A Chemical System that Recognizes the Shape of a Sphere
Giżyński Konrad, Górecki Jerzy *
Institute of Physical Chemistry, Polish Academy of Sciences
Kasprzaka 44/52, 01-224 Warsaw, Poland
*E-mail: jgorecki@ichf.edu.pl
Received:
Received: 24 November 2016; revised: 29 November 2016; accepted: 29 November 2016; published online: 28 December 2016
DOI: 10.12921/cmst.2016.0000057
Abstract:
Unconventional computing devices operating on nonlinear chemical media offer an interesting alternative to standard, semiconductor-based computers. In this work we consider database classifiers formed of interacting droplets in which a photosensitive variant of Belousov-Zhabotinsky (BZ) reaction proceeds. We introduce an evolutionary algorithm that searches for optimal construction of a droplets-based classifier for a given problem. The algorithm is based on maximizing the mutual information between the database and the observed evolution of medium. As an example application of chemical database classifiers we apply the idea to the dataset of points belonging to a unit cube. The dataset contains two output classes: 1 for points belonging to a sphere with radius 0.5 located in the cube center, and 0 for points outside of the sphere. The reliability of optimized chemical classifiers of such database for different numbers of droplets involved in data processing is presented.
Key words:
Belousov-Zhabotinsky reaction, droplets, evolutionary algorithm, mutual information
References:
[1] Gordon E. Moore, Cramming More Components Onto Inte-
grated Circuits, Proc. IEEE 86(1), 82–85, (1998), For recent
data see for example http://en.wikipedia.org/wiki/Moore’s_law.
[2] T. Gramss, S. Bornholdt, M. Gross, M. Mitchell, and T. Pel-
lizzari, Non-Standard Computation: Molecular Computation
– Cellular Automata – Evolutionary Algorithms – Quantum
Computers, Wiley-VCH Verlag GmbH & Co. KGaA, 2005.
[3] Cris Calude and G. Paun, Computing with cells and atoms:
an introduction to quantum, DNA and membrane computing,
CRC Press, 2000.
[4] A. Adamatzky, Ben De L. Costello, and T. Asai, Reaction-
Diffusion Computers, Amsterdam, Netherlands: Elsevier Sci-
ence Ltd., 2005.
[5] A. Adamatzky, L. Bull, and B De L. Costello, Unconven-
tional computing, L. Press, 2007.
[6] Y. Suzuki, M. Hagiya, H. Umeo, and A. Adamatzky, Nat-
ural Computing: 2nd International Workshop on Natural
C. Nagoya, Japan, December 2007, Proceedings, volume 1,
Springer Science & B. Media, 2008.
[7] J. Von Neumann, John von Neumann: selected letters, vol-
ume 27, American Mathematical Soc., 2005.
[8] H. Haken, Brain dynamics(synchronisation and activity pat-
terns in pulse-coupled neural nets with delays and noise),
Springer series in synergetics, (2002).
[9] A.N. Zaikin. A.M. Zhabotinsky, Concentration Wave Propa-
gation in Two-dimensional Liquid-phase Self-oscillating Sys-
tem, Nature 225(5232), 535–537, (1970).
[10] I.R. Epstein, J.A. Pojman, An introduction to nonlinear
chemical dynamics: oscillations, waves, patterns, and chaos,
Oxford University Press N. York, 1998.
[11] J. Lindsay, Richard J. Field, and M. Burger, Oscillations and
traveling waves in chemical systems, Wiley, 1985.
[12] L. Kuhnert, A new optical photochemical memory device in
a light-sensitive chemical active medium, Nature, 319, 393,
(1986).
[13] J. Gorecki, J.N. Gorecka, Computing in Geometrical Con-
strained Excitable C. Systems, In Robert A. Meyers, edi-
tor, Encyclopedia of Complexity and Systems Science, pages
1352–1376 Springer N. York, 2009.
[14] Á. Tóth, K. Showalter, Logic gates in excitable media, J.
Chem. Phys. 103(6), 2058–2066, (1995).
[15] O. Steinbock, Á. Tóth, K. Showalter, Navigating complex
labyrinths: optimal paths from chemical waves, Science
267(5199), 868, (1995).
[16] O. Steinbock, P. Kettunen, and K. Showalter, Chemical Wave
Logic Gates, J. Phys. Chem. 100(49), 18970–18975, (1996).
[17] I. Motoike, K. Yoshikawa, Information operations with an
excitable field, Phys. Rev. E 59(5), 5354, (1999).
[18] J. Sielewiesiuk, J. Gorecki, Logical functions of a cross junc-
tion of excitable chemical media, J. Phys. Chem. A 105(35),
8189–8195, (2001).
[19] A. Adamatzky, B. De L. Costello, Experimental logical gates
in a reaction-diffusion medium: The XOR gate and beyond,
Phys. Rev. E 66(4), 046112, (2002).
[20] K. Yoshikawa, I. Motoike, T. Ichino, T. Yamaguchi,
Y. Igarashi, J. Gorecki, and Joanna N. Gorecka, Basic In-
formation Processing Operations with Pulses of Excitation
in a Reaction-Diffusion System, Int. J. Unconv. Comput., 5,
3–37, (2009).
[21] J. Gorecki, J.N. Gorecka, Information Processing with
Chemical Excitations–from Instant Machines to an Artificial
Chemical Brain., Int. J. Unconv. Comput. 2(4), (2006).
[22] V.K. Vanag, I.R. Epstein, Pattern formation in a tunable
medium: The Belousov-Zhabotinsky reaction in an aerosol
OT microemulsion, Phys. Rev. Lett. 87(22), 228301, (2001).
[23] J. Szymanski, Joanna N. Gorecka, Y. Igarashi, K. Gizyn-
ski, J. Gorecki, Klaus-P. Zauner, and Maurits De Planque,
Droplets with information processing ability, Int. J. Unconv.
Comput. 7(3), 185–200, (2011).
[24] P.H. King, G. Jones, H. Morgan, M.R.R. de Planque, and K.-
P. Zauner, Interdroplet bilayer arrays in millifluidic droplet
traps from 3D-printed moulds, Lab Chip 14(4), 722–729,
(2014).
[25] G. Gruenert, K. Gizynski, G. Escuela, B. Ibrahim, J. Gorecki,
P. Dittrich, Understanding networks of computing chemical
droplet neurons based on information flow., Int. J. Neur. Syst.
25(7), 1450032, (2015).
[26] David B Fogel, Lawrence J Fogel, and VW Porto, Evolving
neural networks, Biol. Cybern. 63(6), 487–493, (1990).
[27] D. Cliff, I. Harvey, and P. Husbands, Incremental evolution
of neural network architectures for adaptive behaviour, In
M. Verleysen, editor, European Symposium on Artificial Neu-
ral Networks (ESANN’93), pages 39–44, Brussels, 1993 D
Facto.
[28] X. Yao, Y. Liu, A new evolutionary system for evolving arti-
ficial neural networks, IEEE Trans. Neural Netw. 8(3), 694–
713, (1997).
[29] C.E. Shannon, A mathematical theory of communication,
Bell Syst. Tech. J., 27, 379–423 and 623–656, (1948).
[30] G. Gruenert, J. Szymanski, J. Holley, G. Escuela, A. Diem,
B. Ibrahim, A. Adamatzky, J. Gorecki, and P. Dittrich, Multi-
scale Modelling of Computers Made from Excitable Chem-
ical Droplets, Int. J. Unconv. Comput. 9(3-4), 237–266,
(2013).
[31] J. Gorecki, J. Szymanski, and Joanna N. Gorecka, Realistic
Parameters for Simple Models of the Belousov–Zhabotinsky
Reaction, J. Phys. Chem. A 115(32), 8855–8859, (2011).
[32] R. Bradbury, M. Nagao, Effect of charge on the mechanical
properties of surfactant bilayers, Soft Matter 12(46), 9383–
9390, (2016).
[33] A. Gadomski, P. Bełdowski, L. Martínez-Balbuena,
I. Santamaría-Holek, and Z. Pawlak, Unravelling a Self-
healing Thermo- and Hydrodynamic Mechanism of Transient
Pore’s Late-stage Closing in Vesicles, and Related Soft-
matter Systems, in Terms of Liaison Between Surface-tension
and Bending Effects, Acta. Phys. Pol. B 47(5), 1341–1356,
(2016).
[34] H.-G. Beyer, H.-P. Schwefel, Evolution strategies – A com-
prehensive introduction, Nat. Comput. 1(1), 3–52, (2002).
[35] H.-P. Schwefel, Numerische Optimierung von Computer-
Modellen mittels der Evolutionsstrategie: mit einer vergle-
ichenden Einführung in die Hill-Climbing-und Zufallsstrate-
gie, Basel, Switzerland: Birkhäuser, 1977.
[36] H.-P. Schwefel, Numerical Optimization of Computer Mod-
els, John Wiley & Sons, Inc., N. York, NY, 1981.
[37] D.E. Goldberg, Genetic Algorithms in Search, Optimization
and Machine Learning, Addison-Wesley Longman Publish-
ing Co., Inc., Boston, MA, first edition, 1989.
[38] D. Thurber, Catfish Are Off the Hook Af-
ter Tokyo Ends 16-Year Earthquake P. Study,
http://articles.latimes.com/1992-04-26/
news/mn-1403_1_major-earthquake, 1992, LA
Times.
Unconventional computing devices operating on nonlinear chemical media offer an interesting alternative to standard, semiconductor-based computers. In this work we consider database classifiers formed of interacting droplets in which a photosensitive variant of Belousov-Zhabotinsky (BZ) reaction proceeds. We introduce an evolutionary algorithm that searches for optimal construction of a droplets-based classifier for a given problem. The algorithm is based on maximizing the mutual information between the database and the observed evolution of medium. As an example application of chemical database classifiers we apply the idea to the dataset of points belonging to a unit cube. The dataset contains two output classes: 1 for points belonging to a sphere with radius 0.5 located in the cube center, and 0 for points outside of the sphere. The reliability of optimized chemical classifiers of such database for different numbers of droplets involved in data processing is presented.
Key words:
Belousov-Zhabotinsky reaction, droplets, evolutionary algorithm, mutual information
References:
[1] Gordon E. Moore, Cramming More Components Onto Inte-
grated Circuits, Proc. IEEE 86(1), 82–85, (1998), For recent
data see for example http://en.wikipedia.org/wiki/Moore’s_law.
[2] T. Gramss, S. Bornholdt, M. Gross, M. Mitchell, and T. Pel-
lizzari, Non-Standard Computation: Molecular Computation
– Cellular Automata – Evolutionary Algorithms – Quantum
Computers, Wiley-VCH Verlag GmbH & Co. KGaA, 2005.
[3] Cris Calude and G. Paun, Computing with cells and atoms:
an introduction to quantum, DNA and membrane computing,
CRC Press, 2000.
[4] A. Adamatzky, Ben De L. Costello, and T. Asai, Reaction-
Diffusion Computers, Amsterdam, Netherlands: Elsevier Sci-
ence Ltd., 2005.
[5] A. Adamatzky, L. Bull, and B De L. Costello, Unconven-
tional computing, L. Press, 2007.
[6] Y. Suzuki, M. Hagiya, H. Umeo, and A. Adamatzky, Nat-
ural Computing: 2nd International Workshop on Natural
C. Nagoya, Japan, December 2007, Proceedings, volume 1,
Springer Science & B. Media, 2008.
[7] J. Von Neumann, John von Neumann: selected letters, vol-
ume 27, American Mathematical Soc., 2005.
[8] H. Haken, Brain dynamics(synchronisation and activity pat-
terns in pulse-coupled neural nets with delays and noise),
Springer series in synergetics, (2002).
[9] A.N. Zaikin. A.M. Zhabotinsky, Concentration Wave Propa-
gation in Two-dimensional Liquid-phase Self-oscillating Sys-
tem, Nature 225(5232), 535–537, (1970).
[10] I.R. Epstein, J.A. Pojman, An introduction to nonlinear
chemical dynamics: oscillations, waves, patterns, and chaos,
Oxford University Press N. York, 1998.
[11] J. Lindsay, Richard J. Field, and M. Burger, Oscillations and
traveling waves in chemical systems, Wiley, 1985.
[12] L. Kuhnert, A new optical photochemical memory device in
a light-sensitive chemical active medium, Nature, 319, 393,
(1986).
[13] J. Gorecki, J.N. Gorecka, Computing in Geometrical Con-
strained Excitable C. Systems, In Robert A. Meyers, edi-
tor, Encyclopedia of Complexity and Systems Science, pages
1352–1376 Springer N. York, 2009.
[14] Á. Tóth, K. Showalter, Logic gates in excitable media, J.
Chem. Phys. 103(6), 2058–2066, (1995).
[15] O. Steinbock, Á. Tóth, K. Showalter, Navigating complex
labyrinths: optimal paths from chemical waves, Science
267(5199), 868, (1995).
[16] O. Steinbock, P. Kettunen, and K. Showalter, Chemical Wave
Logic Gates, J. Phys. Chem. 100(49), 18970–18975, (1996).
[17] I. Motoike, K. Yoshikawa, Information operations with an
excitable field, Phys. Rev. E 59(5), 5354, (1999).
[18] J. Sielewiesiuk, J. Gorecki, Logical functions of a cross junc-
tion of excitable chemical media, J. Phys. Chem. A 105(35),
8189–8195, (2001).
[19] A. Adamatzky, B. De L. Costello, Experimental logical gates
in a reaction-diffusion medium: The XOR gate and beyond,
Phys. Rev. E 66(4), 046112, (2002).
[20] K. Yoshikawa, I. Motoike, T. Ichino, T. Yamaguchi,
Y. Igarashi, J. Gorecki, and Joanna N. Gorecka, Basic In-
formation Processing Operations with Pulses of Excitation
in a Reaction-Diffusion System, Int. J. Unconv. Comput., 5,
3–37, (2009).
[21] J. Gorecki, J.N. Gorecka, Information Processing with
Chemical Excitations–from Instant Machines to an Artificial
Chemical Brain., Int. J. Unconv. Comput. 2(4), (2006).
[22] V.K. Vanag, I.R. Epstein, Pattern formation in a tunable
medium: The Belousov-Zhabotinsky reaction in an aerosol
OT microemulsion, Phys. Rev. Lett. 87(22), 228301, (2001).
[23] J. Szymanski, Joanna N. Gorecka, Y. Igarashi, K. Gizyn-
ski, J. Gorecki, Klaus-P. Zauner, and Maurits De Planque,
Droplets with information processing ability, Int. J. Unconv.
Comput. 7(3), 185–200, (2011).
[24] P.H. King, G. Jones, H. Morgan, M.R.R. de Planque, and K.-
P. Zauner, Interdroplet bilayer arrays in millifluidic droplet
traps from 3D-printed moulds, Lab Chip 14(4), 722–729,
(2014).
[25] G. Gruenert, K. Gizynski, G. Escuela, B. Ibrahim, J. Gorecki,
P. Dittrich, Understanding networks of computing chemical
droplet neurons based on information flow., Int. J. Neur. Syst.
25(7), 1450032, (2015).
[26] David B Fogel, Lawrence J Fogel, and VW Porto, Evolving
neural networks, Biol. Cybern. 63(6), 487–493, (1990).
[27] D. Cliff, I. Harvey, and P. Husbands, Incremental evolution
of neural network architectures for adaptive behaviour, In
M. Verleysen, editor, European Symposium on Artificial Neu-
ral Networks (ESANN’93), pages 39–44, Brussels, 1993 D
Facto.
[28] X. Yao, Y. Liu, A new evolutionary system for evolving arti-
ficial neural networks, IEEE Trans. Neural Netw. 8(3), 694–
713, (1997).
[29] C.E. Shannon, A mathematical theory of communication,
Bell Syst. Tech. J., 27, 379–423 and 623–656, (1948).
[30] G. Gruenert, J. Szymanski, J. Holley, G. Escuela, A. Diem,
B. Ibrahim, A. Adamatzky, J. Gorecki, and P. Dittrich, Multi-
scale Modelling of Computers Made from Excitable Chem-
ical Droplets, Int. J. Unconv. Comput. 9(3-4), 237–266,
(2013).
[31] J. Gorecki, J. Szymanski, and Joanna N. Gorecka, Realistic
Parameters for Simple Models of the Belousov–Zhabotinsky
Reaction, J. Phys. Chem. A 115(32), 8855–8859, (2011).
[32] R. Bradbury, M. Nagao, Effect of charge on the mechanical
properties of surfactant bilayers, Soft Matter 12(46), 9383–
9390, (2016).
[33] A. Gadomski, P. Bełdowski, L. Martínez-Balbuena,
I. Santamaría-Holek, and Z. Pawlak, Unravelling a Self-
healing Thermo- and Hydrodynamic Mechanism of Transient
Pore’s Late-stage Closing in Vesicles, and Related Soft-
matter Systems, in Terms of Liaison Between Surface-tension
and Bending Effects, Acta. Phys. Pol. B 47(5), 1341–1356,
(2016).
[34] H.-G. Beyer, H.-P. Schwefel, Evolution strategies – A com-
prehensive introduction, Nat. Comput. 1(1), 3–52, (2002).
[35] H.-P. Schwefel, Numerische Optimierung von Computer-
Modellen mittels der Evolutionsstrategie: mit einer vergle-
ichenden Einführung in die Hill-Climbing-und Zufallsstrate-
gie, Basel, Switzerland: Birkhäuser, 1977.
[36] H.-P. Schwefel, Numerical Optimization of Computer Mod-
els, John Wiley & Sons, Inc., N. York, NY, 1981.
[37] D.E. Goldberg, Genetic Algorithms in Search, Optimization
and Machine Learning, Addison-Wesley Longman Publish-
ing Co., Inc., Boston, MA, first edition, 1989.
[38] D. Thurber, Catfish Are Off the Hook Af-
ter Tokyo Ends 16-Year Earthquake P. Study,
http://articles.latimes.com/1992-04-26/
news/mn-1403_1_major-earthquake, 1992, LA
Times.
