Catalan's intervals and realizers of triangulations

The Stanley lattice, Tamari lattice and Kreweras lattice are three remarkable orders defined on the set of Catalan objects of a given size. These lattices are ordered by inclusion: the Stanley lattice is an extension of the Tamari lattice which is an extension of the Kreweras lattice. The Stanley order can be defined on the set of Dyck paths of size n as the relation of being above. Hence, intervals in the Stanley lattice are pairs of non-crossing Dyck paths. In a former article, the second author defined a bijection Φ between pairs of non-crossing Dyck paths and the realizers of triangulations (or Schnyder woods). We give a simpler description of the bijection Φ. Then, we study the restriction of Φ to Tamari’s and Kreweras’ intervals. We prove that Φ induces a bijection between Tamari intervals and minimal realizers. This gives a bijection between Tamari intervals and triangulations. We also prove that Φ induces a bijection between Kreweras intervals and the (unique) realizers of stack triangulations. Thus, Φ induces a bijection between Kreweras intervals and stacktriangulations which are known to be in bijection with ternary trees.

Política pública en Francia: prohibición general o parcial del velo integral en el territorio nacional: Proyecto de ley del martes 11 de mayo de 2010

La República francesa se ofende por los burkas y de los niqab deambulando por las calles. Ve a sus principios rectores de Liberté, Égalité, Fraternité mofados, a su democracia desafiada, a su convivencia arriesgada. Por ello, el Gobierno francés ha impulsado desde hace un año una política pública que persigue la prohibición del velo integral -llámese burka o niqab- en el conjunto del espacio público. Años atrás, Francia, país que tanto aprecia los debates, se vio inmersa en la cuestión más general de la identidad nacional desde las reacciones de las banlieues en el 2005. Y por ello, Nicolas Sarkosy, en su programa electoral camino de las presidenciales en el 2007, ya incluía como una prioridad el tema de los valores y principios genuinamente franceses y europeos. Y en esta perspectiva, el Ministerio de Inmigración añadió sus calificativos de Integración e Identidad Nacional. El burka en el espacio público ha asaltado los medios de comunicación y la sociedad en su conjunto, especialmente desde hace dos o tres años. Es un problema sin precedentes en las democracias asentadas -aunque podríamos recordar el motín de Esquilache en 1766 bajo el reinado de Carlos III- sin una Jurisprudencia asentada al respecto, ni un marco normativo que lo prevea directamente. Y por ello, la élite política se divide estos días entre los prudentes y los atrevidos, los que se conforman con una prohibición parcial y los que persiguen una prohibición absoluta. Se trata de una política pública atípica, pues los bienes afectados son en realidad valores, principios y conceptos abstractos. Es la República francesa y la cohesión social los que se ven desafiados. Veremos en un primer momento, la etapa de identificación como problema público y su inclusión en la agenda política, por ende desde un punto de vista técnico, analizaremos brevemente esta política pública Top down limitada, y en el último apartado compararemos los argumentos de las dos alternativas que dispone actualmente el Parlamento para aprobar o no una ley al respecto. Por su parte, la Comisión Parlamentaria alegará principios de índole más filosófica que pragmática, mientras que el Consejo de Estado se centrará exclusivamente en los términos jurídicos y en la Jurisprudencia reduciendo en gran medida el impulso inicial del Gobierno. Quedará por ver estos días de debate en l’Assemblée Nationale1 si la prohibición será total o parcial.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

Smooth multibidding mechanisms

We propose a smooth multibidding mechanism for environments where a group of agents have to choose one out of several projects (possibly with the help of a social planner). Our proposal is related to the multibidding mechanism (Pérez-Castrillo and Wettstein, 2002) but it is "smoother" in the sense that small variations in an agent's bids do not lead to dramatic changes in the probability of selecting a project. This mechanism is shown to possess several interesting properties. Unlike in the study by Pérez Castrillo and Wettstein (2002), the equilibrium outcome is unique. Second, it ensures an equal sharing of the surplus that it induces. Finally, it enables reaching an outcome as close to effciency as is desired.

Multilocus sequence analysis reveals the genetic diversity of European fruit tree phytoplasmas and supports the existence of inter-species recombination

The genetic diversity of three temperate fruit tree phytoplasmas ‘Candidatus Phytoplasma prunorum’, ‘Ca. P. mali’ and ‘Ca. P. pyri’ has been established by multilocus sequence analysis. Among the four genetic loci used, the genes imp and aceF distinguished 30 and 24 genotypes, respectively, and showed the highest variability. Percentage of substitution for imp ranged from 50 to 68% according to species. Percentage of substitution varied between 9 and 12% for aceF, whereas it was between 5 and 6% for pnp and secY. In the case of ‘Ca P. prunorum’ the three most prevalent aceF genotypes were detected in both plants and insect vectors, confirming that the prevalent isolates are propagated by insects. The four isolates known to be hypo-virulent had the same aceF sequence, indicating a possible monophyletic origin. Haplotype network reconstructed by eBURST revealed that among the 34 haplotypes of ‘Ca. P. prunorum’, the four hypo-virulent isolates also grouped together in the same clade. Genotyping of some Spanish and Azerbaijanese ‘Ca. P. pyri’ isolates showed that they shared some alleles with ‘Ca. P. prunorum’, supporting for the first time to our knowledge, the existence of inter-species recombination between these two species.

Sales restriction, quality selection and the mode of competition

A regulator imposing “sales restrictions” on firms competing in oligopolistic markets may enhance quality provision by the firms. Moreover, for most restrictions levels, the impact on quality selection is invariant to the mode of competition

Temporal diffeomorphic free-form deformation: application to motion and strain estimation from 3D echocardiography

This paper presents a new registration algorithm, called Temporal Di eomorphic Free Form Deformation (TDFFD), and its application to motion and strain quanti cation from a sequence of 3D ultrasound (US) images. The originality of our approach resides in enforcing time consistency by representing the 4D velocity eld as the sum of continuous spatiotemporal B-Spline kernels. The spatiotemporal displacement eld is then recovered through forward Eulerian integration of the non-stationary velocity eld. The strain tensor iscomputed locally using the spatial derivatives of the reconstructed displacement eld. The energy functional considered in this paper weighs two terms: the image similarity and a regularization term. The image similarity metric is the sum of squared di erences between the intensities of each frame and a reference one. Any frame in the sequence can be chosen as reference. The regularization term is based on theincompressibility of myocardial tissue. TDFFD was compared to pairwise 3D FFD and 3D+t FFD, bothon displacement and velocity elds, on a set of synthetic 3D US images with di erent noise levels. TDFFDshowed increased robustness to noise compared to these two state-of-the-art algorithms. TDFFD also proved to be more resistant to a reduced temporal resolution when decimating this synthetic sequence. Finally, this synthetic dataset was used to determine optimal settings of the TDFFD algorithm. Subsequently, TDFFDwas applied to a database of cardiac 3D US images of the left ventricle acquired from 9 healthy volunteers and 13 patients treated by Cardiac Resynchronization Therapy (CRT). On healthy cases, uniform strain patterns were observed over all myocardial segments, as physiologically expected. On all CRT patients, theimprovement in synchrony of regional longitudinal strain correlated with CRT clinical outcome as quanti ed by the reduction of end-systolic left ventricular volume at follow-up (6 and 12 months), showing the potential of the proposed algorithm for the assessment of CRT.

Long-range transport of Saharan dust to northern Europe: The 11-16 October 2001 outbreak observed with EARLINET

The spread of mineral particles over southwestern, western, and central Europeresulting from a strong Saharan dust outbreak in October 2001 was observed at10 stations of the European Aerosol Research Lidar Network (EARLINET). For the firsttime, an optically dense desert dust plume over Europe was characterized coherentlywith high vertical resolution on a continental scale. The main layer was located abovethe boundary layer (above 1-km height above sea level (asl)) up to 3–5-km height, andtraces of dust particles reached heights of 7–8 km. The particle optical depth typicallyranged from 0.1 to 0.5 above 1-km height asl at the wavelength of 532 nm, andmaximum values close to 0.8 were found over northern Germany. The lidar observationsare in qualitative agreement with values of optical depth derived from Total OzoneMapping Spectrometer (TOMS) data. Ten-day backward trajectories clearly indicated theSahara as the source region of the particles and revealed that the dust layer observed,e.g., over Belsk, Poland, crossed the EARLINET site Aberystwyth, UK, and southernScandinavia 24–48 hours before. Lidar-derived particle depolarization ratios,backscatter- and extinction-related A ° ngstro¨m exponents, and extinction-to-backscatterratios mainly ranged from 15 to 25%, 0.5 to 0.5, and 40–80 sr, respectively, within thelofted dust plumes. A few atmospheric model calculations are presented showing the dustconcentration over Europe. The simulations were found to be consistent with thenetwork observations.

Filamin depletion blocks endoplasmic spreading and destabilizes force-bearing adhesions

Cell motility is an essential process that depends on a coherent, cross-linked actin cytoskeleton that physically coordinates the actions of numerous structural and signaling molecules. The actin cross-linking protein, filamin (Fln), has been implicated in the support of three-dimensional cortical actin networks capable of both maintaining cellular integrity and withstanding large forces. Although numerous studies have examined cells lacking one of the multiple Fln isoforms, compensatory mechanisms can mask novel phenotypes only observable by further Fln depletion. Indeed, shRNA-mediated knockdown of FlnA in FlnB¿/¿ mouse embryonic fibroblasts (MEFs) causes a novel endoplasmic spreading deficiency as detected by endoplasmic reticulum markers. Microtubule (MT) extension rates are also decreased but not by peripheral actin flow, because this is also decreased in the Fln-depleted system. Additionally, Fln-depleted MEFs exhibit decreased adhesion stability that appears in increased ruffling of the cell edge, reduced adhesion size, transient traction forces, and decreased stress fibers. FlnA¿/¿ MEFs, but not FlnB¿/¿ MEFs, also show a moderate defect in endoplasm spreading, characterized by initial extension followed by abrupt retractions and stress fiber fracture. FlnA localizes to actin linkages surrounding the endoplasm, adhesions, and stress fibers. Thus we suggest that Flns have a major role in the maintenance of actin-based mechanical linkages that enable endoplasmic spreading and MT extension as well as sustained traction forces and mature focal adhesions.

Growth, optical characterization, and laser operation of a stoichiometric crystal KYb(WO4)(2)

We present our recent achievements in the growing and optical characterization of KYb(WO4)2 (hereafter KYbW) crystals and demonstrate laser operation in this stoichiometric material. Single crystals of KYbW with optimal crystalline quality have been grown by the top-seeded-solution growth slow-cooling method. The optical anisotropy of this monoclinic crystal has been characterized, locating the tensor of the optical indicatrix and measuring the dispersion of the principal values of the refractive indices as well as the thermo-optic coefficients. Sellmeier equations have been constructed valid in the visible and near-IR spectral range. Raman scattering has been used to determine the phonon energies of KYbW and a simple physical model is applied for classification of the lattice vibration modes. Spectroscopic studies (absorption and emission measurements at room and low temperature) have been carried out in the spectral region near 1 µm characteristic for the ytterbium transition. Energy positions of the Stark sublevels of the ground and the excited state manifolds have been determined and the vibronic substructure has been identified. The intrinsic lifetime of the upper laser level has been measured taking care to suppress the effect of reabsorption and the intrinsic quantum efficiency has been estimated. Lasing has been demonstrated near 1074 nm with 41% slope efficiency at room temperature using a 0.5 mm thin plate of KYbW. This laser material holds great promise for diode pumped high-power lasers, thin disk and waveguide designs as well as for ultrashort (ps/fs) pulse laser systems.

Le Gravettien de la côte méditerranéenne ibérique

Même si les données disponibles pour le Gravettien méditerranéen ibérique sont réduites et dans des contextes stratigraphiques mal définis, nous présentons dans ce travail les révisions de quelques sites majeurs (Reclau Viver, l"Arbreda, Parpalló, Malladetes, Beneito et Cendres ainsi que de quelques autres gisements. La vision globale du Gravettien méditerranéen ibérique nous montre, dans la période ancienne, une faible présence mais une industrie lithique et osseuse très classique est observée dans les phases moyenne et finale de la période.

Chaotic Kabanov formula for the Azéma martingales

We derive the chaotic expansion of the product of nth- and first-order multiple stochastic integrals with respect to certain normal martingales. This is done by application of the classical and quantum product formulae for multiple stochastic integrals. Our approach extends existing results on chaotic calculus for normal martingales and exhibits properties, relative to multiple stochastic integrals, polynomials and Wick products, that characterize the Wiener and Poisson processes.