Probabilistic Cellular Automata Research Articles

A quantization of interacting particle systems

Interacting particle systems studied in this paper are probabilistic cellular automata with nearest-neighbor interaction including the Domany-Kinzel model. A special case of the Domany-Kinzel model is directed percolation. We regard the interacting particle system as a Markov chain on a graph. Then we present a new quantization of the interacting particle system. After that, we introduce a zeta function of the quantized model and give its determinant expression. Moreover, we calculate the absolute zeta function of the quantized model for the Domany-Kinzel model.

A refined simulation method of building earthquake evacuation processes considering multi-exits and time-variant velocities

This study proposes a refined method for effectively simulating the evacuation processes of multi-story buildings during earthquakes. The method is developed by combining the exit-option algorithm and multi-velocity field model with the previously developed probabilistic network-based floor-field cellular automaton (PN-FFCA) model. Besides, the formula is also proposed for calculating the time-variant moving velocities of evacuees in the buildings subjected to the earthquake loads. Consequently, the refined method can fully consider the effect of multi-exits and time-variant velocities on the random evacuation processes of multi-story buildings during earthquakes. The recorded evacuation process of a school classroom during the 2022 Luding earthquake in China is reproduced using the refined method, which verifies its validity. In addition, the evacuation processes of an actual three-story office building subjected to random earthquake loads are simulated using the refined method. The simulated results are compared with those obtained from the PN-FFCA to demonstrate the advantages and utility of the refined method.

Modeling fatigue-assisted pitting in pipeline steel with PCA-XFEM

We present a localized corrosion and cracking damage mechanism (initiation of the pit, propagation of the pit, pit-to-crack transition, and stable cracking) in a pipeline steel under the application of fatigue loading by using sequential coupling of Probabilistic Cellular Automata (PCA) and eXtended Finite Element Method (XFEM). PCA is utilized for describing the localized corrosion damage mechanism. XFEM is used to simulate arbitrary inhomogeneities (cracks, voids, and soft/hard material interfaces (inclusions)) with the help of Level Set Methods (LSM). In the XFEM, the standard finite element is enriched by additional degrees of freedom by invoking the notion of the partition of unity, which alleviates the burden of mesh conformity to the internal boundaries and avoids re-meshing. LSM is used to locate the voids and material interfaces and track the crack propagation location. A localized strain criterion initiates cracks from the pit surface when the pit reaches a critical strain value.The coupling of PCA and XFEM demonstrates good agreement with experimental data regarding stress-assisted pitting corrosion and pit-induced fatigue cracking in the pipeline steel. The study also investigates the effects of boundaries, and initial pit size on fatigue crack initiation and growth. Boundary effects significantly influence crack initiation life and growth behavior, highlighting the importance of considering both defect characteristics and boundary conditions in assessing fatigue performance and structural integrity. Various initial pit sizes and geometric features further affect crack initiation location and transition time. Furthermore, the PCA-XFEM model effectively captures crack behavior in both short and long crack regimes, demonstrating good agreement with experimental data for a selected pit width of 140μm. By incorporating crack driving parameters derived from experiments, the model accurately predicts crack propagation, further enhancing its reliability and predictive capabilities in assessing fatigue crack behavior. Overall, this approach provides valuable insights for predicting the service life and integrity of pipelines subjected to similar loading conditions, thus aiding in designing and maintaining these critical infrastructure components.

ANALYSIS OF CHANGES IN FRACTAL, STATISTICAL AND KINETIC PARAMETERS DURING THE HETEROANNIHILATION OF PARTICLES ON THE SIMULATED STRUCTURALLY INHOMOGENEOUS SURFACES

To investigate the mechanisms of interaction of particles on structurally inhomogeneous surfaces, the influence of surface morphology, distribution of interacting particles and their mobility on the mechanisms of ongoing processes, various modeling approaches are widely used. The paper presents the results of comparison of kinetic, statistical and fractal parameters changing in the process of heteroannihilation of particles distributed chaotically and multifractally on a simulated structurally inhomogeneous surface. To simulate the complex behavior of particles in time and space during heteroannihilation with changes in their mobility across the surface and various interaction probabilities, a class IV probabilistic cellular automaton method was applied. Based on the simulation results, it is shown that the interaction probability, initial distribution, and mobility of interacting particles influence the formation of kinetic modes at different iterations of the heteroannihilation process. It was found that a decrease in the mobility of interacting particles leads to a longer preservation of spatial heterogeneity in the system. An increase in the mobility of interacting particles and the probability of their interaction increases the rate of change in the fractal dimensionality and the rate coefficients of heteroannihilation kinetics. Decrease of fractal dimensionality during heteroannihilation is accompanied by decrease of asymmetry and increase of excess characterizing shape and degree of symmetry of distribution of interacting particles. At the same time, large values of asymmetry and excess indicate a significant deviation from the normal distribution of interacting particles on the surface.

System reduction: an approach based on probabilistic cellular automata

System reduction: an approach based on probabilistic cellular automata

Generating Loop Patterns with a Genetic Algorithm and a Probabilistic Cellular Automata Rule

The objective is to find a Cellular Automata (CA) rule that can generate “loop patterns”. A loop pattern is given by ones on a zero background showing loops. In order to find out how loop patterns can be locally defined, tentative loop patterns are generated by a genetic algorithm in a preliminary stage. A set of local matching tiles is designed and checked whether they can produce the aimed loop patterns by the genetic algorithm. After having approved a certain set of tiles, a probabilistic CA rule is designed in a methodical way. Templates are derived from the tiles, which then are used in the CA rule for matching. In order to drive the evolution to the desired patterns, noise is injected if the templates do not match or other constraints are not fulfilled. Simulations illustrate that loops and connected loops can be evolved by the CA rule.

Дискретная стохастическая модель гидродинамики потока

For the mathematical description of hydrodynamic conditions in industrial equipment, idealized models are usually used. Upon receipt, a number of simplifying assumptions are made, which, on the one hand, facilitate the use, and on the other hand, the Appearance of the adequacy of the model. All typical models of flow structures are deterministic and continual. At the same time, it became known that the real situation arises in the process of considering possible factors. This trend leads to the need for a wider application of probabilistic approaches to modeling technological processes and apparatuses using modern digital technologies. This article cancels an attempt to create a hydrodynamic model using probabilistic cellular automata. In the model of occurrence, there is one reason for two flow velocities, a decision on the occurrence of a pressure drop, and the other is due to random walks of microvolumes of a moving medium. The described procedure for creating a model contains the results of its use. In particular, the results of modeling of motion trajectories in rare cases, the phenomena of their general movement and detection in rare zones were found. The article presents the results of a comparison of a discrete stochastic model with the types of a diffusion model, in terms of reflecting the physical essence of current flows, the possibilities of determining parameter models, and ease of use. The decisive aspects of the new model, its advantages and revolutions are shown. Possible areas of application of the obtained model. Under investigation are the results of simulation modeling using the proposed model, which reveal repeated results not only consistent with the classical approaches of hydrodynamics, but allow obtaining new data on the course of the processes under study.

Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton.

We develop the notion of Random Domino Automaton, a simple probabilistic cellular automaton model for earthquake statistics, in order to provide a mechanistic basis for the interrelation of Gutenberg-Richter law and Omori law with the waiting time distribution for earthquakes. In this work, we provide a general algebraic solution to the inverse problem for the model and apply the proposed procedure to seismic data recorded in the Legnica-Głogów Copper District in Poland, which demonstrate the adequacy of the method. The solution of the inverse problem enables adjustment of the model to localization-dependent seismic properties manifested by deviations from Gutenberg-Richter law.

MemCA: All-Memristor Design for Deterministic and Probabilistic Cellular Automata Hardware Realization

Inspired by the behavior of natural systems, Cellular Automata (CA) tackle the demanding long-distance information transfer of conventional computers by the massive parallel computation performed by a set of locally-coupled dynamical nodes. Although CA are envisioned as powerful deterministic computers, their intrinsic capabilities are expanded after the memristor’s probabilistic switching is introduced into CA cells, resulting in new hybrid deterministic and probabilistic memristor-based CA (MemCA). In the proposed MemCA hardware realization, memristor devices are incorporated in both the cell and rule modules, composing the very first all-memristor CA hardware, designed with mixed CMOS/Memristor circuits. The proposed implementation accomplishes high operating speed and reduced area requirements, exploiting also memristor as an entropy source in every CA cell. MemCA’s functioning is showcased in deterministic and probabilistic operation, which can be externally modified by the selection of programming voltage amplitude, without changing the design. Also, the proposed MemCA system includes a reconfigurable rule module implementation that allows for spatial and temporal rule inhomogeneity.

Coupling from the past for exponentially ergodic one-dimensional probabilistic cellular automata

Coupling from the past for exponentially ergodic one-dimensional probabilistic cellular automata

Extracellular DNAses Facilitate Antagonism and Coexistence in Bacterial Competitor-Sensing Interference Competition.

Over the last 4 decades, the rate of discovery of novel antibiotics has decreased drastically, ending the era of fortuitous antibiotic discovery. A better understanding of the biology of bacteriogenic toxins potentially helps to prospect for new antibiotics. To initiate this line of research, we quantified antagonists from two different sites at two different depths of soil and found the relative number of antagonists to correlate with the bacterial load and carbon-to-nitrogen (C/N) ratio of the soil. Consecutive studies show the importance of antagonist interactions between soil isolates and the lack of a predicted role for nutrient availability and, therefore, support an in situ role in offense for the production of toxins in environments of high bacterial loads. In addition, the production of extracellular DNAses (exDNases) and the ability to antagonize correlate strongly. Using an in domum-developed probabilistic cellular automaton model, we studied the consequences of exDNase production for both coexistence and diversity within a dynamic equilibrium. Our model demonstrates that exDNase-producing isolates involved in amensal interactions act to stabilize a community, leading to increased coexistence within a competitor-sensing interference competition environment. Our results signify that the environmental and biological cues that control natural-product formation are important for understanding antagonism and community dynamics, structure, and function, permitting the development of directed searches and the use of these insights for drug discovery. IMPORTANCE Ever since the first observation of antagonism by microorganisms by Ernest Duchesne (E. Duchesne, Contribution à l'étude de la concurrence vitale chez les microorganisms. Antagonism entre les moisissures et les microbes, These pour obtenir le grade de docteur en medicine, Lyon, France, 1897), many scientists successfully identified and applied bacteriogenic bioactive compounds from soils to cure infection. Unfortunately, overuse of antibiotics and the emergence of clinical antibiotic resistance, combined with a lack of discovery, have hampered our ability to combat infections. A deeper understanding of the biology of toxins and the cues leading to their production may elevate the success rate of the much-needed discovery of novel antibiotics. We initiated this line of research and discovered that bacterial reciprocal antagonism is associated with exDNase production in isolates from environments with high bacterial loads, while diversity may increase in environments of lower bacterial loads.

Cellular automata rules solving the wireless sensor network coverage problem

The problem of an optimal coverage of a wireless sensor network area is considered. To solve this problem, a Cellular Automata (CA) approach is proposed. More specifically, the objective is to find CA rules which are able to cover the 2D space by a minimum number of so–called “Sensor Tiles”. A sensor tile consists of a von Neumann neighborhood of range 2 centered at sensor “point” and surrounded by 12 sensing “pixels”. Two probabilistic CA rules were designed that can perform this task. Results of an experimental study show that the first rule evolves very fast stable sub-optimal coverings, starting from a random configuration. The second rule finds optimal coverings, however it needs much more time for their evolution. The results are supported by a theoretical study on von Neumann neighborhoods and borrowing either from heuristics or from the spectral theory of circulant graphs.

Locality of the interaction affects dynamics in probabilistic cellular automata

We study a class of one-dimensional probabilistic cellular automata in which each component can be in either state zero or state one. The component interacts with two neighbors: if its neighbors are in an equal state, then the component assumes the same state as its neighbors. If its neighbors are in different states, the following can happen: a one on the right-hand side of a zero, in which case the component becomes one with probability α or zero with probability 1 − α, and conversely, a zero on the right-hand side of a one, in which case the component becomes one with probability β or zero with probability 1 − β. For a set of initial distributions when both neighbors are placed on the right-hand side (respectively, both on the left-hand side) of a component, we prove that the process always converges weakly to the measure concentrated on the configuration where all the components are zeros. When one neighbor is placed on the left-hand side and the other is on the right-hand side, the same convergence happens when β < fN(α), where N is the distance between the neighbors. However, this convergence does not happen for β > 1/2α. Thus, in this case, we get the regimes of ergodicity and non-ergodicity. Moreover, we exhibit another type of phase transition, independent of neighbors’ locations. We also present some numerical studies in which we use mean field approximation and Monte Carlo simulation.

Cellular Automata Machine Modeling to obtain optimal conditions and productivity of microalgae biomass

Microalgae is a promising source of superior biomass for sustainable food sources, high value products, and 3rd generation biofuel. The main factors affecting growth, carbon fixation and biomass production of microalgae are species type, CO2 supply, nutrients, light, temperature, pH and mixing. This paper discusses the precision farming approach in microalgae biomass production using the Cellular Automata Machine modeling, i.e., Probabilistic Cellular Automata. Cellular Automata is a decentralized computing model that provides a useful platform to model the complex dynamic systems such as growth of cells. The application of this method on a large-scale microalgae production system can simulate and model the characteristics of microalgae growth and biomass. In conclusion, the Biological Lattice Gas Cellular Automaton (BIO-LGCA) has been proposed as modeling tools to obtain the optimal conditions and maximum productivity in microalgae biomass production.

Bootstrap Percolation, Probabilistic Cellular Automata and Sharpness

We establish new connections between percolation, bootstrap percolation, probabilistic cellular automata and deterministic ones. Surprisingly, by juggling with these in various directions, we effortlessly obtain a number of new results in these fields. In particular, we prove the sharpness of the phase transition of attractive absorbing probabilistic cellular automata, a class of bootstrap percolation models and kinetically constrained models. We further show how to recover a classical result of Toom on the stability of cellular automata w.r.t. noise and, inversely, how to deduce new results in bootstrap percolation universality from his work.

Fermionic quantum field theories as probabilistic cellular automata

A class of fermionic quantum field theories with interactions is shown to be equivalent to probabilistic cellular automata, namely cellular automata with a probability distribution for the initial states. Probabilistic cellular automata on a one-dimensional lattice are equivalent to two-dimensional quantum field theories for fermions. They can be viewed as generalized Ising models on a square lattice and therefore as classical statistical systems. As quantum field theories they are quantum systems. Thus quantum mechanics emerges from classical statistics. As an explicit example for an interacting fermionic quantum field theory we describe a type of discretized Thirring model as a cellular automaton. The updating rule of the automaton is encoded in the step evolution operator that can be expressed in terms of fermionic annihilation and creation operators. The complex structure of quantum mechanics is associated to particle-hole transformations. The naive continuum limit exhibits Lorentz symmetry. We exploit the equivalence to quantum field theory in order to show how quantum concepts as wave functions, density matrix, noncommuting operators for observables and similarity transformations are convenient and useful concepts for the description of probabilistic cellular automata.

Spatial dynamics of dengue fever spreading for the coexistence of two serotypes with an application to the city of São Paulo, Brazil

Background and objective:Dengue fever is a disease in which individuals’ spatial distribution and Aedes aegypti mosquitoes breeding places are important factors for the disease dynamics. Typically urban, dengue is a problem for least developed countries due to the ineffectiveness in controlling the vector and disorderly urbanization processes. The result is a composition of urban sanitation problems and areas with high demographic densities and intense flows of people. This paper explores the spatial distribution of vector breeding places to evaluate introducing a new dengue serotype to a population at equilibrium for a pre-existing serotype. The paper’s objective is to analyze the spatial dynamics of dengue using variations of the basic reproduction number.Methods:A model based on probabilistic cellular automata is proposed to permitting the necessary flexibility to consider some spatial distributions of vector breeding places. Then, ordinary differential equations are used as a mean-field approach of the model, and the basic reproduction number (R0) is derived considering the next-generation matrix method. A spatial approach for R0 is also proposed, and the model is tested in a neighbourhood from the city of São Paulo, Brazil, to examine the potential risks of vector breeding cells distribution.Results:The results indicated that the more spread out these places, the higher are the values of R0. When the model is applied to a neighbourhood in São Paulo, residential areas may boost the infections and must be under public vigilance to combat vector breeding sites.Conclusions:Considering the mean-field approximation of the cellular automata model by ordinary differential equations, the basic reproduction number derived returned an estimative of the disease dynamics in the population. However, the spatial basic reproduction number was more assertive in showing areas with a higher disease incidence. Moreover, the model could be easily adapted to be used in real maps enabling simulations closer to real problems.

Forecasting interregional youth migration flows

Subject. This article deals with the issues of youth migration, reproduction processes and the potential for the future socio-economic development of areas. Objectives. The article aims to develop a cellular automata model for the medium-term prediction of inter-regional youth migration flows of the 15–19 age cohort. Methods. For the study, we used a statistical analysis and the cellular automata theory. Results. The article presents a probabilistic cellular automata model with rectangular grids of cells without borders, where the number of cells coincides with the 15–19 age cohort number in the respective area. The article also proposes an author-developed cross-platform program in the Go programming language that helps make medium-term forecasts. Conclusions. The cellular automata allow for integrating various patterns of migratory behavior into a general model of area migration flow, and choosing the most adequate patterns of migratory behavior for various age and social groups of migrants.

A fully coupled crystal plasticity-cellular automata model for predicting thermomechanical response with dynamic recrystallization in AISI 304LN stainless steel

A microstructure-based multiscale framework was developed to physically correlate the microstructure evolution and mechanical behavior of AISI 304LN stainless steel during the thermomechanical process. The developed model couples a crystal plasticity finite element method (CPFEM) to simulate heterogeneous deformation and a probabilistic cellular automata (CA) approach with a dynamic recrystallization (DRX) model to simulate microstructure evolution. Specifically, the CA model was built with formulations with physical meaning and combined with CPFEM by updating algorithms with higher robustness. The developed model was validated by comparing it with the experimental results of AISI 304LN stainless steel under thermo-mechanical processing at various temperatures and strain rates. The predicted flow stresses, grain sizes, DRX volume fraction, and deformed texture match well with the experimental data. Additionally, the developed model can simulate microstructure evolution by the DRX process, whereby the evolutions of recrystallized grains and pole figures can be examined. Moreover, the mechanical responses during the nucleation and growth of recrystallized grains can be characterized by in-depth quantitative analysis considering grain-level deformation inhomogeneity.

Quantum fermions from classical bits.

A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically on bit configurations. The genuinely probabilistic character of quantum physics is realized by probabilistic initial conditions. In turn, the probabilistic automaton is equivalent to the classical statistical system of a generalized Ising model. For a description of the probabilistic information at any given time quantum concepts as wave functions and non-commuting operators for observables emerge naturally. Quantum mechanics can be understood as a particular case of classical statistics. This offers prospects to realize aspects of quantum computing in the form of probabilistic classical computing. This article is part of the theme issue 'Quantum technologies in particle physics'.