Analytically solvable processes on networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 1, 2011, Pages

  Smilkov, Daniel ^a   Kocarev, Ljupco ^a,b  

^a Macedonian Academy for Sciences and Arts   (Macedonia)

^b UNIVERSITY OF CALIFORNIA SAN DIEGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICAL EQUATION; EQUILIBRIUM BEHAVIOR; EVOLUTION EQUATIONS; FINITE GRAPHS; INFINITE PARTICLE SYSTEM; LOCAL DYNAMICS; NETWORK TOPOLOGY; RANDOM WALK; STOCHASTIC ISING MODEL; VOTER MODELS;

CELLULAR AUTOMATA; ELECTRIC NETWORK TOPOLOGY; ISING MODEL; PATTERN RECOGNITION SYSTEMS; TOPOLOGY;

STOCHASTIC MODELS;

EID: 79961122968     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.016104     Document Type: Article

References (27)

1. A. Barrat, M. Barthelemy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).
2. D. Ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems, 1st ed. (Cambridge University Press, Cambridge, 2000).
3. H. C. Tuckwell, Introduction to Theoretical Neurobiology (Cambridge University Press, Cambridge, 1988).
4. A. L. Lloyd and R. M. May, Science SCIEAS 0036-8075 10.1126/science. 1061076 292, 1316 (2001). (Pubitemid 32476209)
5. O. Benichou, M. Coppey, M. Moreau, P. H. Suet, and R. Voituriez, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.198101 94, 198101 (2005). (Pubitemid 41493011)
6. M. F. Shlesinger, Nature (London) NATUAS 0028-0836 10.1038/443281a 443, 281 (2006). (Pubitemid 44435133)
7. I. Eliazar, T. Koren, and J. Klafter, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/19/6/065140 19, 065140 (2007). (Pubitemid 46478517)
8. L. A. Adamic, R. M. Lukose, A. R. Puniyani, and B. A. Huberman, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.046135 64, 046135 (2001).
9. R. Guimera, A. Diaz-Guilera, F. Vega-Redondo, A. Cabrales, and A. Arenas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.248701 89, 248701 (2002).
10. N. A. Lynch, Distributed Algorithms (San Francisco, Morgan Kaufmann, 1997).
11. M. H. DeGroot, J. Am. Stat., Assoc. 0162-1459 10.2307/2285509 69, 118 (1974).
12. J. A. Benediktsson and P. H. Swain, IEEE Trans. Circuit Syst. 22, 688 (1992).
13. S. C. Weller and N. C. Mann, Med. Decision Making PRLTAO 0272-989X 10.1177/0272989X9701700108 17, 71 (1997). (Pubitemid 27020141)
14. V. Borkar and P. Varaiya, IEEE Trans. Autom. Control IETAA9 0018-9286 10.1109/TAC.1982.1102982 AC-27, 650 (1982).
15. J. N. Tsitsiklis, Ph.D. dissertation, Massachusetts Institute of Technology, 1984.
16. K. Binder, in Encyclopaedia of Mathematics, edited by, M. Hazewinkel, (Kluwer Academic, Dordrecht, 2001).
17. B. Chopard and M. Droz, Cellular Automata Modeling of Physical Systems (Cambridge University Press, Cambridge, 1998).
18. R. Durrett, Stochast. Proc. Appl. STOPB7 0304-4149 10.1016/0304-4149(81) 90001-6 11, 109 (1981).
19. R. D. McKelvey, J. Econ. Theory JECTAQ 0022-0531 10.1016/0022-0531(76) 90040-5 12, 472 (1976).
20. A. Clauset, C. Moore, and M. E. J. Newman, Nature (London) NATUAS 0028-0836 10.1038/nature06830 453, 98 (2008). (Pubitemid 351630323)
21. H. Simon, Proc. Am. Philos. Soc. 106, 467 (1962).
22. E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barabasi, Science SCIEAS 0036-8075 10.1126/science.1073374 30, 1551 (2002). (Pubitemid 34971002)
23. A. Clauset, M. E. J. Newman, and C. Moore, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.066111 70, 066111 (2004). (Pubitemid 40429799)
24. R. Guimera and L. A. N. Amaral, Nature (London) NATUAS 0028-0836 10.1038/nature03288 433, 895 (2005). (Pubitemid 40314902)
25. M. C. Lagomarsino, P. Jona, B. Bassetti, and H. Isambert, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0609023104 104, 5516 (2001).
26. L. Page, S. Brin, R. Motwani, and T. Winograd, Stanford Digital Libraries Working Paper (1998) [http://ilpubs.stanford.edu:8090/422/].
27. I. C. F. Ipsen and T. M. Selee, SIAM J. Matrix Anal. Appl. SJMAEL 0895-4798 10.1137/060664331 29, 1281 (2007).