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Associative Memory in Reaction-Diffusion Chemistry

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Advances in Unconventional Computing

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 23))

Abstract

Unconventional computing paradigms are typically very difficult to program. By implementing efficient parallel control architectures such as artificial neural networks, we show that it is possible to program unconventional paradigms with relative ease. The work presented implements correlation matrix memories (a form of artificial neural network based on associative memory) in reaction-diffusion chemistry, and shows that implementations of such artificial neural networks can be trained and act in a similar way to conventional implementations.

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References

  1. Adamatzky, A.: Computing in Nonlinear Media and Automata Collectives. IoP Publishing, Bristol, UK (2001)

    Book  MATH  Google Scholar 

  2. Adamatzky, A.: If BZ medium did spanning trees these would be the same trees as Physarum built. Phys. Lett. A 373(10), 952–956 (2009)

    Article  MATH  Google Scholar 

  3. Adamatzky, A., De Lacy Costello, B., Asai, T.: Reaction-Diffusion Computers. Elsevier Science, Amsterdam (2005)

    Google Scholar 

  4. Adamatzky, A., Wuensche, A., De Lacy Costello, B.: Glider-based computing in reaction-diffusion hexagonal cellular automata. Chaos, Solitons Fractals 27(2), 287–295 (2006)

    Google Scholar 

  5. Adleman, L.: Molecular computation of solutions to combinatorial problems. Science 266(5187), 1021–1024 (1994)

    Article  Google Scholar 

  6. Agladze, K., Aliev, R.R., Yamaguchi, T., Yoshikawa, K.: Chemical diode. J. Phys. Chem. 100, 13,895–13,897 (1996)

    Google Scholar 

  7. Asai, T., De Lacy Costello, B., Adamatzky, A.: Silicon implementation of a chemical reaction-diffusion processor for computation of Voronoi diagram. Int. J. Bifurc. Chaos 15(10), 3307–3320 (2005)

    Google Scholar 

  8. Austin, J., Stonham, T.J.: Distributed associative memory for use in scene analysis. Image Vis. Comput. 5(4), 251–260 (1987)

    Article  Google Scholar 

  9. Belousov, B.P.: A Periodic Reaction and Its Mechanism. Med Publ, Moscow (1959)

    Google Scholar 

  10. Carpenter, G.A.: Neural network models for pattern recognition and associative memory. Neural Netw. 2(4), 243–257 (1989)

    Article  Google Scholar 

  11. Conrad, M.: The brain-machine disanalogy. Biosystems 22(3), 197–213 (1989)

    Article  Google Scholar 

  12. Conrad, M., Zauner, K.: Conformation-based computing: A rationale and a recipe. In: Sienko, T., Adamatzky, A., Rambidi, N., Conrad, M. (eds.) Molecular Computing, chap 1. MIT Press, Massachusetts, pp. 1–31 (2003)

    Google Scholar 

  13. Dolnik, M., Marek, M., Epstein, I.R.: Resonances in periodically forced excitable systems. J. Phys. Chem. 96(8), 3218–3224 (1992)

    Article  Google Scholar 

  14. Field, R.J., Janz, R.D., Vanecek, D.J.: Composite double oscillation in a modified version of the Oregonator model of the Belousov-Zhabotinsky reaction. J. Chem. Phys. 73(7), 3132–3138 (1980)

    Article  MathSciNet  Google Scholar 

  15. Gilreath, W.F., Laplante, P.A.: Historical review of OISC. In: Computer Architecture: A Minimalist Perspective. The Kluwer International Series in Engineering and Computer Science, vol. 730, pp. 51–54. Springer, US (2003)

    Google Scholar 

  16. Gorecki, J., Yoshikawa, K., Igarashi, Y.: On chemical reactors that can count. J. Phys. Chem. A 107(10), 1664–1669 (2003)

    Article  Google Scholar 

  17. Gorecki, J., Gorecka, J., Igarashi, Y.: Information processing with structured excitable medium. Nat. Comput. 8, 473–492 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Haykin, S.: Neural Networks: A Comprehensive Foundation, 1st edn. Prentice Hall PTR, Upper Saddle River (1994)

    MATH  Google Scholar 

  19. Holley, J., Adamatzky, A., Bull, L., De Lacy Costello, B., Jahan, I.: Computational modalities of Belousov–Zhabotinsky encapsulated vesicles. ArXiv e-prints (2010)

    Google Scholar 

  20. Kohonen, T.: Correlation matrix memories. IEEE Trans. Comput. C-21(4), 353–359 (1972)

    Google Scholar 

  21. Kuhnert, L.: A new optical photochemical memory device in a light-sensitive chemical active medium. Nature 319(6052), 393–394 (1986)

    Article  Google Scholar 

  22. Kuhnert, L.: Photochemische manipulation von chemischen wellen (in German). Naturwissenschaften 73, 96–97 (1986)

    Article  Google Scholar 

  23. Kuhnert, L., Agladze, K.I., Krinsky, V.I.: Image processing using light-sensitive chemical waves. Nature 337(6204), 244–247 (1989)

    Article  Google Scholar 

  24. Laplante, J., Pemberton, M., Hjelmfelt, A., Ross, J.: Experiments on pattern recognition by chemical kinetics. J. Phys. Chem. 99(25), 10,063–10,065 (1995)

    Google Scholar 

  25. Lázár, A., Noszticzius, Z., Farkas, H., Försterling, H.D.: Involutes: the geometry of chemical waves rotating in annular membranes. Chaos 5(2), 443–447 (1995)

    Article  Google Scholar 

  26. Motoike, I., Yoshikawa, K.: Information operations with an excitable field. Phys. Rev. E 59, 5354–5360 (1999)

    Article  Google Scholar 

  27. Müller, U.: Brainfuck—an eight-instruction Turing-complete programming language. http://www.muppetlabs.com/~breadbox/bf/ (1993)

  28. Nakagaki, T., Yamada, H., Tóth, Á.: Path finding by tube morphogenesis in an amoeboid organism. Biophys. Chem. 92(1–2), 47–52 (2001)

    Article  Google Scholar 

  29. Rambidi, N.: Chemical-based computing and problems of high computational complexity: the reaction-diffusion paradigm. In: Sienko, T., Adamatzky, A., Rambidi, N., Conrad, M. (eds.) Molecular Computing, chap 4, pp. 91–152. MIT Press, Massachusetts (2003)

    Google Scholar 

  30. Rovinsky, A.B., Zhabotinsky, A.M.: Mechanism and mathematical model of the oscillating bromate-ferroin-bromomalonic acid reaction. J. Phys. Chem. 88(25), 6081–6084 (1984)

    Article  Google Scholar 

  31. Steinbock, O., Tóth, Á., Showalter, K.: Navigating complex labyrinths: optimal paths from chemical waves. Science 267(5199), 868–871 (1995)

    Article  Google Scholar 

  32. Stepney, S.: Unconventional computer programming. In: Symposium on Natural/Unconventional Computing and Its Philosophical Significance (2012)

    Google Scholar 

  33. Stepney, S., Abramsky, S., Adamatzky, A., Johnson, C., Timmis, J.: Grand challenge 7: journeys in non-classical computation. In: Visions of Computer Science, London, UK, September 2008, pp. 407–421 (2008)

    Google Scholar 

  34. Stovold, J., O’Keefe, S.: Simulating neurons in reaction-diffusion chemistry. In: Lones, M., Smith, S., Teichmann, S., Naef, F., Walker, J., Trefzer, M. (eds.) Information Processing in Cells and Tissues. Lecture Notes in Computer Science, vol. 7223, pp. 143–149. Springer, Berlin (2012)

    Google Scholar 

  35. Tolmachiev, D., Adamatzky, A.: Chemical processor for computation of Voronoi diagram. Adv. Mater. Opt. Electron. 6(4), 191–196 (1996)

    Article  Google Scholar 

  36. Tóth, Á., Showalter, K.: Logic gates in excitable media. J. Chem. Phys. 103(6), 2058–2066 (1995)

    Article  Google Scholar 

  37. Turing, A.M.: The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond. Ser. B, Biol. Sci. 237(641), 37–72 (1952)

    Article  Google Scholar 

  38. Willshaw, D.J., Buneman, O.P., Longuet-Higgins, H.C.: Non-holographic associative memory. Nature 222(5197), 960–962 (1969)

    Article  Google Scholar 

  39. Zhabotinsky, A., Zaikin, A.: Autowave processes in a distributed chemical system. J. Theor. Biol. 40(1), 45–61 (1973)

    Article  Google Scholar 

  40. Zhabotinsky, A.M.: Periodic course of the oxidation of malonic acid in a solution (studies on the kinetics of Belousov’s reaction). Biofizika 9 (1964)

    Google Scholar 

  41. Zhabotinsky, A.M.: A history of chemical oscillations and waves. Chaos: Interdiscip. J. Nonlinear Sci. 1(4), 379–386 (1991)

    Article  Google Scholar 

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Correspondence to Simon O’Keefe .

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Stovold, J., O’Keefe, S. (2017). Associative Memory in Reaction-Diffusion Chemistry. In: Adamatzky, A. (eds) Advances in Unconventional Computing. Emergence, Complexity and Computation, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-33921-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-33921-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-33920-7

  • Online ISBN: 978-3-319-33921-4

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