Complejidad Dia 8

1. Complejidad Dia 8 Geofisica Biología MacroEconomía Psicologia Meteorología Ecología UBA, Junio 26, 2012.

2. Martes 26: 1era parte More on preprocessing of fmri images 2da Parte Redes, desdeEguiluz a Tagliazuchi. Jueves 28 1era parte anomalous scaling and phase transition 2da parte Modeling “Our brain is a network. A very efficient network to be precise. It is a network of a large number of different brain regions that each have their own task and function, but who are continuously sharing information with each other. As such, they form a complex integrative network in which information is continuously processed and transported between structurally and functionally linked brain regions: the brain network” Where is the router?

3. conventional task-related fMRI Resting state fMRI From: Exploring the brain network: A review on resting-state fMRI functional connectivity. Martijn P. van den Heuvel, Hilleke E. Hulshoff Pol. European Neuropsychopharmacology, 20 (2010) 519–534

4. modeling the brain as a functional network with connections between regions that are functionally linked

5. Graph, clustering-coefficient, characteristic path length, connectivity degree, centrality and modularity. Graph clustering-coefficient characteristic path length connectivity degree modularity centrality

6. Network topologies: regular, random, small-world, scale-free and modular networks.

8. the “small-world” phenomenon • 1011 neurons • 104 synapses per neuron • On average two neurons are only 2 ~ 3 “synapses” apart • Connectivity is sparse (i.e., 104 / 1011 ) • Most connections are local (high clustering coefficient) • The distance between any two network nodes is still relatively small: how is possible?

9. How to extract functional brain networks? fMRI (I) (III) (II) From Eguiluz et al, Phys. Rev. Letters (2005).

10. Undirected Degree (k) fMRI Indicate “airports” My brain’s network (finger tapping) Nodes spatial location Colors indicate the number of links (or “degree”) of each node. yellow=1, green 2, red=3, blue=4, etc From Eguiluz et al, Phys. Rev. Letters (2005).

11. fMRI Brain networks are small-word Group statistics fM RI-results “Small-world” • C >> Crand • L ~ Lrand Previous related results From Eguiluz et al, Phys. Rev. Letters (2005).

12. fMRI Brain’s degree distribution (i.e., how many links each node have) Scale-free k-gwithg ~2 From Eguiluz et al, Phys. Rev. Letters (2005).

13. g=2 fMRI Average Degree Distribution n=22 from 7 subjects Few but very well connected brain sites From Eguiluz et al, Phys. Rev. Letters (2005).

14. fMRI Average Links Length Distribution Probability of finding a link between two nodes separated by a distance x < D k(D) ~ 1/x2 “~ Brain radius” Voxel length From Eguiluz et al, Phys. Rev. Letters (2005).

15. fMRI Something that bother us: Degree vs Clustering Clustering relatively independent of connectivity Recall that clustering estimates the proportion of nodes forming “triangles”. Assortative From Eguiluz et al, Phys. Rev. Letters (2005).

16. fMRI (Directed links) A node tends to be either an in-hub or an out-hub few “airports” out-hub vs und. in-hub vs und. From Cecchi et al, BME (2007).

17. fMRI (Directed links) From Cecchi et al, BME (2007).

18. lattice brain random (Directed links) Assortative? From Cecchi et al, BME (2007).

19. Networks are scale free across different tasks Finger tapping vs. Music • Different tasks • Different networks • Similar scaling From Eguiluz et al, Phys. Rev. Letters (2005). And during “resting state” =>

20. Summary until now: The large scale brain network extracted from correlations seems to be scale-free and small word But what about dynamics?

21. Even in resting state, each positively correlated clique have a negatively correlated contrapart Areas coloured redish have significant positive correlation with seed regions and are significantly anticorrelated with regions coloured blueish (Fox et al , PNAS, 102, 2005)

22. Each positively correlated clique have a negatively correlated contrapart Healthy Controls Chronic Pain Patients Chialvo et al. 2007, “Beyond feeling: chronic pain hurts the brain disrupting the default-mode network dynamics”

23. ~ 1 Chialvo et al., “Beyond feeling: chronic pain hurts the brain disrupting the default-mode network dynamics” J.Neuroscience (2008)

24. What is special about being critical? Recall the Ferromagnetic-paramagnetic Phase-Transition T<TC T~TC T>TC Critical Point order disorder TC Snapshots of spins states in the Ising model. Long range correlations emerges at the critical point Subcritical Critical SuperCritical Snapshots of spins states in a model system (Ising)

25. Critical Ising networks ~ brain networks E=-JS<i,j> Si Sj – B Sk Sk Critical SubCritical SuperCritical Positive correlated networks Ising Brain Only local positive interactions Chialvo DR, Balenzuela P, Fraiman D. The brain: What is critical about it? (arXiv.org/ cond-mat/0804.0032) Fraiman D, Balenzuela P, Foss J. Chialvo DR, Ising like dynamics in large-scale brain networks. (arXiv.org/ cond-mat/0811.3721)

26. Critical Ising networks ~ brain networks Brains Ising

27. Critical Ising networks ~ brain networks Negative correlated networks Critical SubCritical SuperCritical Ising Brain Negative correlations with fat tails similar to the brain data appear in the Ising data, despite the absence of negative “structural” interactions (i.e. no “inhibitory” connectivity).

28. Assortativity

29. Critical Ising networks ~ brain networks

30. Resting-state networks. (functionally linked resting-state networks during rest identified using different methods (e.g. seed, ICA or clustering)

31. Laspia 2007 Easy problem # 2: Define a (reasonable) heuristic order parameter for the large scale brain dynamics seen in the fMRI experiments Price: A year postdoct salary in Chicago (renewable) 2007

32. Related results

34. 1/x2 replicated independently with fMRI Average Links Length Distribution agrees with recent results (in resting condition) interhemispheric PC(D)~1/x2 intrahemispheric Functional connectivity vs. anatomical distance. ( Symmetric interhemispheric) From Salvador et al, (Cerebral Cortex, 2005.)

35. C/Crandom = 2.08 L/Lrandom = 1.09

36. EEG 2 1 3 4 C threshold L Synchronization I Graph

37. Path length is related to cognitive score Control subjects Clustering Path Length cognitive score Alzheimer patients

38. Clauset, Newman & Moore Algorithm*