An improved model of tumour-immune system interactions

The immune system plays an important role in defending the body against tumours and other threats. Currently, mechanisms involved in immune system interactions with tumour cells are not fully understood. Here we develop a mathematical tool that can be used in aiding to address this shortfall in understanding. This paper de- scribes a hybrid cellular automata model of the interaction between a growing tumour and cells of the innate and specific immune system including the effects of chemokines that builds on previous models of tumour-immune system interactions. In particular, the model is focused on the response of immune cells to tumour cells and how the dynamics of the tumour cells change due to the immune system of the host. We present results and predictions of in silico experiments including simulations of Kaplan-Meier survival-like curves.

On the effect of topology on cellular automata rule spaces

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2. Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space. The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

Modelling the potential spread of Solenopsis invicta Buren (Hymenoptera: Formicidae) (red imported fire ant) in Australia

Quantifying the potential spread and density of an invading organism enables decision-makers to determine the most appropriate response to incursions. We present two linked models that estimate the spread of Solenopsis invicta Buren (red imported fire ant) in Australia based on limited data gathered after its discovery in Brisbane in 2001. A stochastic cellular automaton determines spread within a location (100 km by 100 km) and this is coupled with a model that simulates human-mediated movement of S. invicta to new locations. In the absence of any control measures, the models predict that S. invicta could cover 763 000–4 066 000 km2 by the year 2035 and be found at 200 separate locations around Australia by 2017–2027, depending on the rate of spread. These estimated rates of expansion (assuming no control efforts were in place) are higher than those experienced in the USA in the 1940s during the early invasion phases in that country. Active control efforts and quarantine controls in the USA (including a concerted eradication attempt in the 1960s) may have slowed spread. Further, milder winters, the presence of the polygynous social form, increased trade and human mobility in Australia in 2000s compared with the USA in 1940s could contribute to faster range expansion.

Cellular Automata Models of Traffic Behavior in Presence of Speed Breaking Structures

In this article, we study traffic flow in the presence of speed breaking structures. The speed breakers are typically used to reduce the local speed of vehicles near certain institutions such as schools and hospitals. Through a cellular automata model we study the impact of such structures on global traffic characteristics. The simulation results indicate that the presence of speed breakers could reduce the global flow under moderate global densities. However, under low and high global density traffic regime the presence of speed breakers does not have an impact on the global flow. Further the speed limit enforced by the speed breaker creates a phase distinction. For a given global density and slowdown probability, as the speed limit enforced by the speed breaker increases, the traffic moves from the reduced flow phase to maximum flow phase. This underlines the importance of proper design of these structures to avoid undesired flow restrictions.

A constitutive model for transversely isotropic foams, and its application to the indentation of balsa wood

An elastic-plastic constitutive model for transversely isotropic compressible solids (foams) has been developed. A quadratic yield surface with four parameters and one hardening function is proposed. Associated plastic flow is assumed and the yield surface evolves in a self-similar manner calibrated by the uniaxial compressive (or tensile) response of the cellular solid in the axial direction. All material constants in the model (elastic and plastic) can be determined from a combination of a total of four uniaxial and shear tests. The model is used to predict the indentation response of balsa wood to a conical indenter. For the three cone angles considered in this study, very good agreement is found between the experimental measurements and the finite element (FE) predictions of the transversely isotropic cellular solid model. On the other hand, an isotropic foam model is shown to be inadequate to capture the indentation response. © 2005 Elsevier Ltd. All rights reserved.

Preliminary comparison of natural versus model-predicted recovery of vessel-generated seagrass injuries in Florida Keys National Marine Sanctuary

Each year, more than 500 motorized vessel groundings cause widespread damage to seagrasses in Florida Keys National Marine Sanctuary (FKNMS). Under Section 312 of the National Marine Sanctuaries Act (NMSA), any party responsible for the loss, injury, or destruction of any Sanctuary resource, including seagrass, is liable to the United States for response costs and resulting damages. As part of the damage assessment process, a cellular automata model is utilized to forecast seagrass recovery rates. Field validation of these forecasts was accomplished by comparing model-predicted percent recovery to that which was observed to be occurring naturally for 30 documented vessel grounding sites. Model recovery forecasts for both Thalassia testudinum and Syringodium filiforme exceeded natural recovery estimates for 93.1% and 89.5% of the sites, respectively. For Halodule wrightii, the number of over- and under-predictions by the model was similar. However, where under-estimation occurred, it was often severe, reflecting the well-known extraordinary growth potential of this opportunistic species. These preliminary findings indicate that the recovery model is consistently generous to Responsible Parties in that the model forecasts a much faster recovery than was observed to occur naturally, particularly for T. testudinum, the dominant seagrass species in the region and the species most often affected. Environmental setting (i.e., location, wave exposure) influences local seagrass landscape pattern and may also play a role in the recovery dynamics for a particular injury site. An examination of the relationship between selected environmental factors and injury recovery dynamics is currently underway. (PDF file contains 20 pages.)

Cellular automata: Simulating alpine tundra vegetation dynamics in response to global warming

This study attempts to model alpine tundra vegetation dynamics in a tundra region in the Qinghai Province of China in response to global warming. We used Raster-based cellular automata and a Geographic Information System to study the spatial and temporal vegetation dynamics. The cellular automata model is implemented with IDRISI's Multi-Criteria Evaluation functionality to simulate the spatial patterns of vegetation change assuming certain scenarios of global mean temperature increase over time. The Vegetation Dynamic Simulation Model calculates a probability surface for each vegetation type, and then combines all vegetation types into a composite map, determined by the maximum likelihood that each vegetation type should distribute to each raster unit. With scenarios of global temperature increase of I to 3 degrees C, the vegetation types such as Dry Kobresia Meadow and Dry Potentilla Shrub that are adapted to warm and dry conditions tend to become more dominant in the study area.

Information Processing and Transmission in Cellular Automata

A cellular automaton is an iterative array of very simple identical information processing machines called cells. Each cell can communicate with neighboring cells. At discrete moments of time the cells can change from one state to another as a function of the states of the cell and its neighbors. Thus on a global basis, the collection of cells is characterized by some type of behavior. The goal of this investigation was to determine just how simple the individual cells could be while the global behavior achieved some specified criterion of complexity ??ually the ability to perform a computation or to reproduce some pattern. The chief result described in this thesis is that an array of identical square cells (in two dimensions), each cell of which communicates directly with only its four nearest edge neighbors and each of which can exist in only two states, can perform any computation. This computation proceeds in a straight forward way. A configuration is a specification of the states of all the cells in some area of the iterative array. Another result described in this thesis is the existence of a self-reproducing configuration in an array of four-state cells, a reduction of four states from the previously known eight-state case. The technique of information processing in cellular arrays involves the synthesis of some basic components. Then the desired behaviors are obtained by the interconnection of these components. A chapter on components describes some sets of basic components. Possible applications of the results of this investigation, descriptions of some interesting phenomena (for vanishingly small cells), and suggestions for further study are given later.

Cellular automata and non-static image processing for embodied robot systems on a massively parallel processor array

Huelse, M, Barr, D R W, Dudek, P: Cellular Automata and non-static image processing for embodied robot systems on a massively parallel processor array. In: Adamatzky, A et al. (eds) AUTOMATA 2008, Theory and Applications of Cellular Automata. Luniver Press, 2008, pp. 504-510. Sponsorship: EPSRC

Reliable Cellular Automata with Self-Organization

In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information for more than a constant number of steps is nontrivial, even in an infinite automaton. Still, there is a solution in 2 dimensions, and this solution can be used to construct a simple 3-dimensional discrete-time universal fault-tolerant cellular automaton. This technique does not help much to solve the following problems: remembering a bit of information in 1 dimension; computing in dimensions lower than 3; computing in any dimension with non-synchronized transitions. Our more complex technique organizes the cells in blocks that perform a reliable simulation of a second (generalized) cellular automaton. The cells of the latter automaton are also organized in blocks, simulating even more reliably a third automaton, etc. Since all this (a possibly infinite hierarchy) is organized in "software", it must be under repair all the time from damage caused by errors. A large part of the problem is essentially self-stabilization recovering from a mess of arbitrary-size and content caused by the faults. The present paper constructs an asynchronous one-dimensional fault-tolerant cellular automaton, with the further feature of "self-organization". The latter means that unless a large amount of input information must be given, the initial configuration can be chosen to be periodical with a small period.

The stochastic nature of predator-prey cycles

We study by numerical simulations the time correlation function of a stochastic lattice model describing the dynamics of coexistence of two interacting biological species that present time cycles in the number of species individuals. Its asymptotic behavior is shown to decrease in time as a sinusoidal exponential function from which we extract the dominant eigenvalue of the evolution operator related to the stochastic dynamics showing that it is complex with the imaginary part being the frequency of the population cycles. The transition from the oscillatory to the nonoscillatory behavior occurs when the asymptotic behavior of the time correlation function becomes a pure exponential, that is, when the real part of the complex eigenvalue equals a real eigenvalue. We also show that the amplitude of the undamped oscillations increases with the square root of the area of the habitat as ordinary random fluctuations. (C) 2009 Elsevier B.V. All rights reserved.

Universaidade em sistemas da mecâniaestatística de não equilíbrio com estados absorventes e percolação geográfica

Complex systems have stimulated much interest in the scientific community in the last twenty years. Examples this area are the Domany-Kinzel cellular automaton and Contact Process that are studied in the first chapter this tesis. We determine the critical behavior of these systems using the spontaneous-search method and short-time dynamics (STD). Ours results confirm that the DKCA e CP belong to universality class of Directed Percolation. In the second chapter, we study the particle difusion in two models of stochastic sandpiles. We characterize the difusion through diffusion constant D, definite through in the relation h(x)2i = 2Dt. The results of our simulations, using finite size scalling and STD, show that the diffusion constant can be used to study critical properties. Both models belong to universality class of Conserved Directed Percolation. We also study that the mean-square particle displacement in time, and characterize its dependence on the initial configuration and particle density. In the third chapter, we introduce a computacional model, called Geographic Percolation, to study watersheds, fractals with aplications in various areas of science. In this model, sites of a network are assigned values between 0 and 1 following a given probability distribution, we order this values, keeping always its localization, and search pk site that percolate network. Once we find this site, we remove it from the network, and search for the next that has the network to percole newly. We repeat these steps until the complete occupation of the network. We study the model in 2 and 3 dimension, and compare the bidimensional case with networks form at start real data (Alps e Himalayas)

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.

On estimating the basic reproduction number in distinct stages of a contagious disease spreading

In epidemiology, the basic reproduction number R-0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition. R-0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R-0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R-0 >1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable: when R-0 <1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R-0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptibleinfective-recovered (SIR) model described in terms of ODE and also 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. The values of R-0 obtained from both approaches are compared, showing good agreement. (C) 2012 Elsevier B.V. All rights reserved.

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.