Simulating non-Markovian stochastic processes

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

Volumn 90, Issue 4, 2014, Pages

  Boguñá, Marian ^a   Lafuerza, Luis F ^b   Toral, Raúl ^c   Serrano, M Ángeles ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

^c UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

NON-MARKOVIAN;

EID: 84907835173     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.90.042108     Document Type: Article

References (44)

1. D. T. Gillespie, J. Comput. Phys. 22, 403 (1976). JCTPAH 0021-9991 10.1016/0021-9991(76)90041-3
2. D. T. Gillespie, J. Phys. Chem. 81, 2340 (1977). JPCHAX 0022-3654 10.1021/j100540a008
3. D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001). JCPSA6 0021-9606 10.1063/1.1378322
4. I. A. Ushakov, Probabilistic Reliability Models (Wiley, Hoboken, New Jersey, 2012).
5. O. Kella and W. Stadje, Statist. Prob. Lett. 76, 1914 (2006). 0167-7152 10.1016/j.spl.2006.04.041
6. J.-P. Eckmann, E. Moses, and D. Sergi, Proc. Natl. Acad. Sci. (USA) 101, 14333 (2004). PNASA6 0027-8424 10.1073/pnas.0405728101
7. A.-L. Barabasi, Nature (London) 435, 207 (2005). NATUAS 0028-0836 10.1038/nature03459
8. R. Dean Malmgren, D. B. Stouffer, A. E. Motter, and L. A. N. Amaral, Proc. Natl. Acad. Sci. (USA) 105, 18153 (2008). PNASA6 0027-8424 10.1073/pnas.0800332105
9. D. Rybski, S. V. Buldyrev, S. Havlin, F. Liljeros, and H. A. Makse, Proc. Natl. Acad. Sci. (USA) 106, 12640 (2009). PNASA6 0027-8424 10.1073/pnas.0902667106
10. R. Dean Malmgren, D. B. Stouffer, A. S. L. O. Campanharo, and L. A. Nunes Amaral, Science 325, 1696 (2009). SCIEAS 0036-8075 10.1126/science.1174562
11. J. Stehlé, A. Barrat, and G. Bianconi, Phys. Rev. E 81, 035101 (2010). PLEEE8 1539-3755 10.1103/PhysRevE.81.035101
12. K. Zhao, J. Stehlé, G. Bianconi, and A. Barrat, Phys. Rev. E 83, 056109 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.83.056109
13. J. Fernández-Gracia, V. M. Eguíluz, and M. San Miguel, Phys. Rev. E 84, 015103 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.015103
14. M. Salathé, M. Kazandjieva, J. W. Lee, P. Levis, M. W. Feldman, and J. H. Jones, Proc. Natl. Acad. Sci. (USA) 107, 22020 (2010). PNASA6 0027-8424 10.1073/pnas.1009094108
15. A. Gautreau, A. Barrat, and M. Barthélemy, Proc. Natl. Acad. Sci. (USA) 106, 8847 (2009). PNASA6 0027-8424 10.1073/pnas.0811113106
16. M. H. Jensen, K. Sneppen, and G. Tiana, FEBS Lett. 541, 176 (2003). FEBLAL 0014-5793 10.1016/S0014-5793(03)00279-5
17. D. Bratsun, D. Volfson, L. S. Tsimring, and J. Hasty, Proc. Natl. Acad. Sci. (USA) 102, 14593 (2005). PNASA6 0027-8424 10.1073/pnas.0503858102
18. M. Barrio, K. Burrage, A. Leier, and T. Tian, PLoS Comput. Biol. 2, e117 (2006). 1553-734X 10.1371/journal.pcbi.0020117
19. M. R. Roussel and R. Zhu, Phys. Biol. 3, 274 (2006). 1478-3975 10.1088/1478-3975/3/4/005
20. X. Cai, J. Chem. Phys. 126, 124108 (2007). JCPSA6 0021-9606 10.1063/1.2710253
21. D. F. Anderson, J. Chem. Phys. 127, 214107 (2007). JCPSA6 0021-9606 10.1063/1.2799998
22. T. Brett and T. Galla, Phys. Rev. Lett. 110, 250601 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.250601
23. J. Miekisz, J. Poleszczuk, M. Bodnar, and U. Forys, Bull. Math. Biol. 73, 2231 (2011). BMTBAP 0092-8240 10.1007/s11538-010-9622-4
24. L. F. Lafuerza and R. Toral, Phys. Rev. E 84, 051121 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.051121
25. L. F. Lafuerza and R. Toral, Phys. Rev. E 84, 021128 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.021128
26. L. F. Lafuerza and R. Toral, Philos. Trans. A 371, 20120458 (2013). PTRMAD 1364-503X 10.1098/rsta.2012.0458
27. P. Van Mieghem and R. van de Bovenkamp, Phys. Rev. Lett. 110, 108701 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.108701
28. D. R. Cox and H. D. Miller, The Theory of Stochastic Processes (CRC, Boca Raton, FL, 1965).
29. D. R. Cox and W. L. Smith, Biometrika 41, 91 (1954). BIOKAX 0006-3444 10.1093/biomet/41.1-2.91
30. D. Cox, Renewal Theory (Methuen & Co., London, 1970).
31. R. M. Anderson and R. M. May, Infectious Diseases of Humans (Oxford University Press, Oxford, 1991).
32. A. Vazquez, B. Rácz, A. Lukács, and A.-L. Barabási, Phys. Rev. Lett. 98, 158702 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.158702
33. B. Min, K.-I. Goh, and A. Vazquez, Phys. Rev. E 83, 036102 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.83.036102
34. A. Barrat, M. Barthélemy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).
35. M. E. J. Newman, Networks: An Introduction (Oxford University Press, Oxford, 2010).
36. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.3200
37. M. E. J. Newman, Phys. Rev. E 66, 016128 (2002). 1063-651X 10.1103/PhysRevE.66.016128
38. M. Boguñá and R. Pastor-Satorras, Phys. Rev. E 66, 047104 (2002). 1063-651X 10.1103/PhysRevE.66.047104
39. M. Boguñá, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. Lett. 90, 028701 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.90.028701
40. M. Boguñá, R. Pastor-Satorras, and A. Vespignani, in Statistical Mechanics of Complex Networks, edited by R. Pastor-Satorras, J. M. Rubí, and A. Díaz-Guilera, Lecture Notes in Physics Vol. 625 (Springer-Verlag, Berlin, 2003).
41. P. Erdös and P. Rényi, Publ. Math-Debrecen. 6, 290 (1959).
42. J. O. Kephart and S. R. White, in Proceedings of the 1991 IEEE Computer Society Symposium on Research in Security and Privacy (IEEE, Piscataway, NJ, 1991), pp. 343-359.
43. S. Fedotov and V. Méndez, Phys. Rev. Lett. 101, 218102 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.218102
44. M. A. Gibson and J. Bruck, J. Phys. Chem. A 104, 1876 (2000). JPCAFH 1089-5639 10.1021/jp993732q