scholarly journals A low level analysis of Cellular Automata and Random Boolean Networks as a computational architecture

2000 ◽  
Author(s):  
Prateen Damera
Keyword(s):  
Cellular Automata ◽  
Boolean Networks ◽  
Random Boolean Networks ◽  
Low Level ◽  
Computational Architecture ◽  
Level Analysis

scholarly journals A neuro-inspired general framework for the evolution of stochastic dynamical systems: Cellular automata, random Boolean networks and echo state networks towards criticality

2020 ◽  
Vol 14 (5) ◽  
pp. 657-674
Author(s):  
Sidney Pontes-Filho ◽  
Pedro Lind ◽  
Anis Yazidi ◽  
Jianhua Zhang ◽  
Hugo Hammer ◽  
...  
Keyword(s):  
Deep Learning ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
General Framework ◽  
Dynamical Behavior ◽  
Boolean Networks ◽  
Stochastic Dynamical Systems ◽  
Random Boolean Networks ◽  
Echo State Networks ◽  
Computing Paradigm

Abstract Although deep learning has recently increased in popularity, it suffers from various problems including high computational complexity, energy greedy computation, and lack of scalability, to mention a few. In this paper, we investigate an alternative brain-inspired method for data analysis that circumvents the deep learning drawbacks by taking the actual dynamical behavior of biological neural networks into account. For this purpose, we develop a general framework for dynamical systems that can evolve and model a variety of substrates that possess computational capacity. Therefore, dynamical systems can be exploited in the reservoir computing paradigm, i.e., an untrained recurrent nonlinear network with a trained linear readout layer. Moreover, our general framework, called EvoDynamic, is based on an optimized deep neural network library. Hence, generalization and performance can be balanced. The EvoDynamic framework contains three kinds of dynamical systems already implemented, namely cellular automata, random Boolean networks, and echo state networks. The evolution of such systems towards a dynamical behavior, called criticality, is investigated because systems with such behavior may be better suited to do useful computation. The implemented dynamical systems are stochastic and their evolution with genetic algorithm mutates their update rules or network initialization. The obtained results are promising and demonstrate that criticality is achieved. In addition to the presented results, our framework can also be utilized to evolve the dynamical systems connectivity, update and learning rules to improve the quality of the reservoir used for solving computational tasks and physical substrate modeling.

ASYNCHRONOUS RANDOM BOOLEAN NETWORK MODEL WITH VARIABLE NUMBER OF PARENTS BASED ON ELEMENTARY CELLULAR AUTOMATA RULE 126

2006 ◽  
Vol 20 (08) ◽  
pp. 897-923 ◽  
Author(s):  
MIHAELA T. MATACHE
Keyword(s):  
Cellular Automata ◽  
Network Model ◽  
Boolean Network ◽  
Random Variable ◽  
Variable Number ◽  
Boolean Networks ◽  
Random Boolean Networks ◽  
Elementary Cellular Automata ◽  
Boolean Network Model ◽  
Point Analysis

A Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which can vary from one node to another, is considered. This is a generalization of previous results obtained for a constant number of parent nodes, by Matache and Heidel in "Asynchronous Random Boolean Network Model Based on Elementary Cellular Automata Rule 126", Phys. Rev. E71, 026 232, 2005. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. The Boolean rule is a generalization of rule 126 of elementary cellular automata, and is assumed to be the same for all the nodes. We provide a model for the probability of finding a node in state 1 at a time t for the class of generalized asynchronous random Boolean networks (GARBN) in which a random number of nodes can be updated at each time point. We generate consecutive states of the network for both the real system and the models under the various schemes, and use simulation algorithms to show that the results match well. We use the model to study the dynamics of the system through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the GARBN's dynamics range from order to chaos, depending on the type of random variable generating the asynchrony and the parameter combinations.

scholarly journals Classification of Discrete Dynamical Systems Based on Transients

2021 ◽  
pp. 1-26
Author(s):  
Barbora Hudcová ◽  
Tomáš Mikolov
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Complex Dynamics ◽  
Computation Time ◽  
Boolean Networks ◽  
Random Boolean Networks ◽  
Average Computation Time ◽  
Design Systems ◽  
Computational Systems

Abstract In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Channon, 2006; Ofria & Wilke, 2004; Ray, 1991).

scholarly journals Dynamical properties and path dependence in a gene-network model of cell differentiation

2020 ◽  
Author(s):  
Michele Braccini ◽  
Andrea Roli ◽  
Marco Villani ◽  
Roberto Serra
Keyword(s):  
Cell Differentiation ◽  
Network Model ◽  
Gene Network ◽  
Path Dependence ◽  
Control Mechanism ◽  
Boolean Networks ◽  
Biological Cells ◽  
Random Boolean Networks ◽  
Dynamical Properties

Abstract In this work, we explore the properties of a control mechanism exerted on random Boolean networks that takes inspiration from the methylation mechanisms in cell differentiation and consists in progressively freezing (i.e. clamping to 0) some nodes of the network. We study the main dynamical properties of this mechanism both theoretically and in simulation. In particular, we show that when applied to random Boolean networks, it makes it possible to attain dynamics and path dependence typical of biological cells undergoing differentiation.

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