Advertisement

Natural Computing

, Volume 10, Issue 4, pp 1219–1244 | Cite as

Greedy versus social: resource-competing oscillator network as a model of amoeba-based neurocomputer

  • Masashi Aono
  • Yoshito Hirata
  • Masahiko Hara
  • Kazuyuki Aihara
Article

Abstract

A single-celled amoeboid organism, the true slime mold Physarum polycephalum, exhibits rich spatiotemporal oscillatory behavior and sophisticated computational capabilities. The authors previously created a biocomputer that incorporates the organism as a computing substrate to search for solutions to combinatorial optimization problems. With the assistance of optical feedback to implement a recurrent neural network model, the organism changes its shape by alternately growing and withdrawing its photosensitive branches so that its body area can be maximized and the risk of being illuminated can be minimized. In this way, the organism succeeded in finding the optimal solution to the four-city traveling salesman problem with a high probability. However, it remains unclear how the organism collects, stores, and compares information on light stimuli using the oscillatory dynamics. To study these points, we formulate an ordinary differential equation model of the amoeba-based neurocomputer, considering the organism as a network of oscillators that compete for a fixed amount of intracellular resource. The model, called the “Resource-Competing Oscillator Network (RCON) model,” reproduces well the organism’s experimentally observed behavior, as it generates a number of spatiotemporal oscillation modes by keeping the total sum of the resource constant. Designing the feedback rule properly, the RCON model comes to face a problem of optimizing the allocation of the resource to its nodes. In the problem-solving process, “greedy” nodes having the highest competitiveness are supposed to take more resource out of other nodes. However, the resource allocation pattern attained by the greedy nodes cannot always achieve a “socially optimal” state in terms of the public cost. We prepare four test problems including a tricky one in which the greedy pattern becomes “socially unfavorable” and investigate how the RCON model copes with these problems. Comparing problem-solving performances of the oscillation modes, we show that there exist some modes often attain socially favorable patterns without being trapped in the greedy one.

Keywords

Physarum polycephalum Neural network Resource allocation Chaos Coupled oscillators 

References

  1. Adamatzky A (2008) Developing proximity graphs by Physarum Polycephalum: does the plasmodium follow Toussaint hierarchy? Parallel Process Lett 19:105–127MathSciNetCrossRefGoogle Scholar
  2. Aono M, Gunji Y-P (2003) Beyond input-output computings: error-driven emergence with parallel non-distributed slime mold computer. BioSystems 71:257–287CrossRefGoogle Scholar
  3. Aono M, Hara M (2007) Amoeba-based nonequilibrium neurocomputer utilizing fluctuations and instability. In: Aki SG et al (eds) UC 2007, LNCS, vol 4618. Springer-Verlag, Berlin, pp 41–54Google Scholar
  4. Aono M, Hara M (2008) Spontaneous deadlock breaking on amoeba-based neurocomputer. BioSystems 91:83–93CrossRefGoogle Scholar
  5. Aono M, Hara M, Aihara K (2007) Amoeba-based neurocomputing with chaotic dynamics. Commun ACM 50(9):69–72CrossRefGoogle Scholar
  6. Aono M, Hirata Y, Hara M, Aihara K (2009a) Amoeba-based chaotic neurocomputing: combinatorial optimization by coupled biological oscillators. New Gener Comput 27:129–157zbMATHCrossRefGoogle Scholar
  7. Aono M, Hirata Y, Hara M, Aihara K (2009b) Resource-competing oscillator network as a model of amoeba-based neurocomputer. In: Calude C et al (eds) UC 2009, LNCS, vol 5715. Springer-Verlag, Berlin, pp 56–69Google Scholar
  8. Aono M, Hara M, Aihara K, Munakata T (2010a) Amoeba-based emergent computing: combinatorial optimization and autonomous meta-problem solving. Int J Unconv Comput 6:89–108Google Scholar
  9. Aono M, Hirata Y, Hara M, Aihara K (2010b) A model of amoeba-based neurocomputer. J Comput Chem Japan 9(3):143–156CrossRefGoogle Scholar
  10. Arbib MA (ed) (2003) The handbook of brain theory and neural networks, 2nd edn. The MIT Press, CambridgezbMATHGoogle Scholar
  11. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W. H. Freeman and co, New YorkzbMATHGoogle Scholar
  12. Golubitsky M, Stewart I (2002) The symmetry perspective. Birkhauser, BaselGoogle Scholar
  13. Hirata Y, Aono M, Hara M, Aihara K (2010) Spontaneous mode switching in coupled oscillators competing for constant amounts of resources. Chaos 20:013117CrossRefGoogle Scholar
  14. Hopfield JJ, Tank DW (1986) Computing with neural circuits: a model. Science 233:625–633CrossRefGoogle Scholar
  15. Jones J (2009) Approximating the behaviours of Physarum polycephalum for the construction and minimisation of synthetic transport networks. In: Calude C et al (eds) Unconventional computation 2009, UC 2009, LNCS, vol 5715. Springer-Verlag, Berlin, pp 191–208Google Scholar
  16. Kaneko K, Tsuda I (2003) Chaotic itinerancy in focus issue: chaotic itinerancy. Chaos 13:926–936MathSciNetzbMATHCrossRefGoogle Scholar
  17. Kessler D (1982) Plasmodial structure and motility. In: Aldrich HC, Daniel JW (eds) Cell biology of physarum and didymium, vol 1. Academic Press Inc, New York, pp 145–208Google Scholar
  18. Kim S-J, Aono M, Hara M (2010a) Tug-of-war model for two-bandit problem: nonlocally correlated parallel exploration via resource conservation. BioSystems 101:29–36CrossRefGoogle Scholar
  19. Kim S-J, Aono M, Hara M (2010b) Tug-of-war model for multi-armed Bandit problem. In: Calude C et al (eds) UC 2010, LNCS, vol 6079. Springer-Verlag, Berlin, pp 69–80Google Scholar
  20. Kuznetsov YA (2004) Elements of applied bifurcation theory. Springer-Verlag, New York, USAzbMATHGoogle Scholar
  21. Nakagaki T, Yamada H, Toth A (2000) Maze-solving by an amoeboid organism. Nature 407:470CrossRefGoogle Scholar
  22. Nakagaki T, Iima M, Ueda T, Nishiura Y, Saigusa T, Tero A, Kobayashi R, Showalter K (2007) Minimum-risk path finding by an adaptive amoebal network. Phys Rev Lett 99:068104CrossRefGoogle Scholar
  23. Nisan N, Roughgarden T, Tardos E, Vazirani VV (eds) (2007) Algorithmic game theory. Cambridge University Press, CambridgezbMATHGoogle Scholar
  24. Roughgarden T (2005) Selfish routing and the price of anarchy. The MIT Press, CambridgeGoogle Scholar
  25. Saigusa T, Tero A, Nakagaki T, Kuramoto Y (2008) Amoebae anticipate periodic events. Phys Rev Lett 100:018101CrossRefGoogle Scholar
  26. Takamatsu A (2006) Spontaneous switching among multiple spatio-temporal patterns in three-oscillator systems constructed with oscillatory cells of true slime mold. Physica D 223:180–188CrossRefGoogle Scholar
  27. Takamatsu A, Fujii T, Endo I (2000) Time delay effect in a living coupled oscillator system with the plasmodium of Physarum polycephalum. Phys Rev Lett 85:2026–2029CrossRefGoogle Scholar
  28. Takamatsu A, Tanaka R, Yamada H, Nakagaki T, Fujii T, Endo I (2001) Spatiotemporal symmetry in rings of coupled biological oscillators of Physarum plasmodial slime mold. Phys Rev Lett 87:078102CrossRefGoogle Scholar
  29. Tero A, Kobayashi R, Nakagaki T (2006) Physarum solver: a biologically inspired method of road-network navigation. Physica A 363:115–119CrossRefGoogle Scholar
  30. Tero A, Takagi S, Saigusa T, Ito K, Bebber DP, Fricker MD, Yumiki K, Kobayashi R, Nakagaki T (2010) Rules for biologically inspired adaptive network design. Science 327(5964):439–442MathSciNetCrossRefGoogle Scholar
  31. Tsuda S, Zauner KP, Gunji Y-P (2007) Robot control with biological cells. BioSystems 87:215–223CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Masashi Aono
    • 1
  • Yoshito Hirata
    • 2
  • Masahiko Hara
    • 1
  • Kazuyuki Aihara
    • 2
  1. 1.Flucto-Order Functions Research Team, RIKEN-HYU Collaboration Research CenterRIKEN Advanced Science InstituteWakoJapan
  2. 2.Institute of Industrial ScienceThe University of TokyoMeguro-kuJapan

Personalised recommendations