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

The chemical diversity of comets

A fundamental question in cometary science is whether the different dynamical classes of comets have different chemical compositions, which would reflect different initial conditions. From the ground or Earth orbit, radio and infrared spectroscopic observations of a now significant sample of comets indeed reveal deep differences in the relative abundances of cometary ices. However, no obvious correlation with dynamical classes is found. Further results come, or are expected, from space exploration. Such investigations, by nature limited to a small number of objects, are unfortunately focussed on short-period comets (mainly Jupiter-family). But these in situ studies provide "ground truth" for remote sensing. We discuss the chemical differences in comets from our database of spectroscopic radio observations, which has been recently enriched by several Jupiter-family and Halley-type comets.Comment: In press in Earth, Moon and Planets (proceedings of the workshop "Future Ground-based Solar System Research: Synergies with Space Probes and Space Telescopes", Portoferraio, Isola d'Elba, Livorno (Italy), 8-12 September 2008). 6 pages with 2 figure

Improving wafer-scale Josephson junction resistance variation in superconducting quantum coherent circuits

Quantum bits, or qubits, are an example of coherent circuits envisioned for next-generation computers and detectors. A robust superconducting qubit with a coherent lifetime of $O$(100 $\mu$s) is the transmon: a Josephson junction functioning as a non-linear inductor shunted with a capacitor to form an anharmonic oscillator. In a complex device with many such transmons, precise control over each qubit frequency is often required, and thus variations of the junction area and tunnel barrier thickness must be sufficiently minimized to achieve optimal performance while avoiding spectral overlap between neighboring circuits. Simply transplanting our recipe optimized for single, stand-alone devices to wafer-scale (producing 64, 1x1 cm dies from a 150 mm wafer) initially resulted in global drifts in room-temperature tunneling resistance of $\pm$ 30%. Inferring a critical current $I_{\rm c}$ variation from this resistance distribution, we present an optimized process developed from a systematic 38 wafer study that results in $<$ 3.5% relative standard deviation (RSD) in critical current ($\equiv \sigma_{I_{\rm c}}/\left\langle I_{\rm c} \right\rangle$) for 3000 Josephson junctions (both single-junctions and asymmetric SQUIDs) across an area of 49 cm$^2$. Looking within a 1x1 cm moving window across the substrate gives an estimate of the variation characteristic of a given qubit chip. Our best process, utilizing ultrasonically assisted development, uniform ashing, and dynamic oxidation has shown $\sigma_{I_{\rm c}}/\left\langle I_{\rm c} \right\rangle$ = 1.8% within 1x1 cm, on average, with a few 1x1 cm areas having $\sigma_{I_{\rm c}}/\left\langle I_{\rm c} \right\rangle$ $<$ 1.0% (equivalent to $\sigma_{f}/\left\langle f \right\rangle$ $<$ 0.5%). Such stability would drastically improve the yield of multi-junction chips with strict critical current requirements.Comment: 10 pages, 4 figures. Revision includes supplementary materia

On the magnitude of spheres, surfaces and other homogeneous spaces

In this paper we define the magnitude of metric spaces using measures rather than finite subsets as had been done previously and show that this agrees with earlier work with Leinster in arXiv:0908.1582. An explicit formula for the magnitude of an n-sphere with its intrinsic metric is given. For an arbitrary homogeneous Riemannian manifold the leading terms of the asymptotic expansion of the magnitude are calculated and expressed in terms of the volume and total scalar curvature of the manifold. In the particular case of a homogeneous surface the form of the asymptotics can be given exactly up to vanishing terms and this involves just the area and Euler characteristic in the way conjectured for subsets of Euclidean space in previous work.Comment: 21 pages. Main change from v1: details added to proof of Theorem