Tight Bounds for Asymptotic and Approximate Consensus

We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a common value within the convex hull of initial values. This problem, and the related approximate consensus problem, are fundamental building blocks in distributed systems where exact consensus among agents is not required or possible, e.g., man-made distributed control systems, and have applications in the analysis of natural distributed systems, such as flocking and opinion dynamics. We prove tight lower bounds on the contraction rates of asymptotic consensus algorithms in dynamic networks, from which we deduce bounds on the time complexity of approximate consensus algorithms. In particular, the obtained bounds show optimality of asymptotic and approximate consensus algorithms presented in [Charron-Bost et al., ICALP'16] for certain dynamic networks, including the weakest dynamic network model in which asymptotic and approximate consensus are solvable. As a corollary we also obtain asymptotically tight bounds for asymptotic consensus in the classical asynchronous model with crashes. Central to our lower bound proofs is an extended notion of valency, the set of reachable limits of an asymptotic consensus algorithm starting from a given configuration. We further relate topological properties of valencies to the solvability of exact consensus, shedding some light on the relation of these three fundamental problems in dynamic networks

Two-Color Coherent Photodissociation of Nitrogen Oxide in Intense Laser Fields

A simple one-dimensional semi-classical model with a Morse potential is used to investigate the possibility of two-color infrared multi-photon dissociation of vibrationally excited nitrogen oxide. The amplitude ratio effects and adiabatic effects are investigated. Some initial states are found to have thresholds smaller than expected from single-mode considerations and multiple thresholds exist for initial states up to 32. PACS: 42.50.HzComment: 3 pages, old papers, add source files to replace original postscrip

Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series

The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests

Détermination à l'aide d'un modèle récepteur des zones sources à l'origine des concentrations mesurées dans les précipitations collectées en trois sites du réseau MERA (France)

Ces travaux s'inscrivent dans le cadre du programme national de MEsure des Retombées Atmosphériques (MERA). Ils portent sur la recherche de l'origine des précipitations collectées entre 1997 et 1999 dans trois (Morvan, Iraty, Le Casset) des onze stations du réseau MERA localisées en différents points du territoire français. Deux méthodes statistiques ont été utilisées dans cette étude. Les régions à l'origine des fortes concentrations mesurées au site récepteur ont d'abord été déterminées à l'aide d'un modèle (méthode de Seibert) combinant les mesures réalisées sur site et les rétrotrajectoires de masses d'air puis, dans un second temps les différents profils de transport atmosphérique, leur fréquence et concentrations associées ont été évaluées à l'aide d'une classification par Nuées Dynamiques (méthode K-means/distance Euclidienne simple) des rétrotrajectoires de masses d'air. Le test de Kruskal-Wallis a été utilisé pour vérifier si les médianes des concentrations associées à chaque classe sont statistiquement différentes. L'étude réalisée à Iraty (Pyrénées) et au Casset (Alpes) a montré que ces deux stations sont influencées différemment du Morvan. Plus exactement, ces deux sites ne sont pas, ou pratiquement pas, influencés par les zones d'Europe centrale ou du Nord-Ouest fortement émettrices de SO2, de NOx et de NH3. Seul le pH des précipitations collectées à Iraty semble dépendre des émissions de SO2 et de NOx d'une de ces zones. Iraty et le Casset sont très influencées par les émissions anthropiques et par les poussières d'origine terrestres en provenance d'Afrique du Nord. Néanmoins, les niveaux de concentrations mesurés dans les flux en provenance d'Afrique du Nord sont similaires pour Iraty, le Casset et le Morvan (sauf en ions calcium, pour lequel le Casset et Iraty montrent de fortes concentrations). Une autre région européenne peut influencer les niveaux en composés acidifiants mesurés au Casset, il s'agit de l'Italie et de la zone localisée au niveau de l'ex-Yougoslavie. Mais, les niveaux de concentrations qui en résultent sont faibles par rapport à ceux mesurés dans certains flux arrivant au Morvan.The chemistry of precipitation in France was examined using data from the French atmospheric deposition network (MERA). In order to examine the source-receptor relationships responsible for acid rain at three background sites in France, a receptor-oriented model was applied to the precipitation data collected from 1997 to 1999. This methodology combined precipitation and chemical data with air parcel backward trajectories to establish concentration field maps of likely contributing sources. Then, a clustering technique using partitioning methods (K-means/Euclidian distance) was performed to backward trajectories and the distributions of mixing samples associated with backward trajectories in each cluster were compared. The Kruskal-Wallis test was used to verify that the concentration medians associated with each cluster were statistically significant. The results of this study demonstrated that two stations (Iraty and le Casset) were not influenced by the same sources as Morvan. Specifically, these sites were less influenced by high emissions from Central or Northwestern Europe when compared to Morvan. Only the pH seemed under the influence of SO2 and NOx emissions from one of these areas. Iraty and Le casset are very influenced by anthropogenic emissions and the crustal sources around the Mediterranean Basin and North Africa. Other European areas (e.g. Italy) can influence the concentrations recorded at Le Casset but the levels of concentration are lower than those measured at Morvan.This paper represents a complete statistical analysis of wet-only deposition chemistry data for three stations (Iraty, Le Casset and Morvan). Two statistical methods were used in this study. In order to examine the source-receptor relationships responsible for acid rain at these three background sites in France, a receptor-oriented model was applied to the precipitation data collected from 1997 to 1999. This methodology combined chemical data with air parcel backward trajectories to establish concentration field maps of likely contributing sources. This receptor-oriented model was developed by Seibert and it assumes that if a trajectory endpoint falls in a grid cell (i,j), the air mass is assumed to collect components emitted in this cell and once the components are incorporated, they are transported along the trajectory to the receptor site. This model doesn't take into account the atmospheric diffusion and the removal mechanisms occurring during the trajectory from the sources to the receptor. Finally, a concentration field map for the selected species was calculated taking into account all grid cells. For mapping, the grid cells counting fewer than 10 endpoints were not taken in consideration because the confidence of their results was considered too low. The role of three-dimensional backward trajectories is fundamental, so we used three different information sources: the French Institute of Meteorology, Météo-France; the British Atmospheric Data Centre (BADC); and the Atmospheric Environment Service Long Range Transport model of Air Pollution (AES-LRTAP), Canada. These trajectory models were compared for different chemical species. All data were projected in the EMEP grid (150 x 150 km) for establishment of the concentration field map. A clustering technique by partitioning methods (K-means/Euclidian distance) was performed on backward trajectories and the distributions of mixing samples associated with backward trajectories in each cluster were compared. The Kruskal-Wallis test was used to verify that the median concentrations associated with each cluster were statistically significant.The results of this study for Morvan determined five classes of backward trajectories associated with the precipitation collected at this station located in the centre of France. The fluxes from SW and WSW sectors contribute for 52% of events, while the fluxes of NW and E contribute for 31% of events but are mainly responsible for high concentrations of sulphates, nitrates, ammonium and hydronium ion. Regions found to be responsible for rain events coincide with European regions known for their high anthropogenic emissions of SO2 and NOx (Great Britain, North of France, Belgium, The Netherlands and the North of sea).The results for Iraty (South of France) yielded five classes of backward trajectories associated with the precipitation collected in this station. The fluxes from W sectors (NNW, NW, W and WSW) were responsible for 71% of events, while the flux of S (low wind) was responsible for 29% of events but is mainly responsible for high concentrations of sulphates, nitrates, ammonium and calcium. High concentrations of hydronium ion were identified in the NNW sector.The results for Le Casset (East region and mountainous) gave four classes of backward trajectories associated with the precipitation collected in this station. The fluxes from W and WSW sectors were responsible for 35% of events, while the flux of SSW was responsible for 43% and the flux from the SE was responsible for 22% of events. This last sector was mainly responsible for high concentrations of sulphates, nitrates, ammonium and calcium. The concentrations measured at this station were low. Regions found to be responsible for rain events coincide with southern and eastern areas known for their high anthropogenic emissions of SO2 and NOx (north Africa, northern Italy, Yugoslavia).All these results demonstrate that the Iraty and Le Casset stations were not influenced by the same sources as Morvan. Specifically, these sites were less influenced by the high emissions from central or northwestern Europe than Morvan. Only the measurement of pH seemed to be under the influence of SO2 and NOx emissions of one of these areas. Iraty and Le Casset were very influenced by the anthropogenic emissions and the crustal sources around the Mediterranean Basin and North Africa. Other European areas (e.g., Italy) can influence the concentrations recorded at Le Casset but the levels were lower than those measured at Morvan. A relation between sulphates, nitrates and ammonium was identified for Morvan and Le Casset. This observation suggests that aerosol transport of NH4 HSO4, (NH4)2 SO4 and NH4 NO3 is occurring

Theoretical analysis of the implementation of a quantum phase gate with neutral atoms on atom chips

We present a detailed, realistic analysis of the implementation of a proposal for a quantum phase gate based on atomic vibrational states, specializing it to neutral rubidium atoms on atom chips. We show how to create a double--well potential with static currents on the atom chips, using for all relevant parameters values that are achieved with present technology. The potential barrier between the two wells can be modified by varying the currents in order to realize a quantum phase gate for qubit states encoded in the atomic external degree of freedom. The gate performance is analyzed through numerical simulations; the operation time is ~10 ms with a performance fidelity above 99.9%. For storage of the state between the operations the qubit state can be transferred efficiently via Raman transitions to two hyperfine states, where its decoherence is strongly inhibited. In addition we discuss the limits imposed by the proximity of the surface to the gate fidelity.Comment: 9 pages, 5 color figure

Coherent Control of Isotope Separation in HD+ Photodissociation by Strong Fields

The photodissociation of the HD+ molecular ion in intense short- pulsed linearly polarized laser fields is studied using a time- dependent wave-packet approach where molecular rotation is fully included. We show that applying a coherent superposition of the fundamental radiation with its second harmonic can lead to asymmetries in the fragment angular distributions, with significant differences between the hydrogen and deuterium distributions in the long wavelength domain where the permanent dipole is most efficient. This effect is used to induce an appreciable isotope separation.Comment: Physical Review Letters, 1995 (in press). 4 pages in revtex format, 3 uuencoded figures. Full postcript version available at: http://chemphys.weizmann.ac.il/~charron/prl.ps or ftp://scipion.ppm.u-psud.fr/coherent.control/prl.p

Cultured Human Epidermal Cells Do Not Synthesize HLA-DR

All nucleated cells express HLA-A, B, and C antigens. However, only a few cells, including epidermal cells, demonstrate HLA-DR antigens which are potent transplantation immunogens in man. The current study was undertaken to determine if epidermal cells continue to synthesize and/or express HLA-DR antigens after prolonged in vitro culture. Epidermal cells cultured for 7days or more no longer stimulated allogeneic lymphocytes in the epidermal cell-lymphocyte reaction. Indirect immunofluorescence light microscopy of cultured cells using mouse monoclonal antibody to HLA-DR antigen confirmed that these cells do not express HLA-DR antigens whereas they retain β2-microglobulin. Detergent extracts of 12-day cultured epidermal cells biosynthetically labeled with 35S-methionine were immunoprecipitated with monoclonal anti-DR antibody and analyzed by the method of two-dimensional polyacrylamide gel electrophoresis. No radiolabeled proteins were found on these gels in the regions where HLA-DR molecules are known to migrate. These data indicate that HLA-DR antigen is absent from cultured epidermal cells. Finally, we describe a technique for growing epidermal cells on a gelatin membrane which allows subsequent removal of intact cell monolayers from the culture dish. Such monolayers may be useful for purposes of transplantation

Ihog and Boi are essential for Hedgehog signaling in Drosophila

<p>Abstract</p> <p>Background</p> <p>The Hedgehog (Hh) signaling pathway is important for the development of a variety of tissues in both vertebrates and invertebrates. For example, in developing nervous systems Hh signaling is required for the normal differentiation of neural progenitors into mature neurons. The molecular signaling mechanism underlying the function of Hh is not fully understood. In <it>Drosophila</it>, Ihog (Interference hedgehog) and Boi (Brother of Ihog) are related transmembrane proteins of the immunoglobulin superfamily (IgSF) with orthologs in vertebrates. Members of this IgSF subfamily have been shown to bind Hh and promote pathway activation but their exact role in the Hh signaling pathway has remained elusive. To better understand this role <it>in vivo</it>, we generated loss-of-function mutations of the <it>ihog </it>and <it>boi </it>genes, and investigated their effects in developing eye and wing imaginal discs.</p> <p>Results</p> <p>While mutation of either <it>ihog </it>or <it>boi </it>alone had no discernible effect on imaginal tissues, cells in the developing eye disc that were mutant for both <it>ihog </it>and <it>boi </it>failed to activate the Hh pathway, causing severe disruption of photoreceptor differentiation in the retina. In the anterior compartment of the developing wing disc, where different concentrations of the Hh morphogen elicit distinct cellular responses, cells mutant for both <it>ihog </it>and <it>boi </it>failed to activate responses at either high or low thresholds of Hh signaling. They also lost their affinity for neighboring cells and aberrantly sorted out from the anterior compartment of the wing disc into posterior territory. We found that <it>ihog </it>and <it>boi </it>are required for the accumulation of the essential Hh signaling mediator Smoothened (Smo) in Hh-responsive cells, providing evidence that Ihog and Boi act upstream of Smo in the Hh signaling pathway.</p> <p>Conclusions</p> <p>The consequences of <it>boi;ihog </it>mutations for eye development, neural differentiation and wing patterning phenocopy those of <it>smo </it>mutations and uncover an essential role for Ihog and Boi in the Hh signaling pathway.</p