The flow of an electrolyte in a shallow square horizontal cavity subject to a steady current between opposite sides in the presence of an array of external magnets is simulated using a two dimensional lattice Boltzmann equation method for different values of the Chandrasekhar number. The flow is in a viscous regime for small values of Ch and in an advective one for larger values. In this last regime and in a steady state, a fixed number of pairs of initially close ideal tracer particles are added to the flow. We find that the average distance between each pair grows exponentially in time. Then, an average Lyapunov exponent that grows as a power law of the Chandrasekhar number can be defined.
The classification problem predicts labels for input data based on the training dataset. In this paper, the cyclic spaces of first degree reversible cellular automata are used to solve the classification problem. Every dataset of classification problem contains different classes. Based on the class labels in each configuration of cycles of the first degree reversible cellular automaton, they are grouped into different classes. The main advantage of this proposed model is that we can use real-world numerical data directly without doing any type of encoding. When selecting a reversible CA for classification, it is essential to maintain a minimum distance property within the same cycle's configurations, while ensuring a significant distance between configurations from different cycles. This study identifies (linear) CAs that satisfy this criterion. Our model performs well in comparison to the existing machine learning models.
Cellular automata (CAs) and convolutional neural networks (CNNs) are closely related due to the local nature of information processing. The connection between these topics is beneficial to both related fields, for conceptual as well as practical reasons. Our contribution solidifies this connection in the case of non-uniform CAs (nuCAs), simulating a global update in the architecture of the Python package TensorFlow. Additionally, we demonstrate how the highly optimised out-of-the-box multiprocessing in TensorFlow offers interesting computational benefits, especially when simulating large numbers of nuCAs with many cells.
We investigate a regional controllability problem applied to elementary Cellular Automata (CA). We first examine the conditions for boundary control, showing that, at least for small lattice sizes, only peripherally linear or affine CA can be fully controllable. Exploiting linearity, it is possible to develop an algorithm to construct the tree of preimages of a given configuration, therefore explicitly finding the optimal control for any given configuration. We apply then this method to non-linear CA.
This is an extended abstract about the research regarding theory of cellular automata: an overall overview of the past and current investigations along with an outlook on some promising research directions.
Multicomponent or Macroscopic Cellular Automata (MCA) were conceived for modelling and simulating complex “macroscopic” phenomena such as surface flows, forest fires, bioremediation of soils, etc. Many MCA models were developed for risky surface flows of different typology (lava flows, debris/mud/granular flows, lahars, snow avalanches, pyroclastic flows, rain runoff), these models share many “elementary” processes, but differ in some specificities of the particular phenomenon to be simulated. These specificities could be generalized to a single model (SCURRI: Simulation by Cellular Units of the Rheological RIsks) valid for each surface flow we deal with. The base of SCURRI is given by SCIDDICA, including its derivative MCA models LLUNPIY, VALANCA for simulating single phase surface flows (debris/mud/granular flows, lahars, snow avalanches). We introduce viscosity effects in SCURRI by adopting the approach of the MCA model SCIARA for simulating lava flows: a critical height, beyond which the flows become negligible, is introduced in SCURRI now version 01. SCURRI-01 was applied to a real event (of course) different from a lava flow: the secondary lahar of February 2005 of Vascún Valley from Tungurahua. This event had been simulated satisfactorily by LLUNPIY. Simulations were also performed by SCURRI-01 with different values of critical height. Higher values of this parameter, produce clear viscosity increasing effects such as speed decrease which can reach so low values that we can no longer talk about lahars, but rather of slow flow landslide.
We study the synchronisation dynamics of a chain of coupled chaotic maps arranged in a parent-children configuration, with each parent node connected to two children nodes, one of which is also the parent of the next node. We analyse two distinct phenomena: parent-child synchronisation, characterised by the vanishing distance between consecutive nodes, and siblings synchronisation, for which the states of two children coalesce. Our investigation reveals strong differences in the synchronisation mechanisms between these two phenomena, which can be directly linked to the probability distribution of the parent. Theoretical analysis and simulations using the logistic map support our findings. Furthermore, we explore the propagation of perturbations in a synchronised chain by studying the rate of reabsorption of the perturbation.
This paper presents an approach for constructing efficient substitution boxes (S-boxes) for cryptographic applications by combining cellular automata (CA) and reinforcement learning (RL). Semi-bent Boolean functions derived from CA rules are used to generate the S-box output array with desirable cryptographic properties like high nonlinearity. The selection of optimal CA rules is formulated as a Markov Decision Process (MDP), where a reinforcement learning agent explores the state space of rule combinations to maximize a reward signal based on non-linearity and differential uniformity. Various configurations for applying the selected CA rules to generate multi-layered S-boxes are explored. The proposed methodology offers advantages such as reduced memory footprint, exploration of a vast solution space, and inherent parallelism suitable for hardware implementations. Experimental results demonstrate that the generated S-boxes outperform previously proposed CA based S-boxes in terms of cryptographic strength.
A synchronization problem in cellular automata has been known as the Firing Squad Synchronization Problem (FSSP), where the FSSP gives a finite-state protocol for synchronizing a large scale of cellular automata. A quest for smaller state FSSP solutions has been an interesting problem for a long time. It has been shown by Balzer [1967], Sanders [1994], Berthiaume et al. [2004], and Ng [2011] that there exists no 4-state FSSP solution to one-dimensional (1D) arrays and rings. The number four is the state lower bound in the class of FSSP protocols. Umeo, Kamikawa and Yunès [2009], by introducing a notion of full versus partial FSSP solutions, provided a list of the smallest 4-state symmetric powers-of-2 FSSP solutions that can synchronize any 1D ring cellular automata of length n=2^k for any positive integer k ≥ 1 . Afterwards, Ng [2011] also added a list of asymmetric FSSP partial solutions, thus completing the 4-state powers-of-2 FSSP partial solutions. On the other hand, nothing has been explored for the smaller-state 1D array synchronizers. A question whether how many 4-state partial solutions there are for 1D arrays has been remained open. In this paper, we answer the question by providing a new class of the smallest 4-state FSSP partial solutions that can synchronize any 1D arrays of length n=2^k-1 , 2^k , and 2^k+1 for any positive integer k ≥ 2 . We present a class of the smallest 4-state semi-symmetric array synchronizers: 4 solutions for 1D arrays of length n=2^k-1 , 415 solutions for length n=2^k , and 41 solutions for length n=2^k+1 .
This paper presents a novel hybrid approach for desertification control that leverages the strengths of cellular automata (CA) modeling and reinforcement learning (RL). We employ the DESERTICAS software, a specifically designed CA model for simulating desertification dynamics. The model incorporates a variety of factors influencing land degradation, including those from the MEDALUS model, fundamental desertification properties, land-use practices, exploitability, and management. Our key contribution is to introduce a control parameter within the DESERTICAS framework. This allows us to formulate desertification control as an input-output problem and apply control theory principles to CA models. By manipulating the average intensity of a dominant factor (identified as management in this study), we can indirectly influence all other factors and potentially decelerate or even halt land degradation processes. Furthermore, we integrate a Reinforcement Learning (RL) agent into the simulation environment. This virtual entity continuously explores different management strategies, dynamically adjusting its actions based on the observed outcomes. This combination of CA modeling and RL constitutes a hybrid approach to desertification control. The experimental results show promising outcomes, with the inclusion of the RL agent leading to a significant reduction in desertified regions. This study paves the way for further exploration of hybrid CA-RL techniques for environmental applications.
In this paper we suggest a simple algorithm for merging the traffic of a main road with on-ramp traffic. We consider collaborative Connected and Autonomous Vehicles (CAVs). We are interested in the global impact of the merging strategy on the input and output flows of the merging area. We refer to the literature for all local aspects of synchronisation of cars. Our analysis focuses on saturated flows and the control of collective behaviour.
This work relies on DESERTICAS software, which is designed to model desertification dynamics. Spatiotemporal land changes are represented by cellular automata with continuous states. Their transition function incorporates various factors from the MEDALUS model, fundamental desertification properties, and additional factors such as land use practices, exploitability, and ownership considerations. The main contribution of this article is the introduction of a control parameter in the DESERTICAS model to study an input-output problem related to the desertification phenomenon and the application of control theory in cellular automata models. The idea is to act directly on a predominant factor by setting its average intensity. This makes it possible to act indirectly on all the other factors in the model and slow down or halt land degradation processes. In this way, we found that the predominant factor in the study of desertification is management, and we determined its intensity using a genetic algorithm (GA) approach. The aim of combining control problem and GAs is to integrate land protection actions into the desertification simulation, i.e. the DESERTICAS software, and turn it into a decision-support tool.
We propose a novel game-theoretic multi-agent system approach to create a desired 2D pattern. We interpret a pattern formation problem as a variant of the iterated Spatial Prisoner's Dilemma game, where evolutionary competing CA-based agents are used as learning machines. We design a payoff function reflecting a local goal of CA-based agent-players, and we show that the system of competing players is able to reach a Nash equilibrium, providing at the same time the maximization of a global criterion unknown for the agents that is related to the considered pattern formation problem. We provide experimental results showing a high performance of the pattern formation process.
The proposed work presents a cellular automata-based approach to sentiment analysis in code-mixed data. Our method demonstrates promising results in effectively analyzing sentiment across multilingual tweets or sentiments. By leveraging the dynamic properties of cellular automata, our model navigates the complexities of code-mixed data, where multiple languages or dialects are intertwined within the same text. Through extensive experimentation and evaluation, we showcase the robustness and efficacy of our approach in accurately identifying sentiment-bearing components in diverse linguistic contexts. The research contributes to advancing sentiment analysis techniques in the realm of code-mixed data, offering valuable insights for understanding user sentiment in multilingual communities and enhancing communication strategies in linguistically diverse environments. Our supervised classification approach produces 89
The Hiking Optimization Algorithm (HOA) is a newly designed metaheuristic optimization algorithm that stands out for its simplicity and problem-solving capability. Inspired by hiking, HOA draws parallels between the search landscapes of optimization problems and the rugged terrains encountered in nature. In this study, HOA is adapted for binary optimization problems, resulting in the proposal of the Binary Hiking Optimization Algorithm. The proposed algorithm, utilizing S-shaped and V-shaped transfer functions, is applied to Uncapaciated Facility Location Problems, and its performance is assessed. Key metrics such as mean, standard deviation, and GAP values are computed to evaluate the algorithm's effectiveness. Furthermore, an improvement method for the location update strategy is proposed for HOA, inspired by the Moore neighborhood used in cellular automata. The experimental results demonstrate that the binary HOA, strengthened by appropriate transfer functions, serves as a robust approach to tackle complex binary optimization challenges.
The paper solves the problem of effectively organizing the exchange of information in a group of robots, through the use of stream ciphers formed on the basis of cellular automata with active cells. The cellular automata with active cells allows to build a model of a pseudorandom number generator that can simultaneously generate many pseudorandom bit sequences. This makes it possible to organize the transmission of messages from one robot to all robots in the group and vice versa. Messages are exchanged using different self-synchronized stream ciphers generated by one device. Each cellular automata contains the number of active cells, which at the output generate a key gamma and form a stream cipher for the corresponding robot in the group. The number of active cells can either increase or decrease during the functioning of a group of robots, which corresponds to the addition or removal of robots in the group.
This paper explores diploid elementary cellular automata (ECA) systems where the rules of the cellular systems are acquired with a random mixing of two ECAs. However, here, we consider two ECAs from the same family following left to right, 0 to 1, and both transformations. Following the experimental approach, this study classifies the dynamics of (all possible) 300 diploid family couples following Wolfram's and Li and Packard's classification. We investigate the resistance of this diploid system against this family perturbation. As we will see, this study is interesting enough to provide the following rich phenomenon: (1) two-periodic family couple together show chaotic dynamics and vice-versa; (2) some diploid couple changes their class dynamics after a critical value of mixing rate, i.e. class transition; and (3) lastly, these diploid couples are also capable to show continuous or second-order phase transition dynamics.
Engineered Living Materials (ELMs) based on fungal mycelium offer a promising solution to the challenges posed by environmental disruption, resource scarcity, and rising material demands, while also exhibiting interesting computational capabilities. These materials are cost-effective, widely available, and environmentally beneficial due to their biodegradable nature. Using a Field-Programmable Gate Array (FPGA) to create a digital twin could make it much easier to predict growth patterns, find the best conditions for development, and look into possible uses for mycelial ELMs. Digital twins with advanced hardware integration are particularly effective, providing deep insights into the physical and mathematical aspects of these materials. This paper describes the use of Cellular Automata (CAs) and reaction-diffusion systems to model these processes due to their ability to handle the behavior of complex systems with scalability and parallelism. This approach has enabled the high-fidelity simulation of ELMs behaviors and the successful prototype implementation on a FPGA, making it a significant step towards practical applications of mycelial ELMs.
In this paper, we expand upon Cipher Block Chaining (CBC), and explore large cycle reversible non-uniform cellular automata for secure encryption and decryption. Both our encryption and decryption algorithms have an O(n) time complexity. We have conducted statistical tests like NIST, dieharder, and smallCrush to prove its robustness, along with brute force attacks and strict avalanche criterion (SAC) to further test its security. Analysis for known plaintext attack and chosen plaintext attack shows that neither of the attacks are feasible. Lastly, a visual test is conducted to further show the aparant randomness of the ciphertexts.
Engineered living materials (ELMs) and, more specifically, mycelium-based ELMs have been proposed as a solution to address the escalating societal pressures related to human-induced environmental disruption, scarcity of resources, and the anticipated increase in material demand. However, due to the complex biological mechanisms they emulate, their environmental sensitivity, slow supply chain and regulations, these devices present significant challenges for reproduction. Consequently, modeling the phenomena underlying such devices becomes critically important. In this context, we introduce a comprehensive mycelium-based ELM framework that incorporates reaction-diffusion processes and the modeling tool of Cellular Automata (CA). This framework successfully simulates the ELM's unpredictable growth mechanisms and closely resembles the mycelium's biological structure through the exploitation of the reaction-diffusion activator-inhibitor system. Finally, an augmented 3D version is presented that enhances the realism of our findings and strives to provide a deeper understanding of such materials.
