Evolution Of Cellular Automata Research Articles

Route choice model based on cellular automata and cumulative prospect theory

In order to investigate the impact of travelers’ adaptive adjustment behaviors on traffic network flow diversion under the assumption of bounded rationality, a multi-agent route choice model with individual interaction mechanism is established by using cumulative prospect theory and evolutionary cellular automata. In the model, travelers are divided into risk-seeking and risk-aversion ones. Based on the reliability of travel time and the idea of cellular genetic algorithm, the dynamic reference points and their evolution rules for travelers with heterogeneous characteristics are designed to enable individual travelers dynamically adjust their travel time budget according to the changes in the decision-making environment. Finally, the evolution rule of multi-agent reference points is combined with the traditional method of successive average algorithm to design the multi-agent bounded rational route choice evolution algorithm for the solving the problem of traffic flow assignment in a road network. The research main contributions show that the evolution model has well inherited the characteristics of the route flow diversion in the traditional model.

Dynamics in Systems with Modulated Symmetries.

We extend the notions of multipole and subsystem symmetries to more general spatially modulated symmetries. We uncover two instances with exponential and (quasi)periodic modulations and provide simple microscopic models in one, two, and three dimensions. Seeking to understand their effect on the long-time dynamics, we numerically study a stochastic cellular automaton evolution that obeys such symmetries. We prove that, in one dimension, the periodically modulated symmetries lead to a diffusive scaling of correlations modulated by a finite microscopic momentum. In higher dimensions, these symmetries take the form of lines and surfaces of conserved momenta. These give rise to exotic forms of subdiffusive behavior with a rich spatial structure influenced by lattice-scale features. Exponential modulation, on the other hand, can lead to correlations that are infinitely long-lived at the boundary while decaying exponentially in the bulk.

Relating SARS-CoV-2 variants using cellular automata imaging

We classify the main variants of the SARS-CoV-2 virus representing a given biological sequence coded as a symbolic digital sequence and by its evolution by a cellular automata with a properly chosen rule. The spike protein, common to all variants of the SARS-CoV-2 virus, is then by the picture of the cellular automaton evolution yielding a visible representation of important features of the protein. We use information theory Hamming distance between different stages of the evolution of the cellular automaton for seven variants relative to the original Wuhan/China virus. We show that our approach allows to classify and group variants with common ancestors and same mutations. Although being a simpler method, it can be used as an alternative for building phylogenetic trees.

SPATIAL SYNCHRONIZATION OF CELLULAR AUTOMATA IN EVOLUTIONARY PROCESSES SIMULATION TASKS

Manyappliedtasksaresimulatedbydifferenceequationsthatdescribethevectorofsystemstatesevolutionintime. Howeveritisrequiredtotakeintoaccount the spatial structure of simulated processes or systems in some tasks. Inpaperthepossibilityofaspatio-temporalprocessessimulation by cellular automata is considered. The brief review of two-dimensional cellular automataproperties is provided.Theprincipleofthemostfamoustwo-dimensionalcellularautomata“Game of Life”is described.Alsothegeneralwaytosettheseautomatainananalyticalformby Reaction-Diffusion equation is considered. Concrete forms of the Reaction equation and Diffusion equation are constructed and invariant sets for this system are defined. Thegeneralizationofanalyticalcellularautomata representation in total is provided.Asanexample,themodelofpopulationdevelopmentisconsidered. ItutilizestheclassicFerhulstequation, inwhichthespatialstructureistakenintoaccounthavingformofthecumulativeneighbors’impactonpopulationchangesrate.As per using of analytical form of cellular automata, differentschemasofsystemspatio-temporalcharacteristicscontrol aresuggested. Theseschemasarebasedonfeedback: delayedfeedback(thatis one that uses previous system states)and predictive feedback (that is one that uses predicted system states). As aresultthereismanaged to synchronize spatial configuration of cellular automataand it can be interpreted as stable population development. Particularly, cellular automata could work in cycle with cycle length set earlier. For cellular automata evolution visualization the algorithms and their computer implementation aredeveloped.Discrepancy functionis suggested, due to which it is possible to evaluate the synchronization accuracy. Research results and examples of received configurations are presented.

EVOLUTION OF TWO-DIMENSIONAL CELLULAR AUTOMATA. NEW FORMS OF PRESENTATION

The paper considers cellular automata and forms of reflection of their evolution. Forms of evolution of elementary cellular automata are known and widely used, which allowed specialists to model different dynamic processes and behavior of systems in different directions. In the context of the easy construction of the form of evolution of elementary cellular automata, difficulties arise in representing the form of evolution of two-dimensional cellular automata, both synchronous and asynchronous. The evolution of two-dimensional cellular automata is represented by a set of states of two-dimensional forms of cellular automata, which complicates the perception and determination of the dynamics of state change. The aim of this work is to solve the problem of a fixed mapping of the evolution of a two-dimensional cellular automaton in the form of a three-dimensional representation, which is displayed in different colors on a two-dimensional image The paper proposes the evolution of two-dimensional cellular automata in the form of arrays of binary codes for each cell of the field. Each time step of the state change is determined by the state of the logical "1" or "0". Moreover, each subsequent state is determined by increasing the binary digit by one. The resulting binary code identifies the color code that is assigned to the corresponding cell at each step of the evolution iteration. As a result of such coding, a two-dimensional color matrix (color image) is formed, which in its color structure indicates the evolution of a two-dimensional cellular automaton. To represent evolution, Wolfram coding was used, which increases the number of rules for a two-dimensional cellular automaton. The rules were used for the von Neumann neighborhood without taking into account the own state of the analyzed cell. In accordance with the obtained two-dimensional array of codes, a discrete color image is formed. The color of each pixel of such an image is encoded by the obtained evolution code of the corresponding cell of the two-dimensional cellular automaton with the same coordinates. The bitness of the code depends on the number of time steps of evolution. The proposed approach allows us to trace the behavior of the cellular automaton in time depending on its initial states. Experimental analysis of various rules for the von Neumann neighborhood made it possible to determine various rules that allow the shift of an image in different directions, as well as various affine transformations over images. Using this approach, it is possible to describe various dynamic processes and natural phenomena.

Delay propagation cellular automata model based on max-plus algebra for robustness evaluations of non-periodic train operation plans

Based on discrete-event dynamic system theory, train operation events in high-speed railway transportation systems are regarded as the basic elements of these dynamic systems. For non-periodic timetable railways in China, based on a max-plus algebra method, a delay propagation cellular automata model is proposed to evaluate the robustness of high-speed train operation plans. The cellular automata evolution rules that can reproduce the delay propagation state of trains mainly consider train safety headway constraints, passenger transfer constraints, and electric multiple unit (EMU) connection constraints. A simulation analysis of actual cases is performed. The simulation results show that the model can be used to evaluate the robustness of the train operation plan. The numerical results show that in the preparation of train operation plans, the proposed model can predict which trains have significant influences on delays in advance and improve the possibility of reducing the occurrence of delays to maintain high-quality service.

Autonomous Quantum Machines and Finite-Sized Clocks

Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device which we call the "Quasi-Ideal clock", and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an Idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.

Cellular Automata

Cellular automata (CA) are discrete dynamical systems consist of a regular finite grid of cell; each cell encapsulating an equal portion of the state, and arranged spatially in a regular fashion to form an n-dimensional lattice. A cellular automata is like computers, data represented by initial configurations which is processed by time evolution to produce output. This paper is an empirical study of elementary cellular automata which includes concepts of rule equivalence, evolution of cellular automata and classification of cellular automata. In addition, explanation of behaviour of cellular automata is revealed through example.

GPU Projection of ECAS-II Segmenter for Hyperspectral Images Based on Cellular Automata

Segmentation is a key issue in the processing of multidimensional images such as those in the field of remote sensing. Most of the segmentation algorithms developed for multidimensional images begin by reducing the dimensionality of the images, thus loosing information that could be relevant in the segmentation process. Evolutionary cellular automata segmentation (ECAS-II) is an evolutionary approach that provides cellular automata-based segmenters considering all the spectral information contained in a hyperspectral image without applying any technique for dimensionality reduction. This paper presents an efficient graphics processor unit implementation of the type of segmenters produced by ECAS-II for land cover hyperspectral images. The method is evaluated over remote sensing hyperspectral images, introducing it on a spectral–spatial classification scheme based on extreme learning machines. Experiments have shown that the proposed approach achieves better accuracy results for land cover purposes than other spectral–spatial classification techniques based on segmentation.

Stability of Cellular Automata Trajectories Revisited: Branching Walks and Lyapunov Profiles

We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analog of Floquet theory for cellular automata.

Two-steps into energy consumption optimisation due to the mapping of multimedia application to network on chip architecture

Energy-efficiency is becoming one of the most critical issues in embedded system design that target the multimedia application caused by the increasing number of intellectual property IP cores in network on chip NoC. This paper addresses the optimisation of NoC performances in term of power and latency, we proposed an optimisation technique that is an hybrid based-scheduling algorithm that evolve the cellular automata CA with genetic algorithm to solve mapping and scheduling problems where we mixed between GA easiest implementation and achievability of near global optimum solutions with CA simplicity and rigorous mathematical model to achieve our goal. In our algorithm, each transition rule represents a chromosome allowing an automatically programming of the transition rules of the evolutionary cellular automata. Also we have presented new dynamic voltage and frequency scaling technique that automatically detect the voltage change point in order to save power while respecting the timing constraints of the soft real-time multimedia application.

English

English

Foreword: asynchronous behavior of cellular automata and discrete models

This special issue contains a selection of papers presented at the ‘‘Third International Workshop on Asynchronous Cellular Automata and Asynchronous Discrete Models’’ (ACA 2014), held as a satellite workshop of the 11th International Conference on Cellular Automata for Research and Industry (ACRI 2014) in Krakow (Poland) in September 2014. Six papers were selected and, after an additional review process, five of them have been included in this special issue. They are now presented in an extended and improved form with respect to the already refereed workshop version that appeared in the proceedings of the ACRI 2014 conference. The ACA workshop is devoted to the theme of asynchrony, a hot topic, inside Cellular Automata and other Discrete Models as, for instance, Boolean Networks. Cellular Automata are a well-known formal tool for modeling complex systems; they are considered in many scientific fields and industrial applications. Synchronicity is one of the main features of Cellular Automata evolutions. Indeed, in the most common Cellular Automata framework, all cells are updated simultaneously at each discrete time step by means of a same rule. Recent trends consider the modeling of asynchronous systems based on local and possibly non-uniform interactions. The aim of this workshop is to bring together researchers dealing with the theme of the asynchrony inside Cellular Automata and Discrete Models. Typical, but not exclusive, topics of the workshop are dynamics, complexity and computational issues, emergent properties, models of parallelism and distributed systems, and models of real phenomena. The paper ‘‘Local structure approximation as a predictor of second-order phase transitions in asynchronous cellular automata’’ by Henryk Fukś and Nazim Fates considers aasynchronous elementary cellular automata, that is elementary cellular automata in which each cell independently updates with probability a. By means of an extension of the mean-field approximation technique, the authors study the phase transitions in such automata, i.e., the changes of the dynamical behavior which may occur when the parameter a varies. In the paper ‘‘Supercritical probabilistic cellular automata: How effective is the synchronous updating?’’, PierreYves Louis deals with the issue of quantifying the effectiveness of the parallel updating in probabilistic cellular automata, i.e., cellular automata where the local rule is defined by means of a probability. Two interesting classes of probabilistic cellular automata are considered. An analysis of simulation is presented and shows that the behavior of these classes is nearly asynchronous when transition phase phenomena occur. Boolean Networks model the dynamical interaction of components which take a binary state. They have been & Alberto Dennunzio dennunzio@disco.unimib.it

Measure evolution of cellular automata and of finitely anticipative transformations

The evolution of cellular automata and of finitely anticipative transformations is studied by using right sets. These are the sets of symbols that are compatible with a past of a position and the respective coordinate of the transformation. Our main result shows, under some suitable conditions, that if the entropy converges to zero then the right sets increase towards the whole alphabet. We discuss these concepts with Wolfram automata.

The Transition Rules of 2D Linear Cellular Automata Over Ternary Field and Self-Replicating Patterns

In this paper we start with two-dimensional (2D) linear cellular automata (CA) in relation with basic mathematical structure. We investigate uniform linear 2D CA over ternary field, i.e. ℤ3. Present work is related to theoretical and imaginary investigations of 2D linear CA. Even though the basic construction of a CA is a discrete model, its macroscopic level behavior at large times and on large scales could be a close approximation to a continuous system. Considering some statistical properties, someone may also study geometrical aspects of patterns generated by cellular automaton evolution. After iteratively applying the linear rules, CA have been shown capable of producing interesting complex behaviors. Some examples of CA produce remarkably regular behavior on finite configurations. Using some simple initial configurations, the produced pattern can be self-replicating regarding some linear rules. Here we deal with the theory 2D uniform periodic, adiabatic and reflexive boundary CA (2D PB, AB and RB) over the ternary field ℤ3and the applications of image processing for patterns generation. From the visual appearance of the patterns, it is seen that some rules display sensitive dependence on boundary conditions and their rule numbers.

Multi-dimensional Manufacturing Information Based Typical Product Process Route Discovery Method

To solve the difficulty of low reuse value in the traditional process route discovery methods based clustering analysis and to make the extracted process routes support the effective reuse based manufacturing resources, a multi-dimensional manufacturing information based typical product process route discovery method is presented. A process information element and process route information model based multi-dimensional manufacturing information are established, and consequently the lower-dimensional process route model of its own dimensionality is obtained by using kernel principal component analysis(KPCA) to reduce the dimensionality of process information element. Based on the lower-dimensional process route model, a distance calculation method for calculate the similarity between process routes is proposed and evolutionary cellular learning automata was applied to realize the intelligent clustering division of process routes. The typical process routes are extracted from the clustering clusters consequently. Experimental results show that the effectiveness of proposed method is verified.

2D Cellular Automata with an Image Processing Application

This paper investigates the theoretical aspects of two-dimensional linear cellular automata with image applications. We consider geometrical and visual aspects of patterns generated by cellular automata evolution. The present work focuses on the theory of two-dimensional linear cellular automata with respect to uniform periodic and adiabatic boundary cellular automata conditions. Multiple copies of any arbitrary image corresponding to cellular automata nd so many applications in real life situation e.g. textile design, DNA genetics research, etc.

Special section on Cellular Automata

Contrasting natural systems, which eventually evolve to maximal entropy, Cellular Automata are discrete dynamical systems that are known for their strong modeling and self-organizational properties. Defined on an infinite lattice (in the usual onedimensional case, an infinite sequence defined on the integers), even starting with complete disorder, evolution of cellular automata can generate organized structure. Originally developed by John von Neumann in the 1940’s to model biological selfreproduction, cellular automata have long been used in computational, physical, and biological applications. Since 2009 the Workshop on Cellular Automata, Theory and Applications, has been held annually as part of The International Conference on Scientific Computing (CSC). The Workshop has welcomed researchers from many countries around the world to present their results and to participate in the talks and discussions. In

Evolutionary Cellular Automata Algorithm with Hybrid Discrete Variables and its Application to Mechanical Optimization

The optimization design about hybrid discrete variables synthesizing integer, discrete and continuous variables is very significant but also difficult in engineering, mathematics for programming and operational research. Aimed at shortages of existing optimum methods, in this paper, Evolutionary Cellar Automata Algorithm (ECAA) is proposed to complex optimization problem with hybrid discrete variables which has a digging operator and two learning operators (dual arithmetic crossover operator and chaos-peak-jumping operator). The computing examples of mechanical optimization design show that this algorithm has no special requirements on the characteristics of optimal designing problems, it has a fairly good universal adaptability and a reliable operation of program with a strong ability of overall convergence and high efficiency.

A Niche Cellular Genetic Algorithm Based on Evolution Rule

Since the individuals’ reproduction and existing probability can be greatly improved by introducing evolution rule into cellular automata algorithm, this paper presents a new niche cellular genetic algorithm by involving cellular automata evolution rule and introducing niche technique. The results of simulation experiments on some well-known complex benchmarking problems reveal that this algorithm outperforms the basic cellular genetic algorithms (cGAs) and cGAs with evolution rule in terms of diversity, convergence, global optimization and stability.