Exploring Complex Networks
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This document summarizes a presentation on exploring complex networks in the brain. It discusses defining the human connectome at multiple scales from neurons to brain regions. It outlines steps to map the structural and functional connectivity of the brain. It also describes using network measures and models to analyze topological properties of brain networks and detecting community structure. Detecting changes in network measures may help understand diseases.
![2010/4/22WECO Lab, CSIE dept., FJU http://www.weco.net23[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](https://image.slidesharecdn.com/20100422exploringcomplexnetworkswecolab-100422070853-phpapp01/85/Exploring-Complex-Networks-23-320.jpg)
Exploring Complex Networks
- 1. Exploring Complex NetworksSpeaker : Jimmy LuAdvisor : Hsing MeiWeb Computing Laboratory(WECO Lab)Computer Science and Information Engineering DepartmentFu Jen Catholic University
- 2. Outline2010/4/222WECO Lab, CSIE dept., FJU http://www.weco.netThe human connectiome: a structural description of the human brainComplex brain networks: graph theoretical analysis of structural and functional systemsComplex network measures of brain connectivity: uses and interpretationsClasses of network connectivity and dynamicsCommunity structure in social and biological networks
- 3. The Human Connectome(1/2)2010/4/223WECO Lab, CSIE dept., FJU http://www.weco.netWhat is the connectome?ChallengesBrian is a highly complex organBasic structural elements is hard to defineScales and levelsMicroscale: single neurons and synapses Macroscale: brain regions and pathwaysMesoscale: minicolumns and their connection patternsThe first draft should focus on corticalthalamic system
- 4. The Human Connectome(2/2)2010/4/224WECO Lab, CSIE dept., FJU http://www.weco.netSteps toward the human connectomeStep 1: diffusion-weighted image, voxel-wise structural probabilistic connectivity matrixStep 2: correlation analysis of spatially registered, voxel-wise functional connectivity matrixStep 3: cluster analysis, structural-functional relationship, indirect projectionsStep 4: compare result to macaque dataStep 5: validationStep 6–8: population analyses of healthy subjects
- 5. Computational modeling of structural and functional brain netowrks2010/4/225WECO Lab, CSIE dept., FJU http://www.weco.net
- 6. Illustrative anatomical, functional, effective connectivity networks2010/4/226WECO Lab, CSIE dept., FJU http://www.weco.net
- 7. Network measures2010/4/227WECO Lab, CSIE dept., FJU http://www.weco.net
- 8. Measures of network topology2010/4/228WECO Lab, CSIE dept., FJU http://www.weco.net
- 9. Construction of brain networks2010/4/229WECO Lab, CSIE dept., FJU http://www.weco.net
- 10. Structural and functional brain networks2010/4/2210WECO Lab, CSIE dept., FJU http://www.weco.net
- 11. Functional Dynamics2010/4/2211WECO Lab, CSIE dept., FJU http://www.weco.netModelsRandomEntropy: 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 connectivity2010/4/2212WECO Lab, CSIE dept., FJU http://www.weco.net
- 13. Average time course of integration and complexity during graph selection2010/4/2213WECO Lab, CSIE dept., FJU http://www.weco.net
- 14. Parameter variation2010/4/2214WECO Lab, CSIE dept., FJU http://www.weco.net
- 15. Distance matrices and two-dimensional configurations2010/4/2215WECO Lab, CSIE dept., FJU http://www.weco.net
- 16. Plot of characteristic path length2010/4/2216WECO Lab, CSIE dept., FJU http://www.weco.net
- 17. Cellular and whole-brain networks demonstrate consistent topological features2010/4/2217WECO Lab, CSIE dept., FJU http://www.weco.net
- 18. Disease-related disorganization of brain anatomical networks2010/4/2218WECO Lab, CSIE dept., FJU http://www.weco.net
- 19. Detecting Community2010/4/2219WECO Lab, CSIE dept., FJU http://www.weco.netTraditional methodNode-independent, edge-independentdendrogramEdge betweenness and community structuralCalculate the betweenness for all edges in the networkRemove the edge with the highest betweennessRecalculate betweennesses for all edges affected by the removalRepeat from step 2 until no edges remain
- 20. Community structure and dendrogram2010/4/2220WECO Lab, CSIE dept., FJU http://www.weco.net
- 21. http://www.brain-connectivity-toolbox.net2010/4/2221WECO Lab, CSIE dept., FJU http://www.weco.net
- 22. Next Steps2010/4/2222WECO Lab, CSIE dept., FJU http://www.weco.netFrom structures to functionsAnother two type of brain networksDefinition of the brain anatomy on WikipediaTool usageBrainVoygerQXMatlab, BCT, matlabBGLPajek, UCINETWeka
- 23. 2010/4/22WECO Lab, CSIE dept., FJU http://www.weco.net23[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