Gordon Conference on Nonlinear Science Colby College, main, June 26-July 1,2005

1. Gordon Conference on Nonlinear Science Colby College, main, June 26-July 1,2005 Functional Holography of Bio-Networks Activity From Cultures to the Human Brain Eshel Ben-Jacob With Leo Towle, Head Neurology University of Chicago Hospitals Itay Baruchi (PhD student)

2. Bio-Networks Activity N-channels recording Metabolic Networks Gene-Networks Neural-Networks ………..

3. 5 minutes introduction to Neuroscience Great progress in accumulation of detailed information. We have no idea how the brain really works

4. 1011 Neurons 1016 Synapses The brain

5. Probing the brain fMRI EEG ECoG Optical imaging

6. Questions “function-form” relations The challenge: Lifting the perplexity of the complexity Looking for Functional Correlations

7. Cartoon  Math Mathematical representation of the challenge Network of M nodes Recordings Activity Time From N channels where N << M High level of noise

8. Today Tutorial: 1. Correlations, correlation matrix and clustering 2. Dimension Reduction 3. Cross-correlations and temporal ordering 4. Connectivity Networks in Real Space The Functional Holography Analysis 1.The space of Correlations 2. From Correlations to functional correlations 3. Causal Manifolds Epilepsy fMRI and the broken left- right symmetry of the brain Implications about information processing in the brain

9. 3 2 1 Voltage Time Tutorial 1. Correlations Pearson’s correlations

10. Tutorial 1. Correlation matrix and clustering

11. Tutorial 2. Dimensions Reduction Looking for leading vectors of a matrix for maximum information The example of Singular-Value-Decomposition (SVD) (A reminder) Eigenvalues Recorded

12. Illustration of SVD I Original 400x300 pixels 3 eigenvectors 9 81

13. Illustration of SVD II ( For 9 periodic signals + phase shifts + noise) PV1 PV2 SVD Eigenvalues

14. Tutorial 3. Cross-correlations <Xi(t)*Xj(t+∆t)> Cross-correlation ∆t Time delay

15. Tutorial 3. Temporal ordering (Baruchi et al Neuroinformatics Complexity 2005)

16. Tutorial 4. Connectivity Networks in Real Space 3 Colors code 2 1 low Voltage Time C(1,3)=0.15 C(1,2)=0.25 C(2,3)=0.5 (FG11) (FG20) (FG13)

17. End Tutorial What is missing?

18. Another example After collective normalization (Functional Holography)

19. 3 2 3 2 1 1 1 2 3 Space ≡ Matrix Functional Holography FH 1. The Space of Correlations 3 2 1 Baruchi et al Neuroinformatics 2004 Complexity 2005

20. FH 2. From Correlations to Functional correlations Collective normalization Functional Correlations C(i,j) Correlations A(i,j) = D(i,j) Correlation distance D(1,3) 3 2 1

21. What does it mean? 1. Expansion Functional correlations Correlations Correlations Functional Correlations

22. What does it mean? 2. Contraction Correlations High noise tolerance Functional correlations Robustness to lesion

28. Thank you

29. 30micro “Brains” in a Nutshell A lesson from Cultured Neural Networks Regulated spontaneous activity– the basic templates for computability? Segev et al Phy Rev lett 2000,2001,2002,2003 Baruchi et al, Complexity 2005

30. 1ms 100ms Formation of Synchronizes Bursting Events - SBEs

31. From “Brains” in a Nutshell to the Human Brain ECoG recording With Leo Towle (latter in the meeting)

32. Voltage Time From binary sequences to Continuous signals

33. The challenge (inter ictal) From binary sequences to Continuous signals (onset) (ictal)

34. Experimental Unitary Network