprocessing.

Network-motif delay differential analysis of brain activity during seizures

Delay Differential Analysis (DDA) is a nonlinear method for analyzing time series based on principles from nonlinear dynamical systems. DDA is extended here to incorporate network aspects to improve the dynamical characterization of complex systems. To demonstrate its effectiveness, DDA with network capabilities was first applied to the well-known Rössler system under different parameter regimes and noise conditions. Network-motif DDA, based on cortical regions, was then applied to invasive intracranial electroencephalographic data from drug-resistant epilepsy patients undergoing presurgical monitoring. The directional network motifs between brain areas that emerge from this analysis change dramatically before, during, and after seizures. Neural systems provide a rich source of complex data, arising from varying internal states generated by network interactions.

Predicting chromosomal compartments directly from the nucleotide sequence with DNA-DDA

Three-dimensional (3D) genome architecture is characterized by multi-scale patterns and plays an essential role in gene regulation. Chromatin conformation capturing experiments have revealed many properties underlying 3D genome architecture, such as the compartmentalization of chromatin based on transcriptional states. However, they are complex, costly and time consuming, and therefore only a limited number of cell types have been examined using these techniques. Increasing effort is being directed towards deriving computational methods that can predict chromatin conformation and associated structures. Here we present DNA-delay differential analysis (DDA), a purely sequence-based method based on chaos theory to predict genome-wide A and B compartments. We show that DNA-DDA models derived from a 20 Mb sequence are sufficient to predict genome wide compartmentalization at the scale of 100 kb in four different cell types. Although this is a proof-of-concept study, our method shows promise in elucidating the mechanisms responsible for genome folding as well as modeling the impact of genetic variation on 3D genome architecture and the processes regulated thereby.

Quantifying Phase-Amplitude Modulation in Neural Data

Phase-amplitude modulation (the modulation of the amplitude of higher frequency oscillations by the phase of lower frequency oscillations) is a specific type of cross-frequency coupling that has been observed in neural recordings from multiple species in a range of behavioral contexts. Given its potential importance, care must be taken with how it is measured and quantified. Previous studies have quantified phase-amplitude modulation by measuring the distance of the amplitude distribution from a uniform distribution. While this method is of general applicability, it is not targeted to the specific modulation pattern frequently observed with low-frequency oscillations. Here we develop a new method that has increased specificity to detect modulation in the sinusoidal shape commonly observed in neural data.

Precision multidimensional neural population code recovered from single intracellular recordings

Neurons in sensory cortices are more naturally and deeply integrated than any current neural population recording tools (e.g. electrode arrays, fluorescence imaging). Two concepts facilitate efforts to observe population neural code with single-cell recordings. First, even the highest quality single-cell recording studies find a fraction of the stimulus information in high-dimensional population recordings. Finding any of this missing information provides proof of principle. Second, neurons and neural populations are understood as coupled nonlinear differential equations. Therefore, fitted ordinary differential equations provide a basis for single-trial single-cell stimulus decoding. We obtained intracellular recordings of fluctuating transmembrane current and potential in mouse visual cortex during stimulation with drifting gratings. We use mean deflection from baseline when comparing to prior single-cell studies because action potentials are too sparse and the deflection response to drifting grating stimuli (e.g. tuning curves) are well studied. Equation-based decoders allowed more precise single-trial stimulus discrimination than tuning-curve-base decoders. Performance varied across recorded signal types in a manner consistent with population recording studies and both classification bases evinced distinct stimulus-evoked phases of population dynamics, providing further corroboration. Naturally and deeply integrated observations of population dynamics would be invaluable. We offer proof of principle and a versatile framework.

Cycle-by-cycle analysis of neural oscillations

Neural oscillations are widely studied using methods based on the Fourier transform, which models data as sums of sinusoids. This has successfully uncovered numerous links between oscillations and cognition or disease. However, neural data are nonsinusoidal, and these nonsinusoidal features are increasingly linked to a variety of behavioral and cognitive states, pathophysiology, and underlying neuronal circuit properties. We present a new analysis framework, one that is complementary to existing Fourier and Hilbert transform-based approaches, that quantifies oscillatory features in the time domain on a cycle-by-cycle basis. We have released this cycle-by-cycle analysis suite as "bycycle," a fully documented, open-source Python package with detailed tutorials and troubleshooting cases. This approach performs tests to assess whether an oscillation is present at any given moment and, if so, quantifies each oscillatory cycle by its amplitude, period, and waveform symmetry, the latter of which is missed with the use of conventional approaches. In a series of simulated event-related studies, we show how conventional Fourier and Hilbert transform approaches can conflate event-related changes in oscillation burst duration as increased oscillatory amplitude and as a change in the oscillation frequency, even though those features were unchanged in simulation. Our approach avoids these errors. Furthermore, we validate this approach in simulation and against experimental recordings of patients with Parkinson's disease, who are known to have nonsinusoidal beta (12-30 Hz) oscillations.NEW & NOTEWORTHY We introduce a fully documented, open-source Python package, bycycle, for analyzing neural oscillations on a cycle-by-cycle basis. This approach is complementary to traditional Fourier and Hilbert transform-based approaches but avoids specific pitfalls. First, bycycle confirms an oscillation is present, to avoid analyzing aperiodic, nonoscillatory data as oscillations. Next, it quantifies nonsinusoidal aspects of oscillations, increasingly linked to neural circuit physiology, behavioral states, and diseases. This approach is tested against simulated and real data.

Nonlinear dynamics underlying sensory processing dysfunction in schizophrenia

Natural systems, including the brain, often seem chaotic, since they are typically driven by complex nonlinear dynamical processes. Disruption in the fluid coordination of multiple brain regions contributes to impairments in information processing and the constellation of symptoms observed in neuropsychiatric disorders. Schizophrenia (SZ), one of the most debilitating mental illnesses, is thought to arise, in part, from such a network dysfunction, leading to impaired auditory information processing as well as cognitive and psychosocial deficits. Current approaches to neurophysiologic biomarker analyses predominantly rely on linear methods and may, therefore, fail to capture the wealth of information contained in whole EEG signals, including nonlinear dynamics. In this study, delay differential analysis (DDA), a nonlinear method based on embedding theory from theoretical physics, was applied to EEG recordings from 877 SZ patients and 753 nonpsychiatric comparison subjects (NCSs) who underwent mismatch negativity (MMN) testing via their participation in the Consortium on the Genetics of Schizophrenia (COGS-2) study. DDA revealed significant nonlinear dynamical architecture related to auditory information processing in both groups. Importantly, significant DDA changes preceded those observed with traditional linear methods. Marked abnormalities in both linear and nonlinear features were detected in SZ patients. These results illustrate the benefits of nonlinear analysis of brain signals and underscore the need for future studies to investigate the relationship between DDA features and pathophysiology of information processing.