Exploring Complex Networks

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Speaker: Jimmy Lu
Topics: Exploring Complex Networks
Date: 2010.04.22

WECO Lab, CSIE, FJU

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Exploring Complex Networks

  1. 1. Exploring Complex Networks<br />Speaker : Jimmy Lu<br />Advisor : Hsing Mei<br />Web Computing Laboratory(WECO Lab)<br />Computer Science and Information Engineering Department<br />Fu Jen Catholic University<br />
  2. 2. Outline<br />2010/4/22<br />2<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />The human connectiome: a structural description of the human brain<br />Complex brain networks: graph theoretical analysis of structural and functional systems<br />Complex network measures of brain connectivity: uses and interpretations<br />Classes of network connectivity and dynamics<br />Community structure in social and biological networks<br />
  3. 3. The Human Connectome(1/2)<br />2010/4/22<br />3<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />What is the connectome?<br />Challenges<br />Brian is a highly complex organ<br />Basic structural elements is hard to define<br />Scales and levels<br />Microscale: single neurons and synapses <br />Macroscale: brain regions and pathways<br />Mesoscale: minicolumns and their connection patterns<br />The first draft should focus on corticalthalamic system<br />
  4. 4. The Human Connectome(2/2)<br />2010/4/22<br />4<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />Steps toward the human connectome<br />Step 1: diffusion-weighted image, voxel-wise structural probabilistic connectivity matrix<br />Step 2: correlation analysis of spatially registered, voxel-wise functional connectivity matrix<br />Step 3: cluster analysis, structural-functional relationship, indirect projections<br />Step 4: compare result to macaque data<br />Step 5: validation<br />Step 6–8: population analyses of healthy subjects<br />
  5. 5. Computational modeling of structural and functional brain netowrks<br />2010/4/22<br />5<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  6. 6. Illustrative anatomical, functional, effective connectivity networks<br />2010/4/22<br />6<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  7. 7. Network measures<br />2010/4/22<br />7<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  8. 8. Measures of network topology<br />2010/4/22<br />8<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  9. 9. Construction of brain networks<br />2010/4/22<br />9<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  10. 10. Structural and functional brain networks<br />2010/4/22<br />10<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  11. 11. Functional Dynamics<br />2010/4/22<br />11<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />Models<br />Random<br />Entropy: H(X) =0.5ln((2πe)n|COV(X)|)<br />Integration: I(X) =ΣiH(xi) − H(X)<br />Complexity: C(X) = H(X) − ΣiH(xi|X − xi)<br /> = ΣiMI(xi; X − xi) − I(X)<br /> = (n − 1)I(X) − n<I(X − xi)><br />Evelutionary: grah selection<br />
  12. 12. Comparison of structural and functional connectivity<br />2010/4/22<br />12<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  13. 13. Average time course of integration and complexity during graph selection<br />2010/4/22<br />13<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  14. 14. Parameter variation<br />2010/4/22<br />14<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  15. 15. Distance matrices and two-dimensional configurations<br />2010/4/22<br />15<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  16. 16. Plot of characteristic path length<br />2010/4/22<br />16<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  17. 17. Cellular and whole-brain networks demonstrate consistent topological features<br />2010/4/22<br />17<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  18. 18. Disease-related disorganization of brain anatomical networks<br />2010/4/22<br />18<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  19. 19. Detecting Community<br />2010/4/22<br />19<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />Traditional method<br />Node-independent, edge-independent<br />dendrogram<br />Edge betweenness and community structural<br />Calculate the betweenness for all edges in the network<br />Remove the edge with the highest betweenness<br />Recalculate betweennesses for all edges affected by the removal<br />Repeat from step 2 until no edges remain<br />
  20. 20. Community structure and dendrogram<br />2010/4/22<br />20<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  21. 21. http://www.brain-connectivity-toolbox.net<br />2010/4/22<br />21<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />
  22. 22. Next Steps<br />2010/4/22<br />22<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />From structures to functions<br />Another two type of brain networks<br />Definition of the brain anatomy on Wikipedia<br />Tool usage<br />BrainVoygerQX<br />Matlab, BCT, matlabBGL<br />Pajek, UCINET<br />Weka<br />
  23. 23. 2010/4/22<br />WECO Lab, CSIE dept., FJU http://www.weco.net<br />23<br />[1] Olaf Sporns, GiulioTononi, Rolf Kötter, “The human connectiome: a structural description of the human brain”, PLoS Computational Biology 1, e42 (September 2005)<br />[2] Ed Bullmore, Olaf Sporns, “Complex brain networks: graph theoretical analysis of structural and functional systems”, Nature Reviews Neuroscience 10, 186-198 (March 2009)<br />[3] MikailRubinov, Olaf Sporns, “Complex network measures of brain connectivity: uses and interpretations”, NeuroImage (2009)<br />[4] Steven H. Strogatz, “Exploring complex network”, Nature, 410 (March 2001)<br />[5] Olaf Sporns, GiulioTononi, “Classes of network connectivity and dynamics”, Complexity 7 (2002)<br />[6] M. Girvan, M. E. J. Newman, “Community structure in social and biological networks”, PNAS 99 (June 2002)<br />Reference<br />

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