Being Comoplex is Simpler: Event Related Dynamics

1. Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological Sciences

2. Outline • Different event-related scenarios • From time to time-frequency • Examples of pitfalls of current methods • New methods based on complex statistics • Where do we go next?

3. Makeig et al, Science 2002 How did we get here?

4. Event-related scenarios • Event-Related Potential (ERP) • ERBD = ongoing EEG + Additive ERP; • AVG [ + ] = • ERBD = PPR (ongoing EEG); Partial Phase Resetting • AVG [ ] = • Induced Activity: Event-related synchronization and desynchronization (ERS/ERD)

5. 0 0 500 500 1000 1000 ms Hz µV2 µV Time (ms) From time to time-frequency A measure of the distribution of the energy of the signal in time and frequency: STFT, Morlet Wavelet, Hilbert, Gabor, etc Complex coefficients , whose moduli is a measure of the amplitude of the oscillations and whose argument is a measure of their phases.

6. From time to time-frequency Net vector Imag Net Phase Real Each point is a complex wavelet coefficient of a trial at a given frequency and time All trials at a certain t & f form a complex cloud

7. From time to time-frequency Event-related scenarios Change in the position of the cloud  mean vector Change in the shape of the cloud  Eigen structure Change in the dispersion of the cloud  variance Current measures  confound changes

8. Intertrial Phase Coherence Example confound: Mean vector & Phase ITC measures the uniformity of the distribution of angles, wrt the origin - not wrt the centre of the cloud

9. Example confound: Mean vector & Phase Removing Mean Activity Therefore, ITC (and its variants) are NOT a valid tests for inter-trial phase organisation

10. Net vector Imag Imag Variance Real Real Tests on the complex cloud Complex statistics on the features of the cloud (SEPARATELY): mean vector;variance; form

11. Imag Imag Real Real For additive ERP: It has to survive a T-test on the mean (compared to pre-stim) • For PPR: It has to survive the subtraction of the mean vector. • Significant test wrt pre-stim Tests on the complex cloud Necessary conditions

12. Tests on the complex cloud Proposed tests • T-complex mean (test for additive activity) L

13. Tests on the complex cloud Proposed tests L • T-complex variance (test for induced activity) L T-complex mean (test for additive activity)

14. The eigen values of the covariance matrix (2 x L) L Mardia, Kent and Bibby Multivariate analysis, 1979. Tests on the complex cloud Proposed tests • T-Eigenvalue (test for phase similarity) • Generalised correlation

15. L Tests on the complex cloud Proposed tests • T-Eigen value (test for phase similarity - bimodal) • Second trigonometric moment Mardia, Statistics of Directional Data, 1972.

16. Testing the tests: Simulations • ERP • PPR

17. Testing the tests • ERP • PPR

18. Testing the tests • Real Data Visual spatial attention. POz

19. Summary • Current measures (e.g. ITC) cannot distinguish between additive activity and phase resetting. • Statistical tests based on the complex time-frequency are more sensitive to changes event-related brain dynamics. • Separate tests for separate features, to avoid confounds. • Purely descriptive: No mechanistic interpretation.

20. What happens next? • New tests based on comparing models fitted to data. • Neural mass models • Non-parametric time series modeling

21. Non-parametric time series modeling

22. SW linear AR Original LIN-Surr

23. Kernel Regression

24. SW Kernel-AR Original Kernel-NFR

26. Nonstationary Kernel AR

27. Non Stationary NW

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