skip to main content
research-article
Free Access

Natural algorithms and influence systems

Published:01 December 2012Publication History
Skip Abstract Section

Abstract

Algorithms offer a rich, expressive language for modelers of biological and social systems. They lay the grounds for numerical simulations and, crucially, provide a powerful framework for their analysis. The new area of natural algorithms may reprise in the life sciences the role differential equations have long played in the physical sciences. For this to happen, however, an "algorithmic calculus" is needed. We discuss what this program entails in the context of influence systems, a broad family of multiagent models arising in social dynamics.

References

  1. Afek, Y., Alon, N., Barad, O., Hornstein, E., Barkai, N., Bar-Joseph, Z. A biological solution to a fundamental distributed computing problem. Science 331 (2011), 183--185.Google ScholarGoogle ScholarCross RefCross Ref
  2. Bonifaci, V., Mehlhorn, K., Varma, G. Physarum can compute shortest paths. In Proceedings of 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (2012), 233--240. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Camazine, S., Deneubourg, J.L., Franks, N., Sneyd, J., Bonabeau, E., Theraulaz, G. Self-Organization in Biological Systems, Princeton University Press, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Chazelle, B. The convergence of bird flocking, arXiv:0905.4241vl, 2009. Prelim, version in Proceedings of SIAM SODA 2009, with improvements in Proceedings of ACM SoCG 2010.Google ScholarGoogle Scholar
  5. Chazelle, B. The total s-energy of a multiagent system, SIAM J. Control Optim. 49 (2011), 1680--1706.Google ScholarGoogle ScholarCross RefCross Ref
  6. Chazelle, B. The dynamics of influence systems, arXiv:1204.3946v2, 2012. Prelim, version in Proceedings of 53rd FOCS, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Collins, G. E. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Proceedings of 2nd GI Conference on Automata Theory and Formal Languages (1975), Springer-Verlag, New York, 134--183. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Cucker, F., Smale, S. Emergent behavior in flocks. IEEE Trans. Automatic Control 52 (2007), 852--862.Google ScholarGoogle ScholarCross RefCross Ref
  9. Fisher, J., Harel, D., Henzinger, T.A. Biology as reactivity. Commun. ACM 54 (2011), 72--82. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Hegselmann, R., Krause, U. Opinion dynamics and bounded confidence models, analysis, and simulation. J. Artif. Soc. Soc. Simulat. 5 (2002), 3.Google ScholarGoogle Scholar
  11. Hegselmann R, Krause U. Truth and cognitive division of labor: first steps towards a computer aided social epistemology. J. Artif. Soc. Soc. Simulat. 9 (2006).Google ScholarGoogle Scholar
  12. Hendrickx, J.M., Blondel, V.D. Convergence of different linear and non-linear Vicsek models. In Proceedings of 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006) (July 2006, Kyoto, Japan), 1229--1240.Google ScholarGoogle Scholar
  13. Jadbabaie, A., Lin, J., Morse, A.S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automatic Control 48 (2003), 988--1001.Google ScholarGoogle ScholarCross RefCross Ref
  14. Lorenz, J. A stabilization theorem for dynamics of continuous opinions. Phys. Stat. Mech. Appl. 355 (2005), 217--223.Google ScholarGoogle ScholarCross RefCross Ref
  15. Lynch, N.A. Distributed Algorithms, Morgan Kaufmann Publishers Inc., San Francisco, CA, 1996. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Moreau, L. Stability of multiagent systems with time-dependent communication links. IEEE Trans. Automatic Control 50 (2005), 169--182.Google ScholarGoogle ScholarCross RefCross Ref
  17. Navlakha, S., Bar-Joseph, Z. Algorithms in nature: the convergence of systems biology and computational thinking. Mol. Syst. Biol. 7 (2011), 546.Google ScholarGoogle ScholarCross RefCross Ref
  18. Okubo, A., Levin, S.A. Diffusion and Ecological Problems, 2nd edn, Springer, 2002.Google ScholarGoogle Scholar
  19. Parrish, J.K., Hamner, W.M. Animal Groups in Three Dimensions, Cambridge University Press, 1997.Google ScholarGoogle ScholarCross RefCross Ref
  20. Prusinkiewicz, P., Lindenmayer, A., Hanan, J.S., Fracchia, F.D. The Algorithmic Beauty of Plants, Springer-Verlag, 1996. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Reynolds, C.W. Flocks, herds, and schools: a distributed behavioral model. Comput. Graph. 21 (1987), 25--34. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Seneta, E. Non-Negative Matrices and Markov Chains, 2nd edn, Springer, 2006.Google ScholarGoogle Scholar
  23. Strogatz, S.H. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D 143 (2000), 1--20. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O. Novel type of phase transition in a system, of self-driven particles. Phys. Rev. Lett. 75 (1995), 1226--1229.Google ScholarGoogle ScholarCross RefCross Ref
  25. Winfree, A.T. Biological rhythms and the behavior of populations of coupled oscillators. J. Theoret. Biol. 16, 1 (1967), 15--42.Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. Natural algorithms and influence systems

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in

    Full Access

    • Published in

      cover image Communications of the ACM
      Communications of the ACM  Volume 55, Issue 12
      December 2012
      102 pages
      ISSN:0001-0782
      EISSN:1557-7317
      DOI:10.1145/2380656
      Issue’s Table of Contents

      Copyright © 2012 ACM

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 1 December 2012

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article
      • Popular
      • Refereed

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    HTML Format

    View this article in HTML Format .

    View HTML Format