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

Universities and knowledge intensive business services as actors of the creative regional technological infrastructure: The case of the Upper-Rhine Valley

Characterizing the innovative capacity of a territory, and his specific attractivity for external direct investment in new fields, needs the definition of measurable concepts and the design of a proper methodology to gather relevant quantitative data. The aim of the paper is to propose a general theoretical view of the functional characteristics of the various actors and institutions that compose the ?technological infrastructure? of a region, then to show some results of studies made in the Upper-Rhine Valley (in France as well as in Germany) that cast a light on the contribution of certain important players like universities and ?knowledge intensive business services?. Universities have an important and very composite economic impact in their region. As a regular public administration they contribute to local economic activity throug personal incomes, capital expenses and current expenses. But they also attract students, contribute to the image of the city and sometimes propose valuable services for firms. Where universities (and public research centers associated to them) play a very specific role is by training young researchers, who are at the same time inputs and outputs of the research process and fulfill an important role in the cooperation and transfer networks with the most creative local firms. New types of knowledge intensive services are increasingly developed in the environment of industrial firms, either as a result of the process or of ?externalization? of large firms or as an autonomous process of creation ? for instance start-ups initiated by the academic system, but other sorts of services too. These business services could play a crucial role not only for large technology based firms, but also for the small firms at the basis of the regional industrial fabrique. They participate to the technological infrastructure, and more largely to the managerial skills? supply and the innovative climate of the territory.

Computing Integer Powers in Floating-Point Arithmetic

We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).Comment: Laboratoire LIP : CNRS/ENS Lyon/INRIA/Universit\'e Lyon

The Political Economy of International Migration in a Ricardo-Viner Model

Determinants of national policies towards immigration are analysed in the context of an economy open to international trade. Arguments for the existence of an "immigration surplus" are reviewed and followed by an interpretation of the principal contributions of the political economy literature in a Ricardo-Viner model in a direct democracy framework. A median voter model is grafted on several variants of the specific-factor open-economy model to discuss several recent changes in attitudes towards immigration (a stiffened stance, especially towards the unskilled) and in national policies ("melting-pot" vs. guest-worker programs, coexistence of legal and illegal immigrants, lax enforcement towards illegals).

Effects of the vasoactive intestinal peptide (VIP) and related peptides on glioblastoma cell growth in vitro

The growth rate of numerous cancer cell lines is regulated in part by actions of neuropeptides of the vasoactive intestinal peptide (VIP) family, which also includes pituitary adenylate cyclase-activating peptide (PACAP), glucagon, and peptide histidine/isoleucine (PHI). The aim of this work was to investigate the effect of these peptides on the growth of the rat glioblastoma cell line C6 in vitro. We also sought to determine which binding sites were correlated with the effects observed. Proliferation studies performed by means of a CyQuant trade mark assay showed that VIP and PACAP strongly stimulated C6 cell proliferation at most of the concentrations tested, whereas PHI increased cell proliferation only when associated with VIP. Two growth hormone-releasing factor (GRF) derivatives and the VIP antagonist hybrid peptide neurotensin-VIP were able to inhibit VIP-induced cell growth stimulation, even at very low concentrations. Binding experiments carried out on intact cultured C6 cells, using 125I-labeled VIP and PACAP as tracers, revealed that the effects of the peptides on cell growth were correlated with the expression on C6 cells of polyvalent high-affinity VIP-PACAP binding sites and of a second subtype corresponding to very high-affinity VIP-selective binding species. The latter subtype, which interacted poorly with PACAP with a 10,000-fold lower affinity than VIP, might mediate the antagonist effects of neurotensin- VIP and of both GRF derivatives on VIP-induced cell growth stimulation

Strangeness enhancement at LHC

We study production of strangeness in the hot QGP fireball in conditions achieved at LHC, and use these results to obtain soft (strange) hadron multiplicities. We compare the chemical equilibrium and non-equilibrium conditions and identify characteristic experimental observables.Comment: Presented at SQM07, to appear in JPG special issue. One table with prediction