Speaker: Jimmy Lu Topics: Exploring Complex Networks Date: 2010.04.22 WECO Lab, CSIE, FJU

1. Exploring Complex Networks Speaker : Jimmy Lu Advisor : Hsing Mei Web Computing Laboratory(WECO Lab) Computer Science and Information Engineering Department Fu Jen Catholic University

2. Outline 2010/4/22 2 WECO Lab, CSIE dept., FJU http://www.weco.net The human connectiome: a structural description of the human brain Complex brain networks: graph theoretical analysis of structural and functional systems Complex network measures of brain connectivity: uses and interpretations Classes of network connectivity and dynamics Community structure in social and biological networks

3. The Human Connectome(1/2) 2010/4/22 3 WECO Lab, CSIE dept., FJU http://www.weco.net What is the connectome? Challenges Brian is a highly complex organ Basic structural elements is hard to define Scales and levels Microscale: single neurons and synapses Macroscale: brain regions and pathways Mesoscale: minicolumns and their connection patterns The first draft should focus on corticalthalamic system

4. The Human Connectome(2/2) 2010/4/22 4 WECO Lab, CSIE dept., FJU http://www.weco.net Steps toward the human connectome Step 1: diffusion-weighted image, voxel-wise structural probabilistic connectivity matrix Step 2: correlation analysis of spatially registered, voxel-wise functional connectivity matrix Step 3: cluster analysis, structural-functional relationship, indirect projections Step 4: compare result to macaque data Step 5: validation Step 6–8: population analyses of healthy subjects

5. Computational modeling of structural and functional brain netowrks 2010/4/22 5 WECO Lab, CSIE dept., FJU http://www.weco.net

6. Illustrative anatomical, functional, effective connectivity networks 2010/4/22 6 WECO Lab, CSIE dept., FJU http://www.weco.net

7. Network measures 2010/4/22 7 WECO Lab, CSIE dept., FJU http://www.weco.net

8. Measures of network topology 2010/4/22 8 WECO Lab, CSIE dept., FJU http://www.weco.net

9. Construction of brain networks 2010/4/22 9 WECO Lab, CSIE dept., FJU http://www.weco.net

10. Structural and functional brain networks 2010/4/22 10 WECO Lab, CSIE dept., FJU http://www.weco.net

11. Functional Dynamics 2010/4/22 11 WECO Lab, CSIE dept., FJU http://www.weco.net Models Random Entropy: H(X) =0.5ln((2πe)n|COV(X)|) Integration: I(X) =ΣiH(xi) − H(X) Complexity: C(X) = H(X) − ΣiH(xi|X − xi) = ΣiMI(xi; X − xi) − I(X) = (n − 1)I(X) − n<I(X − xi)> Evelutionary: grah selection

12. Comparison of structural and functional connectivity 2010/4/22 12 WECO Lab, CSIE dept., FJU http://www.weco.net

13. Average time course of integration and complexity during graph selection 2010/4/22 13 WECO Lab, CSIE dept., FJU http://www.weco.net

14. Parameter variation 2010/4/22 14 WECO Lab, CSIE dept., FJU http://www.weco.net

15. Distance matrices and two-dimensional configurations 2010/4/22 15 WECO Lab, CSIE dept., FJU http://www.weco.net

16. Plot of characteristic path length 2010/4/22 16 WECO Lab, CSIE dept., FJU http://www.weco.net

17. Cellular and whole-brain networks demonstrate consistent topological features 2010/4/22 17 WECO Lab, CSIE dept., FJU http://www.weco.net

18. Disease-related disorganization of brain anatomical networks 2010/4/22 18 WECO Lab, CSIE dept., FJU http://www.weco.net

19. Detecting Community 2010/4/22 19 WECO Lab, CSIE dept., FJU http://www.weco.net Traditional method Node-independent, edge-independent dendrogram Edge betweenness and community structural Calculate the betweenness for all edges in the network Remove the edge with the highest betweenness Recalculate betweennesses for all edges affected by the removal Repeat from step 2 until no edges remain

20. Community structure and dendrogram 2010/4/22 20 WECO Lab, CSIE dept., FJU http://www.weco.net

21. http://www.brain-connectivity-toolbox.net 2010/4/22 21 WECO Lab, CSIE dept., FJU http://www.weco.net

22. Next Steps 2010/4/22 22 WECO Lab, CSIE dept., FJU http://www.weco.net From structures to functions Another two type of brain networks Definition of the brain anatomy on Wikipedia Tool usage BrainVoygerQX Matlab, BCT, matlabBGL Pajek, UCINET Weka

23. 2010/4/22 WECO Lab, CSIE dept., FJU http://www.weco.net 23 [1] Olaf Sporns, GiulioTononi, Rolf Kötter, “The human connectiome: a structural description of the human brain”, PLoS Computational Biology 1, e42 (September 2005) [2] Ed Bullmore, Olaf Sporns, “Complex brain networks: graph theoretical analysis of structural and functional systems”, Nature Reviews Neuroscience 10, 186-198 (March 2009) [3] MikailRubinov, Olaf Sporns, “Complex network measures of brain connectivity: uses and interpretations”, NeuroImage (2009) [4] Steven H. Strogatz, “Exploring complex network”, Nature, 410 (March 2001) [5] Olaf Sporns, GiulioTononi, “Classes of network connectivity and dynamics”, Complexity 7 (2002) [6] M. Girvan, M. E. J. Newman, “Community structure in social and biological networks”, PNAS 99 (June 2002) Reference