Applications of Information Theory Methods for Evolutionary Optimization of Chemical Computers

Information Processing Using Networks of Chemical Oscillators

I believe the computing potential of systems with chemical reactions has not yet been fully explored. The most common approach to chemical computing is based on implementation of logic gates. However, it does not seem practical because the lifetime of such gates is short, and communication between gates requires precise adjustment. The maximum computational efficiency of a chemical medium is achieved if the information is processed in parallel by different parts of it. In this paper, I review the idea of computing with coupled chemical oscillators and give arguments for the efficiency of such an approach. I discuss how to input information and how to read out the result of network computation. I describe the idea of top-down optimization of computing networks. As an example, I consider a small network of three coupled chemical oscillators designed to differentiate the white from the red points of the Japanese flag. My results are based on computer simulations with the standard two-variable Oregonator model of the oscillatory Belousov−Zhabotinsky reaction. An optimized network of three interacting oscillators can recognize the color of a randomly selected point with >98% accuracy. The presented ideas can be helpful for the experimental realization of fully functional chemical computing networks.

Computing With Networks of Chemical Oscillators and its Application for Schizophrenia Diagnosis

Chemical reactions are responsible for information processing in living organisms, yet biomimetic computers are still at the early stage of development. The bottom-up design strategy commonly used to construct semiconductor information processing devices is not efficient for chemical computers because the lifetime of chemical logic gates is usually limited to hours. It has been demonstrated that chemical media can efficiently perform a specific function like labyrinth search or image processing if the medium operates in parallel. However, the number of parallel algorithms for chemical computers is very limited. Here we discuss top-down design of such algorithms for a network of chemical oscillators that are coupled by the exchange of reaction activators. The output information is extracted from the number of excitations observed on a selected oscillator. In our model of a computing network, we assume that there is an external factor that can suppress oscillations. This factor can be applied to control the nodes and introduce input information for processing by a network. We consider the relationship between the number of oscillation nodes and the network accuracy. Our analysis is based on computer simulations for a network of oscillators described by the Oregonator model of a chemical oscillator. As the example problem that can be solved with an oscillator network, we consider schizophrenia diagnosis on the basis of EEG signals recorded using electrodes located at the patient’s scalp. We demonstrated that a network formed of interacting chemical oscillators can process recorded signals and help to diagnose a patient. The parameters of considered networks were optimized using an evolutionary algorithm to achieve the best results on a small training dataset of EEG signals recorded from 45 ill and 39 healthy patients. For the optimized networks, we obtained over 82% accuracy of schizophrenia detection on the training dataset. The diagnostic accuracy can be increased to almost 87% if the majority rule is applied to answers of three networks with different number of nodes.

Identification of the best medium for experiments on chemical computation with Belousov–Zhabotinsky reaction and ferroin-loaded Dowex beads

Our study is focused on identification of the best medium for future experiments on information processing with Belousov–Zhabotinsky reaction proceeding in Dowex beads with immobilized catalyst inside. The optimum medium should be characterized by long and stable nonlinear behavior, mechanical stability and should allow for control with electric potential. We considered different types of Dowex ion-exchange resins, bead distributions and various initial concentrations of substrates: malonic acid and 1,4-cyclohexanedione. The electric potential on platinum electrodes, stabilized by a potentiostat is used to control medium evolution. A negative electric potential generates activator species HBrO2 on the working electrode according to the reaction: BrO3−  + 2e−  + 3H+  → HBrO2 + H2O, while positive electric potential attracts inhibitor species Br− to the proximity of it. We study oscillation amplitude and period stability in systems with ferroin loaded Dowex 50W-X2 and Dowex 50W-X8 beads during experiments exceeding 16 h. It has been observed, that the above mentioned resins generate a smaller number of CO2 bubbles close to the beads than Dowex 50W-X4, which makes Dowex 50W-X2 and Dowex 50W-X8 more suitable for applications in chemical computing. We report amplitude stability, oscillation frequency, merging and annihilation of travelling waves in a lattice of Dowex 50W-X8 beads (mesh size 50–100) in over 19 h long experiments with equimolar solution of malonic acid and 1,4-cyclohexanedione. This system looks as a promising candidate for chemical computing devices that can operate for a day.

Chemical micro-oscillators based on the Belousov–Zhabotinsky reaction

The results of studies on the development of micro-oscillators (MOs) based on the Belousov –Zhabotinsky (BZ) oscillatory chemical reaction are integrated and systematized. The mechanisms of the BZ reaction and the methods of immobilization of the catalyst of the BZ reaction in micro-volumes are briefly discussed. Methods for creating BZ MOs based on water microdroplets in the oil phase and organic and inorganic polymer microspheres are considered. Methods of control and management of the dynamics of BZ MO networks are described, including methods of MO synchronization. The prospects for the design of neural networks of MOs with intelligent-like behaviour are outlined. Such networks present a new area of nonlinear chemistry, including, in particular, the creation of a chemical ‘computer’.

The bibliography includes 250 references.

How Does a Simple Network of Chemical Oscillators See the Japanese Flag?

Chemical computing is something we use every day (e.g., in the brain), but we can still not explore and master its potential in human-made experiments. It is expected that the maximum computational efficiency of a chemical medium can be achieved if information is processed in parallel by different parts of the medium. In this paper, we use computer simulations to explore the efficiency of chemical computing performed by a small network of three coupled chemical oscillators. We optimize the network to recognize the white and red regions of the Japanese flag. The input information is introduced as the inhibition times of individual oscillators, and the output information is coded in the number of activator maxima observed on a selected oscillator. We have used the Oregonator model to simulate the network time evolution and the evolutionary optimization to find the best network for the considered task. We have found that even a network of three interacting oscillators can recognize the color of a randomly selected point with 95% accuracy.

Information and Statistical Measures in Classical vs. Quantum Condensed-Matter and Related Systems

The presented editorial summarizes in brief the efforts of ten (10) papers collected by the Special Issue (SI) "Condensed-Matter-Principia Based Information & Statistical Measures: From Classical to Quantum". The SI called for papers dealing with condensed-matter systems, or their interdisciplinary analogs, for which well-defined classical statistical vs. quantum information measures can be inferred while based on the entropy concept. The SI has mainly been rested upon objectives addressed by an international colloquium held in October 2019, at the University of Science and Technology (UTP) Bydgoszcz, Poland (see http://zmpf.imif.utp.edu.pl/rci-jcs/rci-jcs-4/), with an emphasis placed on the achievements of Professor Gerard Czajkowski (PGC). PGC commenced his research activity with diffusion-reaction (open) systems under the supervision of Roman S. Ingarden (Toruń), a father of Polish synergetics, and original thermodynamic approaches to self-organization. The active cooperation of PGC mainly with German physicists (Friedrich Schloegl, Aachen; Werner Ebeling, Berlin) ought to be underlined. Then, the development of Czajkowski's research is worth underscoring, moving from statistical thermodynamics to solid state theory, pursued in terms of nonlinear solid-state optics (Franco Bassani, Pisa), and culminating very recently with large quasiparticles, termed Rydberg excitons, and their coherent interactions with light.