Complex Systems
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Volume 26, Number 4 (2017)

On the Dynamics of Excitation and Information Processing in F-actin: Automaton Model
Andrew Adamatzky

A filamentous actin molecule is represented as a graph of finite-state machines (F-actin automata). Each node in the graph takes three states—resting, excited and refractory. All nodes update their states simultaneously and by the same rule. Two rules are considered: the threshold rule—a resting node excites if it has at least one excited neighbor, and the narrow excitation interval rule—a resting node excites if it has exactly one excited neighbor. The distributions of transient periods and lengths of limit cycles in F-actin automata are analyzed. Mechanisms of limit cycle emergence are proposed and we speculate on how these can be used to store information in a single actin unit. It is demonstrated that OR, AND-NOT and XOR gates can be implemented by excitation dynamics in F-actin automata.

Deep Learning with Cellular Automaton-Based Reservoir Computing
Stefano Nichele and Andreas Molund

Recurrent neural networks (RNNs) have been a prominent concept within artificial intelligence. They are inspired by biological neural networks (BNNs) and provide an intuitive and abstract representation of how BNNs work. Derived from the more generic artificial neural networks (ANNs), the recurrent ones are meant to be used for temporal tasks, such as speech recognition, because they are capable of memorizing historic input. However, such networks are very time consuming to train as a result of their inherent nature. Recently, echo state networks and liquid state machines have been proposed as possible RNN alternatives, under the name of reservoir computing (RC). Reservoir computers are far easier to train. In this paper, cellular automata (CAs) are used as a reservoir and are tested on the five-bit memory task (a well-known benchmark within the RC community). The work herein provides a method of mapping binary inputs from the task onto the automata and a recurrent architecture for handling the sequential aspects. Furthermore, a layered (deep) reservoir architecture is proposed. Performances are compared to earlier work, in addition to the single-layer version. Results show that the single cellular automaton (CA) reservoir system yields similar results to state-of-the-art work. The system comprised of two layered reservoirs does show a noticeable improvement compared to a single CA reservoir. This work lays the foundation for implementations of deep learning with CA-based reservoir systems.

Infinite Petri Nets: Part 2, Modeling Triangular, Hexagonal, Hypercube and Hypertorus Structures
Dmitry A. Zaitsev, Ivan D. Zaitsev, and Tatiana R. Shmeleva

A composition and analysis technique was developed for investigation of infinite Petri nets with regular structure introduced for modeling networks, clusters and computing grids that also concerns cellular automata and biological systems. A case study of a hypercube structure composition and analysis is presented; particularities of modeling other structures are discussed: triangular and hexagonal structures on a plane and a hypertorus in a multidimensional space. Parametric description of Petri nets, parametric representation of infinite systems for the calculation of place/transition invariants and solving them in parametric form allow the invariance proof for infinite Petri net models. Complex deadlocks are disclosed and a possibility of the network blocking via ill-intentioned traffic revealed. Prospective directions for future research of infinite Petri nets are formulated and hypotheses advanced.

Cellular Automaton-Based Pseudorandom Number Generator
Zakarya Zarezadeh

This paper is concerned with the study of pseudorandom number generation by an extension of the original cellular automaton, termed nonuniform cellular automata. In order to demonstrate the efficacy of a proposed random number generator, it is usually subject to a battery of empirical and theoretical tests. By using a standard software package for statistically evaluating the quality of random number sequences known as the Diehard battery test suite and TestU01, the results of the proposed model are validated, and we demonstrate that cellular automata can be used to rapidly produce purely random temporal bit sequences to an arbitrary precision.

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