Stochastic Cellular Automaton Model Research Articles

A SCALING LAW RELATING THE RATE OF DESTRUCTION OF A SOLID TUMOR AND THE FRACTAL DIMENSION OF ITS BOUNDARY

In this paper, we investigate the scaling law relating the size of the boundary of a solid tumor and the rate at which it is lysed by a cell population of non-infiltrating cytotoxic lymphocytes. We do it in the context of enzyme kinetics through geometrical, analytical and numerical arguments. Following the Koch island fractal model, a scale-dependent function that describes the constant rate of the decay process and the fractal dimension is obtained. Then, in silico experiments are accomplished by means of a stochastic hybrid cellular automaton model. This model is used to grow several tumors with varying morphology and to test the power decay law when the cell-mediated immune response is effective, confirming its validity.

Stochastic cellular automaton model of culture formation.

We introduce a stochastic cellular automaton as a model for culture and border formation. The model can be conceptualized as a game where the expansion rate of cultures is quantified in terms of their area and perimeter in such a way that approximately geometrically round cultures get a competitive advantage. We first analyze the model with periodic boundary conditions, where we study how the model can end up in a fixed state, i.e., freezes. Then we implement the model on the European geography with mountains and rivers. We see how the model reproduces some qualitative features of European culture formation, namely, that rivers and mountains are more frequently borders between cultures, mountainous regions tend to have higher cultural diversity, and the central European plain has less clear cultural borders.

A stochastic cellular automaton model to describe the evolution of the snow-covered area across a high-elevation mountain catchment.

Variations in the extent and duration of snow cover impinge on surface albedo and snowmelt rate, influencing the energy and water budgets. Monitoring snow coverage is therefore crucial for both optimising the supply of snowpack-derived water and understanding how climate change could impact on this source, vital for sustaining human activities and the natural environment during the dry season. Mountainous sites can be characterised by complex morphologies, cloud cover and forests that can introduce errors into the estimates of snow cover obtained from remote sensing. Consequently, there is a need to develop simulation models capable of predicting how snow coverage evolves across a season. Cellular Automata models have previously been used to simulate snowmelt dynamics, but at a coarser scale that limits insight into the precise factors driving snowmelt at different stages. To address this information gap, we formulate a novel, fine-scale stochastic Cellular Automaton model that describes snow coverage across a high-elevation catchment. Exploiting its refinement, the model is used to explore the interplay between three factors proposed to play a critical role: terrain elevation, sun incidence angle, and the extent of nearby snow. We calibrate the model via a randomised parameter search, fitting simulation data against snow cover masks estimated from Sentinel-2 satellite images. Our analysis shows that.

Cellular-automaton model for tumor growth dynamics: Virtualization of different scenarios

Mathematical Oncology has emerged as a research field that applies either continuous or discrete models to mathematically describe cancer-related phenomena. Such methods are usually expressed in terms of differential equations, however tumor composition involves specific cellular structure and can demonstrate probabilistic nature, often requiring tailor-made approaches. In this context, cell-based models allow monitoring independent single parameters, which might vary in both time and space. By relying on extant tumor growth models in the literature, this study introduces cellular-automata simulation strategies that admit heterogeneous cell population while capturing both single-cell and cluster-cell behaviors. In this agent-based computational model, tumor cells are limited to follow four possible courses of action, namely: proliferation, migration, apoptosis or quiescence. Despite the apparent simplicity of those actions, the model can represent different complex tumor features depending on parameter settings. This study virtualized five different scenarios, showcasing model capabilities of representing tumor dynamics including alternate dormancy periods, cell death instability and cluster formation. Implementation techniques are also explored together with prospective model expansion towards deterministic features. The proposed stochastic cellular automaton model is able to effectively simulate different scenarios regarding tumor growth effectively, figuring as an interesting tool for in silico modeling, with promising capabilities of expansion to support research in mathematical oncology, thus improving diagnosis tools and/or personalized treatment.

Microclimate feedbacks sustain power law clustering of encroaching coastal woody vegetation

The spatial pattern of vegetation patchiness may follow universal characteristic rules when the system is close to critical transitions between alternative states, which improves the anticipation of ecosystem-level state changes which are currently difficult to detect in real systems. However, the spatial patterning of vegetation patches in temperature-driven ecosystems have not been investigated yet. Here, using high-resolution imagery from 1972 to 2013 and a stochastic cellular automata model, we show that in a North American coastal ecosystem where woody plant encroachment has been happening, the size distribution of woody patches follows a power law when the system approaches a critical transition, which is sustained by the local positive feedbacks between vegetation and the surrounding microclimate. Therefore, the observed power law distribution of woody vegetation patchiness may be suggestive of critical transitions associated with temperature-driven woody plant encroachment in coastal and potentially other ecosystems.

Impact of rainfall on the transmission of leptospirosis in Si Sa Ket, Thailand

Leptospirosis is a zoonotic disease found worldwide, but especially in tropical and sub-tropical countries. In Thailand during the rainy season, agricultural and livestock workers are the main occupational risk groups, who are likely to be in contact with contaminated environments. In this study, we aim to examine the impact of rainfall on the transmission of leptospirosis using a stochastic cellular automata model in Si Sa Ket, Thailand, which had the highest number of reported cases from 2014 to 2018. Two bi-dimensional square lattices are created to represent human and contaminated environmental lattices. The reported cases are used to fit in the simulation results by varying transmission probability. The transmission probability depends on sinusoidal function and the rainfall index, the results of which are compared. This study highlighted the way that seasonal rainfall contributed to the transmission dynamics of leptospirosis. The total epidemic size, which is the sum of the overtime cases, was investigated to find the critical transmission probability from the endemic to the epidemic state. Further study of other factors such as flooding and temperature, should be investigated for a better understanding of how the transmission of leptospirosis affects the environment.

Car accident in synchronized traffic flow: A stochastic cellular automaton model

In this paper, we study the probability of car accidents in the modified Nagel–Schreckenberg (mNaSch) under the periodic boundary condition. In order to understand the quality of interaction between vehicles in each phase of the mNaSch, the velocity correlation coefficients were investigated. The effect of the evacuation of damaged vehicles was also studied. The fundamental diagram of the system is constructed in both cases with and without the evacuation. We found that the synchronized phases in the mNaSch are manifested into two aspects. In the first phase, the velocity correlation coefficients are zero where all vehicles move at the same speed. Hence, in the other phase, the speed of vehicles shows a synchronization as the form of clusters of moving vehicles where two speeds predominate simultaneously and the velocity correlation coefficients are higher. In addition, the car accidents in the modified mNaSch depend strongly on the initial configuration especially, if we consider those car accidents really happening in the system. The evacuation of damaged vehicles enhances the traffic situation and qualitatively changes the traffic phases in the mNaSch.

Diffusion of Innovations in Middle Eastern versus Western Markets: A Mathematical Computation Cellular Automata Simulation Model

Simulation modelling has gained ground over the years since it can provide various scenarios applied to any scientific area. In this study, a stochastic cellular automata model is proposed, in which agents fall into three distinct categories (adopters, non-adopters and denials). Based on Hofstede’s cultural dimension individualism, we characterize three major international markets, as perfectly clustered (collective) to perfectly random (individualistic). We investigate innovation diffusion speed, in each network topology. At each time step, the decision of non-adopters to purchase innovative products, is affected by their immediate neighborhood (von Neumman). The speed of diffusion is evaluated using time at which sales reach 50% of market. Effects of simulation parameters on speed of diffusion, are assessed using a log-normal accelerated failure time model. Results demonstrate that diffusion of innovative products accelerates when innovators of a virtual economic system are placed according to a random network and when amount of innovators and imitators in the economic system increases. Slower innovative products’ diffusion process is a result of a large amount of denials and of how imitators are placed in the in the virtual economic system. Diffusion in small-world virtual economic systems lead to small time inflexion points very close to those of a random networked market.

PROPAGATOR: An Operational Cellular-Automata Based Wildfire Simulator

PROPAGATOR is a stochastic cellular automaton model for forest fire spread simulation, conceived as a rapid method for fire risk assessment. The model uses high-resolution information such as topography and vegetation cover considering different types of vegetation. Input parameters are wind speed and direction and the ignition point. Dead fine fuel moisture content and firebreaks—fire fighting strategies can also be considered. The fire spread probability depends on vegetation type, slope, wind direction and speed, and fuel moisture content. The fire-propagation speed is determined through the adoption of a Rate of Spread model. PROPAGATOR simulates independent realizations of one stochastic fire propagation process, and at each time-step gives as output a map representing the probability of each cell of the domain to be affected by the fire. These probabilities are obtained computing the relative frequency of ignition of each cell. The model capabilities are assessed by reproducing a set of past Mediterranean fires occurred in different countries (Italy and Spain), using when available the real fire fighting patterns. PROPAGATOR simulated such scenarios with affordable computational resources and with short CPU-times. The outputs show a good agreement with the real burned areas, demonstrating that the PROPAGATOR can be useful for supporting decisions in Civil Protection and fire management activities.

Assessing the impact of HIV treatment interruptions using stochastic cellular Automata

Chronic HIV infection causes a progressive decrease in the ability to maintain homeostasis resulting, after some time, in eventual break down of immune functions. Recent clinical research has shed light on a significant contribution of the lymphatic tissues, where HIV causes accumulation of collagen, (fibrosis). Specifically, where tissue is populated by certain types of functional stromal cells designated Fibroblastic Reticular Cells (FRCs), these have been found to play a crucial role in balancing out apoptosis and regeneration of naïve T-cells through 2-way cellular signaling. Tissue fibrosis not only impedes this signaling, effectively reducing T-cell levels through increased apoptosis of cells of both T- and FRC type but has been found to be irreversible by current HIV standard treatment (cART). While the therapy aims to block the viral lifecycle, cART-associated increase of T-cell levels in blood appears to conceal existing FRC impairment through fibrosis. This hidden impairment can lead to adverse consequences if treatment is interrupted, e.g. due to poor adherence (missing doses) or through periods recovering from drug toxicities. Formal clinical studies on treatment interruption have indicated possible adverse effects, but quantification of those effects in relation to interruption protocol and patient predisposition remains unclear. Accordingly, the impact of treatment interruption on lymphatic tissue structure and T-cell levels is explored here by means of computer simulation. A novel Stochastic Cellular Automata model is proposed, which utilizes all sources of clinical detail available to us (though sparse in part) for model parametrization. Sources are explicitly referenced and conflicting evidence from previous studies explored. The main focus is on (i) spatial aspects of collagen build up, together with (ii) collagen increase after repeated treatment interruptions to explore the dynamics of HIV-induced fibrosis and T-cell loss.

ESTUDIO COMPARATIVO DE ALGORITMOS DE OPTIMIZACIÓN CON OBJETIVOS MÚLTIPLES PARA UN MODELO DE AUTÓMATA CELULAR

Cellular Automata (CA) models can represent dynamic systems which are discrete in space and time that reflects the effect of intrinsic parameters where individual events are considered to occur from randomness. A CA model of two agents' chemical kinetics has been optimized earlier using NSGA-II based on Evolutionary Algorithm (EA). But the stochastic nature of the CA model along with its high sensitivity on the model parameters requires extensive investigation using different optimization algorithms. For this purpose, in the current study, four more recently developed and popular optimization algorithms based on EA, called NSGA-IIr, NSGA-IIa, AbYSS and MOEA/D, have been considered for investigation based on various performance measuring parameters. The study also compares the performances of the algorithms for different computational efforts with an objective to minimize the required number of objective function evaluations. Simulation results and Friedman rank statistical test show NSGA-IIa and NSGA-IIr as the best choices to optimize the CA stochastic model across any number of objective function evaluations. Though the choice of optimization algorithm does not change with function evaluations, higher function evaluations improve the pseudo-pareto front for the CA optimization problem. Such results will facilitate the use of stochastic CA models to represent complex (bio)-chemical networks.

Spatially constrained tumour growth affects the patterns of clonal selection and neutral drift in cancer genomic data.

Quantification of the effect of spatial tumour sampling on the patterns of mutations detected in next-generation sequencing data is largely lacking. Here we use a spatial stochastic cellular automaton model of tumour growth that accounts for somatic mutations, selection, drift and spatial constraints, to simulate multi-region sequencing data derived from spatial sampling of a neoplasm. We show that the spatial structure of a solid cancer has a major impact on the detection of clonal selection and genetic drift from both bulk and single-cell sequencing data. Our results indicate that spatial constrains can introduce significant sampling biases when performing multi-region bulk sampling and that such bias becomes a major confounding factor for the measurement of the evolutionary dynamics of human tumours. We also propose a statistical inference framework that incorporates spatial effects within a growing tumour and so represents a further step forwards in the inference of evolutionary dynamics from genomic data. Our analysis shows that measuring cancer evolution using next-generation sequencing while accounting for the numerous confounding factors remains challenging. However, mechanistic model-based approaches have the potential to capture the sources of noise and better interpret the data.

Abstract 4232: Spatially constrained tumor growth affects the patterns of clonal selection and neutral drift in cancer genomic data

Abstract Quantification of the effect of spatial tumor sampling on the patterns of mutations detected in next-generation sequencing data is largely lacking. Here we use a spatial stochastic cellular automaton model of tumor growth that accounts for somatic mutations, selection, drift and spatial constrains, to simulate multi-region sequencing data derived from spatial sampling of a neoplasm. We show that the spatial structure of a solid cancer has a major impact on the detection of clonal selection and genetic drift from bulk sequencing data and single-cell sequencing data. Our results indicate that spatial constrains can introduce significant sampling biases when performing multi- region bulk sampling and that such bias becomes a major confounding factor for the measurement of the evolutionary dynamics of human tumors. We present a statistical inference framework that takes into account the spatial effects of a growing tumor and allows inferring the evolutionary dynamics from patient genomic data. Our analysis shows that measuring cancer evolution using next-generation sequencing while accounting for the numerous confounding factors requires a mechanistic model-based approach that captures the sources of noise in the data. Citation Format: Kate Chkhaidze, Timon Heide, Benjamin Werner, Marc J. Williams, Weini Huang, Giulio Caravagna, Ann-Marie Baker, Trevor A. Graham, Andrea Sottoriva. Spatially constrained tumor growth affects the patterns of clonal selection and neutral drift in cancer genomic data [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 4232.

Modeling the effect of visibility on upstairs crowd evacuation by a stochastic FFCA model with finer discretization

In recent years, deep underground buildings appear more often than ever, and stairs are the main facilities for the upward evacuation of crowds from these buildings. As one of the most essential factors, the visibility might play a dominant role in the upward evacuation on stairs. To ensure the safety of the crowd in underground spaces, a finer discrete and stochastic floor field cellular automaton (FFCA) model integrating the visibility influence is established for the simulation of the crowd upward evacuation from a 21-storey staircase. By comparison, the simulation fits well with the observation and experiment, which implies that the model captures the main features of upward evacuations on stairs. Then, from the predicted results, it is found that the visibility reduction has a significant negative impact on the temporal–spatial distribution of pedestrians, especially on the inflow and outflow, while the entrance flow rate shows little impact as long as it is higher than 1.0 ped⋅m−1⋅s−1.

A lattice grain model of hillslope evolution

Abstract. This paper describes and explores a new continuous-time stochastic cellular automaton model of hillslope evolution. The Grain Hill model provides a computational framework with which to study slope forms that arise from stochastic disturbance and rock weathering events. The model operates on a hexagonal lattice, with cell states representing fluid, rock, and grain aggregates that are either stationary or in a state of motion in one of the six cardinal lattice directions. Cells representing near-surface soil material undergo stochastic disturbance events, in which initially stationary material is put into motion. Net downslope transport emerges from the greater likelihood for disturbed material to move downhill than to move uphill. Cells representing rock undergo stochastic weathering events in which the rock is converted into regolith. The model can reproduce a range of common slope forms, from fully soil mantled to rocky or partially mantled, and from convex-upward to planar shapes. An optional additional state represents large blocks that cannot be displaced upward by disturbance events. With the addition of this state, the model captures the morphology of hogbacks, scarps, and similar features. In its simplest form, the model has only three process parameters, which represent disturbance frequency, characteristic disturbance depth, and base-level lowering rate, respectively. Incorporating physical weathering of rock adds one additional parameter, representing the characteristic rock weathering rate. These parameters are not arbitrary but rather have a direct link with corresponding parameters in continuum theory. Comparison between observed and modeled slope forms demonstrates that the model can reproduce both the shape and scale of real hillslope profiles. Model experiments highlight the importance of regolith cover fraction in governing both the downslope mass transport rate and the rate of physical weathering. Equilibrium rocky hillslope profiles are possible even when the rate of base-level lowering exceeds the nominal bare-rock weathering rate, because increases in both slope gradient and roughness can allow for rock weathering rates that are greater than the flat-surface maximum. Examples of transient relaxation of steep, rocky slopes predict the formation of a regolith-mantled pediment that migrates headward through time while maintaining a sharp slope break.

Dynamics of dengue disease with human and vector mobility

Dengue is a vector borne disease transmitted to humans by Aedes aegypti mosquitoes carrying virus of different serotypes. Dengue exhibits complex spatial and temporal dynamics, influenced by various biological, human and environmental factors. In this work, we study the dengue spread for a single serotype (DENV-1) including statistical models of human mobility with exponential step length distribution, by using reaction–diffusion equations and Stochastic Cellular Automata (SCA) approach. We analyze the spatial and temporal spreading of the disease using parameters from field studies. We choose mosquito density data from Ahmedabad city as a proxy for climate data in our SCA model. We find an interesting result that although human mobility makes the infection spread faster, there is an apparent early suppression of the epidemic compared to immobile humans. The disease extinction time is lesser when human mobility is included.

Calibration and validation of cellular automaton traffic flow model with empirical and experimental data

For traffic flow models, calibration and validation are essential. Cellular automaton (CA) models are a special class of models, describing the movement of vehicles in discretised space and time. However, the previous work on calibration and validation does not discuss CA models systematically. This study calibrates and validates a stochastic CA model. The authors use a simple CA model, which only has two important parameters to be calibrated. The methodology for optimisation is to minimise the relative root mean square error between two properties: the averaged velocity and the variation of velocities in a platoon at a given density. Three different sites are used as cases to show the methodology, for which different types of data (video trajectories or GPS data) are available. The authors find that the best model parameters vary for the different locations. This may result from various driving strategies and potential tendencies. Thus, it is concluded that for CA models, various traffic flow phenomena need to be simulated by various parameters.

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.