On external presentations of infinite graphs

The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in particular, for such systems having a finite description, each state of the system is a configuration of some machine. Then most algorithmic approaches rely on the structure of these configurations. Such characterisations are said internal. In order to apply algorithms detecting a structural property (like identifying connected components) one may have first to transform the system in order to fit the description needed for the algorithm. The problem of internal characterisation is that it hides structural properties, and each solution becomes ad hoc relatively to the form of the configurations. On the contrary, external characterisations avoid explicit naming of the vertices. Such characterisation are mostly defined via graph transformations. In this paper we present two kind of external characterisations: deterministic graph rewriting, which in turn characterise regular graphs, deterministic context-free languages, and rational graphs. Inverse substitution from a generator (like the complete binary tree) provides characterisation for prefix-recognizable graphs, the Caucal Hierarchy and rational graphs. We illustrate how these characterisation provide an efficient tool for the representation of infinite state systems

An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata

Cellular Automata (CA) are a class of discrete dynamical systems that have been widely used to model complex systems in which the dynamics is specified at local cell-scale. Classically, CA are run on a regular lattice and with perfect synchronicity. However, these two assumptions have little chance to truthfully represent what happens at the microscopic scale for physical, biological or social systems. One may thus wonder whether CA do keep their behavior when submitted to small perturbations of synchronicity. This work focuses on the study of one-dimensional (1D) asynchronous CA with two states and nearest-neighbors. We define what we mean by ``the behavior of CA is robust to asynchronism'' using a statistical approach with macroscopic parameters. and we present an experimental protocol aimed at finding which are the robust 1D elementary CA. To conclude, we examine how the results exposed can be used as a guideline for the research of suitable models according to robustness criteria.Comment: Version : Feb 13th, 2004, submitted to Complex System

Multi-level agent-based modeling - A literature survey

During last decade, multi-level agent-based modeling has received significant and dramatically increasing interest. In this article we present a comprehensive and structured review of literature on the subject. We present the main theoretical contributions and application domains of this concept, with an emphasis on social, flow, biological and biomedical models.Comment: v2. Ref 102 added. v3-4 Many refs and text added v5-6 bibliographic statistics updated. v7 Change of the name of the paper to reflect what it became, many refs and text added, bibliographic statistics update

Water in Comet 2/2003 K4 (LINEAR) with Spitzer

We present sensitive 5.5 to 7.6 micron spectra of comet C/2003 K4 (LINEAR) obtained on 16 July 2004 (r_{h} = 1.760 AU, Delta_{Spitzer} = 1.409 AU, phase angle 35.4 degrees) with the Spitzer Space Telescope. The nu_{2} vibrational band of water is detected with a high signal-to-noise ratio (> 50). Model fitting to the best spectrum yields a water ortho-to-para ratio of 2.47 +/- 0.27, which corresponds to a spin temperature of 28.5^{+6.5}_{-3.5} K. Spectra acquired at different offset positions show that the rotational temperature decreases with increasing distance from the nucleus, which is consistent with evolution from thermal to fluorescence equilibrium. The inferred water production rate is (2.43 +/- 0.25) \times 10^{29} molec. s^{-1}. The spectra do not show any evidence for emission from PAHs and carbonate minerals, in contrast to results reported for comets 9P/Tempel 1 and C/1995 O1 (Hale-Bopp). However, residual emission is observed near 7.3 micron the origin of which remains unidentified.Comment: 33 pages, including 11 figures, 2 tables, ApJ 2007 accepte