Factorizing the Stochastic Galerkin System

Recent work has explored solver strategies for the linear system of equations arising from a spectral Galerkin approximation of the solution of PDEs with parameterized (or stochastic) inputs. We consider the related problem of a matrix equation whose matrix and right hand side depend on a set of parameters (e.g. a PDE with stochastic inputs semidiscretized in space) and examine the linear system arising from a similar Galerkin approximation of the solution. We derive a useful factorization of this system of equations, which yields bounds on the eigenvalues, clues to preconditioning, and a flexible implementation method for a wide array of problems. We complement this analysis with (i) a numerical study of preconditioners on a standard elliptic PDE test problem and (ii) a fluids application using existing CFD codes; the MATLAB codes used in the numerical studies are available online.Comment: 13 pages, 4 figures, 2 table

Integrated stratigraphy and astrochronology of the Messinian GSSP at Oued Akrech (Atlantic Morocco)

A much improved high-resolution integrated stratigraphy (calcareous plankton biostratigraphy, magnetostratigraphy, cyclostratigraphy) is presented for the classic section of Oued Akrech (Atlantic Morocco) straddling the Tortonian^Messinian boundary. Magnetobiostratigraphic correlations with time-equivalent and astronomically dated sections in the Mediterranean indicate that cyclic alternations of indurated light beige coloured marls and softer, more clayey and reddish coloured marls are dominantly precession-controlled. Characteristic sedimentary cycle patterns, in particular those reflecting precession^obliquity interference, allow for one possible tuning, thus providing accurate astronomical ages for cycles, calcareous plankton events and magnetic reversals. The tuning further indicates that the reddish layers are the equivalent of sapropels in the Mediterranean. The Messinian Global boundary Stratotype Section and Point (GSSP) has recently been formally defined at the base of the reddish layer of cycle No. 15 in section Oued Akrech. This level coincides closely with the first regular occurrence of the Globorotalia miotumida group and is astronomically dated at 7.251 Ma. The global correlation potential is guaranteed by the straightforward calibration of the Oued Akrech magnetostratigraphy to the geomagnetic polarity time scale, locating the GSSP within C3Br.1r. In the marine realm the calcareous nannofossil genus Amaurolithus provides a series of extremely useful events to delimit the boundary on a global scale. The astronomical tuning guarantees a direct first-order calibration of the Messinian GSSP to the standard geological time scale once, as anticipated, the late Miocene part of the astronomical time scale has been incorporated

Computed tomography findings of pneumatosis and portomesenteric venous gas in acute bowel ischemia.

BACKGROUND: To use more representative sample size to evaluate whether computed tomography (CT) scan evidence of the concomitant presence of pneumatosis and portomesenteric venous gas is a predictor of transmural bowel necrosis. METHODS: Data from 208 patients who were referred for a diagnosis of bowel ischemia were retrospectively reviewed. Only patients who underwent a surgical intervention following a diagnosis of bowel ischemia who also had a post-operative histological confirmation of such a diagnosis were included. Patients were split into two groups according to the presence of histological evidence of transmural bowel ischemia (case group) or partial bowel ischemia (control group). CT images were reviewed for findings of ischemia, including mural thickening, pneumatosis, bowel distension, portomesenteric venous gas and arterial or venous thrombi. RESULTS: A total of 248 subjects who underwent surgery for bowel ischemia were identified. Among the 208 subjects enrolled in our study, transmural bowel necrosis was identified in 121 subjects (case group), and partial bowel necrosis was identified in 87 subjects (control group). Based on CT findings, including mural thickening, bowel distension, pneumatosis, pneumatosis plus portomesenteric venous gas and presence of thrombi or emboli, there were no significant differences between the case and control groups. The concomitant presence of pneumatosis and porto-mesenteric venous gas showed an odds ratio of 1.95 (95%CI: 0.491-7.775, P = 0.342) for the presence of transmural necrosis. The presence of pneumatosis plus porto-mesenteric venous gas exhibited good specificity (83%) but low sensitivity (17%) in the identification of transmural bowel infarction. Accordingly, the positive and negative predictive values were 60% and 17%, respectively. CONCLUSION: Although pneumatosis plus porto-mesenteric venous gas is associated with bowel ischemia, we have demonstrated that their co-occurrence cannot be used as diagnostic signs of transmural necrosis