Representing uncertainty regarding satisfaction degrees using possibility distributions

Evaluating flexible criteria on data leads to degrees of satisfaction. If a datum is uncertain, it can be uncertain to which degree it satisfies the criterion. This uncertainty can be modelled using a possibility distribution over the domain of possible degrees of satisfaction. In this work, we discuss the meaningfulness thereof by looking at the semantics of such a representation of the uncertainty. More specifically, it is shown that defuzzification of such a representation, towards usability in (multi-criteria) decision support systems, corresponds to expressing a clear attitude towards uncertainty (optimistic, pessimistic, cautious, etc.

Bipolar querying of valid-time intervals subject to uncertainty

Databases model parts of reality by containing data representing properties of real-world objects or concepts. Often, some of these properties are time-related. Thus, databases often contain data representing time-related information. However, as they may be produced by humans, such data or information may contain imperfections like uncertainties. An important purpose of databases is to allow their data to be queried, to allow access to the information these data represent. Users may do this using queries, in which they describe their preferences concerning the data they are (not) interested in. Because users may have both positive and negative such preferences, they may want to query databases in a bipolar way. Such preferences may also have a temporal nature, but, traditionally, temporal query conditions are handled specifically. In this paper, a novel technique is presented to query a valid-time relation containing uncertain valid-time data in a bipolar way, which allows the query to have a single bipolar temporal query condition

Improving the surface brightness-color relation for early-type stars using optical interferometry

The aim of this work is to improve the SBC relation for early-type stars in the $-1 \leq V-K \leq 0$ color domain, using optical interferometry. Observations of eight B- and A-type stars were secured with the VEGA/CHARA instrument in the visible. The derived uniform disk angular diameters were converted into limb darkened angular diameters and included in a larger sample of 24 stars, already observed by interferometry, in order to derive a revised empirical relation for O, B, A spectral type stars with a V-K color index ranging from -1 to 0. We also took the opportunity to check the consistency of the SBC relation up to $V-K \simeq 4$ using 100 additional measurements. We determined the uniform disk angular diameter for the eight following stars: $\gamma$ Ori, $\zeta$ Per, $8$ Cyg, $\iota$ Her, $\lambda$ Aql, $\zeta$ Peg, $\gamma$ Lyr, and $\delta$ Cyg with V-K color ranging from -0.70 to 0.02 and typical precision of about $1.5\%$. Using our total sample of 132 stars with $V-K$ colors index ranging from about $-1$ to $4$, we provide a revised SBC relation. For late-type stars ($0 \leq V-K \leq 4$), the results are consistent with previous studies. For early-type stars ($-1 \leq V-K \leq 0$), our new VEGA/CHARA measurements combined with a careful selection of the stars (rejecting stars with environment or stars with a strong variability), allows us to reach an unprecedented precision of about 0.16 magnitude or $\simeq 7\%$ in terms of angular diameter.Comment: 13 pages, 5 figures, accepted for publication in A&

The fundamental parameters of the roAp star γ\gamma Equulei

Physical processes working in the stellar interiors as well as the evolution of stars depend on some fundamental stellar properties, such as mass, radius, luminosity, and chemical abundances. A classical way to test stellar interior models is to compare the predicted and observed location of a star on theoretical evolutionary tracks in a H-R diagram. This requires the best possible determinations of stellar mass, radius, luminosity and abundances. To derive its fundamental parameters, we observed the well-known rapidly oscillating Ap star, $\gamma$ Equ, using the visible spectro-interferometer VEGA installed on the optical CHARA array. We computed the calibrated squared visibility and derived the limb-darkened diameter. We used the whole energy flux distribution, the parallax and this angular diameter to determine the luminosity and the effective temperature of the star. We obtained a limb-darkened angular diameter of 0.564~$\pm$~0.017~mas and deduced a radius of $R$~=~2.20~$\pm$~0.12~${\rm R_{\odot}}$. Without considering the multiple nature of the system, we derived a bolometric flux of $(3.12\pm 0.21)\times 10^{-7}$ erg~cm$^{-2}$~s$^{-1}$ and an effective temperature of 7364~$\pm$~235~K, which is below the effective temperature that has been previously determined. Under the same conditions we found a luminosity of $L$~=~12.8~$\pm$~1.4~${\rm L_{\odot}}$. When the contribution of the closest companion to the bolometric flux is considered, we found that the effective temperature and luminosity of the primary star can be, respectively, up to $\sim$~100~K and up to $\sim$~0.8~L$_\odot$ smaller than the values mentioned above.These new values of the radius and effective temperature should bring further constraints on the asteroseismic modelling of the star.Comment: Accepted by A&

An investigation of the close environment of beta Cep with the VEGA/CHARA interferometer

High-precision interferometric measurements of pulsating stars help to characterize their close environment. In 1974, a close companion was discovered around the pulsating star beta Cep using the speckle interferometry technique and features at the limit of resolution (20 milli-arcsecond or mas) of the instrument were mentioned that may be due to circumstellar material. Beta Cep has a magnetic field that might be responsible for a spherical shell or ring-like structure around the star as described by the MHD models. Using the visible recombiner VEGA installed on the CHARA long-baseline interferometer at Mt. Wilson, we aim to determine the angular diameter of beta Cep and resolve its close environment with a spatial resolution up to 1 mas level. Medium spectral resolution (R=6000) observations of beta Cep were secured with the VEGA instrument over the years 2008 and 2009. These observations were performed with the S1S2 (30m) and W1W2 (100m) baselines of the array. We investigated several models to reproduce our observations. A large-scale structure of a few mas is clearly detected around the star with a typical flux relative contribution of 0.23 +- 0.02. Our best model is a co-rotational geometrical thin ring around the star as predicted by magnetically-confined wind shock models. The ring inner diameter is 8.2 +- 0.8 mas and the width is 0.6 +- 0.7 mas. The orientation of the rotation axis on the plane of the sky is PA = 60 +- 1 deg, while the best fit of the mean angular diameter of beta Cep gives UD[V] = 0.22 +- 0.05 mas. Our data are compatible with the predicted position of the close companion of beta Cep. These results bring additional constraints on the fundamental parameters and on the future MHD and asteroseismological models of the star.Comment: Paper accepted for publication in A&A (in press

Spectral and spatial imaging of the Be+sdO binary phi Persei

The rapidly rotating Be star phi Persei was spun up by mass and angular momentum transfer from a now stripped-down, hot subdwarf companion. Here we present the first high angular resolution images of phi Persei made possible by new capabilities in longbaseline interferometry at near-IR and visible wavelengths. We observed phi Persei with the MIRC and VEGA instruments of the CHARA Array. Additional MIRC-only observations were performed to track the orbital motion of the companion, and these were fit together with new and existing radial velocity measurements of both stars to derive the complete orbital elements and distance. The hot subdwarf companion is clearly detected in the near-IR data at each epoch of observation with a flux contribution of 1.5% in the H band, and restricted fits indicate that its flux contribution rises to 3.3% in the visible. A new binary orbital solution is determined by combining the astrometric and radial velocity measurements. The derived stellar masses are 9.6+-0.3Msol and 1.2+-0.2Msol for the Be primary and subdwarf secondary, respectively. The inferred distance (186 +- 3 pc), kinematical properties, and evolutionary state are consistent with membership of phi Persei in the alpha Per cluster. From the cluster age we deduce significant constraints on the initial masses and evolutionary mass transfer processes that transformed the phi Persei binary system. The interferometric data place strong constraints on the Be disk elongation, orientation, and kinematics, and the disk angular momentum vector is coaligned with and has the same sense of rotation as the orbital angular momentum vector. The VEGA visible continuum data indicate an elongated shape for the Be star itself, due to the combined effects of rapid rotation, partial obscuration of the photosphere by the circumstellar disk, and flux from the bright inner disk.Comment: 16 pages, 6 figures, 1 Anne

A randomised double-blind placebo-controlled trial investigating the behavioural effects of vitamin, mineral and n-3 fatty acid supplementation in typically developing adolescent schoolchildren

This material is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2015 The Authors. Published by Cambridge University Press.Nutrient deficiencies have been implicated in anti-social behaviour in schoolchildren; hence, correcting them may improve sociability. We therefore tested the effects of vitamin, mineral and n-3 supplementation on behaviour in a 12-week double-blind randomised placebo-controlled trial in typically developing UK adolescents aged 13–16 years (n 196). Changes in erythrocyte n-3 and 6 fatty acids and some mineral and vitamin levels were measured and compared with behavioural changes, using Conners’ teacher ratings and school disciplinary records. At baseline, the children’s PUFA (n-3 and n-6), vitamin and mineral levels were low, but they improved significantly in the group treated with n-3, vitamins and minerals (P=0·0005). On the Conners disruptive behaviour scale, the group given the active supplements improved, whereas the placebo group worsened (F=5·555, d=0·35; P=0·02). The general level of disciplinary infringements was low, thus making it difficult to obtain improvements. However, throughout the school term school disciplinary infringements increased significantly (by 25 %; Bayes factor=115) in both the treated and untreated groups. However, when the subjects were split into high and low baseline infringements, the low subset increased their offences, whereas the high-misbehaviour subset appeared to improve after treatment. But it was not possible to determine whether this was merely a statistical artifact. Thus, when assessed using the validated and standardised Conners teacher tests (but less clearly when using school discipline records in a school where misbehaviour was infrequent), supplementary nutrition might have a protective effect against worsening behaviour.Peer reviewe