Eminence grise coalitions in opinion dynamics

2014 52nd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2014

Volumn , Issue , 2014, Pages 556-562

  Bolouki, Sadegh ^a   Siami, Milad ^a   Malhame, Roland P ^b   Motee, Nader ^a  

^a LEHIGH UNIVERSITY   (United States)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS TIME SYSTEMS; GRAPH THEORY; SOCIAL ASPECTS;

DYNAMICAL NETWORKS; LINEAR CONTINUOUS-TIME; MULTIPLE CONSENSUS; OPINION DYNAMICS; PUBLIC OPINIONS; TIME-VARYING GRAPHS; UNDERLYING GRAPHS; UPPER AND LOWER BOUNDS;

TIME VARYING NETWORKS;

EID: 84946689306     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ALLERTON.2014.7028504     Document Type: Conference Paper

References (28)

1. S. Chatterjee and E. Seneta, "Towards consensus: Some convergence theorems on repeated averaging," Journal of Applied Probability, pp. 89-97, 1977.
2. S. Bolouki and R. P. Malhamé, "Consensus algorithms and the decomposition-separation theorem," in Proceedings of 52nd IEEE Conference on Decision and Control Conference (CDC 2013), 2013, pp. 1490-1495.
3. B. Touri and A. Nedíc, "On backward product of stochastic matrices," Automatica, vol. 48, no. 8, pp. 1477-1488, 2012.
4. M. H. DeGroot, "Reaching a consensus," Journal of the American Statistical Association, vol. 69, no. 345, pp. 118-121, 1974.
5. J. N. Tsitsiklis, "Problems in decentralized decision making and computation." DTIC Document, Tech. Rep., 1984.
6. J. N. Tsitsiklis, D. P. Bertsekas, M. Athans et al., "Distributed asynchronous deterministic and stochastic gradient optimization algorithms," IEEE transactions on automatic control, vol. 31, no. 9, pp. 803-812, 1986.
7. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and distributed computation: numerical methods. Prentice-Hall, Inc., 1989.
8. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, "Novel type of phase transition in a system of self-driven particles," Physical review letters, vol. 75, no. 6, pp. 1226-1229, 1995.
9. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988-1001, 2003.
10. V. Blondel, J. Hendrickx, A. Olshevsky, and J. Tsitsiklis, "Convergence in multiagent coordination, consensus, and flocking," in Proceedings of 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2005), 2005, pp. 2996-3000.
11. L. Moreau, "Stability of multiagent systems with time-dependent communication links," IEEE Transactions on Automatic Control, vol. 50, no. 2, pp. 169-182, 2005.
12. J. M. Hendrickx and V. Blondel, "Convergence of different linear and nonlinear vicsek models," in Proceedings of 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), 2006, pp. 1229-1240.
13. S. Li, H. Wang, and M. Wang, "Multi-agent coordination using nearest neighbor rules: A revisit to vicsek model," arXiv preprint cs/0407021, 2004.
14. J. Lorenz, "A stabilization theorem for dynamics of continuous opinions," Physica A: Statistical Mechanics and its Applications, vol. 355, no. 1, pp. 217-223, 2005.
15. J. M. Hendrickx and J. N. Tsitsiklis, "Convergence of type-symmetric and cut-balanced consensus seeking systems," IEEE Transactions on Automatic Control, vol. 58, no. 1, pp. 214-218, 2013.
16. B. Touri and A. Nedíc, "On ergodicity, infinite flow, and consensus in random models," IEEE Transactions on Automatic Control, vol. 56, no. 7, pp. 1593-1605, 2011.
17. -, "On approximations and ergodicity classes in random chains," IEEE Transactions on Automatic Control, vol. 57, no. 11, pp. 2718-2730, 2012.
18. -, "Product of random stochastic matrices," IEEE Transactions on Automatic Control, vol. 59, no. 2, pp. 437-448, 2014.
19. S. Bolouki and R. P. Malhamé, "On the limiting behavior of linear or convex combination based updates of multi-agent systems," in Proceedings of 18th IFAC World Congress, 2011, pp. 8819-8823.
20. -, "On consensus with a general discrete time convex combination based algorithm for multi-agent systems," in Proceedings of 19th Mediterranean Conference on Control & Automation (MED 2011), 2011, pp. 668-673.
21. -, "Theorems about ergodicity and class-ergodicity of chains with applications in known consensus models," in Proceedings of 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2012, pp. 1425-1431.
22. -, "Ergodicity and class-ergodicity of balanced asymmetric stochastic chains," GERAD Technical Report G-2012-93, 2012.
23. -, "Consensus algorithms and the decomposition-separation theorem," arXiv:1303.6674v2 [math.DS], 2014.
24. S. Bolouki, R. P. Malhamé, M. Siami, and M. Nader, "A geometric approach towards linear consensus algorithms," in Proceedings of 53rd IEEE Conference on Decision and Control Conference (CDC 2014).
25. I. M. Sonin et al., "The decomposition-separation theorem for finite nonhomogeneous markov chains and related problems," in Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz. Institute of Mathematical Statistics, 2008, pp. 1-15.
26. R. W. Brockett, Finite dimensional linear systems. New York Wiley, 1970.
27. S. Bolouki, R. P. Malhamé, M. Siami, and N. Motee, "éminence grise coalition: on the shaping of public opinion," arXiv:1409.7091v1 math.DS, 2014.
28. A. Kolmogoroff, "Zur theorie der markoffschen ketten," Mathematische Annalen, vol. 112, no. 1, pp. 155-160, 1936.