Finding the "truncated" polynomial that is closest to a function

When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits. And yet, the polynomial approximations that are actually implemented do have coefficients that are represented with a finite - and sometimes small - number of bits: this is due to the finiteness of the floating-point representations (for software implementations), and to the need to have small, hence fast and/or inexpensive, multipliers (for hardware implementations). We then have to consider polynomial approximations for which the degree-$i$ coefficient has at most $m_i$ fractional bits (in other words, it is a rational number with denominator $2^{m_i}$). We provide a general method for finding the best polynomial approximation under this constraint. Then, we suggest refinements than can be used to accelerate our method.Comment: 14 pages, 1 figur

The ‘problem of problem choice’: A model of sequential knowledge production within scientific communities cientific communities.

In this paper we present an original model of sequential problem choice within scientific communities. Disciplinary knowledge is accumulated by solving problems emerging in a growing tree-like web of research areas. Knowledge production is sequential since the problems solved generate new problems that may be handled. The model allows us to study how the reward system in science influences the scientific community in stochastically selecting at each period its research agendas, and the long term resulting disciplines. We present some evidence on a decrease in the generation of new areas, a path dependency in specialization, and circumstances under which collapsing dynamics arise.Sequential Problem Choice; Stochastic Process; Tree; Graph Theory; Scientific Knowledge; Academics; Reward System

The operation of VEGA/CHARA : from the scientific idea to the final products

We describe the data flow in the operation of the VEGA/CHARA instrument. After a brief summary of the main characteristics and scientific objectives of the VEGA instrument, we explain the standard procedure from the scientific idea up to the execution of the observation. Then, we describe the different steps done after the observation, from the raw data to the archives and the final products. Many tools are used and we show how the Virtual Observatory principles have been implemented for the interoperability of these software and databases.Comment: 9 pages, 3 figure

Validity of the one-dimensional limp model for porous materials

A straightforward criterion to determine the limp model validity for porous materials is addressed here. The limp model is an "equivalent fluid" model which gives a better description of the porous behavior than the well known "rigid frame" model. It is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the Frame Stiffness Influence FSI based on porous material properties. The critical values of FSI under which the limp model can be used, are determined using a 1D analytical modeling for a specific boundary set: radiation of a vibrating plate covered by a porous layer.Comment: 12th International Student Conference on Electrical Engineering, Prague : Tch\`eque, R\'epublique (2008

Aspects of Assembly and Cascaded Aspects of Assembly: Logical and Temporal Properties

Highly dynamic computing environments, like ubiquitous and pervasive computing environments, require frequent adaptation of applications. This has to be done in a timely fashion, and the adaptation process must be as fast as possible and mastered. Moreover the adaptation process has to ensure a consistent result when finished whereas adaptations to be implemented cannot be anticipated at design time. In this paper we present our mechanism for self-adaptation based on the aspect oriented programming paradigm called Aspect of Assembly (AAs). Using AAs: (1) the adaptations process is fast and its duration is mastered; (2) adaptations' entities are independent of each other thanks to the weaver logical merging mechanism; and (3) the high variability of the software infrastructure can be managed using a mono or multi-cycle weaving approach.Comment: 14 pages, published in International Journal of Computer Science, Volume 8, issue 4, Jul 2011, ISSN 1694-081

Controllable emission of a dipolar source coupled with a magneto-dielectric resonant subwavelength scatterer

We demonstrate experimentally and theoretically that a local excitation of a single scatterer of relative dielectric permittivity {\epsilon} = 6 permits to excite broad dipolar and quadrupolar electric and magnetic resonances that shape the emission pattern in an un- precedented way. By suitably positioning the feed with respect to the sphere at a ?=3 distance, this compact antenna is able to spectrally sort the electromagnetic emission ei- ther in the forward or in the backward direction, together with a high gain in directivity. Materials with {\epsilon} = 6 can be found in the whole spectrum of frequencies promising Mie antennas to become an enabling technology in numbers of applications, ranging from quantum single photon sources to telecommunications

Correctly rounded multiplication by arbitrary precision constants

We introduce an algorithm for multiplying a floating-point number $x$ by a constant $C$ that is not exactly representable in floating-point arithmetic. Our algorithm uses a multiplication and a fused multiply accumulate instruction. We give methods for checking whether, for a given value of $C$ and a given floating-point format, our algorithm returns a correctly rounded result for any $x$. When it does not, our methods give the values $x$ for which the multiplication is not correctly rounded.Nous proposons un algorithme permettant de multiplier un nombre virgule flottante x par une constante C qui n’est pas exactement représentable en virgule flottante.Notre algorithme nécessite la disponibilité d’une instruction “multiplication-accumulation”. Nous donnons des méthodes pour tester si,pour une constante C et un format virgule flottante donnés, notre algorithme donnera un arrondi correct pour toutes les valeurs de x.Quand ce n’est pas le cas,nos méthodes permettent de connaître toutes les valeurs de x pour lesquelles la multiplication par C n’est pas arrondie correctement