Emergence of bimodality in controlling complex networks

Nature Communications

Volumn 4, Issue , 2013, Pages

  Jia, Tao ^a   Liu, Yang Yu ^a,b   Csóka, Endre ^c   Pósfai, Márton ^a,c,d   Slotine, Jean Jacques ^e,f   Barabási, Albert László ^a,b,g,h  

^a NORTHEASTERN UNIVERSITY   (United States)

^b DANA FARBER CANCER INSTITUTE   (United States)

^c EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^d BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^e MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^f Massachusetts Institute of Technology Cambridge   (United States)

^g BRIGHAM AND WOMEN S HOSPITAL   (United States)

^h CENTRAL EUROPEAN UNIVERSITY   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL FRAMEWORK; CONTROL SYSTEM; NETWORK DESIGN; ORGANIZATIONAL FRAMEWORK; PERTURBATION; PREDICTION; RESEARCH WORK;

ANALYTICAL RESEARCH; ARTICLE; INTERNET PROTOCOL; MOLECULAR DYNAMICS; SCIENCE;

EID: 84879631414     PISSN: None     EISSN: 20411723     Source Type: Journal    
DOI: 10.1038/ncomms3002     Document Type: Article

References (60)

1. Kalman, R. E. Mathematical description of linear dynamical systems. J. Soc. Indus. Appl. Math. Ser. A 1, 152-192 (1963).
2. Luenberger, D. G. Introduction to Dynamic Systems: Theory, Models, & Applications (John Wiley & Sons, 1979).
3. Chui, C. K. & Chen, G. Linear Systems and Optimal Control (Springer-Verlag, 1989).
4. Slotine, J.-J. & Li, W. Applied Nonlinear Control (Prentice-Hall, 1991).
5. Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. Controllability of complex networks. Nature 473, 167-173 (2011).
6. Rajapakse, I., Groudine, M. & Mesbahi, M. Dynamics and control of state-dependent networks for probing genomic organization. Proc. Natl Acad. Sci. 108, 17257-17262 (2011).
7. Lestas, I., Vinnicombe, G. & Paulsson, J. Fundamental limits on the suppression of molecular fluctuations. Nature 467, 174-178 (2010).
8. Nepusz, T. & Vicsek, T. Controlling edge dynamics in complex networks. Nat. Phys. 8, 568-573 (2012).
9. Yan, G., Ren, J., Lai, Y.-C., Lai, C.-H. & Li, B. Controlling complex networks: How much energy is needed? Phys. Rev. Lett. 108, 218703 (2012).
10. Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. Control centrality and hierarchical structure in complex networks. PLoS ONE 7, e44459 (2012).
11. Wang, W.-X., Ni, X., Lai, Y.-C. & Grebogi, C. Optimizing controllability of complex networks by minimum structural perturbations. Phys. Rev. E 85, 026115 (2012).
12. Tang, Y., Gao, H., Zou, W. & Kurths, J. Identifying controlling nodes in neuronal networks in different scales. PLoS ONE 7, e41375 (2012).
13. Cowan, N. J., Chastain, E. J., Vilhena, D. A., Freudenberg, J. S. & Bergstrom, C. T. Nodal dynamics, not degree distributions, determine the structural controllability of complex networks. PLoS ONE 7, e38398 (2012).
14. Gutiérrez, R., Sendiña-Nadal, I., Zanin, M., Papo, D. & Boccaletti, S. Targeting the dynamics of complex networks. Sci. Rep. 2, 396 (2012).
15. Wang, B., Gao, L. & Gao, Y. Control range: a controllability-based index for node significance in directed networks. J. Stat. Mech. : Theor. Exp. 2012, P04011 (2012).
16. Mones, E., Vicsek, L. & Vicsek, T. Hierarchy measure for complex networks. PLoS ONE 7, e33799 (2012).
17. Pu, C.-L., Pei, W.-J. & Michaelson, A. Robustness analysis of network controllability. Physica A: Stat. Mechanics Appl. 391, 4420-4425 (2012).
18. Pósfai, M., Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. Effect of correlations on network controllability. Sci. Rep. 3, 1067 (2013).
19. Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. Observability of complex systems. Proc. Natl Acad. Sci. 110, 2460-2465 (2013).
20. Commault, C., Dion, J. M., Trinh, D. H. & Do, T. H. Sensor classification for the fault detection and isolation, a structural approach. Int. J. Adaptive Control Signal Processing 25, 1-17 (2011).
21. Molloy, M. & Reed, B. A critical point for random graphs with a given degree sequence. Random Struct. Algorithms 6, 161-180 (1995).
22. Newman, M. E. J., Strogatz, S. H. & Watts, D. J. Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118 (2001).
23. Albert, R. & Barabási, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97 (2002).
24. Kim, H., Genio, C. I. D., Bassler, K. E. & Toroczkai, Z. Constructing and sampling directed graphs with given degree sequences. New. J. Phys. 14, 023012 (2012).
25. Liu, Y.-Y., Csóka, E., Zhou, H. & Pósfai, M. Core percolation on complex networks. Phys. Rev. Lett. 109, 205703 (2012).
26. Erdös, P. & Rényi, A. On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17-60 (1960).
27. Barabási, A.-L. & Albert, R. Emergence of scaling in random networks. Science 286, 509-512 (1999).
28. Caldarelli, G. Scale-Free Networks: Complex Webs in Nature and Technology (Oxford Univ. Press, 2007).
29. Hopcroft, J. E. & Karp, R. M. An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2, 225-231 (1973).
30. Milo, R. et al. Network motifs: Simple building blocks of complex networks. Science 298, 824-827 (2002). (Pubitemid 35231534)
31. Balaji, S., Madan Babu, M., Iyer, L., Luscombe, N. & Aravind, L. Principles of combinatorial regulation in the transcriptional regulatory network of yeast. J. Mol. Biol. 360, 213-227 (2006). (Pubitemid 43949401)
32. Gama-Castro, S. et al. Regulondb (version 6. 0): gene regulation model of escherichia coli k-12 beyond transcription, active (experimental) annotated promoters and textpresso navigation. Nucleic. Acids. Res. 36, D120-D124 (2008). (Pubitemid 351149707)
33. White, J. G., Southgate, E., Thomson, J. N. & Brenner, S. The structure of the nervous system of the nematode caenorhabditis elegans. Philos. Trans. R Soc. Lond. B Biol. Sci. 314, 1-340 (1986).
34. Redner, S. How popular is your paper? An empirical study of the citation distribution. Eur. Phys. J. B 4, 131-134 (1998). (Pubitemid 128437505)
35. Leskovec, J. K. J. & Faloutsos, C. In Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining 177-187 (2005).
36. Redner, S. Citation statistics from 110 years of physical review. Phys. Today 58, 49-54 (2005). (Pubitemid 41038281)
37. Albert, R., Jeong, H. & Barabási, A.-L. Diameter of the world wide web. Nature 401, 130-131 (1999).
38. Adamic, L. A. & Glance, N. In Proceedings of the 3rd International Workshop on Link Discovery 36-43 (2005).
39. Leskovec, J., Lang, K., Dasgupta, A. & Mahoney, M. Community structure in large networks: natural cluster sizes and the absence of large well-defined clusters. Preprint at http://arxiv. org/abs/0810. 1355 (2008).
40. Ravasz, E., Somera, A. L., Mongru, D. A., Oltvai, Z. N. & Barabási, A.-L. Hierarchical organization of modularity in metabolic networks. Science 297, 1551-1555 (2002). (Pubitemid 34971002)
41. Newman, M. E. J. Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002).
42. Pastor-Satorras, R., Vázquez, A. & Vespignani, A. Dynamical and correlation properties of the internet. Phys. Rev. Lett. 87, 258701 (2001).
43. Maslov, S. & Sneppen, K. Specificity and stability in topology of protein networks. Science 296, 910-913 (2002). (Pubitemid 34464896)
44. Lee, J.-S., Goh, K.-I., Kahng, B. & Kim, D. Intrinsic degree-correlations in the static model of scale-free networks. Eur. Phys. J. B Condensed Matter Complex Sys. 49, 231-238 (2006). (Pubitemid 43261416)
45. Jeong, H., Tombor, B., Albert, R., Oltvai, Z. N. & Barabási, A.-L. The large-scale organization of metabolic networks. Nature 407, 651-654 (2000).
46. Cesar, A. H. R. Conditions for the emergence of scaling in the inter-event time of uncorrelated and seasonal systems. Physica A: Stat. Mechanics Appl. 369, 877-883 (2006).
47. Onnela, J.-P. et al. Analysis of a large-scale weighted network of one-to-one human communication. New. J. Phys. 9, 179 (2007).
48. Gonzalez, M. C., Hidalgo, C. A. & Barabasi, A.-L. Understanding individual human mobility patterns. Nature 453, 779-782 (2008). (Pubitemid 351793783)
49. Song, C., Qu, Z., Blumm, N. & Barabási, A.-L. Limits of predictability in human mobility. Science 327, 1018-1021 (2010).
50. Jiang, Z.-Q. et al. Calling patterns in human communication dynamics. Proc. Natl Acad. Sci. 110, 1600-1605 (2013).
51. Cross, R. & Parker, A. The Hidden Power of Social Networks (Harvard Business School Press, 2004).
52. Van Duijn, M. A. J., Huisman, M., Stokman, F. N., Wasseur, F. W. & Zeggelink, E. P. H. Evolution of sociology freshmen into a friendship network. J. Math. Sociol. 27, 153-191 (2003). (Pubitemid 36774485)
53. Milo, R. et al. Superfamilies of designed and evolved networks. Science 303, 1538-1542 (2004).
54. Martinez, N. Artifacts or attributes? effects of resolution on the little rock lake food web. Econol. Monogr. 61, 367-392 (1991). (Pubitemid 21905256)
55. Chen, G., Moiola, J. L. & Wang, H. O. Bifurcation control: theories, methods, and applications. Int. J Bifurcation Chaos 10, 511-548 (2000).
56. Dion, J.-M., Commault, C. & van der Woude, J. Generic properties and control of linear structured systems: a survey. Automatica 39, 1125-1144 (2003).
57. Zdeborová, L. & Mézard, M. The number of matchings in random graphs. J. Stat. Mech. : Theory Exp. 05, P05003 (2006).
58. Karp, R. M. & Sipser, M. In Proceedings of the 22nd Annual IEEE Symposium on Foundations of Computer 364-375 (1981).
59. Lovász, L. & Plummer, M. D. Matching Theory (American Mathematical Society, 2009).
60. Goh, K.-I., Kahng, B. & Kim, D. Universal behavior of load distribution in scale-free networks. Phys. Rev. Lett. 87, 278701 (2001).