Reaction–diffusion chemistry implementation of associative memory neural network

References

• A. Adamatzky, Computing in Nonlinear Media and Automata Collectives, IoP Publishing, Bristol, 2001.
   Google Scholar
• A. Adamatzky, If BZ medium did spanning trees these would be the same trees as Physarum built, Phys. Lett. A 373(10) (2009), pp. 952–956.
   Web of Science ®Google Scholar
• A. Adamatzky, B. De Lacy Costello and T. Asai, Reaction–-diffusion Computers, Elsevier Science, Amsterdam, 2005.
   Google Scholar
• A. Adamatzky, B. De Lacy Costello, L. Bull, and J. Holley, Towards arithmetic circuits in sub-excitable chemical media, Isr. J. Chem. 51(1) (2011), pp. 56–66.
   Web of Science ®Google Scholar
• A. Adamatzky, A. Wuensche, A. Wuensche, and B. De Lacy Costello, Glider-based computing in reaction--diffusion hexagonal cellular automata, Chaos, Solitons Fractals 27(2) (2006), pp. 287–295.
   Web of Science ®Google Scholar
• L. Adleman, Molecular computation of solutions to combinatorial problems, Science 266(5187) (1994), pp. 1021–1024.
   PubMed Web of Science ®Google Scholar
• K. Agladze, R.R. Aliev, T. Yamaguchi, and K. Yoshikawa, Chemical diode, J. Phys. Chem. 100 (1996), pp. 13895–13897.
   Web of Science ®Google Scholar
• T. Asai, B. De Lacy Costello, and A. Adamatzky, Silicon implementation of a chemical reaction--diffusion processor for computation of Voronoi diagram, Int. J. Bifurcation Chaos 15(10) (2005), pp. 3307–3320.
   Web of Science ®Google Scholar
• J. Austin and T.J. Stonham, Distributed associative memory for use in scene analysis, Image Vision Comput. 5(4) (1987), pp. 251–260.
   Web of Science ®Google Scholar
• B.P. Belousov, A Periodic Reaction and Its Mechanism, Med Publishing, Moscow, 1959.
   Google Scholar
• G.A. Carpenter, Neural network models for pattern recognition and associative memory, Neural Networks 2(4) (1989), pp. 243–257.
   Web of Science ®Google Scholar
• M. Conrad, The brain-machine disanalogy, Biosystems 22(3) (1989), pp. 197–213.
   PubMed Web of Science ®Google Scholar
• M. Conrad and K. Zauner, Conformation-based computing: A rationale and a recipe, in Molecular Computing, chap 1, T. Sienko, A. Adamatzky, N. Rambidi, and M. Conrad, eds., MIT Press, Cambridge, MA, 2003, pp. 1–31.
   Google Scholar
• M. Dolnik, M. Marek, and I.R. Epstein, Resonances in periodically forced excitable systems, J. Phys. Chem. 96(8) (1992), pp. 3218–3224.
   Web of Science ®Google Scholar
• R.J. Field, R.D. Janz, and D.J. Vanecek, Composite double oscillation in a modified version of the Oregonator model of the Belousov--Zhabotinsky reaction, J. Chem. Phys. 73(7) (1980), pp. 3132–3138.
   Web of Science ®Google Scholar
• P.L. Gentili, V. Horvath, V.K. Vanag, and I.R. Epstein, Belousov--Zhabotinsky “chemical neuron” as a binary and fuzzy logic processor, J. Unconventional Comput. 8 (2012), pp. 177–192.
   Web of Science ®Google Scholar
• W.F. Gilreath and P.A. Laplante, Historical review of OISC, in Computer Architecture: A Minimalist Perspective Vol. 730, The Kluwer International Series in Engineering and Computer Science, New York, Springer, 2003, pp. 51–54.
   Google Scholar
• J. Gorecki, K. Yoshikawa, and Y. Igarashi, On chemical reactors that can count, J. Phys. Chem. A 107(10) (2003), pp. 1664–1669.
   Web of Science ®Google Scholar
• J. Gorecki, J. Gorecka, and Y. Igarashi, Information processing with structured excitable medium, Nat. Comput. 8 (2009), pp. 473–492.
   Google Scholar
• S. Haykin, Neural Networks: A Comprehensive Foundation, 1st ed., Prentice Hall PTR, Upper Saddle River, NJ, 1994.
   Google Scholar
• J. Holley, A. Adamatzky, L. Bull, B. De Lacy Costello, and I. Jahan, Computational modalities of Belousov--Zhabotinsky encapsulated vesicles, (2010). Available at ArXiv e-prints.
   Google Scholar
• E. Katz (ed.), Molecular and Supramolecular Information Processing: From Molecular Switches to Logic Systems, Wiley-VCH, Weinheim, 2012.
   Google Scholar
• T. Kohonen, Correlation matrix memories, IEEE Trans. Comput. C-21 4(1972), pp. 353–359.
   Web of Science ®Google Scholar
• L. Kuhnert, A new optical photochemical memory device in a light-sensitive chemical active medium, Nature 319(6052) (1986), pp. 393–394.
   Web of Science ®Google Scholar
• L. Kuhnert, Photochemische manipulation von chemischen wellen (in German), Naturwissenschaften 73 (1986), pp. 96–97.
   Web of Science ®Google Scholar
• L. Kuhnert, K.I. Agladze, and V.I. Krinsky, Image processing using light-sensitive chemical waves, Nature 337(6204) (1989), pp. 244–247.
   Web of Science ®Google Scholar
• J. Laplante, M. Pemberton, A. Hjelmfelt, and J. Ross, Experiments on pattern recognition by chemical kinetics, J. Phys. Chem. 99(25) (1995), pp. 10063–10065.
   Web of Science ®Google Scholar
• A. Lázár, Z. Noszticzius, H. Farkas, and H.D. Försterling, Involutes: The geometry of chemical waves rotating in annular membranes, Chaos 5(2) (1995), pp. 443–447.
   PubMed Web of Science ®Google Scholar
• I. Motoike and K. Yoshikawa, Information operations with an excitable field, Phys. Rev. E 59 (1999), pp. 5354–5360.
   PubMed Web of Science ®Google Scholar
• U. Müller, Brainfuck---an eight-instruction Turing-complete programming language, 1993. Available at http://www.muppetlabs.com/~breadbox/bf/.
   Google Scholar
• T. Nakagaki, H. Yamada, and Á. Tóth, Path finding by tube morphogenesis in an amoeboid organism, Biophys. Chem. 92(1–2) (2001), pp. 47–52.
   PubMed Web of Science ®Google Scholar
• N. Rambidi, Chemical-based computing and problems of high computational complexity: The reaction--diffusion paradigm, in Molecular Computing, chap 4, T. Sienko, A. Adamatzky, N. Rambidi and M. Conrad, eds., MIT Press, Cambridge, MA, 2003, pp. 91–152.
   Google Scholar
• A.B. Rovinsky and A.M. Zhabotinsky, Mechanism and mathematical model of the oscillating bromate-ferroin-bromomalonic acid reaction, J. Phys. Chem. 88(25) (1984), pp. 6081–6084.
   Web of Science ®Google Scholar
• D. Scalise and R. Schulman, Emulating cellular automata in chemical reaction-diffusion networks, in DNA Computing and Molecular Programming, Vol. 8727, Lecture Notes in Computer Science, S. Murata and S. Kobayashi, eds., Springer, 2014, pp. 67–83.
   Google Scholar
• O. Steinbock, Á. Tóth, and K. Showalter, Navigating complex labyrinths: Optimal paths from chemical waves, Science 267(5199) (1995), pp. 868–871.
   PubMed Web of Science ®Google Scholar
• S. Stepney, Unconventional computer programming, in Symposium on Natural/Unconventional Computing and Its Philosophical Significance, AISB, London, 2012.
   Google Scholar
• S. Stepney, S. Abramsky, A. Adamatzky, C. Johnson, and J. Timmis, Grand challenge 7: Journeys in non-classical computation, in Visions of Computer Science, London, 2008, pp. 407–421.
   Google Scholar
• J. Stovold, and S. O’Keefe, Simulating neurons in reaction-diffusion chemistry, in Information Processing in Cells and Tissues, Vol. 7223, Lecture Notes in Computer Science, M. Lones, S. Smith, S. Teichmann, F. Naef, J. Walker and M. Trefzer, eds., Springer, Berlin / Heidelberg, 2012, pp. 143–149.
   Google Scholar
• D. Tolmachiev, and A. Adamatzky, Chemical processor for computation of Voronoi diagram, Adv. Mater. Opt. Electron. 6(4) (1996), pp. 191–196.
   Google Scholar
• Á. Tóth, and K. Showalter, Logic gates in excitable media, J. Chem. Phys. 103(6) (1995), pp. 2058–2066.
   Web of Science ®Google Scholar
• A.M.Turing, The chemical basis of morphogenesis, Philos. Trans. R. Soc. London Ser. B, Biol. Sci. 237 641(1952), pp. 37–72.
   Web of Science ®Google Scholar
• D.J. Willshaw, O.P. Buneman, and H.C. Longuet-Higgins, Non-holographic associative memory, Nature 222(5197) (1969), pp. 960–962.
   PubMed Web of Science ®Google Scholar
• A. Zhabotinsky, and A. Zaikin, Autowave processes in a distributed chemical system, J. Theor. Biol. 40(1) (1973), pp. 45–61.
   PubMed Web of Science ®Google Scholar
• A.M. Zhabotinsky, Periodic course of the oxidation of malonic acid in a solution (studies on the kinetics of Belousov’s reaction), Biofizika 9 (1964), pp. 306–311.
   PubMedGoogle Scholar
• A.M. Zhabotinsky, A history of chemical oscillations and waves. Chaos: Interdisciplinary, J. Nonlinear Sci. 1(4) (1991), pp. 379–386.
   PubMedGoogle Scholar