Interplay between topology and dynamics in excitation patterns on hierarchical graphs

Frontiers in Neuroinformatics

Volumn 3, Issue SEP, 2009, Pages

  Hütt, Marc Thorsten ^a   Lesne, Annick ^b,c  

^a JACOBS UNIVERSITY BREMEN   (Germany)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

^c SORBONNE UNIVERSITÉ   (France)

Author keywords

Avalanches; Complex networks; Excitable dynamics; Hierarchical networks; Mean field; Modules; Patterns

Indexed keywords

EID: 73949128757     PISSN: 16625196     EISSN: None     Source Type: Journal    
DOI: 10.3389/neuro.11.028.2009     Document Type: Article

References (37)

1. Alon, U. (2007). Network motifs: theory and experimental approaches. Nat. Rev. Genet. 8, 450-461.
2. Anderson, R. M., and May, R. M. (1991). Infectious Diseases of Humans. Oxford, Oxford University Press.
3. Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., and Zhou, C. (2008). Synchronization in complex networks. Phys. Rep. 469, 93-153.
4. Arenas, A., Diaz-Guilera, A., and Perez-Vicente, C. J. (2006). Synchronization reveals topological scales in complex networks. Phys. Rev. Lett. 96, 114102.
5. Armbruster, D., Mikhailov, A. S., and Kaneko, K. (eds) (2005). Networks of Interacting Machines. Singapore, World Scientific Publishing.
6. Bailey, N. T. J. (1975). The Mathematical Theory of Infectious Diseases and its Applications. London, Charles Griffin.
7. Bak, P., Chen, K., and Tang, C. (1990). A forest-fire model and some thoughts on turbulence. Phys. Lett. A 147, 297.
8. Barabási, A. L., and Albert, R. (1999). Emergence of scaling in random networks. Science 286, 509.
9. Barabási, A. L., and Oltvai, Z. N. (2004). Network biology: understanding the cell's functional organization. Nat. Rev. Genet. 5, 101-113.
10. Bornholdt, S. (2005). Systems biology: less is more in modeling large genetic networks. Science 310, 449.
11. Brandman, O., and Meyer, T. (2008). Feedback loops shape cellular signals in space and time. Science 322, 390.
12. Carvunis, A. R., Latapy, M., Lesne, A., Magnien, C., and Pezard, L. (2006). Dynamics of three-state excitable units on poisson vs. power-law random networks. Physica A 367, 595-612.
13. Drossel, B. (2008). Random Boolean networks. In Reviews of Nonlinear Dynamics and Complexity, Chapter 3, Vol. 1, H. G. Schuster, ed. (Weinheim, Wiley VCH), p. 69.
14. Drossel, B., and Schwabl, F. (1992). Selforganized critical forest-fire model. Phys. Rev. Lett. 69, 1629.
15. Graham, I., and Matthai, C. C. (2003). Investigation of the forest-fire model on a small-world network. Phys. Rev. E 68, 036109.
16. Guimera, R., and Amaral, L. A. N. (2005). Functional cartography of complex metabolic networks. Nature 433, 895.
17. Guimera, R., Uzzi, B., Spiro, J., and Amaral, L. A. N. (2005). Team assembly mechanisms determine collaboration network structure and team performance. Science 308, 697-702.
18. Han, J. D. J., Bertin, N., Hao, T., Goldberg, D. S., Berriz, G. F., Zhang, L. V., Dupuy, D., Walhout, A. J. M., Cusick, M. E., and Roth, F. P. (2004). Evidence for dynamically organized modularity in the yeast protein-protein interaction network. Nature 430, 88-93.
19. Hethcote, H. W. (2000). Mathematics of infectious diseases. SIAM Rev. 42, 599.
20. Ipsen, M., and Mikhailov, A. (2002). Evolutionary reconstruction of networks. Phys. Rev. E 66. 046109.
21. Kaiser, M., Görner, M., and Hilgetag, C. (2007). Criticality of spreading dynamics in hierarchical cluster networks without inhibition. New J. Phys. 9, 110.
22. Kearns, M., Suri, S., and Montfort, N. (2006). An experimental study of the coloring problem on human subject networks. Science 313, 824-827.
23. Lee, D. S., Goh, K. I., Kahng, B., and Kim, D. (2004). Sandpile avalanche dynamics on scale-free networks. Physica A 338, 84-91.
24. Levina, A., Ernst, U., and Herrmann, J. M. (2007a). Criticality of avalanche dynamics in adaptive recurrent networks. Neurocomputing 70, 1877-1881.
25. Levina, A., Herrmann, J. M., and Geisel, T. (2007b). Dynamical synapses causing self-organized criticality in neural networks. Nat. Phys. 3, 857-860.
26. Marr, C., and Hütt, M. T. (2005). Topology regulates pattern formation capacity of binary cellular automata on graphs. Physica A 354, 641-662.
27. Milo, R., Itzkovitz, S., Kashtan, N., Levitt, R., Shen-Orr, S., Ayzenshtat, I., Sheffer, M., and Alon, U. (2004). Superfamilies of evolved and designed networks. Science 303, 1538-1542.
28. Moreno, Y., Pastor-Satorras, R., and Vespignani, A. (2002). Epidemic outbreaks in complex heterogeneous networks. Eur. Phys. J. B 26, 521.
29. Müller-Linow, M., Hilgetag, C. C., and Hütt, M. T. (2008). Organization of excitable dynamics in hierarchical biological networks. PLoS Comput. Biol. 4, e1000190. doi: 10.1371/ journal.pcbi.1000190
30. Müller-Linow, M., Marr, C., and Hütt, M. T. (2006). Topology regulates the distribution pattern of excitations in excitable dynamics on graphs. Phys. Rev. E 74, 016112.
31. Pastor-Satorras, R., and Vespignani, A. (2004). Evolution and Structure of the Internet: A Statistical Physics Approach. Cambridge, Cambridge University Press.
32. Ravasz, E., and Barabási, A. L. (2003). Hierarchical organization in complex networks. Phys. Rev. E 67, 1-7.
33. Ravasz, E., Somera, A. L., Mongru, D. A., Oltvai, Z. N., and Barabási, A. L. (2002). Hierarchical organization of modularity in metabolic networks. Science 297, 1551-1555.
34. Roxin, A., Riecke, H., and Solla, A. (2004). Self-sustained activity in a small-world network of excitableneurons. Phys. Rev. Lett. 92, 198101.
35. Sporns, O. (2006). Small-world connectivity, motif composition, and complexity of fractal neuronal connections. Biosystems 85, 55-64.
36. Uchida, S., Drossel, B., and Brose, U. (2007). The structure of food webs with adaptive behaviour. Ecol. Modell. 206, 263-276.
37. Watts, D. J., and Strogatz, S. H. (1998). Collective dynamics of 'small-world' networks. Nature 393, 440.