Distributed Testing of Excluded Subgraphs

We study property testing in the context of distributed computing, under the classical CONGEST model. It is known that testing whether a graph is triangle-free can be done in a constant number of rounds, where the constant depends on how far the input graph is from being triangle-free. We show that, for every connected 4-node graph H, testing whether a graph is H-free can be done in a constant number of rounds too. The constant also depends on how far the input graph is from being H-free, and the dependence is identical to the one in the case of testing triangles. Hence, in particular, testing whether a graph is K_4-free, and testing whether a graph is C_4-free can be done in a constant number of rounds (where K_k denotes the k-node clique, and C_k denotes the k-node cycle). On the other hand, we show that testing K_k-freeness and C_k-freeness for k>4 appear to be much harder. Specifically, we investigate two natural types of generic algorithms for testing H-freeness, called DFS tester and BFS tester. The latter captures the previously known algorithm to test the presence of triangles, while the former captures our generic algorithm to test the presence of a 4-node graph pattern H. We prove that both DFS and BFS testers fail to test K_k-freeness and C_k-freeness in a constant number of rounds for k>4

Boundary conformal field theories and loop models

We propose a systematic method to extract conformal loop models for rational conformal field theories (CFT). Method is based on defining an ADE model for boundary primary operators by using the fusion matrices of these operators as adjacency matrices. These loop models respect the conformal boundary conditions. We discuss the loop models that can be extracted by this method for minimal CFTs and then we will give dilute O(n) loop models on the square lattice as examples for these loop models. We give also some proposals for WZW SU(2) models.Comment: 23 Pages, major changes! title change

η−η′\eta-\eta^\prime mixing and the next-to-leading-order power correction

The next-to-leading-order $O(1/Q^4)$ power correction for $\eta\gamma$ and $\eta^\prime\gamma$ form factors are evaluated and employed to explore the $\eta-\eta^\prime$ mixing. The parameters of the two mixing angle scheme are extracted from the data for form factors, two photon decay widths and radiative $J/\psi$ decays. The $\chi^2$ analysis gives the result: $f_{\eta_1}=(1.16\pm0.06)f_\pi, f_{\eta_8}=(1.33\pm0.23)f_\pi, \theta_1=-9^\circ\pm 3^\circ, \theta_8=-21.3^\circ\pm 2.3^\circ$, where $f_{\eta_{1(8)}}$ and $\theta_{1(8)}$ are the decay constants and the mixing angles for the singlet (octet) state. In addition, we arrive at a stringent range for $f_{\eta^\prime}^c:-10$ MeV$\le f_{\eta^\prime}^c\le -4$ MeV.Comment: 23 pages, 9 figures, To be publshied in Phys. Rev.

Spin states of asteroids in the Eos collisional family

Eos family was created during a catastrophic impact about 1.3 Gyr ago. Rotation states of individual family members contain information about the history of the whole population. We aim to increase the number of asteroid shape models and rotation states within the Eos collision family, as well as to revise previously published shape models from the literature. Such results can be used to constrain theoretical collisional and evolution models of the family, or to estimate other physical parameters by a thermophysical modeling of the thermal infrared data. We use all available disk-integrated optical data (i.e., classical dense-in-time photometry obtained from public databases and through a large collaboration network as well as sparse-in-time individual measurements from a few sky surveys) as input for the convex inversion method, and derive 3D shape models of asteroids together with their rotation periods and orientations of rotation axes. We present updated shape models for 15 asteroids and new shape model determinations for 16 asteroids. Together with the already published models from the publicly available DAMIT database, we compiled a sample of 56 Eos family members with known shape models that we used in our analysis of physical properties within the family. Rotation states of asteroids smaller than ~20 km are heavily influenced by the YORP effect, whilst the large objects more or less retained their rotation state properties since the family creation. Moreover, we also present a shape model and bulk density of asteroid (423) Diotima, an interloper in the Eos family, based on the disk-resolved data obtained by the Near InfraRed Camera (Nirc2) mounted on the W.M. Keck II telescope.Comment: Accepted for publication in ICARUS Special Issue - Asteroids: Origin, Evolution & Characterizatio

SOPHIE velocimetry of Kepler transit candidates XII. KOI-1257 b: a highly eccentric three-month period transiting exoplanet

In this paper we report a new transiting warm giant planet: KOI-1257 b. It was first detected in photometry as a planet-candidate by the ${\it Kepler}$ space telescope and then validated thanks to a radial velocity follow-up with the SOPHIE spectrograph. It orbits its host star with a period of 86.647661 d $\pm$ 3 s and a high eccentricity of 0.772 $\pm$ 0.045. The planet transits the main star of a metal-rich, relatively old binary system with stars of mass of 0.99 $\pm$ 0.05 Msun and 0.70 $\pm$ 0.07 Msun for the primary and secondary, respectively. This binary system is constrained thanks to a self-consistent modelling of the ${\it Kepler}$ transit light curve, the SOPHIE radial velocities, line bisector and full-width half maximum (FWHM) variations, and the spectral energy distribution. However, future observations are needed to confirm it. The PASTIS fully-Bayesian software was used to validate the nature of the planet and to determine which star of the binary system is the transit host. By accounting for the dilution from the binary both in photometry and in radial velocity, we find that the planet has a mass of 1.45 $\pm$ 0.35 Mjup, and a radius of 0.94 $\pm$ 0.12 Rjup, and thus a bulk density of 2.1 $\pm$ 1.2 g.cm$^{-3}$. The planet has an equilibrium temperature of 511 $\pm$ 50 K, making it one of the few known members of the warm-jupiter population. The HARPS-N spectrograph was also used to observe a transit of KOI-1257 b, simultaneously with a joint amateur and professional photometric follow-up, with the aim of constraining the orbital obliquity of the planet. However, the Rossiter-McLaughlin effect was not clearly detected, resulting in poor constraints on the orbital obliquity of the planet.Comment: 39 pages, 17 figures, accepted for publication in Astronomy & Astrophysic

On Discrete Symmetries in su(2) and su(3) Affine Theories and Related Graphs

We classify the possible finite symmetries of conformal field theories with an affine Lie algebra su(2) and su(3), and discuss the results from the perspective of the graphs associated with the modular invariants. The highlights of the analysis are first, that the symmetries we found in either case are matched by the graph data in a perfect way in the case of su(2), but in a looser way for su(3), and second, that some of the graphs lead naturally to projective representations, both in su(2) and in su(3).Comment: 34 pages, 4 eps figure

Influence of UV radiation from a massive YSO on the chemistry of its envelope

We have studied the influence of far ultraviolet (UV) radiation from a massive young stellar object (YSO) on the chemistry of its own envelope by extending the models of Doty et al. (2002) to include a central source of UV radiation. The models are applied to the massive star-forming region AFGL 2591 for different inner UV field strengths. Depth-dependent abundance profiles for several molecules are presented and discussed. We predict enhanced column densities for more than 30 species, especially radicals and ions. Comparison between observations and models is improved with a moderate UV field incident on the inner envelope, corresponding to an enhancement factor G0~10-100 at 200 AU from the star with an optical depth tau~15-17. Subtle differences are found compared with traditional models of Photon Dominated Regions (PDRs) because of the higher temperatures and higher gas-phase H2O abundance caused by evaporation of ices in the inner region. In particular, the CN/HCN ratio is not a sensitive tracer of the inner UV field, in contrast with the situation for normal PDRs: for low UV fields, the extra CN reacts with H2 in the inner dense and warm region and produces more HCN. It is found that the CH+ abundance is strongly enhanced and grows steadily with increasing UV field. High-J lines of molecules like CN and HCN are most sensitive to the inner dense region where UV radiation plays a role. Thus, even though the total column density affected by UV photons is small, comparison of high-J and low-J lines can selectively trace and distinguish the inner UV field from the outer one. In addition, future Herschel-HIFI observations of hydrides can sensitively probe the inner UV field.Comment: Accepted for publication in A&A. 13 pages, 10 figure

Cosmological Backreaction from Perturbations

We reformulate the averaged Einstein equations in a form suitable for use with Newtonian gauge linear perturbation theory and track the size of the modifications to standard Robertson-Walker evolution on the largest scales as a function of redshift for both Einstein de-Sitter and Lambda CDM cosmologies. In both cases the effective energy density arising from linear perturbations is of the order of 10^-5 the matter density, as would be expected, with an effective equation of state w ~ -1/19. Employing a modified Halofit code to extend our results to quasilinear scales, we find that, while larger, the deviations from Robertson-Walker behaviour remain of the order of 10^-5.Comment: 15 pages, 8 figures; replaced by version accepted by JCA

On a Light Spinless Particle Coupled to Photons

A pseudoscalar or scalar particle $\phi$ that couples to two photons but not to leptons, quarks and nucleons would have effects in most of the experiments searching for axions, since these are based on the $a \gamma \gamma$ coupling. We examine the laboratory, astrophysical and cosmological constraints on $\phi$ and study whether it may constitute a substantial part of the dark matter. We also generalize the $\phi$ interactions to possess $SU(2) \times U(1)$ gauge invariance, and analyze the phenomenological implications.Comment: LaTex, 20p., 6 figures. Changes in sections 4, 5 and figure 2, our bounds are now more stringent. To be published in Physical Review