Quantum and classical properties of the fields generated by two interlinked second-order non-linear interactions

We consider two interlinked non-linear interactions occurring simultaneously in a single chi((2)) crystal. Classical and quantum working regimes are considered and their peculiar properties analysed. In particular, we describe an experiment, realized in the classical regime, that verifies the holographic nature of the process, and predict, for the quantum regime, the generation of a fully inseparable tripartite Gaussian state of light that can be used to support a general 1--> 2 continuous variable telecloning protocol.

Gaussian States in Quantum Information

These notes originated out of a set of lectures in Quantum Optics and Quantum Information given by one of us (MGAP) at the University of Napoli and the University of Milano. A quite broad set of issues are covered, ranging from elementary concepts to current research topics, and from fundamental concepts to applications. A special emphasis has been given to the phase space analysis of quantum dynamics and to the role of Gaussian states in continuous variable quantum information.

Macroscopicity in an optomechanical matter-wave interferometer

We analyse a proposal that we have recently put forward for an interface between matter-wave and optomechanical technologies from the perspective of macroscopic quantumness. In particular, by making use of a measure of macroscopicity in quantum superpositions that is particularly well suited for continuous variables systems, we demonstrate the existence of working points for our interface at which a quantum mechanical superposition of genuinely mesoscopic states is achieved. Our proposal thus holds the potential to affirm itself as a viable atom-to-mechanics transducer of quantum coherences.

Missing value imputation in longitudinal measures of alcohol consumption

Attrition in longitudinal studies can lead to biased results. The study is motivated by the unexpected observation that alcohol consumption decreased despite increased availability, which may be due to sample attrition of heavy drinkers. Several imputation methods have been proposed, but rarely compared in longitudinal studies of alcohol consumption. The imputation of consumption level measurements is computationally particularly challenging due to alcohol consumption being a semi-continuous variable (dichotomous drinking status and continuous volume among drinkers), and the non-normality of data in the continuous part. Data come from a longitudinal study in Denmark with four waves (2003-2006) and 1771 individuals at baseline. Five techniques for missing data are compared: Last value carried forward (LVCF) was used as a single, and Hotdeck, Heckman modelling, multivariate imputation by chained equations (MICE), and a Bayesian approach as multiple imputation methods. Predictive mean matching was used to account for non-normality, where instead of imputing regression estimates, "real" observed values from similar cases are imputed. Methods were also compared by means of a simulated dataset. The simulation showed that the Bayesian approach yielded the most unbiased estimates for imputation. The finding of no increase in consumption levels despite a higher availability remained unaltered. Copyright (C) 2011 John Wiley & Sons, Ltd.

Maternal nutrition and the risk of preeclampsia

La prééclampsie est responsable du quart des mortalités maternelles et est la deuxième cause de décès maternels associés à la grossesse au Canada et dans le monde. L’identification d’une stratégie efficace pour la prévention de la prééclampsie est une priorité et un défi primordial dans les milieux de recherche en obstétrique. Le rôle des éléments nutritifs dans le développement de la prééclampsie a récemment reçu davantage d’attention. Plusieurs études cliniques et épidémiologiques ont été menées pour déterminer les facteurs de risque alimentaires potentiels et examiner les effets d’une supplémentation nutritive dans le développement de troubles hypertensifs de la grossesse. Pour déterminer les effets de suppléments antioxydants pris pendant la grossesse sur le risque d’hypertension gestationnelle (HG) et de prééclampsie, un essai multicentrique contrôlé à double insu a été mené au Canada et au Mexique (An International Trial of Antioxidants in the Prevention of Preeclampsia – INTAPP). Les femmes, stratifiées par risque, étaient assignées au traitement expérimental quotidien (1 gramme de vitamine C et 400 UI de vitamine E) ou au placebo. En raison des effets secondaires potentiels, le recrutement pour l’essai a été arrêté avant que l’échantillon complet ait été constitué. Au total, 2640 femmes éligibles ont accepté d’être recrutées, dont 2363 (89.5%) furent incluses dans les analyses finales. Nous n’avons retrouvé aucune évidence qu’une supplémentation prénatale de vitamines C et E réduisait le risque d’HG et de ses effets secondaires (RR 0,99; IC 95% 0,78-1,26), HG (RR 1,04; IC 95% 0,89-1,22) et prééclampsie (RR 1,04; IC 95% 0,75-1,44). Toutefois, une analyse secondaire a révélé que les vitamines C et E augmentaient le risque de « perte fœtale ou de décès périnatal » (une mesure non spécifiée au préalable) ainsi qu’une rupture prématurée des membranes avant terme. Nous avons mené une étude de cohorte prospective chez les femmes enceintes recrutées dans l’INTAPP afin d’évaluer les relations entre le régime alimentaire maternel en début et fin de grossesse et le risque de prééclampsie et d’HG. Un questionnaire de fréquence alimentaire validé était administré deux fois pendant la grossesse (12-18 semaines, 32-34 semaines). Les analyses furent faites séparément pour les 1537 Canadiennes et les 799 Mexicaines en raison de l’hétérogénéité des régimes alimentaires des deux pays. Parmi les canadiennes, après ajustement pour l’indice de masse corporelle (IMC) précédant la grossesse, le groupe de traitement, le niveau de risque (élevé versus faible) et les autres facteurs de base, nous avons constaté une association significative entre un faible apport alimentaire (quartile inférieur) de potassium (OR 1,79; IC 95% 1,03-3,11) et de zinc (OR 1,90; IC 95% 1,07-3,39) et un risque augmenté de prééclampsie. Toujours chez les Canadiennes, le quartile inférieur de consommation d’acides gras polyinsaturés était associé à un risque augmenté d’HG (OR 1,49; IC 95% 1,09-2,02). Aucun des nutriments analysés n’affectait les risques d’HG ou de prééclampsie chez les Mexicaines. Nous avons entrepris une étude cas-témoins à l’intérieur de la cohorte de l’INTAPP pour établir le lien entre la concentration sérique de vitamines antioxydantes et le risque de prééclampsie. Un total de 115 cas de prééclampsie et 229 témoins ont été inclus. Les concentrations de vitamine E ont été mesurées de façon longitudinale à 12-18 semaines (avant la prise de suppléments), à 24-26 semaines et à 32-34 semaines de grossesse en utilisant la chromatographie liquide de haute performance. Lorsqu’examinée en tant que variable continue et après ajustement multivarié, une concentration de base élevée de gamma-tocophérol était associée à un risque augmenté de prééclampsie (quartile supérieur vs quartile inférieur à 24-26 semaines : OR 2,99, IC 95% 1,13-7,89; à 32-34 semaines : OR 4,37, IC 95% 1,35-14,15). Nous n’avons pas trouvé de lien entre les concentrations de alpha-tocophérol et le risque de prééclampsie. En résumé, nous n’avons pas trouvé d’effets de la supplémentation en vitamines C et E sur le risque de prééclampsie dans l’INTAPP. Nous avons toutefois trouvé, dans la cohorte canadienne, qu’une faible prise de potassium et de zinc, tel qu’estimée par les questionnaires de fréquence alimentaire, était associée à un risque augmenté de prééclampsie. Aussi, une plus grande concentration sérique de gamma-tocophérol pendant la grossesse était associée à un risque augmenté de prééclampsie.

Laser granulometry of Holocene estuarine silts: effects of hydrogen peroxide treatment

The Holocene estuarine silts of the Severn Estuary Levels (southwest Britain) are representative of their kind in northwest Europe. They contain two broad types of plant material: particles codeposited with mineral grains from the estuarine water body, and extraneous debris (stems of indigenous prior plants; post depositional root matter) which is difficult to remove completely by physical means. Treatment with hydrogen peroxide before laser granulometry removes all plant material regardless of kind, drastically reduces values for the mean grain size and median size relative to untreated samples, but has little effect on the mode, except for a restricted group of bimodal-platykurtic, medium-coarse silts. It is concluded that, in the case of sediments of the general kind examined, no advantages acrue from the treatment of samples with hydrogen peroxide prior to analysis. Although a discrete rather than continuous variable, values of the mode obtained from untreated sediments are suggested to be acceptable for most purposes where a measure of central tendency is required.

A randomised crossover study investigating the effects of galacto-oligosaccharides on the faecal microbiota in men and women over 50 years of age

Faecal microbial changes associated with ageing include reduced bifidobacteria numbers. These changes coincide with an increased risk of disease development. Prebiotics have been observed to increase bifidobacteria numbers within humans. The present study aimed to determine if prebiotic galacto-oligosaccharides (GOS) could benefit a population of men and women of 50 years and above, through modulation of faecal microbiota, fermentation characteristics and faecal water genotoxicity. A total of thirty-seven volunteers completed this randomised, double-blind, placebo-controlled crossover trial. The treatments – juice containing 4 g GOS and placebo – were consumed twice daily for 3 weeks, preceded by 3-week washout periods. To study the effect of GOS on different large bowel regions, three-stage continuous culture systems were conducted in parallel using faecal inocula from three volunteers. Faecal samples were microbially enumerated by quantitative PCR. In vivo, following GOS intervention, bifidobacteria were significantly more compared to post-placebo (P = 0·02). Accordingly, GOS supplementation had a bifidogenic effect in all in vitro system vessels. Furthermore, in vessel 1 (similar to the proximal colon), GOS fermentation led to more lactobacilli and increased butyrate. No changes in faecal water genotoxicity were observed. To conclude, GOS supplementation significantly increased bifidobacteria numbers in vivo and in vitro. Increased butyrate production and elevated bifidobacteria numbers may constitute beneficial modulation of the gut microbiota in a maturing population.

Stability of stationary solutions of the forced Navier-Stokes equations on the two-torus

We study the linear and nonlinear stability of stationary solutions of the forced two-dimensional Navier-Stokes equations on the domain [0,2π]x[0,2π/α], where α ϵ(0,1], with doubly periodic boundary conditions. For the linear problem we employ the classical energy{enstrophy argument to derive some fundamental properties of unstable eigenmodes. From this it is shown that forces of pure χ2-modes having wavelengths greater than 2π do not give rise to linear instability of the corresponding primary stationary solutions. For the nonlinear problem, we prove the equivalence of nonlinear stability with respect to the energy and enstrophy norms. This equivalence is then applied to derive optimal conditions for nonlinear stability, including both the high-and low-Reynolds-number limits.

An in vitro study of the effect of probiotics, prebiotics and synbiotics on the elderly faecal microbiota

The use of dietary intervention in the elderly in order to beneficially modulate their gut microbiota has not been extensively studied. The influence of two probiotics (Bifidobacterium longum and Lactobacillus fermentum) and two prebiotics [isomaltooligosaccharides (IMO) and short-chain fructooligosaccharides (FOS)], individually and in synbiotic combinations (B. longum with IMO, L. fermentum with FOS) on the gut microbiota of elderly individuals was investigated using faecal batch cultures and three-stage continuous culture systems. Population changes of major bacterial groups were enumerated using fluorescent in situ hybridisation (FISH). B. longum and IMO alone significantly increased the Bifidobacterium count after 5 and 10 h of fermentation and their synbiotic combination significantly decreased the Bacteroides count after 5 h of fermentation. L. fermentum and FOS alone significantly increased the Bifidobacterium count after 10 h and 5, 10 and 24 h of fermentation respectively. B. longum with IMO as well as B. longum and IMO alone significantly increased acetic acid concentration during the fermentation in batch cultures. In the three-stage continuous culture systems, both synbiotic combinations increased the Bifidobacterium and Lactobacillus count in the third vessel representing the distal colon. In addition, the synbiotic combination of L. fermentum with scFOS resulted in a significant increase in the concentration of acetic acid. The results show that the elderly gut microbiota can be modulated in vitro with the appropriate pro-, pre- and synbiotics.

Energy consistent discontinuous Galerkin methods for the Navier–Stokes–Korteweg system

We design consistent discontinuous Galerkin finite element schemes for the approximation of the Euler-Korteweg and the Navier-Stokes-Korteweg systems. We show that the scheme for the Euler-Korteweg system is energy and mass conservative and that the scheme for the Navier-Stokes-Korteweg system is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to viscous effects, that is, there is no numerical dissipation. In this sense the methods are consistent with the energy dissipation of the continuous PDE systems. - See more at: http://www.ams.org/journals/mcom/2014-83-289/S0025-5718-2014-02792-0/home.html#sthash.rwTIhNWi.dpuf

ADRB2 and LEPR Gene Polymorphisms: Synergistic Effects on the Risk of Obesity in Japanese

The objective of the present study was to validate a recently reported synergistic effect between variants located in the leptin receptor (LEPR) gene and in the beta-2 adrenergic receptor (ADRB2) gene on the risk of overweight/obesity. We studied a middle-aged/ elderly sample of 4,193 nondiabetic Japanese subjects stratified according gender (1,911 women and 2,282 men). The LEPR Gln223Arg (rs1137101) variant as well as both ADRB2 Arg16Gly (rs1042713) and Gln27Glu (rs1042714) polymorphisms were analyzed. The primary outcome was the risk of overweight/obesity defined as BMI >= 25 kg/m(2), whereas secondary outcomes included the risk of a BMI >= 27 kg/m(2) and BMI as a continuous variable. None of the studied polymorphisms showed statistically significant individual effects, regardless of the group or phenotype studied. Haplotype analysis also did not disclose any associations of ADRB2 polymorphisms with BMI. However, dimensionality reduction-based models confirmed significant interactions among the investigated variants for BMI as a continuous variable as well as for the risk of obesity defined as BMI >= 27 kg/m(2). All disclosed interactions were found in men only. Our results provide external validation for a male specific ADRB2-LEPR interaction effect on the risk of overweight/obesity, but indicate that effect sizes associated with these interactions may be smaller in the population studied.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

TRANSITIVE CIRCLE EXCHANGE TRANSFORMATIONS WITH FLIPS

We study the existence of transit we exchange transformations with flips defined on the unit circle S(1). We provide a complete answer to the question of whether there exists a transitive exchange transformation of S(1) defined on a subintervals and having f flips.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

HOMEOMORPHISMS OF THE ANNULUS WITH A TRANSITIVE LIFT II

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the in finite strip (A) over tilde which is transitive. We show that, if the rotation number of (f) over tilde restricted to both boundary components of A is strictly positive, then there exists a closed nonempty connected set Gamma subset of (A) over tilde such that Gamma subset of] - infinity,0] x [0,1], Gamma is unbounded, the projection of to Gamma A is dense, Gamma - (1, 0) subset of Gamma and (f) over tilde(Gamma) subset of Gamma. Also, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of Gamma, lim sup (n ->infinity) p(1)((f) over tilde (n) ((Z) over tilde)) - p(1) ((Z) over tilde)/n < -d.