1. Are worms more complex than humans? Rodrigo Quian Quiroga Sloan-Swartz Center for Theoretical Neurobiology. Caltech

3. Complexity measures Shannon information (entropy) Algorithmic complexity (length of the shortest code). Logical deep (time taken by the shortest code) Correlation dimension (topologic dimension of an attractor). Kolmogorov entropy. Neural Complexity (functional clustering)

4. Is it complex? 3 1 4 1 5 9 2 6 5 3 … X1( 1 ) = 0.1 X2( 1 ) = 0.3 DO I = 1, N X1(I+1) = 1.4 - X1(I)**2 + 0.3 * X2(I) X2(I+1) = X1(I) END DO X1(I) I

5. Claims: 1.There is no unique measure of complexity.

6. Amplitude distributions Amplitude Which one is more complex? Data points Frequency Power spectra Phase space reconstruction

7. Which one is more complex? Data points Amplitude distribution Amplitudes Frequency Power spectra Phase space reconstruction

8. Claims: 1.There is no unique measure of complexity. 2.Complexity depends on how we measure and represent the data.

9. Which one is more complex? Complexity Disorder Adapted from P. Grassberger, ‘89

10. Claims: 1.There is no unique measure of complexity. 2.Complexity depends on how we measure and represent the data. 3.Complexity is low both for order and randomness.

11. Which one is more complex? Complexity Disorder V1V1 V4V4 V3V3 T ~ V1V1 V2V2 Classical mechanics Statistical mechanics

12. Tossing a coin

13. Claims: 1.There is no unique measure of complexity. 2.Complexity depends on how we measure and represent the data. 3.Complexity is low both for order and randomness. But randomness is relative! (it depends on measurements, analysis tools, computer power, etc.)

14. Complexity of the brain Images from D. van Essen’s lab

15. Complexity of the brain Oztia! The brain is simple, Just half a kilo of matter.

16. Complexity  Evolution Complexity  Behavior Complexity  Consciousness Complexity of the brain Google: 374000 hits Can we measure this from brain data?

17. Complexity and consciousness

20. Complexity Disorder Seizure EEG Normal EEG Complexity and consciousness

21. Quian Quiroga et al, 2001

22. Claims: 1.There is no unique measure of complexity. 2.Complexity depends on how we measure and represent the data. 3.Complexity is low both for order and randomness. (?!?!?!) 4.Is it useful?

23. 30 sec EEG Frequency (Hz) Complexity and Behavior AwakeDeep sleep

24. Thalamo-cortical networks They generate sleep spindles and spike wave discharges Adapted from M. Steriade’s work

25. Why worms can be more complex than humans? Ideally: –Background activity  random (functional) conectivity –Complex behavior  activation of a complex network In practice: –A very complex network may look random, whereas a simpler one may show high complexity. –This depends on: measurement (# of neurons, noise, etc.), analysis tools, definition of complexity, etc.

26. Claims: (open for discussion) 1.There is no unique measure of complexity. 2.Complexity depends on how we measure and represent the data. 3.Complexity is low both for order and randomness. (?!?!?!) 4.Is it useful?

27. Which one is more complex?