Mortality, Redundancy, and Diversity in Stochastic Search

Physical Review Letters

Volumn 114, Issue 19, 2015, Pages

  Meerson, Baruch ^a   Redner, S ^b,c  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b USA   (United States)

^c SANTA FE INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOCHEMISTRY; STOCHASTIC SYSTEMS; TIME MEASUREMENT;

MORTALITY RATE; MOST LIKELY; ONE DIMENSION; SEARCH TIME; STOCHASTIC SEARCH; STOCHASTIC SEARCH PROCESS; TIME-SCALES; TOY MODELS;

REDUNDANCY;

EID: 84930221818     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.114.198101     Document Type: Article

References (39)

1. O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, Rev. Mod. Phys. 83, 81 (2011). RMPHAT 0034-6861 10.1103/RevModPhys.83.81
2. O. G. Berg, R. B. Winter, and P. H. Von Hippel, Biochemistry 20, 6929 (1981). BICHAW 0006-2960 10.1021/bi00527a028
3. P.H. Von Hippel, Annu. Rev. Biophys. Biomol. Struct. 36, 79 (2007). ABBSE4 1056-8700 10.1146/annurev.biophys.34.040204.144521
4. L. Mirny, Nat. Phys. 4, 93 (2008). NPAHAX 1745-2473 10.1038/nphys848
5. E. L. Charnov, Theor. Popul. Biol. 9, 129 (1976). TLPBAQ 0040-5809 10.1016/0040-5809(76)90040-X
6. W. J. Bell, Searching Behaviour: The Behavioural Ecology of Finding Resources (Chapman and Hall, London, 1991).
7. W. J. O'Brien, H. I. Browman, and B. I. Evans, Am. Sci. 78, 152 (1990). AMSCAC 0003-0996
8. G. M. Viswanathan, S. V. Buldyrev, S. Havlin, M. G. E. Da Luz, E. P. Raposo, and H. E. Stanley, Nature (London) 401, 911 (1999). NATUAS 0028-0836 10.1038/44831
9. O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, Phys. Rev. E 74, 020102 (2006). PRESCM 1539-3755 10.1103/PhysRevE.74.020102
10. M. von Smoluchowski, Z. Phys. Chem. 92, 129 (1917). 0942-9352
11. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990). RMPHAT 0034-6861 10.1103/RevModPhys.62.251
12. H. R. Richardson and L. D. Stone, Naval Research Logistics Quarterly 18, 141 (1971). NRLQAR 0028-1441 10.1002/nav.3800180202
13. J. R. Frost and L. D. Stone, http://www.uscg.mil/acquisition/rdc/reports/2001/CGD1501Report.pdf.
14. M. F. Shlesinger, J. Phys. A 42, 434001 (2009). JPAMB5 1751-8113 10.1088/1751-8113/42/43/434001
15. R. F. Bonner, R. Nossal, S. Havlin, and G. H. Weiss, J. Opt. Soc. Am. A 4, 423 (1987). JOAOD6 0740-3232 10.1364/JOSAA.4.000423
16. S. B. Yuste, E. Abad, and K. Lindenberg, Phys. Rev. Lett. 110, 220603 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.220603
17. E. Abad, S. B. Yuste, and K. Lindenberg, Phys. Rev. E 88, 062110 (2013). PRESCM 1539-3755 10.1103/PhysRevE.88.062110
18. B. Meerson, arXiv:1502.02813.
19. O. Bénichou and S. Redner, Phys. Rev. Lett. 113, 238101 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.238101
20. M. Eisenbach and L. C. Giojalas, Nat. Rev. Mol. Cell Biol. 7, 276 (2006). NRMCBP 1471-0072 10.1038/nrm1893
21. K. Reynaud, Z. Schuss, N. Rouach, and D. Holcman, arXiv:1409.7941.
22. G. Zumofen, J. Klafter, and A. Blumen, J. Chem. Phys. 79, 5131 (1983). JCPSA6 0021-9606 10.1063/1.445637
23. S. Redner and K. Kang, J. Phys. A 17, L451 (1984). JPHAC5 0305-4470 10.1088/0305-4470/17/8/012
24. A. Blumen, G. Zumofen, and J. Klafter, Phys. Rev. B 30, 5379(R) (1984). PRBMDO 0163-1829 10.1103/PhysRevB.30.5379
25. R. A. Blythe and A. J. Bray, Phys. Rev. E 67, 041101 (2003). PRESCM 1539-3755 10.1103/PhysRevE.67.041101
26. A. J. Bray, S. N. Majumdar, and G. Schehr, Adv. Phys. 62, 225 (2013). ADPHAH 0001-8732 10.1080/00018732.2013.803819
27. S. Redner and B. Meerson, J. Stat. Mech. (2014) P06019. JSMTC6 1742-5468 10.1088/1742-5468/2014/06/P06019
28. B. Meerson, A. Vilenkin, and P. L. Krapivsky, Phys. Rev. E 90, 022120 (2014). PRESCM 1539-3755 10.1103/PhysRevE.90.022120
29. K. Lindenberg, V. Seshadri, K. E. Shuler, and G. H. Weiss, J. Stat. Phys. 23, 11 (1980). JSTPBS 0022-4715 10.1007/BF01014427
30. S. Redner and P. L. Krapivsky, Am. J. Phys. 67, 1277 (1999). AJPIAS 0002-9505 10.1119/1.19115
31. P. L. Krapivsky, S. N. Majumdar, and A. Rosso, J. Phys. A 43, 315001 (2010). JPAMB5 1751-8113 10.1088/1751-8113/43/31/315001
32. C. Mejia-Monasterio, G. Oshanin, and G. Schehr, J. Stat. Mech. (2011) P06022. JSMTC6 1742-5468 10.1088/1742-5468/2011/06/P06022
33. B. Meerson and S. Redner, J. Stat. Mech. (2014) P08008. JSMTC6 1742-5468 10.1088/1742-5468/2014/8/P08008
34. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, England, 2001).
35. Wolfram Research, Inc., Mathematica, Version 10.0, 2014.
36. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists, 7th ed. (Academic Press, New York, 2012).
37. C. Álvarez, J. A. Castilla, L. Martínez, J. P. Ramírez, F. Vergara, and J. J. Gaforio, Human Reprod. 18, 2082 (2003); HUREEE 0268-1161 10.1093/humrep/deg430
38. Sperm Biology: An Evolutionary Perspective, edited by T. R. Birkhead, D. J. Hosken, and S. S. Pitnick (Academic Press, Burlington, MA, 2009).
39. The derivation is similar to that for a distribution of diffusivities, as presented in the material associated with Eq.(16).