Amoeba-based Chaotic Neurocomputing: Combinatorial Optimization by Coupled Biological Oscillators

Takamatsu, A., Fujii, T. and Endo, I., “Time Delay Effect in a Living Coupled Oscillator System with the Plasmodium of Physarum Polycephalum,” Phys. Rev. Lett. 85, pp. 2026-2029, 2000.

Takamatsu, A., Tanaka, R., Yamada, H., Nakagaki, T., Fujii, T. and Endo, I., “Spatiotemporal Symmetry in Rings of Coupled Biological Oscillators of Physarum Plasmodial Slime Mold,” Phys. Rev. Lett. 87, pp. 078102, 2001.

Takamatsu, A., Tanaka, R. and Fujii, T., “Hidden Symmetry in Chains of Biological Coupled Oscillators,” Phys. Rev. Lett. 92, pp. 228102, 2004.

Takamatsu, A. “Spontaneous Switching Among Multiple Spatio-Temporal Patterns in Three-Oscillator Systems Constructed with Oscillatory Cells of True Slime Mold,” Physica D 223, pp. 180-188, 2006.

Nakagaki, T., Yamada, H. and Toth, A., “Maze-Solving by an Amoeboid Organism,” Nature 407, pp. 470, 2000.

Nakagaki, T., Yamada, H. and Hara, M., “Smart Network Solutions in an Amoeboid Organism,” Biophys. Chem. 107, pp. 1-5, 2004.

Nakagaki, T., Iima, M., Ueda, T., Nishiura, Y., Saigusa, T., Tero, A., Kobayashi, R. and Showalter, K., “Minimum-Risk Path Finding by an Adaptive Amoebal Network,” Phys. Rev. Lett. 99, pp. 068104, 2007.

Saigusa, T., Tero, A., Nakagaki, T. and Kuramoto, Y., “Amoebae Anticipate Periodic Events,” Phys. Rev. Lett. 100, pp. 018101, 2008.

Aono, M. and Gunji, Y-P. “Beyond Input-Output Computings: Error-Driven Emergence with Parallel Non-Distributed Slime Mold Computer,” BioSystems 71, pp. 257-287, 2003.

Aono, M. and Hara, M. “Dynamic Transition among Memories on Neurocomputer Composed of Amoeboid Cell with Optical Feedback,” in Proceedings of The 2006 International Symposium on Nonlinear Theory and its Applications, pp. 763-766, 2006.

Aono, M. and Hara, M., “Amoeba-based Nonequilibrium Neurocomputer Utilizing Fluctuations and Instability,” in UC 2007, LNCS, 4618 (Aki, S. G., et al. eds.), pp. 41-54. Springer-Verlag, Berlin, 2007.

Aono, M., Hara, M. and Aihara, K., “Amoeba-based Neurocomputing with Chaotic Dynamics,” Commun. ACM 50, 9, pp. 69-72, 2007.

Aono, M. and Hara, M., “Spontaneous Deadlock Breaking on Amoeba-Based Neurocomputer,” BioSystems 91, pp. 83-93, 2008.

Aono, M., Hara, M., Aihara, K. and Munakata, T, “Amoeba-Based Emergent Computing: Combinatorial Optimization and Autonomous Meta-Problem Solving,” to appear in International Journal of Unconventional Computing, 2009.

Tsuda, S., Aono, M. and Gunji, Y-P., “Robust and emergent Physarum logical-computing,” BioSystems 73, pp. 45-55, 2004.

Tsuda, S., Zauner, K. P. and Gunji, Y-P., “Robot Control with Biological Cells,” in Proceedings of Sixth International Workshop on Information Processing in Cells and Tissues, pp. 202-216, 2005.

Tero, A., Kobayashi, R. and Nakagaki, T., “Physarum Solver: A Biologically Inspired Method of Road-Network Navigation,” Physica A 363, pp. 115-119, 2006.

Adamatzky, A., “Physarum machine: Implementation of a Kolmogorov-Uspensky machine on a biological substrate,” to appear in Parallel Processing Letters (PPL), 17, 4, pp. 455–467, 2007.

Ohl, C. and Stockem, W., “Distribution and Function of Myosin II as a Main Constituent of the Microfilament System in Physarum Polycephalum,” Europ. J. Protistol, 31, pp. 208-222, 1995.

Nakamura, A. and Kohama, K., “Calcium Regulation of the Actin-Myosin Interaction of Physarum Polycephalum,” International Review of Cytology, 191, pp. 53-98, 1999.

Ueda, T., Matsumoto, K., Akitaya, T. and Kobatake, Y., “Spatial and Temporal Organization of Intracellular Adenine Nucleotides and Cyclic Nucleotides in Relation to Rhythmic Motility in Physarum Polycephalum,” Exp. Cell Res. 162, 2, pp. 486-494, 1986.

Ueda, T., Mori, Y. and Kobatake, Y., “Patterns in the Distribution of Intracellular ATP Concentration in Relation to Coordination of Amoeboid Cell Behavior in Physarum Polycephalum,” Exp. Cell Res. 169, 1, pp. 191-201, 1987.

Nakagaki, T., Yamada, H. and Ueda, T., “Interaction Between Cell Shape and Contraction Pattern,” Biophys. Chem. 84, pp. 195-204, 2000.

Arbib, M. A. (ed.). The Handbook of Brain Theory and Neural Networks (Second Edition), The MIT Press, Cambridge, Massachusetts, 2003.

Hopfield, J. J. and Tank, D. W., “Computing with Neural Circuits: A model,” Science 233, pp. 625-633, 1986.

Holland, J. H., Adaptation in Natural and Artificial Systems (Second Edition), The MIT Press, Cambridge, Massachusetts, 1992.

Bonabeau, E., Dorigo, M. and Theraulaz, G., Swarm Intelligence: From Natural to Artificial Systems, Oxford University Press, New York, 1999.

Munakata, T.,Fundamentals of the New Artificial Intelligence: Neural, Evolutionary, Fuzzy and More (Second Edition), Springer-Verlag, Berlin, 2008.

Garey, M. R. and Johnson, D. S., Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and co., New York, 1979.

Ueda, T., Mori, Y., Nakagaki, T. and Kobatake, Y., “Action Spectra for Superoxide Generation and UV and Visible Light Photoavoidance in Plasmodia of Physarum Polycephalum,” Photochem. Photobiol. 48, pp. 705-709, 1988.

Ott, E., Chaos in Dynamical Systems (2nd edition), Cambridge University Press, Cambridge, 2002.

Scheinkman, A. and LeBaron, B., “Nonlinear Dynamics and Stock Returns,” J. Business 62, pp. 311-337, 1989.

Schreiber, T. and Schmitz, A., “Improved Surrogate Data for Nonlinearity Tests,” Phys. Rev. Lett. 77, pp. 635-638, 1996.

Small, M., Yu, D. and Harrison, R. G., “Surrogate Test for Psuedoperiodic Time Series Data,”Phys. Rev. Lett. 87, pp. 188101, 2001.

Luo X., Nakamura T., Small M., “Surrogate Test to Distinguish between Chaotic and Pseudoperiodic Time Series,”. Phys. Rev. E 71: 026230, 2005.

Thiel, M., Romano, M. C., Kurths, J., Rolfs, M. and Kliegl, R., “Twin Surrogates to Test for Complex Synchronisation,” Europhys. Lett. 75 pp. 535-541, 2006.

Kennel, M. B., “Statistical Test for Dynamical Nonstationarity in Observed Time-Series Data,” Phys. Rev. E 56, pp. 316-321, 1997.

Wayland, R., Bromley, D., Pickett, D. and Passamante, A., “Recognizing Determinism in a Time Series,” Phys. Rev. Lett. 70, pp. 580-582, 1993.

Rosetnstein, M. T., Collins, J. J. and De Luca, C. J., “A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets,” Physica D 65, pp. 117-134, 1993.

Hegger, R., Kantz, H. and Schreiber, T., “Practical Implementation of Nonlinear Time Series Methods: The TISEAN Package,” Chaos 9, pp. 413-435, 1999.

Ott, E., Grebogi, C. and Yorke, J., “Controlling Chaos,” Phys. Rev. Lett. 64, pp. 1196, 1990.

Kaneko, K. and Tsuda, I., Complex Systems: Chaos and Beyond - A Constructive Approach with Applications in Life Sciences, Springer-Verlag, New York, 2001.

Aihara, K., Takabe, T. and Toyoda, M., “Chaotic Neural Networks,” Phys. Lett. A 144, pp. 333-340, 1990.

Hasegawa, M., Ikeguchi, T. and Aihara, K., “Combination of Chaotic Neurodynamics with the 2-opt Algorithm to Solve Traveling Salesman Problems,” Phys. Rev. Lett. 79, pp. 2344-2347, 1997.

Steinbock, O., Toth, A. amd Showalter, K., “Navigating Complex Labyrinths: Optimal Paths from Chemical Waves,” Science, 267, pp. 868-871, 1995.

Motoike, I. and Yoshikawa, K., “Information Operations with an Excitable Field,” Phys. Rev. E, 59, pp. 5354-5360, 1999.

Adamatzky, A., De Lacy Costello, B. and Asai, T. Reaction-Diffusion Computers, Elsevier, Amsterdam, 2005.

Abelson, H., Allen, D., Coore, D., Hanson, C., Homsy, G., Knight, T. F. Jr., Nagpal, R., Rauch, E., Sussman, G. J. and Weiss, R., “Amorphous Computing,” Commun. ACM 43, 5, pp. 74-82, 2000.

Reif, J. H. and Labean, T. H., “Autonomous Programmable Biomolecular Devices using Self-Assembled DNA Nanostructures,” Commun. ACM 50, 9, pp. 46–53, 2007.

Conrad, M., “On Design Principles for a Molecular Computer,” Commun. ACM 28, 5, pp. 464-480, 1985.

Christodoulides, N., Lederer, F. and Silberberg, Y., “Discritizing Light Behaviour in Linear and Nonlinear Waveguide Lattices,” Nature 424, pp. 817-823, 2003.