Stochastic Cellular Automaton Model Research Articles

A stochastic cellular automata model of tautomer equilibria

ABSTRACTMany chemical substances, including drugs and biomolecules, exist in solution not as a single species, but as a collection of tautomers and related species. Importantly, each of these species is an independent compoundwith its own specific biochemical and physicochemical properties. The species interconvert in a dynamic and often complicated manner, making modelling the overall species composition difficult. Agent-based cellular automata models are uniquely suited to meet this challenge, allowing the equilibria to be simulated using simple rulesand at the same time capturing the inherent stochasticity of the natural phenomenon. In the present example a stochastic cellular automata model is employed to simulate the tautomer equilibria of 9-anthrone and 9-anthrol in the presence of their common anion. The observed KE of the 9-anthrone ⇌ 9-anthrol tautomerisation along with the measured tautomer pKa values were used to model the equilibria at pH values 4, 7 and 10. At pH 4 and 7, the anthrone comprises >99% of the total species population, while at pH 10the anthrone and the anion each represent just under half of the total population. The advantages of the cellular automata approach over the customary coupled differential equation approach are discussed.

確率交通流セルオートマトンモデルの示す開放系相図と臨界点(応用,応用可積分系, 平成19年研究部連合発表会)

確率交通流セルオートマトンモデルの示す開放系相図と臨界点(応用,応用可積分系, 平成19年研究部連合発表会)

Simple stochastic cellular automaton model for starved beds and implications about formation of sand topographic features in terms of sand flux

A simple stochastic cellular automaton model is proposed for simulating bedload transport, especially for cases with a low transport rate and where available sediments are very sparse on substrates in a subaqueous system. Numerical simulations show that the bed type changes from sheet flow through sand patches to ripples as the amount of sand increases; this is consistent with observations in flume experiments and in the field. Without changes in external conditions, the sand flux calculated for a given amount of sand decreases over time as bedforms develop from a flat bed. This appears to be inconsistent with the general understanding that sand flux remains unchanged under the constant-fluid condition, but it is consistent with the previous experimental data. For areas of low sand abundance, the sand flux versus sand amount (flux–density relation) in the simulation shows a single peak with an abrupt decrease, followed by a long tail; this is very similar to the flux–density relation seen in automobile traffic flow. This pattern (the relation between segments of the curve and the corresponding bed states) suggests that sand sheets, sand patches, and sand ripples correspond respectively to the free-flow phase, congested phase, and jam phase of traffic flows. This implies that sand topographic features on starved beds are determined by the degree of interference between sand particles. Although the present study deals with simple cases only, this can provide a simplified but effective modeling of the more complicated sediment transport processes controlled by interference due to contact between grains, such as the pulsatory migration of grain-size bimodal mixtures with repetition of clustering and scattering.

On Mechanistic Explanation of the Shape of the Universal Curve of Earthquake Recurrence Time Distributions

This paper outlines an idea for an explanation of a mechanism underlying the shape of the universal curve of the Earthquake Recurrence Time Distributions. The proposed simple stochastic cellular automaton model is reproducing the gamma distribution fit with the proper value of parameter γ characterizing the Earth’s seismicity and also imitates a deviation from the fit at short interevent times, as observed in real data. Thus the model suggests an explanation of the universal pattern of rescaled Earthquake Recurrence Time Distributions in terms of combinatorial rules for accumulation and abrupt release of seismic energy.

A cellular automata model of Ebola virus dynamics

We construct a stochastic cellular automaton (SCA) model for the spread of the Ebola virus (EBOV). We make substantial modifications to an existing SCA model used for HIV, introduced by others and studied by the authors. We give a rigorous analysis of the similarities between models due to the spread of virus and the typical immune response to it, and the differences which reflect the drastically different timing of the course of EBOV. We demonstrate output from the model and compare it with clinical data.

Stochastic cellular automata simulation of oscillations and autowaves in reaction-diffusion systems

In this paper, the investigations on stochastic cellular automata models of stable oscillations and autowaves in active media are summarized to formulate a concept of stochastic cellular automaton (CA) corresponding to asynchronous CAs with probabilistic transition rules. A formal description of a stochastic CA and a stochastic CA model is given. The properties and methods of synthesis of CA models for a specified set of elementary physical and chemical transformations are described. Some possibilities of simulating autowave and oscillatory processes are demonstrated using, as an example, a carbon monoxide oxidation reaction on a platinum catalyst with surface restructuring. The CA-simulation has made it possible to reveal the range of reaction parameter values with stable oscillations of reagent concentrations and to observe autowaves on the platinum surface. Special attention is given to providing a highly efficient parallel implementation of the stochastic CA algorithm. For this, the asynchronous mode must be preliminarily transformed to a block-synchronous one. Its equivalence to the asynchronous mode is justified. This is done for the CA reaction model by a comparative statistical analysis of the simulation results.

Stochastic model showing a transition to self-controlled particle-deposition state induced by optical near-fields

We study a stochastic model for the self-controlled particle-deposition process induced by optical near-fields. This process was experimentally realized by Yukutake et al. on an electrode of a novel photovoltaic device as Ag deposition under light illumination, in which the wavelength of incident light is longer than the long-wavelength cutoff of the materials composing the device. Naruse et al. introduced a stochastic cellular automaton model to simulate underlying nonequilibrium processes which are necessary to formulate unique granular Ag film in this deposition process. In the present paper, we generalize their model and clarify the essential role of optical near-fields generated on the electrode surface. We introduce a parameter $b$ indicating the incident light power per site and a function representing the resonance effect of optical near-fields depending on the Ag-cluster size on the surface. Numerical simulation shows a transition from a trivial particle-deposition state to a nontrivial self-controlled particle-deposition state at a critical value $b_{\rm c}$, and only in the latter state optical near-fields are effectively generated. The properties of transition in this mesoscopic surface model in nonequilibrium are studied by the analogy of equilibrium phase transitions associated with critical phenomena, and the criteria of transition are reported.

Early warning signals of desertification transitions in semiarid ecosystems.

The identification of early warning signals for regime shifts in ecosystems is of crucial importance given their impact in terms of economic and social effects. We present here the results of a theoretical study on the desertification transition in semiarid ecosystems under external stress. We performed numerical simulations based on a stochastic cellular automaton model, and we studied the dynamics of the vegetation clusters in terms of percolation theory, assumed as an effective tool for analyzing the geometrical properties of the clusters. Focusing on the role played by the strength of external stresses, measured by the mortality rate m, we followed the progressive degradation of the ecosystem for increasing m, identifying different stages: first, the fragmentation transition occurring at relatively low values of m, then the desertification transition at higher mortality rates, and finally the full desertification transition corresponding to the extinction of the vegetation and the almost complete degradation of the soil, attained at the maximum value of m. For each transition we calculated the spanning probabilities as functions of m and the percolation thresholds according to different spanning criteria. The identification of the different thresholds is proposed as an useful tool for monitoring the increasing degradation of real-world finite-size systems. Moreover, we studied the time fluctuations of the sizes of the biggest clusters of vegetated and nonvegetated cells over the entire range of mortality values. The change of sign in the skewness of the size distributions, occurring at the fragmentation threshold for the biggest vegetation cluster and at the desertification threshold for the nonvegetated cluster, offers new early warning signals for desertification. Other new and robust indicators are given by the maxima of the root-mean-square deviation of the distributions, which are attained respectively inside the fragmentation interval, for the vegetated biggest cluster, and inside the desertification interval, for the nonvegetated cluster.

The Study of Traffic Rules Based on Cellular Automata Traffic Wave Model

The traffic control problem is a hot issue in recent years. We investigate the effectiveness of three traffic rules in assuring safety and improve traffic flow. We utilize a cellular automata method of traffic flow to investigate and simulate the vehicle performance and use a linear weighting approach to weigh safety and traffic flow comprehensively. We establish overtaking models of a two-lane freeway on the basis of the stochastic traffic cellular automaton (STCA) model. Using the cellular automata method, we simulate the relationships between the traffic flows, the average vehicle velocity, and the vehicle density. We propose two new traffic rules, which in the premise of ensuring safety and improve traffic flow.

Derivation of a stochastic cellular automaton model for the dynamics of bistable units with global and asymmetric local interactions

Derivation of a stochastic cellular automaton model for the dynamics of bistable units with global and asymmetric local interactions

A simple stochastic cellular automaton for synchronized traffic flow

We present a very simple stochastic traffic cellular automaton (CA) model to reproduce synchronized traffic. This model aims to be nearly as simple as the well-known Nagel–Schreckenberg model, but to overcome to shortcomings of the latter: The Nagel–Schreckenberg model (NaSch) and its variants achieve collision-free driving by explicitly allowing for unlimited braking capabilities. However, it is rather natural to view the collision-free traffic flow as a consequence of moderate driving instead of infinite braking capabilities. Therefore, our new CA model limits the vehicles’ acceleration and deceleration rates to realistic values. Moreover, our model is able to reproduce several important features of synchronized traffic flow.Earlier models achieve identical goals only by using relatively complicated rules of motion. Our model, however, introduces slight modifications of the easily comprehensible NaSch. These modifications lead to very stable states where all vehicles tend to synchronize their speed. Even though, or perhaps precisely because, the states of synchronized flow are stable in our model, it allows to study several features of this traffic phase in great detail.

Traffic disruption and recovery in road networks

We study the impact of disruptions on road networks, and the recovery process after the disruption is removed from the system. Such disruptions could be caused by vehicle breakdown or illegal parking. We analyze the transient behavior using domain wall theory, and compare these predictions with simulations of a stochastic cellular automaton model. We find that the domain wall model can reproduce the time evolution of flow and density during the disruption and the recovery processes, for both one-dimensional systems and two-dimensional networks.

A comparative study of Macroscopic Fundamental Diagrams of arterial road networks governed by adaptive traffic signal systems

Using a stochastic cellular automaton model for urban traffic flow, we study and compare Macroscopic Fundamental Diagrams (MFDs) of arterial road networks governed by different types of adaptive traffic signal systems, under various boundary conditions. In particular, we simulate realistic signal systems that include signal linking and adaptive cycle times, and compare their performance against a highly adaptive system of self-organizing traffic signals which is designed to uniformly distribute the network density. We find that for networks with time-independent boundary conditions, well-defined stationary MFDs are observed, whose shape depends on the particular signal system used, and also on the level of heterogeneity in the system. We find that the spatial heterogeneity of both density and flow provide important indicators of network performance. We also study networks with time-dependent boundary conditions, containing morning and afternoon peaks. In this case, intricate hysteresis loops are observed in the MFDs which are strongly correlated with the density heterogeneity. Our results show that the MFD of the self-organizing traffic signals lies above the MFD for the realistic systems, suggesting that by adaptively homogenizing the network density, overall better performance and higher capacity can be achieved.

Modeling urban land use conversion of Daqing City, China: a comparative analysis of “top-down” and “bottom-up” approaches

During the past decades, Daqing City, China has experienced unprecedented urban expansion due to the rapid development of petroleum industry. With rapid urbanization and lack of strategic planning, Daqing is facing many socio-economic and environmental problems, and it is essential to examine the process of urbanization, and to develop policy recommendations for sustainable development. To address this problem, this paper examined the urbanization process of Daqing City through developing two multi-level models: an integrated system dynamic (SD) and CLUE-S model (SD-CLUES), and an integrated SD and stochastic cellular automata model (SD-CA). Analysis of results suggests that these two models generate significantly different results. With the SD-CLUES model, new urban developments are clustered in the downtown area or along major transportation networks, indicating exogenous driving forces playing an important role in shaping urban spatial dynamics. With the SD-CA model, on the contrary, the resultant new urban cells are spread over the entire study area, and associated with existing urban areas. Further, visual comparisons and validations indicate that the SD-CA model is a better alternative in explaining the urbanization mechanism of Daqing City. In addition, analysis of results suggests that the stochastic factor in the CA model has significant impact on the modeling accuracy.

THE DYNAMICAL MODELS OF ACTIVATED SLUDGE SYSTEM: STOCHASTIC CELLULAR AUTOMATON AND DIFFERENTIAL EQUATIONS

A stochastic cellular automaton (CA) model for activated sludge system (ASS) is formulated by a series of transition functions upon realistic treatment processes, and it is tested by comparing with ordinary differential equations (ODEs) of ASS. CA system performed by empirical parameters can reflect the characteristics of fluctuation, complexity and strong non-linearity of ASS. The results show that the predictions of CA are approximately similar to the dynamical behaviors of ODEs. Based on the extreme experimental system with complete cell recycle in model validation, the dynamics of biomass and substrate are predicted accurately by CA, but the large errors exist in ODEs except for integrating more spatially complicated factors. This is due to that the strong mechanical stress from spatial crowding effect is ignored in ODEs, while CA system as a spatially explicit model takes account of local interactions. Despite its extremely simple structure, CA still can capture the essence of ASS better than ODEs, thus it would be very useful in predicting long-term dynamics in other similar systems.

Using Cellular Automata to study the effect of competition for epidemic diseases

Abstract Cellular Automata (CA) has shown to be a valuable approach in ecological modeling, in particular when dealing with local interactions between species and their environment. A stochastic cellular automata model, which included two competitors (the inferior species which is immune to a disease and the superior one which is sensitive to the disease), is constructed. Through time series analysis and spatial pattern analysis, the influence of competition effect upon the behavior of epidemic diseases has been investigated to know whether the competition effect is in favor of epidemics control. Then, some strategies for introducing competitors to the infectious system are explored. The result shows that introducing some right competitors into the infection region may be a considerable policy. The population with high colonization rate, low extinction rate and long colonization radius is introduced preferably. The result may give us some suggestions for epidemic control in conservation of wild populations.

A CARBON-CYCLE-BASED STOCHASTIC CELLULAR AUTOMATA CLIMATE MODEL

In this paper a stochastic cellular automata model is examined, which has been developed to study a "small" world, where local changes may noticeably alter global characteristics. This is applied to a climate model, where global temperature is determined by an interplay between atmospheric carbon dioxide and carbon stored by plant life. The latter can be released by forest fires, giving rise to significant changes of global conditions within short time.

Stochastic cellular automata model and Monte Carlo simulations of CD4 + T cell dynamics with a proposed alternative leukapheresis treatment for HIV/AIDS

Acquired Immunodeficiency Syndrome (AIDS) is responsible for millions of deaths worldwide. To date, many drug treatment regimens have been applied to AIDS patients but none has resulted in a successful cure. This is mainly due to the fact that free HIV particles are frequently in mutation, and infected CD4 + T cells normally reside in the lymphoid tissue where they cannot (so far) be eradicated. We present a stochastic cellular automaton (CA) model to computationally study what could be an alternative treatment, namely Leukapheresis (LCAP), to remove HIV infected leukocytes in the lymphoid tissue. We base our investigations on Monte Carlo computer simulations. Our major objective is to investigate how the number of infected CD4 + T cells changes in response to LCAP during the short-time (weeks) and long-time (years) scales of HIV/AIDS progression in an infected individual. To achieve our goal, we analyze the time evolution of the CD4 + T cell population in the lymphoid tissue (i.e., the lymph node) for HIV dynamics in treatment situations with various starting times and frequencies and under a no treatment condition. Our findings suggest that the effectiveness of the treatment depends mainly on the treatment starting time and the frequency of the LCAP. Other factors (e.g., the removal proportion, the treatment duration, and the state of removed cells) that likely influence disease progression are subjects for further investigation.

A Bayesian MCMC approach to reconstruct spatial vegetation dynamics from sparse vegetation maps

In studies of vegetation dynamics, data points describing the changes are often sparse, because changes were not recognized in early stages or investigations were part of different projects. The snapshots at hand often leave the nature of the dynamics unrevealed and only give a rough estimation of the directions of changes. Extrapolation of the dynamics with traditional cellular automaton modeling is also complicated in such cases, because rules often cannot be deduced from field data for each interaction. We developed a Bayesian MCMC method, using a discrete time stochastic cellular automaton model to reconstruct vegetation dynamics between vegetation maps available and provide estimation of vegetation pattern in years not surveyed. Spread capability of each vegetation type was characterized by a lateral spread parameter and another for establishment from species pool. The method was applied to a series of three vegetation maps depicting vegetation change at a grassland site following abandonment of grazing in north-eastern Hungary. The Markov chain explored the missing data space (missing maps) as well as the parameter space. Transitions by lateral expansion had a greater importance than the appearance of new vegetation types without spatial constraints at our site. We estimated the trajectory of change for each vegetation type, which bore a considerable non-linear element in most cases. To our best knowledge, this is the first work that tries to estimate vegetation transition parameters in a stochastic cellular automaton based on field measurements and provides a tool to reconstruct past dynamics from observed pattern.

Two-lane traffic-flow model with an exact steady-state solution

We propose a stochastic cellular-automaton model for two-lane traffic flow based on the misanthrope process in one dimension. The misanthrope process is a stochastic process allowing for an exact steady-state solution; hence, we have an exact flow-density diagram for two-lane traffic. In addition, we introduce two parameters that indicate, respectively, driver's driving-lane preference and passing-lane priority. Due to the additional parameters, the model shows a deviation of the density ratio for driving-lane use and a biased lane efficiency in flow. Then, a mean-field approach explicitly describes the asymmetric flow by the hop rates, the driving-lane preference, and the passing-lane priority. Meanwhile, the simulation results are in good agreement with an observational data, and we thus estimate these parameters. We conclude that the proposed model successfully produces two-lane traffic flow particularly with the driving-lane preference and the passing-lane priority.