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.  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? Outline

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

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

5.  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. 05001000 µV Time (ms) 05001000 ms µV 2 Hz From time to time-frequency

6. Real Imag Net vector From time to time-frequency 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 Net Phase

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

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

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

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

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

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

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

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

16.  ERP  PPR Testing the tests: Simulations

17.  ERP  PPR Testing the tests

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

19.  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. Summary

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. 22 Original LIN-Surr SW linear AR

23. Kernel Regression

24. 24 Original Kernel-NFR SW Kernel-AR

25. 25

26. 26 Nonstationary Kernel AR

27. 27 Non Stationary NW

28. 28 Appearance of Limit Cycle in Epilepsy LH RA