On homotopies with triple points of classical knots

We consider a knot homotopy as a cylinder in 4-space. An ordinary triple point $p$ of the cylinder is called {\em coherent} if all three branches intersect at $p$ pairwise with the same index. A {\em triple unknotting} of a classical knot $K$ is a homotopy which connects $K$ with the trivial knot and which has as singularities only coherent triple points. We give a new formula for the first Vassiliev invariant $v_2(K)$ by using triple unknottings. As a corollary we obtain a very simple proof of the fact that passing a coherent triple point always changes the knot type. As another corollary we show that there are triple unknottings which are not homotopic as triple unknottings even if we allow more complicated singularities to appear in the homotopy of the homotopy.Comment: 10 pages, 13 figures, bugs in figures correcte

On the functional form of the metallicity-giant planet correlation

It is generally accepted that the presence of a giant planet is strongly dependent on the stellar metallicity. A stellar mass dependence has also been investigated, but this dependence does not seem as strong as the metallicity dependence. Even for metallicity, however, the exact form of the correlation has not been established. In this paper, we test several scenarios for describing the frequency of giant planets as a function of its host parameters. We perform this test on two volume-limited samples (from CORALIE and HARPS). By using a Bayesian analysis, we quantitatively compared the different scenarios. We confirm that giant planet frequency is indeed a function of metallicity. However, there is no statistical difference between a constant or an exponential function for stars with subsolar metallicities contrary to what has been previously stated in the literature. The dependence on stellar mass could neither be confirmed nor be discarded.Comment: 5 pages, 2 figures, accepted in A&

A new analysis of the WASP-3 system: no evidence for an additional companion

In this work we investigate the problem concerning the presence of additional bodies gravitationally bounded with the WASP-3 system. We present eight new transits of this planet and analyse all the photometric and radial velocity data published so far. We did not observe significant periodicities in the Fourier spectrum of the observed minus calculated (O-C) transit timing and radial velocity diagrams (the highest peak having false-alarm probabilities of 56 per cent and 31 per cent, respectively) or long-term trends. Combining all the available information, we conclude that the radial velocity and transit timing techniques exclude, at 99 per cent confidence limit, any perturber more massive than M \gtrsim 100 M_Earth with periods up to 10 times the period of the inner planet. We also investigate the possible presence of an exomoon on this system and determined that considering the scatter of the O-C transit timing residuals a coplanar exomoon would likely produce detectable transits. This hypothesis is however apparently ruled out by observations conducted by other researchers. In case the orbit of the moon is not coplanar the accuracy of our transit timing and transit duration measurements prevents any significant statement. Interestingly, on the basis of our reanalysis of SOPHIE data we noted that WASP-3 passed from a less active (log R'_hk=-4.95) to a more active (log R'_hk=-4.8) state during the 3 yr monitoring period spanned by the observations. Despite no clear spot crossing has been reported for this system, this analysis claims for a more intensive monitoring of the activity level of this star in order to understand its impact on photometric and radial velocity measurements.Comment: MNRAS accepted (14/08/2012

Ultratransparent glass-ceramics: the structure factor and the quenching of the Rayleigh scattering

Glass-ceramics with nanocrystals present a transparency higher than that expected from the theory of Rayleigh scattering. This ultra-transparency is attributed to the spatial correlation of the nanoparticles. The structure factor is calculated for a simple model system, the random sequential addition of equal spheres, at different volume filling factor. The spatial correlation given by the constraint that particles cannot superimpose produces a diffraction peak with a low $S(q)$ in its low-$q$ tail, which is relevant for light scattering. The physical mechanism producing high transparency in glass-ceramics is demonstrated to be the low density fluctuation in the number of scatterers.Comment: 9 pages, 2 fi

Beyond Node Degree: Evaluating AS Topology Models

This is the accepted version of 'Beyond Node Degree: Evaluating AS Topology Models', archived originally at arXiv:0807.2023v1 [cs.NI] 13 July 2008.Many models have been proposed to generate Internet Autonomous System (AS) topologies, most of which make structural assumptions about the AS graph. In this paper we compare AS topology generation models with several observed AS topologies. In contrast to most previous works, we avoid making assumptions about which topological properties are important to characterize the AS topology. Our analysis shows that, although matching degree-based properties, the existing AS topology generation models fail to capture the complexity of the local interconnection structure between ASs. Furthermore, we use BGP data from multiple vantage points to show that additional measurement locations significantly affect local structure properties, such as clustering and node centrality. Degree-based properties, however, are not notably affected by additional measurements locations. These observations are particularly valid in the core. The shortcomings of AS topology generation models stems from an underestimation of the complexity of the connectivity in the core caused by inappropriate use of BGP data

New and updated stellar parameters for 71 evolved planet hosts. On the metallicity - giant planet connection

It is still being debated whether the well-known metallicity - giant planet correlation for dwarf stars is also valid for giant stars. For this reason, having precise metallicities is very important. Different methods can provide different results that lead to discrepancies in the analysis of planet hosts. To study the impact of different analyses on the metallicity scale for evolved stars, we compare different iron line lists to use in the atmospheric parameter derivation of evolved stars. Therefore, we use a sample of 71 evolved stars with planets. With these new homogeneous parameters, we revisit the metallicity - giant planet connection for evolved stars. A spectroscopic analysis based on Kurucz models in local thermodynamic equilibrium (LTE) was performed through the MOOG code to derive the atmospheric parameters. Two different iron line list sets were used, one built for cool FGK stars in general, and the other for giant FGK stars. Masses were calculated through isochrone fitting, using the Padova models. Kolmogorov-Smirnov tests (K-S tests) were then performed on the metallicity distributions of various different samples of evolved stars and red giants. All parameters compare well using a line list set, designed specifically for cool and solar-like stars to provide more accurate temperatures. All parameters derived with this line list set are preferred and are thus adopted for future analysis. We find that evolved planet hosts are more metal-poor than dwarf stars with giant planets. However, a bias in giant stellar samples that are searched for planets is present. Because of a colour cut-off, metal-rich low-gravity stars are left out of the samples, making it hard to compare dwarf stars with giant stars. Furthermore, no metallicity enhancement is found for red giants with planets ($\log g < 3.0$\,dex) with respect to red giants without planets.Comment: 22 pages, 10 figures, 12 tables, accepted to A&

New and updated stellar parameters for 90 transit hosts. The effect of the surface gravity

Context. Precise stellar parameters are crucial in exoplanet research for correctly determining of the planetary parameters. For stars hosting a transiting planet, determining of the planetary mass and radius depends on the stellar mass and radius, which in turn depend on the atmospheric stellar parameters. Different methods can provide different results, which leads to different planet characteristics.}%Spectroscopic surface gravities have shown to be poorly constrained, but the photometry of the transiting planet can provide an independent measurement of the surface gravity. Aims. In this paper, we use a uniform method to spectroscopically derive stellar atmospheric parameters, chemical abundances, stellar masses, and stellar radii for a sample of 90 transit hosts. Surface gravities are also derived photometrically using the stellar density as derived from the light curve. We study the effect of using these different surface gravities on the determination of the chemical abundances and the stellar mass and radius. Methods. A spectroscopic analysis based on Kurucz models in LTE was performed through the MOOG code to derive the atmospheric parameters and the chemical abundances. The photometric surface gravity was determined through isochrone fitting and the use of the stellar density, directly determined from the light curve. Stellar masses and radii are determined through calibration formulae. Results. Spectroscopic and photometric surface gravities differ, but this has very little effect on the precise determination of the stellar mass in our spectroscopic analysis. The stellar radius, and hence the planetary radius, is most affected by the surface gravity discrepancies. For the chemical abundances, the difference is, as expected, only noticable for the abundances derived from analyzing of lines of ionized species.Comment: 12 pages, 6 figures, 5 tables, accepted to A&