We present new observations of the nuclear star cluster in the central parsec of the Galaxy with the adaptive optics assisted, integral field spectrograph SINFONI on the ESO/VLT. Our work allows the spectroscopic detection of early and late type stars to m K ≥ 16, more than 2 magnitudes deeper than our previous data sets. Our observations result in a total sample of 177 bona fide early-type stars. We find that most of these Wolf Rayet (WR), O-and B-stars reside in two strongly warped disks between 0.8" and 12" from SgrA*, as well as a central compact concentration (the S-star cluster) centered on SgrA*. The later type B stars (m K > 15) in the radial interval between 0.8" and 12" seem to be in a more isotropic distribution outside the disks. The observed dearth of late type stars in the central few arcseconds is puzzling, even when allowing for stellar collisions. The stellar mass function of the disk stars is extremely top heavy with a best fit power law of dN/dm ∝ m −0.45±0.3 .Since at least the WR/O-stars were formed in situ in a single star formation event ∼6 Myrs ago, this mass function probably reflects the initial mass function (IMF). The mass functions of the S-stars inside 0.8" and of the early-type stars at distances beyond 12" are compatible with a standard Salpeter/Kroupa IMF (best fit power law of dN/dm ∝ m −2.15±0.3 ).

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High speed trains are currently meant to run faster and to carry heavier loads, while being less energy consuming and still respecting the security and comfort certification criteria. To face these challenges, a better understanding of the interaction between the dynamic train behavior and the track geometry is needed. As during its lifecycle, the train faces a great variability of track conditions, this dynamic behavior has indeed to be characterized on track portions sets that are representative of the whole railway network. This paper is thus devoted to the development of a stochastic modeling of the track geometry and its identification with experimental measurements. Based on a spatial and statistical decomposition, this model allows the spatial and statistical variability and dependency of the track geometry to be taken into account. Moreover, it allows the generation of realistic track geometries that are representative of a whole railway network. First, this paper describes a practical implementation of the proposed method and then applies this method to the modeling of a particular French high speed line, for which experimental data are available.