An extinction-survival-type phase transition in the probabilistic cellular automaton p182-q200

We investigate the critical behaviour of a probabilistic mixture of cellular automata (CA) rules 182 and 200 (in Wolfram`s enumeration scheme) by mean-field analysis and Monte Carlo simulations. We found that as we switch off one CA and switch on the other by the variation of the single parameter of the model, the probabilistic CA (PCA) goes through an extinction-survival-type phase transition, and the numerical data indicate that it belongs to the directed percolation universality class of critical behaviour. The PCA displays a characteristic stationary density profile and a slow, diffusive dynamics close to the pure CA 200 point that we discuss briefly. Remarks on an interesting related stochastic lattice gas are addressed in the conclusions.

Cellular automaton model for molecular traffic jams

We consider the time evolution of an exactly solvable cellular automaton with random initial conditions both in the large-scale hydrodynamic limit and on the microscopic level. This model is a version of the totally asymmetric simple exclusion process with sublattice parallel update and thus may serve as a model for studying traffic jams in systems of self-driven particles. We study the emergence of shocks from the microscopic dynamics of the model. In particular, we introduce shock measures whose time evolution we can compute explicitly, both in the thermodynamic limit and for open boundaries where a boundary-induced phase transition driven by the motion of a shock occurs. The motion of the shock, which results from the collective dynamics of the exclusion particles, is a random walk with an internal degree of freedom that determines the jump direction. This type of hopping dynamics is reminiscent of some transport phenomena in biological systems.

A Cellular Automaton Approach to Spatial Electric Load Forecasting

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Accelerating precursory activity within a class of earthquake analogue automata

A statistical fractal automaton model is described which displays two modes of dynamical behaviour. The first mode, termed recurrent criticality, is characterised by quasi-periodic, characteristic events that are preceded by accelerating precursory activity. The second mode is more reminiscent of SOC automata in which large events are not preceded by an acceleration in activity. Extending upon previous studies of statistical fractal automata, a redistribution law is introduced which incorporates two model parameters: a dissipation factor and a stress transfer ratio. Results from a parameter space investigation indicate that a straight line through parameter space marks a transition from recurrent criticality to unpredictable dynamics. Recurrent criticality only occurs for models within one corner of the parameter space. The location of the transition displays a simple dependence upon the fractal correlation dimension of the cell strength distribution. Analysis of stress field evolution indicates that recurrent criticality occurs in models with significant long-range stress correlations. A constant rate of activity is associated with a decorrelated stress field.

Recurrence interval statistics of cellular automaton seismicity models

The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.

The Effect of Spatial Scale on Predicting Time Series: A Study on Epidemiological System Identification

A susceptible-infective-recovered (SIR) epidemiological model based on probabilistic cellular automaton (PCA) is employed for simulating the temporal evolution of the registered cases of chickenpox in Arizona, USA, between 1994 and 2004. At each time step, every individual is in one of the states S, I, or R. The parameters of this model are the probabilities of each individual (each cell forming the PCA lattice ) passing from a state to another state. Here, the values of these probabilities are identified by using a genetic algorithm. If nonrealistic values are allowed to the parameters, the predictions present better agreement with the historical series than if they are forced to present realistic values. A discussion about how the size of the PCA lattice affects the quality of the model predictions is presented. Copyright (C) 2009 L. H. A. Monteiro et al.

System Identification and Prediction of Dengue Fever Incidence in Rio de Janeiro

Identification, prediction, and control of a system are engineering subjects, regardless of the nature of the system. Here, the temporal evolution of the number of individuals with dengue fever weekly recorded in the city of Rio de Janeiro, Brazil, during 2007, is used to identify SIS (susceptible-infective-susceptible) and SIR (susceptible-infective-removed) models formulated in terms of cellular automaton (CA). In the identification process, a genetic algorithm (GA) is utilized to find the probabilities of the state transition S -> I able of reproducing in the CA lattice the historical series of 2007. These probabilities depend on the number of infective neighbors. Time-varying and non-time-varying probabilities, three different sizes of lattices, and two kinds of coupling topology among the cells are taken into consideration. Then, these epidemiological models built by combining CA and GA are employed for predicting the cases of sick persons in 2008. Such models can be useful for forecasting and controlling the spreading of this infectious disease.

A vaccination game based on public health actions and personal decisions

Susceptible-infective-removed (SIR) models are commonly used for representing the spread of contagious diseases. A SIR model can be described in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. Here, this framework is employed for investigating the consequences of applying vaccine against the propagation of a contagious infection, by considering vaccination as a game, in the sense of game theory. In this game, the players are the government and the susceptible newborns. In order to maximize their own payoffs, the government attempts to reduce the costs for combating the epidemic, and the newborns may be vaccinated only when infective individuals are found in their neighborhoods and/or the government promotes an immunization program. As a consequence of these strategies supported by cost-benefit analysis and perceived risk, numerical simulations show that the disease is not fully eliminated and the government implements quasi-periodic vaccination campaigns. (C) 2011 Elsevier B.V. All rights reserved.

Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases

There are several ways of controlling the propagation of a contagious disease. For instance, to reduce the spreading of an airborne infection, individuals can be encouraged to remain in their homes and/or to wear face masks outside their domiciles. However, when a limited amount of masks is available, who should use them: the susceptible subjects, the infective persons or both populations? Here we employ susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations and probabilistic cellular automata in order to investigate how the deletion of links in the random complex network representing the social contacts among individuals affects the dynamics of a contagious disease. The inspiration for this study comes from recent discussions about the impact of measures usually recommended by health public organizations for preventing the propagation of the swine influenza A (H1N1) virus. Our answer to this question can be valid for other eco-epidemiological systems. (C) 2010 Elsevier BM. All rights reserved.

Monitoring growth in rapidly urbanizing areas using remotely sensed data

Urbanization and the ability to manage for a sustainable future present numerous challenges for geographers and planners in metropolitan regions. Remotely sensed data are inherently suited to provide information on urban land cover characteristics, and their change over time, at various spatial and temporal scales. Data models for establishing the range of urban land cover types and their biophysical composition (vegetation, soil, and impervious surfaces) are integrated to provide a hierarchical approach to classifying land cover within urban environments. These data also provide an essential component for current simulation models of urban growth patterns, as both calibration and validation data. The first stages of the approach have been applied to examine urban growth between 1988 and 1995 for a rapidly developing area in southeast Queensland, Australia. Landsat Thematic Mapper image data provided accurate (83% adjusted overall accuracy) classification of broad land cover types and their change over time. The combination of commonly available remotely sensed data, image processing methods, and emerging urban growth models highlights an important application for current and next generation moderate spatial resolution image data in studies of urban environments.

A 2D numerical model for simulating the physics of fault systems

Simulations provide a powerful means to help gain the understanding of crustal fault system physics required to progress towards the goal of earthquake forecasting. Cellular Automata are efficient enough to probe system dynamics but their simplifications render interpretations questionable. In contrast, sophisticated elasto-dynamic models yield more convincing results but are too computationally demanding to explore phase space. To help bridge this gap, we develop a simple 2D elastodynamic model of parallel fault systems. The model is discretised onto a triangular lattice and faults are specified as split nodes along horizontal rows in the lattice. A simple numerical approach is presented for calculating the forces at medium and split nodes such that general nonlinear frictional constitutive relations can be modeled along faults. Single and multi-fault simulation examples are presented using a nonlinear frictional relation that is slip and slip-rate dependent in order to illustrate the model.

MapScript: A map algebra programming language incorporating neighborhood analysis

Map algebra is a data model and simple functional notation to study the distribution and patterns of spatial phenomena. It uses a uniform representation of space as discrete grids, which are organized into layers. This paper discusses extensions to map algebra to handle neighborhood operations with a new data type called a template. Templates provide general windowing operations on grids to enable spatial models for cellular automata, mathematical morphology, and local spatial statistics. A programming language for map algebra that incorporates templates and special processing constructs is described. The programming language is called MapScript. Example program scripts are presented to perform diverse and interesting neighborhood analysis for descriptive, model-based and processed-based analysis.

An atomistic simulation of solid state sintering using Monte Carlo methods

This paper presents results on the simulation of the solid state sintering of copper wires using Monte Carlo techniques based on elements of lattice theory and cellular automata. The initial structure is superimposed onto a triangular, two-dimensional lattice, where each lattice site corresponds to either an atom or vacancy. The number of vacancies varies with the simulation temperature, while a cluster of vacancies is a pore. To simulate sintering, lattice sites are picked at random and reoriented in terms of an atomistic model governing mass transport. The probability that an atom has sufficient energy to jump to a vacant lattice site is related to the jump frequency, and hence the diffusion coefficient, while the probability that an atomic jump will be accepted is related to the change in energy of the system as a result of the jump, as determined by the change in the number of nearest neighbours. The jump frequency is also used to relate model time, measured in Monte Carlo Steps, to the actual sintering time. The model incorporates bulk, grain boundary and surface diffusion terms and includes vacancy annihilation on the grain boundaries. The predictions of the model were found to be consistent with experimental data, both in terms of the microstructural evolution and in terms of the sintering time. (C) 2002 Elsevier Science B.V. All rights reserved.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.