On the Signed 22-independence Number of Graphs

In this paper, we study the signed 2-independence number in graphs and give new sharp upper and lower bounds on the signed 2-independence number of a graph by a simple uniform approach. In this way, we can improve and generalize some known results in this area

Bayesian model averaging with fixed and flexible priors: theory, concepts, and calibration experiments for rainfall-runoff modeling

This paper introduces for the first time the concept of Bayesian Model Averaging (BMA) with multiple prior structures, for rainfall‐runoff modeling applications. The original BMA model proposed by Raftery et al. (2005) assumes that the prior probability density function (pdf) is adequately described by a mixture of Gamma and Gaussian distributions. Here we discuss the advantages of using BMA with fixed and flexible prior distributions. Uniform, Binomial, Binomial‐Beta, Benchmark, and Global Empirical Bayes priors along with Informative Prior Inclusion and Combined Prior Probabilities were applied to calibrate daily streamflow records of a coastal plain watershed in the South‐East USA. Various specifications for Zellner's g prior including Hyper, Fixed, and Empirical Bayes Local (EBL) g priors were also employed to account for the sensitivity of BMA and derive the conditional pdf of each constituent ensemble member. These priors were examined using the simulation results of conceptual and semi‐distributed rainfall‐runoff models. The hydrologic simulations were first coupled with a new sensitivity analysis model and a parameter uncertainty algorithm to assess the sensitivity and uncertainty associated with each model. BMA was then used to subsequently combine the simulations of the posterior pdf of each constituent hydrological model. Analysis suggests that a BMA based on combined fixed and flexible priors provides a coherent mechanism and promising results for calculating a weighted posterior probability compared to individual model calibration. Furthermore, the probability of Uniform and Informative Prior Inclusion priors received significantly lower predictive error whereas more uncertainty resulted from a fixed g prior (i.e. EBL)

Bounds on the signed distance--domination number of graphs

Abstract Let , be a graph with vertex set of order and edge set . A -dominating set of is a subset such that each vertex in \ has at least neighbors in . If is a vertex of a graph , the open -neighborhood of , denoted by , is the set , . is the closed -neighborhood of . A function 1, 1 is a signed distance--dominating function of , if for every vertex , ∑ 1. The signed distance--domination number, denoted by , , is the minimum weight of a signed distance--dominating function of . In this paper, we give lower and upper bounds on , of graphs. Also, we determine the signed distance--domination number of graph , (the graph obtained from the disjoint union by adding the edges , ) when 2

The solar-like CoRoT target HD 170987: spectroscopic and seismic observations

The CoRoT mission is in its third year of observation and the data from the second long run in the galactic centre direction are being analysed. The solar-like oscillating stars that have been observed up to now have given some interesting results, specially concerning the amplitudes that are lower than predicted. We present here the results from the analysis of the star HD 170987.The goal of this research work is to characterise the global parameters of HD 170987. We look for global seismic parameters such as the mean large separation, maximum amplitude of the modes, and surface rotation because the signal-to-noise ratio in the observations do not allow us to measure individual modes. We also want to retrieve the stellar parameters of the star and its chemical composition.We have studied the chemical composition of the star using ground-based observations performed with the NARVAL spectrograph. We have used several methods to calculate the global parameters from the acoustic oscillations based on CoRoT data. The light curve of the star has been interpolated using inpainting algorithms to reduce the effect of data gaps. We find power excess related to p modes in the range [400 - 1200]muHz with a mean large separation of 55.2+-0.8muHz with a probability above 95% that increases to 55.9 +-0.2muHz in a higher frequency range [500 - 1250] muHz and a rejection level of 1%. A hint of the variation of this quantity with frequency is also found. The rotation period of the star is estimated to be around 4.3 days with an inclination axis of i=50 deg +20/-13. We measure a bolometric amplitude per radial mode in a range [2.4 - 2.9] ppm around 1000 muHz. Finally, using a grid of models, we estimate the stellar mass, M=1.43+-0.05 Msun, the radius, R=1.96+-0.046 Rsun, and the age ~2.4 Gyr.Comment: 12 pages, 15 figures, accepted for publication in A&

Solar-like oscillations with low amplitude in the CoRoT target HD 181906

Context: The F8 star HD 181906 (effective temperature ~6300K) was observed for 156 days by the CoRoT satellite during the first long run in the centre direction. Analysis of the data reveals a spectrum of solar-like acoustic oscillations. However, the faintness of the target (m_v=7.65) means the signal-to-noise (S/N) in the acoustic modes is quite low, and this low S/N leads to complications in the analysis. Aims: To extract global variables of the star as well as key parameters of the p modes observed in the power spectrum of the lightcurve. Methods: The power spectrum of the lightcurve, a wavelet transform and spot fitting have been used to obtain the average rotation rate of the star and its inclination angle. Then, the autocorrelation of the power spectrum and the power spectrum of the power spectrum were used to properly determine the large separation. Finally, estimations of the mode parameters have been done by maximizing the likelihood of a global fit, where several modes were fit simultaneously. Results: We have been able to infer the mean surface rotation rate of the star (~4 microHz) with indications of the presence of surface differential rotation, the large separation of the p modes (~87 microHz), and therefore also the ridges corresponding to overtones of the acoustic modes.Comment: Paper Accepted to be published in A&A. 10 Pages, 12 figure

Spin down of the core rotation in red giants

The space mission Kepler provides us with long and uninterrupted photometric time series of red giants. We are now able to probe the rotational behaviour in their deep interiors using the observations of mixed modes. We aim to measure the rotational splittings in red giants and to derive scaling relations for rotation related to seismic and fundamental stellar parameters. We have developed a dedicated method for automated measurements of the rotational splittings in a large number of red giants. Ensemble asteroseismology, namely the examination of a large number of red giants at different stages of their evolution, allows us to derive global information on stellar evolution. We have measured rotational splittings in a sample of about 300 red giants. We have also shown that these splittings are dominated by the core rotation. Under the assumption that a linear analysis can provide the rotational splitting, we observe a small increase of the core rotation of stars ascending the red giant branch. Alternatively, an important slow down is observed for red-clump stars compared to the red giant branch. We also show that, at fixed stellar radius, the specific angular momentum increases with increasing stellar mass. Ensemble asteroseismology indicates what has been indirectly suspected for a while: our interpretation of the observed rotational splittings leads to the conclusion that the mean core rotation significantly slows down during the red giant phase. The slow-down occurs in the last stages of the red giant branch. This spinning down explains, for instance, the long rotation periods measured in white dwarfsComment: Accepted in A&

Inferring mode inertias in evolved solar-like stars

Asteroseismology of evolved solar-like stars is experiencing a growing interest due to the wealth of observational data from space-borne instruments such as the \emph{CoRoT} and \emph{Kepler} spacecraft. In particular, the recent detection of mixed modes, which probe both the innermost and uppermost layers of stars, paves the way for inferring the internal structure of stars along their evolution through the subgiant and red giant phases. Mixed modes can also place stringent constraints on the physics of such stars and on their global properties (mass, age, etc...). Here, using two \emph{Kepler} stars (KIC 4351319 and KIC 6442183), we demonstrate that measurements of mixed mode characteristics allow us to estimate the mode inertias, providing a new and additional diagnostics on the mode trapping and subsequently on the internal structure of evolved stars. We however stress that the accuracy may be sensitive to non-adiabatic effects.Comment: ApJ Lette

A search for p-modes and other variability in the binary system 85 Pegasi using MOST photometry

Context: Asteroseismology has great potential for the study of metal-poor stars due to its sensitivity to determine stellar ages. Aims: Our goal was to detect p-mode oscillations in the metal-poor sub-dwarf 85 Peg A and to search for other variability on longer timescales. Methods: We have obtained continuous high-precision photometry of the binary system 85 Pegasi with the MOST space telescope in two seasons (2005 & 2007). Furthermore, we redetermined vsini for 85 Peg A using high resolution spectra obtained through the ESO archive, and used photometric spot modeling to interpret long periodic variations. Results: Our frequency analysis yields no convincing evidence for p-modes significantly above a noise level of 4 ppm. Using simulated p-mode patterns we provide upper RMS amplitude limits for 85 Peg A. The light curve shows evidence for variability with a period of about 11 d and this periodicity is also seen in the follow up run in 2007; however, as different methods to remove instrumental trends in the 2005 run yield vastly different results, the exact shape and periodicity of the 2005 variability remain uncertain. Our re-determined vsini value for 85 Peg A is comparable to previous studies and we provide realistic uncertainties for this parameter. Using these values in combination with simple photometric spot models we are able to reconstruct the observed variations. Conclusions: The null-detection of p-modes in 85 Peg A is consistent with theoretical values for pulsation amplitudes in this star. The detected long-periodic variation must await confirmation by further observations with similar or better precision and long-term stability. If the 11 d periodicity is real, rotational modulation of surface features on one of the components is the most likely explanation.Comment: 11 pages, 9 figures, accepted for publication in A&