All scale-free networks are sparse

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.Comment: 4 pages, 2 figure

Feedback control of spin systems

The feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary and deterministic closed loop. The Lyapunov-based feedback design presented does not require spins that are selectively addressable. With this method, it is possible to obtain control inputs also for difficult tasks, like suppressing undesired couplings in identical spin systems.Comment: 16 pages, 15 figure

Increased glycation and oxidative damage to apolipoprotein B100 of LDL cholesterol in patients with type 2 diabetes and effect of metformin

OBJECTIVE The aim of this study was to investigate whether apolipoprotein B100 of LDL suffers increased damage by glycation, oxidation, and nitration in patients with type 2 diabetes, including patients receiving metformin therapy. RESEARCH DESIGN AND METHODS For this study, 32 type 2 diabetic patients and 21 healthy control subjects were recruited; 13 diabetic patients were receiving metformin therapy (median dose: 1.50 g/day). LDL was isolated from venous plasma by ultracentrifugation, delipidated, digested, and analyzed for protein glycation, oxidation, and nitration adducts by stable isotopic dilution analysis tandem mass spectrometry. RESULTS Advanced glycation end product (AGE) content of apolipoprotein B100 of LDL from type 2 diabetic patients was higher than from healthy subjects: arginine-derived AGE, 15.8 vs. 5.3 mol% (P < 0.001); and lysine-derived AGE, 2.5 vs. 1.5 mol% (P < 0.05). Oxidative damage, mainly methionine sulfoxide residues, was also increased: 2.5 vs. 1.1 molar equivalents (P < 0.001). 3-Nitrotyrosine content was decreased: 0.04 vs. 0.12 mol% (P < 0.05). In diabetic patients receiving metformin therapy, arginine-derived AGE and methionine sulfoxide were lower than in patients not receiving metformin: 19.3 vs. 8.9 mol% (P < 0.01) and 2.9 vs. 1.9 mol% (P < 0.05), respectively; 3-nitrotyrosine content was higher: 0.10 vs. 0.03 mol% (P < 0.05). Fructosyl-lysine residue content correlated positively with fasting plasma glucose. Arginine-derived AGE residue contents were intercorrelated and also correlated positively with methionine sulfoxide. CONCLUSIONS Patients with type 2 diabetes had increased arginine-derived AGEs and oxidative damage in apolipoprotein B100 of LDL. This was lower in patients receiving metformin therapy, which may contribute to decreased oxidative damage, atherogenicity, and cardiovascular disease

Thirty-two Goldbach Variations

We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.Comment: v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and Witten zeta functions. Errors in the second section on Complex Line Integrals are corrected. To appear in International Journal of Number Theory. Title change

Quantifying Entanglement Production of Quantum Operations

The problem of entanglement produced by an arbitrary operator is formulated and a related measure of entanglement production is introduced. This measure of entanglement production satisfies all properties natural for such a characteristic. A particular case is the entanglement produced by a density operator or a density matrix. The suggested measure is valid for operations over pure states as well as over mixed states, for equilibrium as well as nonequilibrium processes. Systems of arbitrary nature can be treated, described either by field operators, spin operators, or any other kind of operators, which is realized by constructing generalized density matrices. The interplay between entanglement production and phase transitions in statistical systems is analysed by the examples of Bose-Einstein condensation, superconducting transition, and magnetic transitions. The relation between the measure of entanglement production and order indices is analysed.Comment: 20 pages, Revte

SOPHIE velocimetry of Kepler transit candidates XVII. The physical properties of giant exoplanets within 400 days of period

While giant extrasolar planets have been studied for more than two decades now, there are still some open questions such as their dominant formation and migration process, as well as their atmospheric evolution in different stellar environments. In this paper, we study a sample of giant transiting exoplanets detected by the Kepler telescope with orbital periods up to 400 days. We first defined a sample of 129 giant-planet candidates that we followed up with the SOPHIE spectrograph (OHP, France) in a 6-year radial velocity campaign. This allow us to unveil the nature of these candidates and to measure a false-positive rate of 54.6 +/- 6.5 % for giant-planet candidates orbiting within 400 days of period. Based on a sample of confirmed or likely planets, we then derive the occurrence rates of giant planets in different ranges of orbital periods. The overall occurrence rate of giant planets within 400 days is 4.6 +/- 0.6 %. We recover, for the first time in the Kepler data, the different populations of giant planets reported by radial velocity surveys. Comparing these rates with other yields, we find that the occurrence rate of giant planets is lower only for hot jupiters but not for the longer period planets. We also derive a first measurement on the occurrence rate of brown dwarfs in the brown-dwarf desert with a value of 0.29 +/- 0.17 %. Finally, we discuss the physical properties of the giant planets in our sample. We confirm that giant planets receiving a moderate irradiation are not inflated but we find that they are in average smaller than predicted by formation and evolution models. In this regime of low-irradiated giant planets, we find a possible correlation between their bulk density and the Iron abundance of the host star, which needs more detections to be confirmed.Comment: To appear in Astronomy and Astrophysic

Analysis of two-player quantum games in an EPR setting using geometric algebra

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.Comment: 20 pages, no figure, revise

Les cégépiens ayant des troubles d'apprentissage face aux TIC

Rapport final présenté au Fonds de recherche du Québec - Société et culture (FRQSC) et le ministère de l'Éducation, du Loisir et du Sport (MELS)Également disponible en version papier.Titre de l'écran-titre (visionné le 10 oct. 2012

N-player quantum games in an EPR setting

The $N$-player quantum game is analyzed in the context of an Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for $N$-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the mixed Nash equilibrium and the payoffs are determined. Players' payoffs are then defined with linear functions so that common two-player games can be easily extended to the $N$-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners' Dilemma game for general $N \ge 2$. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs.Comment: 26 pages, 2 figure