Towards Google matrix of brain

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 374, Issue 31-32, 2010, Pages 3206-3209

  Shepelyansky, D L ^a,b   Zhirov, O V ^c  

^a UNIVERSITÉ PAUL SABATIER   (France)

^b CNRS   (France)

^c BUDKER INSTITUTE OF NUCLEAR PHYSICS   (Russian Federation)

Author keywords

Google matrix; Neuronal networks; Page rank; World wide web

Indexed keywords

BRAIN MODELS; EIGENVALUES AND EIGENFUNCTIONS; NEURONS; WORLD WIDE WEB;

DAMPING FACTORS; EIGENSTATES; EIGENVALUES; GOOGLE MATRIXES; NEURONAL NETWORKS; PAGE RANKS; PAGERANK; RELAXATION MODES;

NEURAL NETWORKS;

EID: 77955320548     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2010.06.007     Document Type: Article

References (40)

1. J. von Neumann The Computer and the Brain 1958 Yale Univ. Press New Haven, CT
2. F.C. Hoppensteadt, and E.M. Izhikevich Weakly Connected Neural Networks 1997 Springer-Verlag
3. E.M. Izhikevich Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting 2007 The MIT Press Cambridge, MA
4. O. Sporns Brain connectivity Scholarpedia 2 10 2007 4695
5. D.J. Felleman, and D.C. van Essen Cereb. Cortex 1 1991 1
6. S.B. Laughlin, and T.J. Sejnowski Science 301 2003 1870
7. O. Sporns, D.R. Chialvo, M. Kaiser, and C.C. Hilgetag TRENDS Cognitive Sci. 8 2004 418
8. C.J. Honey, R. Kötter, M. Breakspear, and O. Sporns PNAS 104 2007 10240
9. M. Kaiser Phil. Trans. R. Soc. A 365 2007 3033
10. P. Hagmann, L. Cammoun, X. Gigandet, R. Meuli, C.J. Honey, V.J. Weeden, and O. Sporns PLOS Biol. 6 2008 1479
11. E.M. Izhikevich, and G.M. Edelman PNAS 105 2008 3593
12. Q. Wen, A. Stepanyants, G.N. Elston, A.Y. Grosberg, and D.B. Chklovskii PNAS 106 2009 12536
13. S. Cocco, S. Leibler, and R. Monasson PNAS 106 2009 14058
14. S. Brin, and L. Page Comput. Networks ISDN Syst. 30 1998 107
15. A.M. Langville, and C.D. Meyer Google's PageRank and Beyond: The Science of Search Engine Rankings 2006 Princeton University Press Princeton
16. D. Austin AMS Feature Columns, available at http://www.ams.org/ featurecolumn/archive/pagerank.html 2008
17. I.P. Cornfeld, S.V. Fomin, and Y.G. Sinai Ergodic Theory 1982 Springer
18. M. Brin, and G. Stuck Introduction to Dynamical Systems 2002 Cambridge Univ. Press Cambridge, UK
19. D.L. Shepelyansky, and O.V. Zhirov Phys. Rev. E 81 2010 036213
20. L. Ermann, and D.L. Shepelyansky Phys. Rev. E 81 2010 036221
21. D. Donato, L. Laura, S. Leonardi, and S. Millozzi Eur. Phys. J. B 38 2004 239
22. G. Pandurangan, P. Raghavan, and E. Upfal Internet Math. 3 2005 1
23. P. Boldi, M. Santini, and S. Vigna A. Ellis, T. Hagino, Proceedings of the 14th International Conference on World Wide Web 2005 ACM Press New York 557
24. S. Vigna A. Ellis, T. Hagino, Proceedings of the 14th International Conference on World Wide Web 2005 ACM Press New York 976
25. K. Avrachenkov, and D. Lebedev Internet Math. 3 2006 207
26. K. Avrachenkov, N. Litvak, and K.S. Pham A. Bonato, F.R.K. Chung, Algorithms and Models for the Web-Graph: Proceedings of the 5th International Workshop, WAW 2007, San Diego, CA
27. Lecture Notes Computer Sci. vol. 4863 2007 Springer-Verlag Berlin 16
28. N. Litvak, W.R.W. Scheinhardt, and Y. Volkovich Internet Math. 4 2007 175
29. K. Avrachenkov, D. Donato, N. Litvak, Algorithms and Models for the Web-Graph: Proceedings of the 6th International Workshop, WAW 2009, Barcelona
30. Lecture Notes Computer Sci. vol. 5427 2009 Springer-Verlag Berlin
31. N. Perra, and S. Fortunato Phys. Rev. E 78 2008 036107
32. S.N. Dorogovtsev, and J.F.F. Mendes Evolution of Networks 2003 Oxford Univ. Press Oxford
33. P. Chen, H. Xie, S. Maslov, and S. Redner J. Infometrics 1 2007 8
34. F. Radicchi, S. Fortunato, B. Markines, and A. Vespignani Phys. Rev. E 80 2009 056103
35. E.M. Izhikevich, private communication, August 2009: the links between neurons have been generated by E.M. Izhikevich on the basis of the brain model described in [11]; the links are available at Quantware Library, K. Frahm, D. Shepelyansky (Eds.), Section QNR15 at http://www.quantware.ups-tlse.fr/QWLIB
36. B. Georgeot, O. Giraud, and D.L. Shepelyansky preprint arXiv:1002.3342 [cs.IR] 2010
37. A.D. Chepelianskii arXiv:1003.5455 [cs.SE] 2010
38. F. Evers, and A.D. Mirlin Rev. Mod. Phys. 80 2008 1355
39. O. Giraud, B. Georgeot, and D.L. Shepelyansky Phys. Rev. E 80 2009 026107
40. B.V. Chirikov Creating chaos and the life, preprint arXiv:physics/0503072 2005