the power spectrum & the autocorrelation function (ACF) of a signal are heavily related. so, spectral & ACF measures will capture similar aspects of the data. shown here: how changes in spectral exponent lead to changes in ACF full width at half-maximum amplitude. pic.twitter.com/mYqpYe5pOl
— Natalie Schaworonkow (@nschawor) December 22, 2020
a sine wave is amplitude-modulated by a sinc-function of increasing frequency. the spectral peak of resulting signal starts to broaden, as a narrow sine spectral peak is convolved with the sinc box-car frequency response (time domain multiplication = frequency domain convolution) pic.twitter.com/2VLGEEeNE1
— Natalie Schaworonkow (@nschawor) December 15, 2020
after some discussions, maybe a simpler way to look at this: numerical values for phase throughout the whole interval, but bursts with clear troughs and peaks only at certain times in the below signal. pic.twitter.com/4kLAiADpEH
— Natalie Schaworonkow (@nschawor) December 11, 2020
2 different signals, for which the phase is extracted via the hilbert transform. one will get some numerical values for phase in any case, but these values are not always meaningful in a physiological sense, without an oscillation present. pic.twitter.com/UhDStvlwgt
— Natalie Schaworonkow (@nschawor) December 9, 2020
built a spikeling: a model neuron that runs on a small arduino nano chip & can fire action potentials. for instance, by shining light on a photodiode the neuron can be excited (1st half of video) or inhibited (2nd half). love the sound output! pic.twitter.com/ZZ3uc2qI4R
— Natalie Schaworonkow (@nschawor) December 1, 2020
EEG analysis in sensor space may yield distorted measures. 2 rhythms (at red & blue locations) with slightly different peak frequency mix across space. the power spectrum of the signal recorded at the green electrode now has 2 peaks in the alpha band. 🤔 pic.twitter.com/jc3HMjMWNs
— Natalie Schaworonkow (@nschawor) November 25, 2020
the power spectrum shows only half the picture: signals which differ in only with respect to phase shifts of their constituent components will have the same power spectrum. (here: 10 Hz sine wave + phase shifted 20 Hz sine wave for simulating different waveform shape) pic.twitter.com/nwTkir23JX
— Natalie Schaworonkow (@nschawor) November 23, 2020
calculating power spectra with Welch's method entails splitting the signal into segments of a certain length and averaging across segments. too short segments: low frequency resolution. low number of segments: noisy estimates. the sweet spot: somewhere in between. 🤔 pic.twitter.com/KQqBEG6YSj
— Natalie Schaworonkow (@nschawor) November 21, 2020
discrete Fourier transform, illustrated geometrically. for each frequency, the dot product of the signal with a sine as well as a cosine is calculated. the power at that frequency corresponds to the length of the vector that has the 2 dot products as x- and y-entries. pic.twitter.com/goF0TsO0I5
— Natalie Schaworonkow (@nschawor) November 19, 2020
invasive recording over the human visual cortex: a beautiful alpha-rhythm. a visual stimulus is shown during the shaded intervals, the stimulus attenuates the rhythm. the rhythm returns when the stimulus is turned off. (neat to see this classic effect so clearly in ECoG ♥️) pic.twitter.com/oGQH6XV3ro
— Natalie Schaworonkow (@nschawor) November 13, 2020
a simple LFP model made up of 1 inhibitory and 1 excitatory current, each with different synaptic kernel time constants. changing excitation/inhibition-ratio pushes the LFP 1/f-exponent (from a narrow freq. band) towards the exponent of the current with increasing contribution. pic.twitter.com/eE2vkljPdj
— Natalie Schaworonkow (@nschawor) November 10, 2020
a simple LFP model: several white noise spike trains are convolved with a synaptic kernel & the resulting signals are added. changing the decay time of the synaptic kernel changes LFP timescale. ⏲️ pic.twitter.com/J3NyiPt0Cb
— Natalie Schaworonkow (@nschawor) November 9, 2020
behavioral and neuronal measures acquired over the course of an experiment display fluctuations on fast as well as slow scales. if one computes a correlation between two _independent_ sets of such measurements, very likely strong spurious correlations will be seen. pic.twitter.com/C2muytZDhF
— Natalie Schaworonkow (@nschawor) October 16, 2020
example: a simple compound signal (red) made out of two frequency components. if you extract instantaneous amplitude and phase from the analytic signal of the compound, its phase and amplitude correspond to the circular mean of the analytic signal from individual components. pic.twitter.com/945XCXGthj
— Natalie Schaworonkow (@nschawor) October 11, 2020
the analytic signal obtained via the hilbert transform for broadband 🌸 and narrowband 🔴 filtered data. pic.twitter.com/ptZPNc3vsQ
— Natalie Schaworonkow (@nschawor) October 9, 2020
besides occipital alpha- & sensorimotor mu-rhythms, there are also other ~10 Hz rhythms in the human brain. for instance, tau-rhythms originating in the temporal lobe, which have been linked to auditory function. have not seen a temporal rhythm so clearly before. ECoG ❤️! pic.twitter.com/05GOZZXKG3
— Natalie Schaworonkow (@nschawor) September 1, 2020
IRASA is a method for separating 1/f & oscillatory parts in power spectra. timeseries are up- and downsampled with non-integer sampling rates. resulting PSDs are then averaged across different rates, which leads to dispersion of oscillatory peaks (to some extent). pic.twitter.com/PVDLBsncF6
— Natalie Schaworonkow (@nschawor) August 28, 2020
lots of EEG studies are looking at changes in oscillatory alpha-power. but different types of time domain changes can manifest as changes in alpha-power. for instance, de-/increases in:
— Natalie Schaworonkow (@nschawor) August 21, 2020
- duration or
- number or
- amplitude of oscillatory bursts. pic.twitter.com/voHmOvac9e
a small side project that I've been working on: an analysis of aperiodic activity and alpha oscillations in an open-data longitudinal infant EEG dataset: https://t.co/RBBSDux6ST 1/n
— Natalie Schaworonkow (@nschawor) August 19, 2020
adults have pronounced alpha-oscillations in the EEG, but young infants lack them. oscillations only emerge gradually during the first year of life. so, in the EEG power spectrum of a 2 month year old baby, there are no pronounced peaks, only the characteristic 1/f-part. 2/n pic.twitter.com/tlSaLxL3pr
— Natalie Schaworonkow (@nschawor) August 19, 2020
to counter EEG volume conduction, a spatial filter can be used, e.g. a Laplacian filter (1 electrode activity minus mean of surrounding ones). but if strong distant sources are present, they may still predominantly contribute to the filtered trace, yielding a non-local signal. pic.twitter.com/HldamITd6X
— Natalie Schaworonkow (@nschawor) August 6, 2020
lots of temporal correlations are present in response times over the course of an experiment, showing fast and slow fluctuations & reflecting different underlying processes: training effects, motor preparedness, sleepiness induced by long & boring experiments. 🙂 pic.twitter.com/AnyEz3A3It
— Natalie Schaworonkow (@nschawor) August 4, 2020
oscillations recorded with EEG electrodes are a mixture of different sources. therefore, phase of sensor space signals does not necessarily reflect the phase of a singular oscillation; swinging back & forth in phase space, depending on synchronization of underlying rhythms. pic.twitter.com/3Nd4DqXUlo
— Natalie Schaworonkow (@nschawor) July 21, 2020
wrapping around the axes of a univariate circular measure results in a polar plot. for a bivariate measure, this results in a torus 🍩. here, a waveform shape donut shows a fixed phase offset of a harmonic beta-component to a base alpha-oscillation. pic.twitter.com/ZvYauTFG06
— Natalie Schaworonkow (@nschawor) July 9, 2020
some neat waveforms from human ECoG recordings: triangular alpha-rhythm and arc-shaped sensorimotor mu-rhythm. (traces from different participants) pic.twitter.com/CnEcmiw4wP
— Natalie Schaworonkow (@nschawor) June 22, 2020
for me, the hardest step is always averaging over subjects, since they display large heterogeneity. here an example of how alpha-power is related to visual target detection (the classical result: lower occipital power for hit trials), in the average & for some selected subjects. pic.twitter.com/9oykK5z8pU
— Natalie Schaworonkow (@nschawor) June 18, 2020
many rhythms in the same frequency band are active simultaneously in the cortex. they mix and a summation of them is measured. this leads to distortions with respect to waveform shape (for instance), depending on the temporal relationships between the rhythms. pic.twitter.com/yDhdd5O1Z2
— Natalie Schaworonkow (@nschawor) May 28, 2020
the spectral profiles of three different types of line noise from today. 'standard' one with very narrow-band peak. a bursting type and one with weird amplitude modulation, with a broader bandwidth of the peak. pic.twitter.com/Un2EOQ7ixV
— Natalie Schaworonkow (@nschawor) May 27, 2020
illustration of two non-sinusoidal sources added together with different time delays. the time delay determines whether the oscillation in the alpha-band is enhanced or attenuated, with only the harmonic beta-component remaining. pic.twitter.com/VYzemimu7C
— Natalie Schaworonkow (@nschawor) May 25, 2020
oscillations and ERPs often feel like separate worlds, but in some ways, they are different sides of 1 coin. according to the baseline shift account, late ERPs arise because of the non-zero mean property of oscillations, which change their power in the presence of stimuli. pic.twitter.com/uvgXkGJ8d2
— Natalie Schaworonkow (@nschawor) May 23, 2020
the sensorimotor mu-rhythm shows a lot of pronounced 1/f-fluctuations in amplitude, resulting in a bursty appearance. today, I was surprised by the relative lack of amplitude modulation in hippocampal theta, with a more stable cycle amplitude over time. 🤔 (mu: human, theta: rat) pic.twitter.com/JClFCySWBX
— Natalie Schaworonkow (@nschawor) May 19, 2020
the Wasserstein metric can aid in comparing two probability distributions. it reflects the minimum amount of total work required to turn one into the other (being lazy, but smart). metric = shaded yellow area between the CDFs. (1D is easy, >1D requires more planning to stay lazy) pic.twitter.com/kbf3imh2Ug
— Natalie Schaworonkow (@nschawor) May 18, 2020
same frequency spectra, but very different time domain signals. simulation: non-sinusoidal mu-rhythm vs. sinusoidal mu-rhythm + beta-bursts. 🤔 pic.twitter.com/ElDfgAhIQp
— Natalie Schaworonkow (@nschawor) May 12, 2020
When stimulation is applied with a magnetic coil over the motor cortex, it is possible to elicit a small muscle twitch. This motor evoked potential can be measured with electromyography. (300 trials, 20–45 ms after stimulation, normalized by amplitude) Nice waveform! 🙂 pic.twitter.com/fl0wsYlSWr
— Natalie Schaworonkow (@nschawor) May 8, 2020
A single ion channel is stochastic; but looking at many of them at once will reveal regularities, slowly approaching a time course as described by the Hodgkin-Huxley model. (here: delayed rectifier potassium channels in a voltage clamp setup; inspired by rereading Dayan & Abbott) pic.twitter.com/AoAIWkJg19
— Natalie Schaworonkow (@nschawor) May 3, 2020
peak frequencies of rhythms vary across people, but how consistent are rhythms over species? currently looking at some LFP from mouse visual cortex: the most prominent rhythm there goes away with visual stimulation but has a broad frequency peak at 4.5 Hz. 🤔 nice sharp troughs! pic.twitter.com/1wMivrISwB
— Natalie Schaworonkow (@nschawor) April 30, 2020
typo: dipole is placed in primary somatosensory cortex!
when recording EEG, the orientation of underlying dipoles will heavily influence what kind of field will be picked up on the sensor level. (single dipole placed in hand knob area of primary motor cortex) pic.twitter.com/cSbk95MLa7
— Natalie Schaworonkow (@nschawor) April 24, 2020
the two hemispheres have their own neuronal rhythms. sometimes they swing together for a bit, then drift apart again. (EEG, resting state sensorimotor mu-rhythms) pic.twitter.com/ihsvMG7FLo
— Natalie Schaworonkow (@nschawor) April 20, 2020
a glimpse on the electric orchestra that is playing all the time in the brain, with EEG rhythms appearing and disappearing concurrently. for all of them: distinct peak frequencies and waveforms, distinct spatial topography, distinct modulation by behavior. 🌊 pic.twitter.com/biITJKyuNB
— Natalie Schaworonkow (@nschawor) April 14, 2020
The peak frequency for visual alpha-oscillations is typically between 8 and 12 Hz. So, a person with a peak frequency of 8 Hz will traverse through 480 up and downs per minute, while a person with a 12 Hz peak will traverse through much more, 720. Will it make a difference? 🤔 pic.twitter.com/N5eJKRL5Tp
— Natalie Schaworonkow (@nschawor) April 7, 2020
tables, the original open data. extracted a data table from Henry (1944) with longitudinal EEG recordings (spanning years!), showing increasing alpha frequency over childhood & adolescence. thinking about using it for a mixed model fitting exercise. 🤔 https://t.co/wqRGsCzHEy pic.twitter.com/naTfZ3ifde
— Natalie Schaworonkow (@nschawor) April 6, 2020
Effects of increasing the noise level for oscillatory signals: the harmonic frequency SNR of a non-sinusoidal oscillation deteriorates faster than the base frequency SNR, scrambling estimates of peak-trough asymmetry. 🤔 pic.twitter.com/7RP7TtoAzW
— Natalie Schaworonkow (@nschawor) April 1, 2020
#piday! The red sinusoidal oscillation has constant angular velocity, moving with a steady rate in the complex plane. In contrast, the blue non-sinusoidal signal accelerates at troughs and slows down at peaks during an oscillation cycle. pic.twitter.com/DmMJ6KLHOs
— Natalie Schaworonkow (@nschawor) March 14, 2020
EEG mu-oscillations from electrodes across left and right sensorimotor cortex. @introspection, some neuronal waves for you. :-) pic.twitter.com/jCoZNO5VtQ
— Natalie Schaworonkow (@nschawor) February 26, 2020
Sensorimotor oscillations are not passively idling, they modulate cortical excitability with behavioral consequences. Magnetic stimulation given at the trough of the EEG mu-rhythm results in much larger muscle responses compared to peak stimulation. https://t.co/tcgzQLyhlu pic.twitter.com/H1vmCjK0oD
— Natalie Schaworonkow (@nschawor) February 14, 2020
EEG alpha peak frequency varies as a function of alpha power for some subjects, as shown by below spectra computed for segments sorted by power in alpha band. I wonder how this could influence gradients in peak frequency along posterior-anterior axis. 🤔 https://t.co/uHqUf7mOw8 pic.twitter.com/QRVA4l1wdK
— Natalie Schaworonkow (@nschawor) February 6, 2020
Projecting signals with weights obtained by principal or independent component analysis geometrically corresponds to a rotation in an n-dimensional space, n=number of signals. 🌀 pic.twitter.com/qr9Tj2e4IP
— Natalie Schaworonkow (@nschawor) January 30, 2020
Across participants, there is a large range of measurable EEG oscillation strength. For some participants, oscillations are very pronounced, for others miniscule. One can exclude participants for the sake of good measurement, but then the generalizability suffers. Tough choice! pic.twitter.com/dXiPS5XJqP
— Natalie Schaworonkow (@nschawor) January 23, 2020
Reproducing really old results (~1930s): EEG visual alpha frequency increases over development.
— Natalie Schaworonkow (@nschawor) January 10, 2020
So many subjects in one scatter plot 😮. All of the extensive data wrangling by Voytek lab graduate rotation student Andrew Bender. pic.twitter.com/iMmuuWVdr1