Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, e.g., the number of digits of the integer to be factored.Comment: 28 pages, LaTeX. This is an expanded version of a paper that appeared in the Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, Nov. 20--22, 1994. Minor revisions made January, 199

Segregation of a major gene influencing ovulation in progeny of Lacaune meat sheep

Inheritance of the ovulation rate (OR) in the Lacaune meat breed was studied through records from a small nucleus of 36 hyper-prolific ewes screened on farms on the basis of their natural litter size, and from progeny data of three selected Lacaune sires. These sires were chosen at the AI centre according to their breeding values estimated for the mean and the variability of their daughters' litter size. Non-carrier Lacaune dairy ewes were inseminated to produce 121 F1 daughters and 27 F1 sons. Twelve sons (four from each sire) were used in turn to inseminate non-carrier Lacaune dairy ewes providing 260 BC progeny ewes. F1 and BC progeny were brought from private farms and gathered after weaning on an experimental farm where ovulation rates were recorded in the first and second breeding seasons. With an average of 6.5 records each, the mean OR of hyper-prolific ewes was very high (5.34), and 38.4% of records showed a rate of 6 or more. F1 data showed high repeatability of OR (r = 0.54) within ewe, with significant variability among ewes. High OR (≥ 4) were observed in each family. A segregation analysis provided a significant likelihood ratio and classified the three founders as heterozygous. BC ewes also displayed high repeatability of OR (r = 0.47) and the mean OR varied considerably between families (from 1.24 to 1.78). Seven of the 12 BC families presented high-ovulating ewes (at least one record ≥ 4) and segregation analysis yielded a highly significant likelihood ratio as compared to an empirical test distribution. The high variability of the mean ovulation rate shown by a small group of daughters of BC ewes inseminated by putative carrier F1 rams, and the very high ovulation rate observed for some of these ewe lambs, confirmed the segregation of a major gene with two co-dominant alleles borne by an autosome. The difference between homozygous non-carriers and heterozygous ewes was about one ovulation on the observed scale and 2.2 standard deviations on the underlying scale

French Roadmap for complex Systems 2008-2009

This second issue of the French Complex Systems Roadmap is the outcome of the Entretiens de Cargese 2008, an interdisciplinary brainstorming session organized over one week in 2008, jointly by RNSC, ISC-PIF and IXXI. It capitalizes on the first roadmap and gathers contributions of more than 70 scientists from major French institutions. The aim of this roadmap is to foster the coordination of the complex systems community on focused topics and questions, as well as to present contributions and challenges in the complex systems sciences and complexity science to the public, political and industrial spheres

Des sous-univers du discours, qui seraient dégagés à la fois du sens et de la forme. Applications en syntaxe

Lecerf Yves. Des sous-univers du discours, qui seraient dégagés à la fois du sens et de la forme. Applications en syntaxe. In: Langages, 12ᵉ année, n°55, 1979. Analyse de discours et linguistique générale, sous la direction de Jean-Marie Marandin. pp. 89-123

Structure cristalline de γ Cu2 (OH)2 Cr4

The crystal structure of γ Cu₂ (OH)₂ CrO₄, the monoclinic form of copper hydroxy chromate, has been investigated by the « heavy atom » method. The refinement carried out by the least-squares method, leads to good agreement between calculated and observed structure factors (R = 0,10). In this structure the coordination polyhedron of copper is a deformed octahedron. The oxygen and OH form a distorted hexagonal close packing array in which Cu⁺⁺ and Cr[vi] partially fill the octehedral and tetrahedral sites. There are two cationic layers : in the first one the octahedral sites are half filled by Cu⁺⁺ ions, in the second one 1/4 of the octahedral sites are filled by Cu⁺⁺ and 1/8 of the tetrahedral sites by Cr[vi]. A study of the bonding shows perfect cohesion of the structure, which explains the great stability of this form, as opposed to the other metastable β form in which cohesion is very poor.La structure de γ Cu₂ (OH)₂ CrO₄, variété monoclinique stable de l'hydroxychromate de cuivre, a été déterminée par la méthode de « l'atome lourd ». L'affinement réalisé par la méthode des moindres carrés conduit à un bon accord entre facteurs de structure calculés et observés (R = 0,10). Dans cette structure le polyèdre de coordination du cuivre est un octaèdre déformé. Les atomes d'oxygène et OH forment un empilement qui dérive directement d'un assemblage hexagonal compact, les cations Cu²⁺ et Cr[vi] occupant certains sites octaédriques et tétraédriques de cet empilement. Il existe alors deux types de couches cationiques, dans la première la moitié des sites octaédriques sont occupés par des ions Cu⁺⁺, dans la seconde, le quart des sites octaédriques sont occupés par Cu⁺⁺ et le huitième des sites tétraédriques sont occupés par Cr[vi]. L'étude de l'enchaînement montre une parfaite cohésion de la structure, ce qui explique la grande stabilité de cette variété, contrairement à l'autre variété β métastable, où la cohésion est mal assurée.Riou Amédée, Gérault Yves, Lecerf André. Structure cristalline de γ Cu2 (OH)2 Cr4. In: Bulletin de la Société française de Minéralogie et de Cristallographie, volume 96, 1, 1973. pp. 25-29

IX. La fouille d’Er Grah : problématique et stratégie

Le Roux Charles Tanguy, Lecerf Yannick, Tinévez Jean-Yves. IX. La fouille d’Er Grah : problématique et stratégie. In: Gallia préhistoire. Suppléments, supplément 38, 2006. Monuments mégalithiques à Locmariaquer (Morbihan). Le long tumulus d’Er Grah dans son environnement. pp. 77-80

XIII. La fréquentation tardive des lieux

Le Roux Charles Tanguy, Lecerf Yannick, Tinévez Jean-Yves. XIII. La fréquentation tardive des lieux. In: Gallia préhistoire. Suppléments, supplément 38, 2006. Monuments mégalithiques à Locmariaquer (Morbihan). Le long tumulus d’Er Grah dans son environnement. pp. 147-149

XIII. La fréquentation tardive des lieux

Le Roux Charles Tanguy, Lecerf Yannick, Tinévez Jean-Yves. XIII. La fréquentation tardive des lieux. In: Gallia préhistoire. Suppléments, supplément 38, 2006. Monuments mégalithiques à Locmariaquer (Morbihan). Le long tumulus d’Er Grah dans son environnement. pp. 147-149

XI. Er Grah : Les structures prémonumentales

Le Roux Charles Tanguy, Lecerf Yannick, Tinévez Jean-Yves. XI. Er Grah : Les structures prémonumentales. In: Gallia préhistoire. Suppléments, supplément 38, 2006. Monuments mégalithiques à Locmariaquer (Morbihan). Le long tumulus d’Er Grah dans son environnement. pp. 109-121