Representation of Nelson Algebras by Rough Sets Determined by Quasiorders

In this paper, we show that every quasiorder $R$ induces a Nelson algebra $\mathbb{RS}$ such that the underlying rough set lattice $RS$ is algebraic. We note that $\mathbb{RS}$ is a three-valued {\L}ukasiewicz algebra if and only if $R$ is an equivalence. Our main result says that if $\mathbb{A}$ is a Nelson algebra defined on an algebraic lattice, then there exists a set $U$ and a quasiorder $R$ on $U$ such that $\mathbb{A} \cong \mathbb{RS}$.Comment: 16 page

Information completeness in Nelson algebras of rough sets induced by quasiorders

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson algebra can be obtained by applying the well-known construction by Sendlewski. We prove that if the set of all $R$-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by a quasiorder forms an effective lattice, that is, an algebraic model of the logic $E_0$, which is characterised by a modal operator grasping the notion of "to be classically valid". We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder.Comment: 15 page

Asymmetricity of ground-based GPS slant delay data

International audienceThe ground-based measurements of the Global Positioning System (GPS) allow estimation of the tropospheric delay along the slanted signal paths through the atmosphere. The meteorological exploitation of such slant delay (SD) observations relies on the hypothesis of azimuthal asymmetry of the information content. This article addresses the validity of the hypothesis. A new concept of asymmetricity is introduced for studying the SD observations and their model counterparts. The asymmetricity is defined as the ratio of the absolute asymmetric delay component to total SD. The model counterparts are determined from 3-h forecasts of a numerical weather prediction (NWP) model, run with four different horizontal resolutions. The SD observations are compared with their model counterparts with emphasis on cases of high asymmetricity in order to see whether the observed asymmetry is a real atmospheric signature. The asymmetricity is found to be of the order of a few parts per thousand. Thus, the asymmetric delay component barely exceeds the assumed standard deviation of the SD observation error. However, the observed asymmetric delay components show a statistically significant meteorological signal. Benefit of the asymmetric SD observations is therefore expected to be taken in future, when NWP systems will explicitly represent the small-scale atmospheric features revealed by the SD observations

Renal Tumor Invasion Depth and Diameter are the Two Most Accurate Anatomical Features Regarding the Choice of Radical Versus Partial Nephrectomy

Background and Aims: To evaluate simple tumor characteristics (renal tumor diameter and parenchymal invasion depth) compared with more complex classifications, that is, Renal Tumor Invasion Index (RTII) and Preoperative Aspects and Dimensions Used for an Anatomical classification, in predicting the type of nephrectomy (radical vs partial) performed. Material and Methods: A total of 915 patients who had undergone either partial nephrectomy (n=388, 42%) or radical nephrectomy (n=527, 58%) were identified from the Helsinki University Hospital kidney tumor database between 1 January 2006 and 31 December 2014. Tumor maximum diameter and depth of invasion into the parenchyma were estimated from computed tomography or magnetic resonance imaging images and compared with Preoperative Aspects and Dimensions Used for an Anatomical and Renal Tumor Invasion Index. Logistic regression and receiver operating curves were used to compare the parameters at predicting the type of nephrectomy. Results and conclusion: All the anatomical variables of receiver operating curve/area under the curve analyses were significant predictors for the type of nephrectomy. Parenchymal invasion (area under the curve 0.91; 95% confidence interval, 0.89-0.93), RTII (area under the curve 0.91; 95% confidence interval, 0.89-0.93), and diameter (area under the curve 0.91; 95% confidence interval, 0.89-0.93) performed significantly better than Preoperative Aspects and Dimensions Used for an Anatomical classification (area under the curve 0.88; 95% confidence interval, 0.85-0.89). In multivariable analysis, invasion depth was the best predictor of nephrectomy type (percentage correct, 85.6%). Addition of one anatomic parameter into the model of non-anatomical cofactors improved the accuracy of the model significantly, but the addition of more parameters did not. Parenchymal invasion depth and tumor diameter are the most accurate anatomical features for predicting the nephrectomy type. All potential anatomical classification systems should be tested against these two simple characteristics.Peer reviewe

Azimuthal asymmetry in ground-based GPS slant delay observations and their NWP model counterparts

International audienceThe ground-based measurements of the Global Positioning System (GPS) allow estimation of the tropospheric delay along the slanted signal paths through the atmosphere. The meteorological exploitation of such slant delay (SD) observations relies on the hypothesis of azimuthal asymmetry of the information content. This article addresses the validity of the hypothesis. The asymmetric properties of the SD observations and their model counterparts are investigated. In this study, the model counterparts are based on 3-h forecasts of a numerical weather prediction (NWP) model, run with four different horizontal resolutions. The SD observations are compared with their model counterparts with emphasis on cases of high asymmetry in order to see whether the observed asymmetry is a real atmospheric signature. The asymmetric delay component is found to be of the order of a few parts per thousand of the absolute SD value, thus barely exceeding the assumed standard deviation of the SD observation error. However, the observed asymmetric delay components show a statistically significant meteorological signal. Benefit of the asymmetric SD observations is therefore expected to be taken in future, when NWP systems will explicitly represent the small-scale atmospheric features revealed by the SD observations

A combined HST and XMM-Newton campaign for the magnetic O9.7 V star HD 54879: towards constraining the weak-wind problem of massive stars

Context: HD 54879 (O9.7 V) is one of a dozen O-stars for which an organized atmospheric magnetic field has been detected. To gain insights into the interplay between atmospheres, winds, and magnetic fields of massive stars, we acquired UV and X-ray data of HD 54879 using the Hubble Space Telescope and the XMM-Newton satellite. In addition, 35 optical amateur spectra were secured to study the variability of HD 54879. A multiwavelength (X-ray to optical) spectral analysis is performed using the Potsdam Wolf-Rayet (PoWR) model atmosphere code and the xspec software. Results: The photospheric parameters are typical for an O9.7 V star. The microturbulent, macroturbulent, and projected rotational velocities are lower than previously suggested (<4 km/s). An initial mass of 16$\,M_\odot$ and an age of 5 Myr are inferred from evolutionary tracks. We derive a mean X-ray emitting temperature of $\log T_{\rm X} = 6.7\,$[K] and an X-ray luminosity of $\log L_\text{X} = 32\,$[erg/s]. Short- and long-scale variability is seen in the H-alpha line, but only a very long period of $P \approx 5\,$yr could be estimated. Assessing the circumstellar density of HD 54879 using UV spectra, we can roughly estimate the mass-loss rate HD 54879 would have in the absence of a magnetic field as $\log \dot{M}_{B=0}\approx -9.0\,[{M_\odot}/{\rm yr}]$. The magnetic field traps the stellar wind up to the Alfv\'en radius > $12\,R_\odot$, implying that its true mass-loss rate is $\log \dot{M}< -10.2\,[{M_\odot}/{\rm yr}]$. Hence, density enhancements around magnetic stars can be exploited to estimate mass-loss rates of non-magnetic stars of similar spectral types, essential for resolving the weak wind problem. Conclusions: Our study confirms that strongly magnetized stars lose little or no mass, and supplies important constraints on the weak-wind problem of massive main sequence stars.Comment: Accepted for publication in A&A on Aug. 9, 2017, 12 + 1 pages, 15 figures. Paper replaced due to typos and missing acknowledgment

Doppler images and the underlying dynamo. The case of AF Leporis

The (Zeeman-)Doppler imaging studies of solar-type stars very often reveal large high-latitude spots. This also includes F stars that possess relatively shallow convection zones, indicating that the dynamo operating in these stars differs from the solar dynamo. We aim to determine whether mean-field dynamo models of late-F type dwarf stars can reproduce the surface features recovered in Doppler maps. In particular, we wish to test whether the models can reproduce the high-latitude spots observed on some F dwarfs. The photometric inversions and the surface temperature maps of AF Lep were obtained using the Occamian-approach inversion technique. Low signal-to-noise spectroscopic data were improved by applying the least-squares deconvolution method. The locations of strong magnetic flux in the stellar tachocline as well as the surface fields obtained from mean-field dynamo solutions were compared with the observed surface temperature maps. The photometric record of AF Lep reveals both long- and short-term variability. However, the current data set is too short for cycle-length estimates. From the photometry, we have determined the rotation period of the star to be 0.9660+-0.0023 days. The surface temperature maps show a dominant, but evolving, high-latitude (around +65 degrees) spot. Detailed study of the photometry reveals that sometimes the spot coverage varies only marginally over a long time, and at other times it varies rapidly. Of a suite of dynamo models, the model with a radiative interior rotating as fast as the convection zone at the equator delivered the highest compatibility with the obtained Doppler images.Comment: accepted for publication in Astronomy & Astrophysic