Understanding Networks of Computing Chemical Droplet Neurons Based on Information Flow

In this paper, we present general methods that can be used to explore the information processing potential of a medium composed of oscillating (self-exciting) droplets. Networks of Belousov-Zhabotinsky (BZ) droplets seem especially interesting as chemical reaction-diffusion computers because their time evolution is qualitatively similar to neural network activity. Moreover, such networks can be self-generated in microfluidic reactors. However, it is hard to track and to understand the function performed by a medium composed of droplets due to its complex dynamics. Corresponding to recurrent neural networks, the flow of excitations in a network of droplets is not limited to a single direction and spreads throughout the whole medium. In this work, we analyze the operation performed by droplet systems by monitoring the information flow. This is achieved by measuring mutual information and time delayed mutual information of the discretized time evolution of individual droplets. To link the model with reality, we use experimental results to estimate the parameters of droplet interactions. We exemplarily investigate an evolutionary generated droplet structure that operates as a NOR gate. The presented methods can be applied to networks composed of at least hundreds of droplets.

[1]  Susan Stepney,et al.  Programming Unconventional Computers: Dynamics, Development, Self-Reference , 2012, Entropy.

[2]  Rodrigo Quian Quiroga,et al.  Nonlinear multivariate analysis of neurophysiological signals , 2005, Progress in Neurobiology.

[3]  William Bialek,et al.  Entropy and Information in Neural Spike Trains , 1996, cond-mat/9603127.

[4]  Andrew Adamatzky,et al.  Multi-scale Modelling of Computers Made from Excitable Chemical Droplets , 2013, Int. J. Unconv. Comput..

[5]  Ursula Kummer,et al.  Information transfer in signaling pathways: A study using coupled simulated and experimental data , 2008, BMC Bioinformatics.

[6]  George Sugihara,et al.  Detecting Causality in Complex Ecosystems , 2012, Science.

[7]  Klaus-Peter Zauner,et al.  Molecular Information Technology , 2005 .

[8]  Ferrante Neri,et al.  An Optimization Spiking Neural P System for Approximately Solving Combinatorial Optimization Problems , 2014, Int. J. Neural Syst..

[9]  M. Hallett,et al.  Linear and nonlinear information flow based on time-delayed mutual information method and its application to corticomuscular interaction , 2010, Clinical Neurophysiology.

[10]  Walter Senn,et al.  Code-Specific Learning Rules Improve Action Selection by Populations of Spiking Neurons , 2014, Int. J. Neural Syst..

[11]  Richard M. Noyes,et al.  Oscillations in chemical systems. I. Detailed mechanism in a system showing temporal oscillations , 1972 .

[12]  Andrew Adamatzky,et al.  Information coding with frequency of oscillations in Belousov-Zhabotinsky encapsulated disks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Andrew Adamatzky,et al.  Vesicle computers: Approximating Voronoi diagram on Voronoi automata , 2011, ArXiv.

[14]  Randall D. Beer,et al.  Information Dynamics of Evolved Agents , 2010, SAB.

[15]  Henry Markram,et al.  Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations , 2002, Neural Computation.

[16]  Alexander K. Vidybida,et al.  Testing of information condensation in a model reverberating spiking neural network , 2010, Int. J. Neural Syst..

[17]  David B. Fogel,et al.  An introduction to simulated evolutionary optimization , 1994, IEEE Trans. Neural Networks.

[18]  Jan Szymanski,et al.  Droplets with Information Processing Ability , 2011, Int. J. Unconv. Comput..

[19]  Andrew Adamatzky,et al.  Computing in nonlinear media and automata collectives , 2001 .

[20]  R. Kass,et al.  Multiple neural spike train data analysis: state-of-the-art and future challenges , 2004, Nature Neuroscience.

[21]  Antoni Morro,et al.  Studying the Role of Synchronized and Chaotic Spiking Neural Ensembles in Neural Information Processing , 2014, Int. J. Neural Syst..

[22]  R. Solé,et al.  The large-scale organization of chemical reaction networks in astrophysics , 2004, cond-mat/0406137.

[23]  M. Roulston.  Estimating the errors on measured entropy and mutual information , 1999 .

[24]  Matthäus Staniek,et al.  Symbolic transfer entropy. , 2008, Physical review letters.

[25]  R. Quiroga,et al.  Extracting information from neuronal populations : information theory and decoding approaches , 2022 .

[26]  Jan Szymanski,et al.  Realistic parameters for simple models of the Belousov-Zhabotinsky reaction. , 2011, The journal of physical chemistry. A.

[27]  Tuning active emulsion dynamics via surfactants and topology , 2013, The European physical journal. E, Soft matter.

[28]  Randall D. Beer,et al.  Nonnegative Decomposition of Multivariate Information , 2010, ArXiv.

[29]  John R. Koza,et al.  Hierarchical Genetic Algorithms Operating on Populations of Computer Programs , 1989, IJCAI.

[30]  Andrew Adamatzky,et al.  Logical and arithmetic circuits in Belousov-Zhabotinsky encapsulated disks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Edgar N. Sánchez,et al.  A New Neural Observer for an Anaerobic Bioreactor , 2010, Int. J. Neural Syst..

[32]  Hywel Morgan,et al.  Formation of artificial lipid bilayers using droplet dielectrophoresis. , 2008, Lab on a chip.

[33]  Gottfried Jetschke,et al.  Mathematik der Selbstorganisation , 1989 .

[34]  Stefano Panzeri,et al.  Analytical estimates of limited sampling biases in different information measures. , 1996, Network.

[35]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[36]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[37]  Christof Teuscher,et al.  Online Learning in a Chemical Perceptron , 2013, Artificial Life.

[38]  Albert Y. Zomaya,et al.  Local information transfer as a spatiotemporal filter for complex systems. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Henry Markram,et al.  On the computational power of circuits of spiking neurons , 2004, J. Comput. Syst. Sci..

[40]  Wofgang Maas,et al.  Networks of spiking neurons: the third generation of neural network models , 1997 .

[41]  Peter Dittrich,et al.  Chemical Computing , 2004, UPP.

[42]  Karsten Weicker,et al.  Evolutionäre Algorithmen, 2. Auflage , 2007, Leitfäden der Informatik.

[43]  Jochen Kaiser,et al.  Transfer entropy in magnetoencephalographic data: quantifying information flow in cortical and cerebellar networks. , 2011, Progress in biophysics and molecular biology.

[44]  William Bialek,et al.  Entropy and information in neural spike trains: progress on the sampling problem. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Wolfgang Banzhaf,et al.  Learning to Move a Robot with Random Morphology , 1998, EvoRobot.

[46]  J Gorecki,et al.  Sensing the distance to a source of periodic oscillations in a nonlinear chemical medium with the output information coded in frequency of excitation pulses. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  Alexander Dimitrov,et al.  Natural time scales for neural encoding , 2000, Neurocomputing.

[48]  Andrew Adamatzky,et al.  Computational modalities of Belousov-Zhabotinsky encapsulated vesicles , 2010, Nano Commun. Networks.

[49]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[50]  Hojjat Adeli,et al.  Spiking Neural Networks , 2009, Int. J. Neural Syst..

[51]  Christopher J. Rozell,et al.  Optimal Sparse Approximation with Integrate and Fire Neurons , 2014, Int. J. Neural Syst..

[52]  Alexander Borst,et al.  Information theory and neural coding , 1999, Nature Neuroscience.

[53]  Wolfgang Maass,et al.  Networks of Spiking Neurons: The Third Generation of Neural Network Models , 1996, Electron. Colloquium Comput. Complex..

[54]  A. Zhabotinsky,et al.  Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System , 1970, Nature.

[55]  Peter Dittrich,et al.  Symbol representations and signal dynamics in evolving droplet computers , 2014, Natural Computing.