Cellular automata-based spatial dynamic modeling for analyzing urban land use change

This paper analyzes land use change in Rio Claro City and its surroundings, located in the southeastern state of Sao Paulo, in the period from 1988 to 1995, using air-borne digital imagery and a cellular automata model. The simulation experiment was carried out in the Dinamica EGO platform and the results revealed a constrained urban sprawl, resulting from both the densification of residential areas implemented in previous years and the economic recession that led to an internal financial crisis in Brazil during the early 1990s. The simulation outputs were validated using a multi-resolution procedure based on a fuzzy similarity index and showed a satisfactory fitness in relation to the historical reference data. © 2013 IEEE.

Modeling the kinetics of the coalescence of water droplets in crude oil emulsions subject to an electric field, with the cellular automata technique

In this study, the concept of cellular automata is applied in an innovative way to simulate the separation of phases in a water/oil emulsion. The velocity of the water droplets is calculated by the balance of forces acting on a pair of droplets in a group, and cellular automata is used to simulate the whole group of droplets. Thus, it is possible to solve the problem stochastically and to show the sequence of collisions of droplets and coalescence phenomena. This methodology enables the calculation of the amount of water that can be separated from the emulsion under different operating conditions, thus enabling the process to be optimized. Comparisons between the results obtained from the developed model and the operational performance of an actual desalting unit are carried out. The accuracy observed shows that the developed model is a good representation of the actual process. (C) 2010 Published by Elsevier Ltd.

On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

We study the spreading of contagious diseases in a population of constant size using susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R(0)) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R(0) cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations. (C) 2009 Elsevier B.V. All rights reserved.

Small-World Effect in Epidemics Using Cellular Automata

The spread of an infectious disease in a population involves interactions leading to an epidemic outbreak through a network of contacts. Extending on Watts and Strogatz (1998) who showed that short-distance connections create a small-world effect, a model combining short-and long-distance probabilistic and regularly updated contacts helps considering spatial heterogeneity. The method is based on cellular automata. The presence of long-distance connections accelerates the small-world effect, as if the world shrank in proportion of their total number.

Towards robust network based complex systems : from evolutionary cellular automata to biological models

Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.

Behavioural queueing : cellular automata and a laboratory experiment

Dans cette thèse, nous étudions les aspects comportementaux d'agents qui interagissent dans des systèmes de files d'attente à l'aide de modèles de simulation et de méthodologies expérimentales. Chaque période les clients doivent choisir un prestataire de servivce. L'objectif est d'analyser l'impact des décisions des clients et des prestataires sur la formation des files d'attente. Dans un premier cas nous considérons des clients ayant un certain degré d'aversion au risque. Sur la base de leur perception de l'attente moyenne et de la variabilité de cette attente, ils forment une estimation de la limite supérieure de l'attente chez chacun des prestataires. Chaque période, ils choisissent le prestataire pour lequel cette estimation est la plus basse. Nos résultats indiquent qu'il n'y a pas de relation monotone entre le degré d'aversion au risque et la performance globale. En effet, une population de clients ayant un degré d'aversion au risque intermédiaire encoure généralement une attente moyenne plus élevée qu'une population d'agents indifférents au risque ou très averses au risque. Ensuite, nous incorporons les décisions des prestataires en leur permettant d'ajuster leur capacité de service sur la base de leur perception de la fréquence moyenne d'arrivées. Les résultats montrent que le comportement des clients et les décisions des prestataires présentent une forte "dépendance au sentier". En outre, nous montrons que les décisions des prestataires font converger l'attente moyenne pondérée vers l'attente de référence du marché. Finalement, une expérience de laboratoire dans laquelle des sujets jouent le rôle de prestataire de service nous a permis de conclure que les délais d'installation et de démantèlement de capacité affectent de manière significative la performance et les décisions des sujets. En particulier, les décisions du prestataire, sont influencées par ses commandes en carnet, sa capacité de service actuellement disponible et les décisions d'ajustement de capacité qu'il a prises, mais pas encore implémentées. - Queuing is a fact of life that we witness daily. We all have had the experience of waiting in line for some reason and we also know that it is an annoying situation. As the adage says "time is money"; this is perhaps the best way of stating what queuing problems mean for customers. Human beings are not very tolerant, but they are even less so when having to wait in line for service. Banks, roads, post offices and restaurants are just some examples where people must wait for service. Studies of queuing phenomena have typically addressed the optimisation of performance measures (e.g. average waiting time, queue length and server utilisation rates) and the analysis of equilibrium solutions. The individual behaviour of the agents involved in queueing systems and their decision making process have received little attention. Although this work has been useful to improve the efficiency of many queueing systems, or to design new processes in social and physical systems, it has only provided us with a limited ability to explain the behaviour observed in many real queues. In this dissertation we differ from this traditional research by analysing how the agents involved in the system make decisions instead of focusing on optimising performance measures or analysing an equilibrium solution. This dissertation builds on and extends the framework proposed by van Ackere and Larsen (2004) and van Ackere et al. (2010). We focus on studying behavioural aspects in queueing systems and incorporate this still underdeveloped framework into the operations management field. In the first chapter of this thesis we provide a general introduction to the area, as well as an overview of the results. In Chapters 2 and 3, we use Cellular Automata (CA) to model service systems where captive interacting customers must decide each period which facility to join for service. They base this decision on their expectations of sojourn times. Each period, customers use new information (their most recent experience and that of their best performing neighbour) to form expectations of sojourn time at the different facilities. Customers update their expectations using an adaptive expectations process to combine their memory and their new information. We label "conservative" those customers who give more weight to their memory than to the xiv Summary new information. In contrast, when they give more weight to new information, we call them "reactive". In Chapter 2, we consider customers with different degree of risk-aversion who take into account uncertainty. They choose which facility to join based on an estimated upper-bound of the sojourn time which they compute using their perceptions of the average sojourn time and the level of uncertainty. We assume the same exogenous service capacity for all facilities, which remains constant throughout. We first analyse the collective behaviour generated by the customers' decisions. We show that the system achieves low weighted average sojourn times when the collective behaviour results in neighbourhoods of customers loyal to a facility and the customers are approximately equally split among all facilities. The lowest weighted average sojourn time is achieved when exactly the same number of customers patronises each facility, implying that they do not wish to switch facility. In this case, the system has achieved the Nash equilibrium. We show that there is a non-monotonic relationship between the degree of risk-aversion and system performance. Customers with an intermediate degree of riskaversion typically achieve higher sojourn times; in particular they rarely achieve the Nash equilibrium. Risk-neutral customers have the highest probability of achieving the Nash Equilibrium. Chapter 3 considers a service system similar to the previous one but with risk-neutral customers, and relaxes the assumption of exogenous service rates. In this sense, we model a queueing system with endogenous service rates by enabling managers to adjust the service capacity of the facilities. We assume that managers do so based on their perceptions of the arrival rates and use the same principle of adaptive expectations to model these perceptions. We consider service systems in which the managers' decisions take time to be implemented. Managers are characterised by a profile which is determined by the speed at which they update their perceptions, the speed at which they take decisions, and how coherent they are when accounting for their previous decisions still to be implemented when taking their next decision. We find that the managers' decisions exhibit a strong path-dependence: owing to the initial conditions of the model, the facilities of managers with identical profiles can evolve completely differently. In some cases the system becomes "locked-in" into a monopoly or duopoly situation. The competition between managers causes the weighted average sojourn time of the system to converge to the exogenous benchmark value which they use to estimate their desired capacity. Concerning the managers' profile, we found that the more conservative Summary xv a manager is regarding new information, the larger the market share his facility achieves. Additionally, the faster he takes decisions, the higher the probability that he achieves a monopoly position. In Chapter 4 we consider a one-server queueing system with non-captive customers. We carry out an experiment aimed at analysing the way human subjects, taking on the role of the manager, take decisions in a laboratory regarding the capacity of a service facility. We adapt the model proposed by van Ackere et al (2010). This model relaxes the assumption of a captive market and allows current customers to decide whether or not to use the facility. Additionally the facility also has potential customers who currently do not patronise it, but might consider doing so in the future. We identify three groups of subjects whose decisions cause similar behavioural patterns. These groups are labelled: gradual investors, lumpy investors, and random investor. Using an autocorrelation analysis of the subjects' decisions, we illustrate that these decisions are positively correlated to the decisions taken one period early. Subsequently we formulate a heuristic to model the decision rule considered by subjects in the laboratory. We found that this decision rule fits very well for those subjects who gradually adjust capacity, but it does not capture the behaviour of the subjects of the other two groups. In Chapter 5 we summarise the results and provide suggestions for further work. Our main contribution is the use of simulation and experimental methodologies to explain the collective behaviour generated by customers' and managers' decisions in queueing systems as well as the analysis of the individual behaviour of these agents. In this way, we differ from the typical literature related to queueing systems which focuses on optimising performance measures and the analysis of equilibrium solutions. Our work can be seen as a first step towards understanding the interaction between customer behaviour and the capacity adjustment process in queueing systems. This framework is still in its early stages and accordingly there is a large potential for further work that spans several research topics. Interesting extensions to this work include incorporating other characteristics of queueing systems which affect the customers' experience (e.g. balking, reneging and jockeying); providing customers and managers with additional information to take their decisions (e.g. service price, quality, customers' profile); analysing different decision rules and studying other characteristics which determine the profile of customers and managers.

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.

Evolutionary modeling of larval dispersal in blowflies using non-uniform cellular automata

When the food supply flnishes, or when the larvae of blowflies complete their development and migrate prior to the total removal of the larval substrate, they disperse to find adequate places for pupation, a process known as post-feeding larval dispersal. Based on experimental data of the Initial and final configuration of the dispersion, the reproduction of such spatio-temporal behavior is achieved here by means of the evolutionary search for cellular automata with a distinct transition rule associated with each cell, also known as a nonuniform cellular automata, and with two states per cell in the lattice. Two-dimensional regular lattices and multivalued states will be considered and a practical question is the necessity of discovering a proper set of transition rules. Given that the number of rules is related to the number of cells in the lattice, the search space is very large and an evolution strategy is then considered to optimize the parameters of the transition rules, with two transition rules per cell. As the parameters to be optimized admit a physical interpretation, the obtained computational model can be analyzed to raise some hypothetical explanation of the observed spatiotemporal behavior. © 2006 IEEE.

Modelling fungus dispersal scenarios using cellular automata

This study focused on representing spatio-temporal patterns of fungal dispersal using cellular automata. Square lattices were used, with each site representing a host for a hypothetical fungus population. Four possible host states were allowed: resistant, permissive, latent or infectious. In this model, the probability of infection for each of the healthy states (permissive or resistant) in a time step was determined as a function of the host's susceptibility, seasonality, and the number of infectious sites and the distance between them. It was also assumed that infected sites become infectious after a pre-specified latency period, and that recovery is not possible. Several scenarios were simulated to understand the contribution of the model's parameters and the spatial structure on the dynamic behaviour of the modelling system. The model showed good capability for representing the spatio-temporal pattern of fungus dispersal over planar surfaces. With a specific problem in mind, the model can be easily modified and used to describe field behaviour, which can contribute to the conservation and development of management strategies for both natural and agricultural systems. © 2012 Elsevier B.V.

LATTICE BOLTZMANN METHOD AND CELLULAR AUTOMATA SIMULATION OF PARTICLE MOTION AND DEPOSITION IN 2-D CASE

This technical report discusses the application of the Lattice Boltzmann Method (LBM) and Cellular Automata (CA) simulation in fluid flow and particle deposition. The current work focuses on incompressible flow simulation passing cylinders, in which we incorporate the LBM D2Q9 and CA techniques to simulate the fluid flow and particle loading respectively. For the LBM part, the theories of boundary conditions are studied and verified using the Poiseuille flow test. For the CA part, several models regarding simulation of particles are explained. And a new Digital Differential Analyzer (DDA) algorithm is introduced to simulate particle motion in the Boolean model. The numerical results are compared with a previous probability velocity model by Masselot [Masselot 2000], which shows a satisfactory result.

Integrating spatial optimization and cellular automata for evaluating urban change

Urban growth and change presents numerous challenges for planners and policy makers. Effective and appropriate strategies for managing growth and change must address issues of social, environmental and economic sustainability. Doing so in practical terms is a difficult task given the uncertainty associated with likely growth trends not to mention the uncertainty associated with how social and environmental structures will respond to such change. An optimization based approach is developed for evaluating growth and change based upon spatial restrictions and impact thresholds. The spatial optimization model is integrated with a cellular automata growth simulation process. Application results are presented and discussed with respect to possible growth scenarios in south east Queensland, Australia.

Forecasting enrollment in differential assessment programs using cellular automata

Urban growth models have been used for decades to forecast urban development in metropolitan areas. Since the 1990s cellular automata, with simple computational rules and an explicitly spatial architecture, have been heavily utilized in this endeavor. One such cellular-automata-based model, SLEUTH, has been successfully applied around the world to better understand and forecast not only urban growth but also other forms of land-use and land-cover change, but like other models must be fed important information about which particular lands in the modeled area are available for development. Some of these lands are in categories for the purpose of excluding urban growth that are difficult to quantify since their function is dictated by policy. One such category includes voluntary differential assessment programs, whereby farmers agree not to develop their lands in exchange for significant tax breaks. Since they are voluntary, today’s excluded lands may be available for development at some point in the future. Mapping the shifting mosaic of parcels that are enrolled in such programs allows this information to be used in modeling and forecasting. In this study, we added information about California’s Williamson Act into SLEUTH’s excluded layer for Tulare County. Assumptions about the voluntary differential assessments were used to create a sophisticated excluded layer that was fed into SLEUTH’s urban growth forecasting routine. The results demonstrate not only a successful execution of this method but also yielded high goodness-of-fit metrics for both the calibration of enrollment termination as well as the urban growth modeling itself.

Sensitivity to noise and ergodicity of an assembly line of cellular automata that classifies density

We investigate the sensitivity of the composite cellular automaton of H. Fuks [Phys. Rev. E 55, R2081 (1997)] to noise and assess the density classification performance of the resulting probabilistic cellular automaton (PCA) numerically. We conclude that the composite PCA performs the density classification task reliably only up to very small levels of noise. In particular, it cannot outperform the noisy Gacs-Kurdyumov-Levin automaton, an imperfect classifier, for any level of noise. While the original composite CA is nonergodic, analyses of relaxation times indicate that its noisy version is an ergodic automaton, with the relaxation times decaying algebraically over an extended range of parameters with an exponent very close (possibly equal) to the mean-field value.

Typhoid fever as cellular microbiological model

The knowledge about typhoid fever pathogenesis is growing in the last years, mainly about the cellular and molecular phenomena that are responsible by clinical manifestations of this disease. In this article are discussed several recent discoveries, as follows: a) Bacterial type III protein secretion system; b) The five virulence genes of Salmonella spp. that encoding Sips (Salmonella invasion protein) A, B, C, D and E, which are capable of induce apoptosis in macrophages; c) The function of Toll R2 and Toll R4 receptors present in the macrophage surface (discovered in the Drosophila). The Toll family receptors are critical in the signalizing mediated by LPS in macrophages in association with LBP and CD14; d) The lines of immune defense between intestinal lumen and internal organs; e) The fundamental role of the endothelial cells in the inflammatory deviation from bloodstream into infected tissues by bacteria. In addition to above subjects, the authors comment the correlation between the clinical features of typhoid fever and the cellular and molecular phenomena of this disease, as well as the therapeutic consequences of this knowledge.

Hysteresis and return-point memory in deterministic cellular automata

We have investigated hysteresis and the return-point memory (RPM) property in deterministic cellular automata with avalanche dynamics. The RPM property reflects a partial ordering of metastable states, preserved by the dynamics. Recently, Sethna et al. [Phys. Rev. Lett. 70, 3347 (1993)] proved this behavior for a homogeneously driven system with static disorder. This Letter shows that the partial ordering and the RPM can be displayed as well by systems driven heterogeneously, as a result of its own evolution dynamics. In particular, we prove the RPM property for a deterministic 2D sandpile automaton driven at a central site.