On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.Comment: 27 pages; 1 figur

A Hierarchical Recurrent Encoder-Decoder For Generative Context-Aware Query Suggestion

Users may strive to formulate an adequate textual query for their information need. Search engines assist the users by presenting query suggestions. To preserve the original search intent, suggestions should be context-aware and account for the previous queries issued by the user. Achieving context awareness is challenging due to data sparsity. We present a probabilistic suggestion model that is able to account for sequences of previous queries of arbitrary lengths. Our novel hierarchical recurrent encoder-decoder architecture allows the model to be sensitive to the order of queries in the context while avoiding data sparsity. Additionally, our model can suggest for rare, or long-tail, queries. The produced suggestions are synthetic and are sampled one word at a time, using computationally cheap decoding techniques. This is in contrast to current synthetic suggestion models relying upon machine learning pipelines and hand-engineered feature sets. Results show that it outperforms existing context-aware approaches in a next query prediction setting. In addition to query suggestion, our model is general enough to be used in a variety of other applications.Comment: To appear in Conference of Information Knowledge and Management (CIKM) 201

Polarimetric variations of binary stars. III Periodic polarimetric variations of the Herbig Ae/Be star MWC 1080

We present polarimetric observations of a massive pre-main sequence short-period binary star of the Herbig Ae/Be type, MWC 1080. The mean polarization at 7660 A is 1.60% at 81.6 deg, or 0.6% at 139 deg if an estimate of the interstellar polarization is subtracted. The intrinsic polarization points to an asymmetric geometry of the circumstellar or circumbinary environment while the 139 deg intrinsic position angle traces the axis of symmetry of the system and is perpendicular to the position angle of the outflow cavity. The polarization and its position angle are clearly variable, at all wavelengths, and on time scales of hours, days, months, and years. Stochastic variability is accompanied by periodic variations caused by the orbital motion of the stars in their dusty environment. These periodic polarimetric variations are the first phased-locked ones detected for a pre-main sequence binary. The variations are not simply double-periodic (seen twice per orbit) but include single-periodic (seen once per orbit) and higher-order variations. The presence of single-periodic variations could be due to non equal mass stars, the presence of dust grains, an asymmetric configuration of the circumstellar or circumbinary material, or the eccentricity of the orbit. MWC 1080 is an eclipsing binary with primary and secondary eclipses occurring at phases 0.0 and 0.55. The signatures of the eclipses are seen in the polarimetric observations.Comment: 30 pages, 8 figures, to be published in the Astronomical Journa

Ring Formation in Magnetically Subcritical Clouds and Multiple Star Formation

We study numerically the ambipolar diffusion-driven evolution of non-rotating, magnetically subcritical, disk-like molecular clouds, assuming axisymmetry. Previous similar studies have concentrated on the formation of single magnetically supercritical cores at the cloud center, which collapse to form isolated stars. We show that, for a cloud with many Jeans masses and a relatively flat mass distribution near the center, a magnetically supercritical ring is produced instead. The supercritical ring contains a mass well above the Jeans limit. It is expected to break up, through both gravitational and possibly magnetic interchange instabilities, into a number of supercritical dense cores, whose dynamic collapse may give rise to a burst of star formation. Non-axisymmetric calculations are needed to follow in detail the expected ring fragmentation into multiple cores and the subsequent core evolution. Implications of our results on multiple star formation in general and the northwestern cluster of protostars in the Serpens molecular cloud core in particular are discussed.Comment: 25 pages, 4 figures, to appear in Ap

Fronts and interfaces in bistable extended mappings

We study the interfaces' time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the convolution with a function of bounded variation. We prove the existence of travelling wave interfaces, namely fronts, and the uniqueness of the corresponding selected velocity and shape. This selected velocity is shown to be the propagating velocity for any interface, to depend continuously on the couplings and to increase with the symmetry parameter of the local nonlinearity. We apply the results to several examples including discrete and continuous couplings, and the planar fronts' dynamics in multi-dimensional Coupled Map Lattices. We eventually emphasize on the extension to other kinds of fronts and to a more general class of bistable extended mappings for which the couplings are allowed to be nonlinear and the local map to be smooth.Comment: 27 pages, 3 figures, submitted to Nonlinearit

The JCMT Gould Belt Survey: the effect of molecular contamination in SCUBA-2 observations of Orion A

Thermal emission from cold dust grains in giant molecular clouds can be used to probe the physical properties, such as density, temperature and emissivity in star-forming regions. We present the SCUBA-2 shared-risk observations at 450 $\mu$m and 850 $\mu$m of the Orion A molecular cloud complex taken at the James Clerk Maxwell Telescope (JCMT). Previous studies showed that molecular emission lines can contribute significantly to the measured fluxes in those continuum bands. We use the HARP $^{12}$CO J=3-2 integrated intensity map for Orion A in order to evaluate the molecular line contamination and its effects on the SCUBA-2 maps. With the corrected fluxes, we have obtained a new spectral index $\alpha$ map for the thermal emission of dust in the well-known integral-shaped filament. Furthermore, we compare a sample of 33 sources, selected over the Orion A molecular cloud complex for their high $^{12}$CO J=3-2 line contamination, to 27 previously identified clumps in OMC-4. This allows us to quantify the effect of line contamination on the ratio of 850 $\mu$m to 450 $\mu$m flux densities and how it modifies the deduced spectral index of emissivity $\beta$ for the dust grains. We also show that at least one Spitzer-identified protostellar core in OMC-5 has a $^{12}$CO J=3-2 contamination level of 16 %. Furthermore, we find the strongest contamination level (44 %) towards a young star with disk near OMC-2. This work is part of the JCMT Gould Belt Legacy Survey.Comment: 13 pages, 6 figures, Accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS

Existence and Stability of Steady Fronts in Bistable CML

We prove the existence and we study the stability of the kink-like fixed points in a simple Coupled Map Lattice for which the local dynamics has two stable fixed points. The condition for the existence allows us to define a critical value of the coupling parameter where a (multi) generalized saddle-node bifurcation occurs and destroys these solutions. An extension of the results to other CML's in the same class is also displayed. Finally, we emphasize the property of spatial chaos for small coupling.Comment: 18 pages, uuencoded PostScript file, J. Stat. Phys. (In press

Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of white noise. For strong coupling (of the order N^2), the system synchronises, in the sense that all oscillators assume almost the same position in their respective local potential most of the time. In a previous paper, we showed that the transition from strong to weak coupling involves a sequence of symmetry-breaking bifurcations of the system's stationary configurations, and analysed in particular the behaviour for coupling intensities slightly below the synchronisation threshold, for arbitrary N. Here we describe the behaviour for any positive coupling intensity \gamma of order N^2, provided the particle number N is sufficiently large (as a function of \gamma/N^2). In particular, we determine the transition time between synchronised states, as well as the shape of the "critical droplet", to leading order in 1/N. Our techniques involve the control of the exact number of periodic orbits of a near-integrable twist map, allowing us to give a detailed description of the system's potential landscape, in which the metastable behaviour is encoded

Extensive collection of femtoliter pad secretion droplets in beetle Leptinotarsa decemlineata allows nanoliter microrheology

Pads of beetles are covered with long, deformable setae, each ending in a micrometric terminal plate coated with secretory fluid. It was recently shown that the layer of the pad secretion covering the terminal plates is responsible for the generation of strong attractive forces. However, less is known about the fluid itself because it is produced in extremely small quantity. We here present a first experimental investigation of the rheological properties of the pad secretion in the Colorado potato beetle {\it Leptinotarsa decemlineata}. Because the secretion is produced in an extremely small amount at the level of the terminal plate, we first develop a procedure based on capillary effects to collect the secretion. We then manage to incorporate micrometric beads, initially in the form of a dry powder, and record their thermal motion to determine the mechanical properties of the surrounding medium. We achieve such a quantitative measurement within the collected volume, much smaller than the $1 {\rm \mu}$l sample volume usually required for this technique. Surprisingly, the beetle secretion was found to behave as a purely viscous liquid, of high viscosity. This suggests that no specific complex fluid behaviour is needed during beetle locomotion. We build a scenario for the contact formation between the spatula at the setal tip and a substrate, during the insect walk. We show that the attachment dynamics of the insect pad computed from the high measured viscosity is in good agreement with observed insect pace. We finally discuss the consequences of the secretion viscosity on the insect adhesion

Kinks Dynamics in One-Dimensional Coupled Map Lattices

We examine the problem of the dynamics of interfaces in a one-dimensional space-time discrete dynamical system. Two different regimes are studied : the non-propagating and the propagating one. In the first case, after proving the existence of such solutions, we show how they can be described using Taylor expansions. The second situation deals with the assumption of a travelling wave to follow the kink propagation. Then a comparison with the corresponding continuous model is proposed. We find that these methods are useful in simple dynamical situations but their application to complex dynamical behaviour is not yet understood.Comment: 17pages, LaTex,3 fig available on cpt.univ-mrs.fr directory pub/preprints/94/dynamical-systems/94-P.307