An error estimate of Gaussian Recursive Filter in 3Dvar problem

Computational kernel of the three-dimensional variational data assimilation (3D-Var) problem is a linear system, generally solved by means of an iterative method. The most costly part of each iterative step is a matrix-vector product with a very large covariance matrix having Gaussian correlation structure. This operation may be interpreted as a Gaussian convolution, that is a very expensive numerical kernel. Recursive Filters (RFs) are a well known way to approximate the Gaussian convolution and are intensively applied in the meteorology, in the oceanography and in forecast models. In this paper, we deal with an oceanographic 3D-Var data assimilation scheme, named OceanVar, where the linear system is solved by using the Conjugate Gradient (GC) method by replacing, at each step, the Gaussian convolution with RFs. Here we give theoretical issues on the discrete convolution approximation with a first order (1st-RF) and a third order (3rd-RF) recursive filters. Numerical experiments confirm given error bounds and show the benefits, in terms of accuracy and performance, of the 3-rd RF.Comment: 9 page

Reclassification of the nearest quasar pair candidate: SDSS J15244+3032 - RXS J15244+3032

We present optical spectroscopy of the nearest quasar pair listed in the 13th edition of the Veron-Cetty & Veron catalogue, i.e. the two quasars SDSS J15244+3032 and RXS J15244+3032 (redshift z~0.27, angular separation ~7 arcsec, and line-of-sight velocity difference ~1900 km/s). This system would be an optimal candidate to investigate the mutual interaction of the host galaxies with ground based optical imaging and spectroscopy. However, new optical data demonstrate that RXS J15244+3032 is indeed a star of spectral type G. This paper includes data gathered with the Asiago 1.82m telescope (Cima Ekar Observatory, Asiago, Italy).Comment: 5 pages, 2 figures, 1 table. Accepted for publication in APS

On the cool gaseous haloes of quasars

We present optical spectroscopy of projected QSO pairs to investigate the MgII and the CIV absorption features imprinted on the spectrum of the background object by the gaseous halo surrounding the foreground QSO. We observed 13 projected pairs in the redshift range 0.7<z<2.2 spanning projected separations between 60 kpc and 120 kpc. In the spectra of the background QSOs, we identify MgII intervening absorption systems associated to the foreground QSOs in 7 out of 10 pairs, and 1 absorption system out of 3 is found for CIV. The distribution of the equivalent width as a function of the impact parameter shows that, unlike the case of normal galaxies, some strong absorption systems (EWr > 1 Ang) are present also beyond a projected radius of ~70 kpc. If we take into account the mass of the galaxies as an additional parameter that influence the extent of the gaseous haloes, the distribution of the absorptions connected to the QSOs is consistent to that of galaxies. In the spectra of the foreground QSOs we do not detect any MgII absorption lines originated by the gas surrounding the QSO itself, but in 2 cases these features are present for CIV. The comparison between the absorption features observed in the transverse direction and those along the line of sight allows us to comment on the distribution of the absorbing gas and on the emission properties of the QSOs. Based on observations undertaken at the European Southern Observatory (ESO) Very Large Telescope (VLT) under Programmes 085.B-0210(A) and 086.B-0028(A).Comment: 15 pages, 3 tables, 9 figures. Accepted to be published on MNRA

Advances in surface EMG signal simulation with analytical and numerical descriptions of the volume conductor

Surface electromyographic (EMG) signal modeling is important for signal interpretation, testing of processing algorithms, detection system design, and didactic purposes. Various surface EMG signal models have been proposed in the literature. In this study we focus on 1) the proposal of a method for modeling surface EMG signals by either analytical or numerical descriptions of the volume conductor for space-invariant systems, and 2) the development of advanced models of the volume conductor by numerical approaches, accurately describing not only the volume conductor geometry, as mainly done in the past, but also the conductivity tensor of the muscle tissue. For volume conductors that are space-invariant in the direction of source propagation, the surface potentials generated by any source can be computed by one-dimensional convolutions, once the volume conductor transfer function is derived (analytically or numerically). Conversely, more complex volume conductors require a complete numerical approach. In a numerical approach, the conductivity tensor of the muscle tissue should be matched with the fiber orientation. In some cases (e.g., multi-pinnate muscles) accurate description of the conductivity tensor may be very complex. A method for relating the conductivity tensor of the muscle tissue, to be used in a numerical approach, to the curve describing the muscle fibers is presented and applied to representatively investigate a bi-pinnate muscle with rectilinear and curvilinear fibers. The study thus propose an approach for surface EMG signal simulation in space invariant systems as well as new models of the volume conductor using numerical methods

One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in RN^N

In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. We also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities

Thyroid ultrasonography reporting: consensus of Italian Thyroid Association (AIT), Italian Society of Endocrinology (SIE), Italian Society of Ultrasonography in Medicine and Biology (SIUMB) and Ultrasound Chapter of Italian Society of Medical Radiology (SIRM)

Thyroid ultrasonography (US) is the gold standard for thyroid imaging and its widespread use is due to an optimal spatial resolution for superficial anatomic structures, a low cost and the lack of health risks. Thyroid US is a pivotal tool for the diagnosis and follow-up of autoimmune thyroid diseases, for assessing nodule size and echostructure and defining the risk of malignancy in thyroid nodules. The main limitation of US is the poor reproducibility, due to the variable experience of the operators and the different performance and settings of the equipments. Aim of this consensus statement is to standardize the report of thyroid US through the definition of common minimum requirements and a correct terminology. US patterns of autoimmune thyroid diseases are defined. US signs of malignancy in thyroid nodules are classified and scored in each nodule. We also propose a simplified nodule risk stratification, based on the predictive value of each US sign, classified and scored according to the strength of association with malignancy, but also to the estimated reproducibility among different operators