The Mystery of Two Straight Lines in Bacterial Genome Statistics. Release 2007

In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy. The main challenge now is to explain the observed high accuracy. The new phenomenon of complementary symmetry for codon position--specific nucleotide frequencies is observed. The results of analysis of several codon usage models are presented. We demonstrate that the mean--field approximation, which is also known as context--free, or complete independence model, or Segre variety, can serve as a reasonable approximation to the real codon usage. The first two principal components of codon usage correlate strongly with genomic G+C content and the optimal growth temperature respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. First three eigenvalues in codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and archaeal genomes codon usage is clearly distributed along two third order curves with genomic G+C content as a parameter.Comment: Significantly extended version with new data for all the 348 distinct bacterial genomes available in Genbank in April 200

Approaches to analysis with infinitesimals following Robinson, Nelson, and others

This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and the Intended Interpretation hypothesis. We highlight some applications including (1) Loeb's approach to the Lebesgue measure, (2) a radically elementary approach to the vibrating string, (3) true infinitesimal differential geometry. We explore the relation of Robinson's and related frameworks to the multiverse view as developed by Hamkins. Keywords: axiomatisations, infinitesimal, nonstandard analysis, ultraproducts, superstructure, set-theoretic foundations, multiverse, naive integers, intuitionism, soritical properties, ideal elements, protozoa

A Bayesian framework to objectively combine metrics when developing stressor specific multimetric indicator

In the context of the European Water Framework Directive (WFD), monitoring programs and related indicators have been developed to assess anthropogenic impacts on various components of aquatic ecosystems. While great precautions are usually taken when selecting and calculating relevant core metrics, little attention is generally paid to the generation of the multimetric indicator, i.e. the combination of the different core metrics. Indeed, most multimetric indicators are generated by simply averaging or summing metrics, without taking into account their sensitivity and their variability. Moreover, few indicators provide a rigorous estimate of the uncertainty of the assessments, while this estimation is essential for managers. In this context, we developed a Bayesian framework to build multimetric indicators aiming at improving those two weaknesses. This framework is based on two phases. First, pressure-impact statistical models are developed to quantify the impact of pressure on various fish metrics. Then the Bayesian theorem is applied to estimate probabilities of being at a certain anthropogenic pressure level from fish observation and pressure-impact models outputs. The Bayesian theorem allows to combine objectively the different core metrics, taking into account their sensitivity and their variability, and to provide rigorous uncertainty quantification, which is especially valuable in the WFD context. The method is applied as illustrative example on transitional French water bodies to demonstrate its relevance, especially in the Water Framework Directive context though the method is generic enough to be applied in various contexts

Hydrodynamic Coupling of Two Brownian Spheres to a Planar Surface

We describe direct imaging measurements of the collective and relative diffusion of two colloidal spheres near a flat plate. The bounding surface modifies the spheres' dynamics, even at separations of tens of radii. This behavior is captured by a stokeslet analysis of fluid flow driven by the spheres' and wall's no-slip boundary conditions. In particular, this analysis reveals surprising asymmetry in the normal modes for pair diffusion near a flat surface.Comment: 4 pages, 4 figure

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Component-Based Real-Time Operating System for Embedded Applications

Acceptance rate: 37%, Rank (CORE): AInternational audienceAs embedded systems must constantly integrate new functionalities, their developement cycles must be based on high-level abstractions, making the software design more flexible. CBSE provides an approach to these new requirements. However, low-level services provided by operating systems are an integral part of embedded applications, furthermore deployed on resource-limited devices. Therefore, the expected benefits of CBSE must not impact on the constraints imposed by the targetted domain, such as memory footprint, energy consumption, and execution time. In this paper, we present the componentization of a legacy industry-established Real-Time Operating System, and how component-based applications are built on top of it. We use the Think framework that allows to produce flexible systems while paying for flexibility only where desired. Performed experimentions show that the induced overhead is negligeable

Higher order glass-transition singularities in colloidal systems with attractive interactions

The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line, and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third order bifurcation point, i.e. in a A_3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth order A_4 (swallow-tail) singularity at a critical well width. Close to the A_3 and A_4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.Comment: 19 pages, 12 figures, Phys. Rev. E, in prin

Incorporating prior knowledge improves detection of differences in bacterial growth rate

BACKGROUND: Robust statistical detection of differences in the bacterial growth rate can be challenging, particularly when dealing with small differences or noisy data. The Bayesian approach provides a consistent framework for inferring model parameters and comparing hypotheses. The method captures the full uncertainty of parameter values, whilst making effective use of prior knowledge about a given system to improve estimation. RESULTS: We demonstrated the application of Bayesian analysis to bacterial growth curve comparison. Following extensive testing of the method, the analysis was applied to the large dataset of bacterial responses which are freely available at the web-resource, ComBase. Detection was found to be improved by using prior knowledge from clusters of previously analysed experimental results at similar environmental conditions. A comparison was also made to a more traditional statistical testing method, the F-test, and Bayesian analysis was found to perform more conclusively and to be capable of attributing significance to more subtle differences in growth rate. CONCLUSIONS: We have demonstrated that by making use of existing experimental knowledge, it is possible to significantly improve detection of differences in bacterial growth rate

Almost exponential maps and integrability results for a class of horizontally regular vector fields

We show a higher order integrability theorem for distributions generated by a family of vector fields under a horizontal regularity assumption on their coefficients. We use as chart a class of almost exponential maps which we discuss in detailsComment: arXiv admin note: material from arXiv:1106.2410v1, now three separate articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520