Diffusion Maps, Spectral Clustering and Eigenfunctions of Fokker-Planck operators

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of the corresponding Markov matrix is optimal under a certain mean squared error criterion. Furthermore, assuming that data points are random samples from a density p(\x) = e^{-U(\x)} we identify these eigenvectors as discrete approximations of eigenfunctions of a Fokker-Planck operator in a potential 2U(\x) with reflecting boundary conditions. Finally, applying known results regarding the eigenvalues and eigenfunctions of the continuous Fokker-Planck operator, we provide a mathematical justification for the success of spectral clustering and dimensional reduction algorithms based on these first few eigenvectors. This analysis elucidates, in terms of the characteristics of diffusion processes, many empirical findings regarding spectral clustering algorithms.Comment: submitted to NIPS 200

An intercomparison of measured pressure-broadening, pressure shifting parameters of carbon dioxide and their temperature dependence

International audienceAn intercomparison of measured pressure-broadening and pressure-shifting coefficients for carbon dioxide absorption lines was done. The work focuses on collision systems where a significant number of data can be found (CO2-N2, CO2-O2, CO2-air, and CO2-CO2) and yield information important to applications related to Earth's atmosphere. The literature was searched for measured line shape parameter data for the collision systems mentioned above. Databases were created for each perturbing gas with the ro-vibrational transition as the key. Using these databases intercomparisons of the measurements of half-widths, their temperature dependence, and line shifts were made. The data allow the investigations of trends in the data with respect to the vibrational and the rotational quantum numbers, various line shape models, and isotopologue effects

Observations sur le cycle du detérminisme de la production chez la Vigne à l'occasion de la mise au point d'une méthode d'infection artificielle par le mildiou (Plasmopara viticola) pour l'évaluation des fongicides au champ

L'étude biométrique d'un essai destine à la mise au point d'une méthode d'appreciation de la valeur de produits fongicides (anti-mildiou), montre que la technique de brumisation permet de faire des essais valides même dans des conditions climatiques peu propices au mildiou car on obtient une infection sévère et uniforme, et l'ordre de classement des produits est sensiblement Je meme qu'en conditions naturelles.Les plantes ayant subi des destructions du feuillage très diverses suivant les traitements on été étudiées pendant trois ans. Cette étude démontre l'existence du cycle de trois ans: constitution de réserves, initiation florale, production de grappes déjà postulé par ailleurs.Observations on the cycle determining the yield of the grapevine made while perfecting a method of artificial infection by mildew (Plasmopara viticola) in order to evaluate fungicides in the fieldSpraying a water mist ("brumisation") during the summer months results in a strong and even downy mildew infection on one year old rooted vine cuttings grown in the field. This makes comparative trials of fungicides possible even in unfavourable (dry) years.Such a trial, involving four levels (spray formulations) of the fungicides factor, two levels (with or without) of the mist factor, with five replications in plots of six plants, resulted in a set of plants having suffered various degrees of foliage destruction. Measuring these plants during three successive years, starting with the differential treatment year, provided the basis for checking an hypothesis on the determination of yield in the grapevine.Progressive analysis of variance of regressions (WooLF 1951) was used in the interpretation of results.Vigour in the second year was negatively correlated with foliar damage in the first year. In turn, number of bunches in the third year was correlated with vigour in the second year, hence with foliar damage in the first year.This lends support to the hypothesis that, in the grapevine, there is a three year cycle leading to the harvested clusters.On an adult plant, three cycles are simultaneously at work at every moment. These cycles are competing for energy fixed by photosynthesls; hormonal correlations that may be correlated with energy (carbohydrates) storage, for instance through its influence on root system volume, are also at play.The implications of these results, especially for experimental work with the grapevine, are discussed

Keck Observatory Laser Guide Star Adaptive Optics Discovery and Characterization of a Satellite to the Large Kuiper Belt Object 2003 EL_(61)

The newly commissioned laser guide star adaptive optics system at Keck Observatory has been used to discover and characterize the orbit of a satellite to the bright Kuiper Belt object 2003 EL_(61). Observations over a 6 month period show that the satellite has a semimajor axis of 49,500 ± 400 km, an orbital period of 49.12 ± 0.03 days, and an eccentricity of 0.050 ± 0.003. The inferred mass of the system is (4.2 ± 0.1) × 10^(21) kg, or ~32% of the mass of Pluto and 28.6% ± 0.7% of the mass of the Pluto-Charon system. Mutual occultations occurred in 1999 and will not occur again until 2138. The orbit is fully consistent neither with one tidally evolved from an earlier closer configuration nor with one evolved inward by dynamical friction from an earlier more distant configuration

A hydrodynamic study of the circumstellar envelope of alpha Scorpii

Context: Both the absolute mass-loss rates and the mechanisms that drive the mass loss of late-type supergiants are still not well known. Binaries such as alpha Sco provide the most detailed empirical information about the winds of these stars. Aims: The goal was to improve the binary technique for the determination of the mass-loss rate of alpha Sco A by including a realistic density distribution and velocity field from hydrodynamic and plasma simulations. Methods: We performed 3D hydrodynamic simulations of the circumstellar envelope of alpha Sco in combination with plasma simulations accounting for the heating, ionization, and excitation of the wind by the radiation of alpha Sco B. These simulations served as the basis for an examination of circumstellar absorption lines in the spectrum of alpha Sco B as well as of emission lines from the Antares nebula. Results: The present model of the extended envelope of alpha Sco reproduces some of the structures that were observed in the circumstellar absorption lines in the spectrum of alpha Sco B. Our theoretical density and velocity distributions of the outflow deviate considerably from a spherically expanding model, which was used in previous studies. This results in a higher mass-loss rate of (2 +/- 0.5) x 10^-6 M_sun/yr. The hot H II region around the secondary star induces an additional acceleration of the wind at large distances from the primary, which is seen in absorption lines of Ti II and Cr II at -30 km/s.Comment: 12 pages, 14 figures, accepted for publication in A&

Satellites of the largest Kuiper Belt objects

We have searched the four brightest objects in the Kuiper Belt for the presence of satellites using the newly commissioned Keck Observatory Laser Guide Star Adaptive Optics system. Satellites are seen around three of the four objects: Pluto (whose satellite Charon is well-known and whose recently discovered smaller satellites are too faint to be detected), 2003 EL61 (where a second satellite is seen in addition to the previously known satellite), and 2003 UB313 (where a satellite is seen for the first time). The object 2005 FY9, the brightest Kuiper Belt object (KBO) after Pluto, does not have a satellite detectable within 0".4 with a brightness of more than 1% of the primary. The presence of satellites around three of the four brightest KBOs is inconsistent with the fraction of satellites in the Kuiper Belt at large at the 99.2% confidence level, suggesting a different formation mechanism for these largest KBO satellites. The two satellites of 2003 EL61, and the one satellite of 2003 UB313, with fractional brightnesses of 5% and 1.5%, and 2%, of their primaries, respectively, are significantly fainter relative to their primaries than other known KBO satellites, again pointing to possible differences in their origin

Forces on Dust Grains Exposed to Anisotropic Interstellar Radiation Fields

Grains exposed to anisotropic radiation fields are subjected to forces due to the asymmetric photon-stimulated ejection of particles. These forces act in addition to the ``radiation pressure'' due to absorption and scattering. Here we model the forces due to photoelectron emission and the photodesorption of adatoms. The ``photoelectric'' force depends on the ambient conditions relevant to grain charging. We find that it is comparable to the radiation pressure when the grain potential is relatively low and the radiation spectrum is relatively hard. The calculation of the ``photodesorption'' force is highly uncertain, since the surface physics and chemsitry of grain materials are poorly understood at present. For our simple yet plausible model, the photodesorption force dominates the radiation pressure for grains with size >~0.1 micron exposed to starlight from OB stars. We find that the anisotropy of the interstellar radiation field is ~10% in the visible and ultraviolet. We estimate size-dependent drift speeds for grains in the cold and warm neutral media and find that micron-sized grains could potentially be moved across a diffuse cloud during its lifetime.Comment: LaTeX(41 pages, 19 figures), submitted to Ap

Playing fast and loose with music recognition

We report lessons from iteratively developing a music recognition system to enable a wide range of musicians to embed musical codes into their typical performance practice. The musician composes fragments of music that can be played back with varying levels of embellishment, disguise and looseness to trigger digital interactions. We collaborated with twenty-three musicians, spanning professionals to amateurs and working with a variety of instruments. We chart the rapid evolution of the system to meet their needs as they strove to integrate music recognition technology into their performance practice, introducing multiple features to enable them to trade-off reliability with musical expression. Collectively, these support the idea of deliberately introducing ‘looseness’ into interactive systems by addressing the three key challenges of control, feedback and attunement, and highlight the potential role for written notations in other recognition-based systems

New light on the S235A-B star forming region

The S235A-B star forming region has been extensively observed in the past from the radio to the near-IR, but what was happening in the immediate surroundings of the water maser, placed in between the two nebulosities, was still unclear because of insufficient resolution especially in the spectral range from the Far-IR to the mm, even though there were sound indications that new young stellar objects (YSOs) are being formed there. We present here new high resolution maps at mm wavelengths in different molecules (HCO+, C34S, H2CS, SO2 and CH3CN), as well as in the 1.2 and 3.3 mm continuum obtained with the Plateau de Bure interferometer, and JCMT observations at 450 micron and 850 micron that unambiguously reveal the presence of new YSOs placed in between the two HII regions S235A and S235B and associated with the water maser. A molecular core and an unresolved source in the mm and in the sub-mm are centred on the maser, with indication of mass infall onto the core. Two molecular bipolar outflows and a jet originate from the same position. Weak evidence is found for a molecular rotating disk perpendicular to the direction of the main bipolar outflow. The derived parameters indicate that one of the YSOs is an intermediate luminosity object (L~1000 Lsun) in a very early evolutionary phase, embedded in a molecular core of ~100 Msun, with a temperature of 30 K. The main source of energy for the YSO could come from gravitational infall, thus making of this YSO a rare example of intermediate luminosity protostar representing a link between the earliest evolutionary phases of massive stars and low mass protostars of class 0-I.Comment: 19 pages, 22 figures, to be published in Astronomy & Astrophysic