Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban...
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![Page 1: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/1.jpg)
Being Comoplex is Simpler: Event Related Dynamics
Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences CentreWael El-Deredy School of Psychological Sciences
![Page 2: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/2.jpg)
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
![Page 3: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/3.jpg)
How did we get here?
Makeig et al, S
cience 2002
![Page 4: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/4.jpg)
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
![Page 5: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/5.jpg)
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.
arctan Im( ) Re( )ift iftx x| |iftxiftx
0 500 1000
µV
Time (ms)0 500 1000 ms
µV
2
Hz
From time to time-frequency
![Page 6: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/6.jpg)
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
![Page 7: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/7.jpg)
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
![Page 8: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/8.jpg)
ITC measures the uniformity of the distribution of angles, wrt the origin - not wrt the centre of the cloud
Example confound: Mean vector & Phase
1 1
1 1ITC ift
L Lj ift
fti i ift
xe
L L x
Intertrial Phase Coherence
![Page 9: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/9.jpg)
Removing Mean Activity
1 1
1 1ITC ift
L Lj ift
fti i ift
xe
L L x
Example confound: Mean vector & Phase
Therefore, ITC (and its variants) are NOT a valid tests for inter-trial phase organisation
![Page 10: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/10.jpg)
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
![Page 11: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/11.jpg)
Tests on the complex cloudNecessary 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)
![Page 12: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/12.jpg)
T-complex mean (test for additive activity)*
2
( )( )1
pre preft f ft f
ft
ft
x x x xT N
1
1 L
ft ifti
x xL
Tests on the complex cloudProposed tests
L
![Page 13: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/13.jpg)
T-complex mean (test for additive activity)*
2
( )( )1
pre preft f ft f
ft
ft
x x x xT N
2
2 2( )1
ft
preft f
ft preT N
STD
2 *
1
1( )( )
1
L
ft ift ft ift fti
x x x xL
1
1 L
ft ifti
x xL
T-complex variance (test for induced activity)
Tests on the complex cloudProposed tests
L
L
![Page 14: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/14.jpg)
T-Eigenvalue (test for phase similarity)• Generalised correlation
1 2 2 1 2( 15 6) log ( ) 4ft ft ft ft ftL
Tests on the complex cloudProposed tests
The eigen values of the covariance matrix (2 x L)
Mardia, Kent and Bibby Multivariate analysis, 1979.
L
![Page 15: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/15.jpg)
T-Eigen value (test for phase similarity - bimodal)• Second trigonometric moment
2
21
1ift
Lj
fti
R eL
Tests on the complex cloudProposed tests
Mardia, Statistics of Directional Data, 1972.
L
![Page 16: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/16.jpg)
ERP
PPR
Testing the tests: Simulations
![Page 17: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/17.jpg)
ERP
PPR
Testing the tests
![Page 18: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/18.jpg)
Real Data
Visual spatial attention. POz
Testing the tests
![Page 19: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/19.jpg)
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
![Page 20: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/20.jpg)
What happens next? New tests based on comparing models fitted to data.
○ Neural mass models○ Non-parametric time series modeling
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Non-parametric time series modeling
![Page 22: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/22.jpg)
22
Original LIN-Surr
SW linear AR
![Page 23: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/23.jpg)
Kernel Regression
![Page 24: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/24.jpg)
24
Original Kernel-NFR
SW Kernel-AR
![Page 25: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/25.jpg)
25
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26
Nonstationary Kernel AR
0 01
0 0
0 01
;
ˆ ;x t
x t
t t t
N
t h htN
h ht
v f t
v K L t tf t
K L t t
x
x xx
x x
0
* * *; 1 0
ˆ ;t t t tv f t x
0
** **; 1 0
ˆ ;t t tv f t x
![Page 27: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/27.jpg)
27
Non Stationary NW **
; , , ,kt t kv t A B C D
![Page 28: Being Comoplex is Simpler: Event Related Dynamics Pedro Valdes-Sosa Eduardo Martínez-Montes Cuban Neurosciences Centre Wael El-Deredy School of Psychological.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649e215503460f94b0dc2c/html5/thumbnails/28.jpg)
28
Appearance of Limit Cycle in Epilepsy
LH
RA
LH t
ra t
**
;limmax s ts
t
abs v