Euler-Lagrange correspondence of generalized Burgers cellular automaton

Recently, we have proposed a {\em Euler-Lagrange transformation} for cellular automata(CA) by developing new transformation formulas. Applying this method to the Burgers CA(BCA), we have succeeded in obtaining the Lagrange representation of the BCA. In this paper, we apply this method to multi-value generalized Burgers CA(GBCA) which include the Fukui-Ishibashi model and the quick-start model associated with traffic flow. As a result, we have succeeded in clarifying the Euler-Lagrange correspondence of these models. It turns out, moreover that the GBCA can naturally be considered as a simple model of a multi-lane traffic flow.Comment: 11 pages, 6 figures; accepted for publication in Int. J. Mod. Phys.

Non-deterministic density classification with diffusive probabilistic cellular automata

We present a probabilistic cellular automaton (CA) with two absorbing states which performs classification of binary strings in a non-deterministic sense. In a system evolving under this CA rule, empty sites become occupied with a probability proportional to the number of occupied sites in the neighborhood, while occupied sites become empty with a probability proportional to the number of empty sites in the neighborhood. The probability that all sites become eventually occupied is equal to the density of occupied sites in the initial string.Comment: 4 pages, 4 figure

Max-plus analysis on some binary particle systems

We concern with a special class of binary cellular automata, i.e., the so-called particle cellular automata (PCA) in the present paper. We first propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2 and 4-3 are solved exactly and their general solutions are found in terms of max-plus expressions. Finally, we analyze the asymptotic behaviors of general solutions and prove the fundamental diagrams exactly.Comment: 24 pages, 5 figures, submitted to J. Phys.

Parity Problem With A Cellular Automaton Solution

The parity of a bit string of length $N$ is a global quantity that can be efficiently compute using a global counter in ${O} (N)$ time. But is it possible to find the parity using cellular automata with a set of local rule tables without using any global counter? Here, we report a way to solve this problem using a number of $r=1$ binary, uniform, parallel and deterministic cellular automata applied in succession for a total of ${O} (N^2)$ time.Comment: Revtex, 4 pages, final version accepted by Phys.Rev.

Stochastic boundary conditions in the deterministic Nagel-Schreckenberg traffic model

We consider open systems where cars move according to the deterministic Nagel-Schreckenberg rules and with maximum velocity ${v}_{max} > 1$, what is an extension of the Asymmetric Exclusion Process (ASEP). It turns out that the behaviour of the system is dominated by two features: a) the competition between the left and the right boundary b) the development of so-called "buffers" due to the hindrance an injected car feels from the front car at the beginning of the system. As a consequence, there is a first-order phase transition between the free flow and the congested phase accompanied by the collapse of the buffers and the phase diagram essentially differs from that of ${v}_{max} = 1$ (ASEP).Comment: 29 pages, 26 figure

Evaluating the Influence of Epidemiological Parameters and Host Ecology on the Spread of Phocine Distemper Virus through Populations of Harbour Seals

Catriona Harris was supported by a grant from the UK Natural Environment Research Council. The funders had no role in study design, data collections and analysis, decision to publish, or preparation of the manuscript.Background: Outbreaks of phocine distemper virus (PDV) in Europe during 1988 and 2002 were responsible for the death of around 23,000 and 30,000 harbour seals, respectively. These epidemics, particularly the one in 2002, provided an unusual opportunity to estimate epidemic parameters for a wildlife disease. There were marked regional differences in the values of some parameters both within and between epidemics. Methodology and Principal Findings: We used an individual-based model of seal movement that allowed us to incorporate realistic representations of space, time and animal behaviour into a traditional epidemiological modelling framework. We explored the potential influence of a range of ecological (foraging trip duration, time of epidemic onset, population size) and epidemiological (length of infectious period, contact rate between infectious and susceptible individuals, case mortality) parameters on four readily-measurable epidemic characteristics (number of dead individuals, duration of epidemic, peak mortality date and prevalence) and on the probability that an epidemic would occur in a particular region. We analysed the outputs as if they were the results of a series of virtual experiments, using Generalised Linear Modelling. All six variables had a significant effect on the probability that an epidemic would be recognised as an unusual mortality event by human observers. Conclusions: Regional and temporal variation in contact rate was the most likely cause of the observed differences between the two epidemics. This variation could be a consequence of differences in the way individuals divide their time between land and sea at different times of the year.Publisher PDFPeer reviewe

Asynchronous cellular automata

This text has been proposed for the Encyclopedia of Complexity and Systems Science edited by Springer Nature and should appear in 2018.International audienceThis text is intended as an introduction to the topic of asynchronous cellular automata. We start from the simple example of the Game of Life and examine what happens to this model when it is made asynchronous (Sec. 1). We then formulate our definitions and objectives to give a mathematical description of our topic (Sec. 2). Our journey starts with the examination of the shift rule with fully asynchronous updating and from this simple example, we will progressively explore more and more rules and gain insights on the behaviour of the simplest rules (Sec. 3). As we will meet some obstacles in having a full analytical description of the asynchronous behaviour of these rules, we will turn our attention to the descriptions offered by statistical physics, and more specifically to the phase transition phenomena that occur in a wide range of rules (Sec. 4). To finish this journey, we will discuss the various problems linked to the question of asynchrony (Sec. 5) and present some openings for the readers who wish to go further (Sec. 6)

Evaluating the Quality of Local Structure Approximation Using Elementary Rule 14

International audienceCellular automata (CA) can be viewed as maps in the space of probability measures. Such maps are normally infinitely-dimensional, and in order to facilitate investigations of their properties, especially in the context of applications, finite-dimensional approximations have been proposed. The most commonly used one is known as the local structure theory, developed by H. Gutowitz et al. in 1987. In spite of the popularity of this approximation in CA research, examples of rigorous evaluations of its accuracy are lacking. In an attempt to fill this gap, we construct a local structure approximation for rule 14, and study its dynamics in a rigorous fashion, without relying on numerical experiments. We then compare the outcome with known exact results