1. Measuring Activation and Causality using multiple Prior Information Pedro A. Valdés-Sosa Cuban Neuroscience Center

2. Mapping

3. Brain Maps

4. Multimodal T1-Nissl-cryotomy-PET-myelin stain

5. Localization versus Connectivity Hiparcus ( II BC) Jackson US air Traffic Luria

6. Localization versus Connection AnatomicalPhysiological Localization Morphometry: Voxel based Region based Cortical thickness Activation: EEEG/MEG fMRI Connection Anatomical Connectivity Diffusion Weighted Functional Connectivity Effective Connectivity

7. Brain Tomographies Physical Model of some brain characteristic Prediction of measurement Direct Problem Image of some brain characteristic measurement Inverse Problem a Priori Information

8. EEG/MEG Forward Problem Primary current j EEG/MEG v

9. EEG inverse Problem Bayesian Inference!!

10. Methods for Regression Data VARETA LORETA ICA Non Negative Matrix Factorization In fact can be unified or combined

11. L0 Norm “Sparsness” AIC, BIC, TIC, RIC “subset selection”“Matching Purusit”“Dipoles”

12. L1 Norm “Sparseness” “Lasso”“Basis Pursuit”“FOCUSS” Connection with ICA

13. Fast LARS Algorithm (Friedman, Hastie, Tibshirani) Regularization path for diabetes data

14. L2 Norm “Minimum Norm” “Ridge”“Frames”“Minimum Norm”

15. Simplest EEG inverse Problem Bayesian Inference!!

16. Multiple Priors SparsenessMinimal Norm Non smoothDipoles=FOCUSSMinimum Norm SmoothVARETALORETA

17. Which inverse solution to choose?: let the data decide combining all solutions

18. Bayesian Model Averaging For 69 compartments

19. Simulations with Bayesian Model Averaging

20. BMA during concurrent EEG/fMRI

21. Combining Priors Fused Lasso VARETA-LORETA

22. Combining penalties (L1,I) (L1,L)

23. Between LORETA and VARETA LORETA VARETA Solution Chosen

24. Further Combination: Multiple Priors plus (semi) Non Negative Matrix Factorization Non Negative Matrix Factorizations used for data reduction Equivalent to Cluster Analysis

25. Multiple Priors plus (semi) Non Negative Matrix Factorization

26. Fast Non-negative LARS Algorithm (Morup) Regularization paths for diabetes data

27. Results for a Simulation 64 Channels, 1 Patch complex time series BIC Regularization path

28. Results of a Simulation

29. Localization versus Connection AnatomicalPhysiological Localization Morphometry: Voxel based Region based Cortical thickness Activation: EEEG/MEG fMRI Connection Anatomical Connectivity Diffusion Weighted Functional Connectivity Effective Connectivity

30. Effective vs. Functional Connectivity (Karl Friston)

31. Statistical Analysis of Causal Modeling "Beyond such discarded fundamentals as 'matter' and 'force' lies still another fetish amidst the inscrutable arcana of modern science, namely, the category of cause and effect.“ Karl Pearson (1911)

32. Granger (Non) Causality for TWO time series 1212 1212 Granger Non Causality t t-1 t =1,…,N

33. Granger Causality of EEG signals Freiwald et al. (1999) J. Neurosci. Methods. 94:105-119 C3 C4 t t-1

34. What happens when you have a LOT of time series? 12…p12…p … t t-1 t =1,…,N Long history: Bressler, Baccala, Kaminski, Eichler, Goebel

35. Problems with the Multivariate Autoregressive Model for Brain Manifolds p→∞p→∞ # of parameters likelihood

36. Regions of Interest Alemán-Gómez Y. et al. PS0103

37. Point influence Measures is the simple test

38.  38 Spike and Wave

39.  39 Spike and Wave

40. What happens when you have a LOT of time series? 12…p12…p … t t-1 t =1,…,N Long history: Bressler, Baccala, Kaminski, Eichler, Goebel

41. a) Teat CG as a Random Field Concept applied to correlation fields by Worsley Usual SPM: RF is the brain New Idea RF is Cartesian product of Brain by Brain = = X

42. Granger Causality must be measured on a MANIFOLD

43. Influence Measures defined on a Manifold An influence field is a multiple test and all for a given

44. Discretization of the Continuos AR Model

45. Influence Fields and Bayesian Estimation Influence field likelihood prior

46. Influence Fields Outield Infield

47. Priors for Influence Fields maximal SMOOTHNESS Valdés-Sosa PA Neuroinformatics (2004) 2:1-12 Valdés-Sosa PA et al. Phil. Trans R. Soc. B (2005) 360: 969-981 Minimum norm I Minimum spatial laplacian L prior

48. vs FFA Amigdala Fear Static + Fear Dynamic Neutral Neural basis of emotional expression processing

49. Emotional Network (Dipole)

50. Cuban Neuroscience Center Concurrent EEG-fMRI recordings Fine time scale

51. Cuban Neuroscience Center Concurrent EEG-fMRI (  Rhythm)

52. Basis of concurrent EEG/MEG-fMRI analysis-voxel level Trujillo et al. IJBEM (2001)  BOLD  Vasomotor Feed Forward Signal  VFFS  Ensemble of Postsynaptic Potentials  ePSP  net Primary Current Density  nPCD  EEG/MEG

53. EEG/MEG-fMRI-voxel Inverese solution Association  BOLD  VFF S  ePSP  nPCD  EEG/MEG

54. correlationlog BOLD-log j

55. First order Autoregressive Model for fMRI and EEG

56. Estimated A for fMRI-EEG (f,s) using L1 regularizer

57. EEG-fMRI influence Fields Maximal Evidence dipole MN non smooth smooth nonsmooth+smooth dipole+MN

58. http://journals.royalsociety.org/content/md5e04y6bgm8 /

59. Localization versus Connection AnatomicalPhysiological Localization Morphometry: Voxel based Region based Cortical thickness Activation: EEEG/MEG fMRI Connection Anatomical Connectivity Diffusion Weighted Functional Connectivity Effective Connectivity