On-line relational SOM for dissimilarity data

International audienceIn some applications and in order to address real world situations better, data may be more complex than simple vectors. In some examples, they can be known through their pairwise dissimilarities only. Several variants of the Self Organizing Map algorithm were introduced to generalize the original algorithm to this framework. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual combination of all elements in the data set. However, this latter approach suffers from two main drawbacks. First, its complexity can be large. Second, only a batch version of this algorithm has been studied so far and it often provides results having a bad topographic organization. In this article, an on-line version of relational SOM is described and justified. The algorithm is tested on several datasets, including categorical data and graphs, and compared with the batch version and with other SOM algorithms for non vector data

AGB subpopulations in the nearby globular cluster NGC 6397

It has been well established that Galactic Globular clusters (GCs) harbour more than one stellar population, distinguishable by the anti-correlations of light element abundances (C-N, Na-O, and Mg-Al). These studies have been extended recently to the asymptotic giant branch (AGB). Here we investigate the AGB of NGC 6397 for the first time. We have performed an abundance analysis of high-resolution spectra of 47 RGB and 8 AGB stars, deriving Fe, Na, O, Mg and Al abundances. We find that NGC 6397 shows no evidence of a deficit in Na-rich AGB stars, as reported for some other GCs - the subpopulation ratios of the AGB and RGB in NGC 6397 are identical, within uncertainties. This agrees with expectations from stellar theory. This GC acts as a control for our earlier work on the AGB of M 4 (with contrasting results), since the same tools and methods were used.Comment: 10 pages, 7 figures, 8 tables (2 online-only). Accepted for publication in MNRA

A new method for the spectroscopic identification of stellar non-radial pulsation modes. II. Mode identification of the Delta Scuti star FG Virginis

We present a mode identification based on new high-resolution time-series spectra of the non-radially pulsating Delta Scuti star FG~Vir (HD 106384, V = 6.57, A5V). From 2002 February to June a global Delta Scuti Network (DSN) campaign, utilizing high-resolution spectroscopy and simultaneous photometry has been conducted for FG~Vir in order to provide a theoretical pulsation model. In this campaign we have acquired 969 Echelle spectra covering 147 hours at six observatories. The mode identification was carried out by analyzing line profile variations by means of the Fourier parameter fit method, where the observational Fourier parameters across the line are fitted with theoretical values. This method is especially well suited for determining the azimuthal order m of non-radial pulsation modes and thus complementary with the method of Daszynska-Daszkiewicz (2002) which does best at identifying the degree l. 15 frequencies between 9.2 and 33.5 c/d were detected spectroscopically. We determined the azimuthal order m of 12 modes and constrained their harmonic degree l. Only modes of low degree (l <= 4) were detected, most of them having axisymmetric character mainly due to the relatively low projected rotational velocity of FG Vir. The detected non-axisymmetric modes have azimuthal orders between -2 and 1. We derived an inclination of 19 degrees, which implies an equatorial rotational rate of 66 km/s.Comment: 14 pages, 26 figure

Nanostructures in Ti processed by severe plastic deformation

Metals and alloys processed by severe plastic deformation (SPD) can demonstrate superior mechanical properties, which are rendered by their unique defect structures. In this investigation, transmission electron microscopy and x-ray analysis were used to systematically study the defect structures, including grain and subgrain structures, dislocation cells, dislocation distributions, grain boundaries, and the hierarchy of these structural features, in nanostructured Ti produced by a two-step SPD procedure-warm equal channel angular pressing followed by cold rolling. The effects of these defect structures on the mechanical behaviors of nanostructured Ti are discussed

Observation of the Halo of NGC 3077 Near the "Garland" Region Using the Hubble Space Telescope

We report the detection of upper main sequence stars and red giant branch stars in the halo of an amorphous galaxy, NGC3077. The observations were made using Wide Field Planetary Camera~2 on board the Hubble Space Telescope. The red giant branch luminosity function in I-band shows a sudden discontinuity at I = 24.0 +- 0.1 mag. Identifying this with the tip of the red giant branch (TRGB), and adopting the calibration provided by Lee, Freedman, & Madore (1993) and the foreground extinction of A_B = 0.21 mag, we obtain a distance modulus of (m-M)_0 = 27.93 +- 0.14(random) +- 0.16(sys). This value agrees well with the distance estimates of four other galaxies in the M81 Group. In addition to the RGB stars, we observe a concentration of upper main sequence stars in the halo of NGC3077, which coincides partially with a feature known as the ``Garland''. Using Padua isochrones, these stars are estimated to be <150 Myrs old. Assuming that the nearest encounter between NGC3077 and M81 occurred 280 Myrs ago as predicted by the numerical simulations (Yun 1997), the observed upper main sequence stars are likely the results of the star formation triggered by the M81-NGC3077 tidal interaction.Comment: 15 pages, 8 figures. Accepted for publication in Astrophysical Journa

Geometrically Frustrated Crystals: Elastic Theory and Dislocations

Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is pointed out and the phase diagram of the ring-crystal, which depends on radius and thickness, is discussed.Comment: 4 pages, 3 figure

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

On the AGB stars of M 4: A robust disagreement between spectroscopic observations and theory

Several recent spectroscopic investigations have presented conflicting results on the existence of Na-rich asymptotic giant branch (AGB) stars in the Galactic globular cluster M4 (NGC6121). The studies disagree on whether or not Na-rich red giant branch (RGB) stars evolve to the AGB. For a sample of previously published HER- MES/AAT AGB and RGB stellar spectra we present a re-analysis of O, Na, and Fe abundances, and a new analysis of Mg and Al abundances; we also present CN band strengths for this sample, derived from low-resolution AAOmega spectra. Following a detailed literature comparison, we find that the AGB samples of all studies consistently show lower abundances of Na and Al, and are weaker in CN, than RGB stars in the cluster. This is similar to recent observations of AGB stars in NGC 6752 and M 62. In an attempt to explain this result, we present new theoretical stellar evolutionary models for M 4; however, these predict that all stars, including Na-rich RGB stars, evolve onto the AGB. We test the robustness of our abundance results using a variety of atmospheric models and spectroscopic methods; however, we do not find evidence that systematic modelling uncertainties can explain the apparent lack of Na- rich AGB stars in M4. We conclude that an unexplained, but robust, discordance between observations and theory remains for the AGB stars in M 4.Comment: 25 pages, 21 figures, 15 tables, accepted for publication in MNRA