Large scale detection of half-flats in CAT(0)-spaces

For a k-flat F inside a locally compact CAT(0)-space X, we identify various conditions that ensure that F bounds a (k+1)-dimensional half flat in X. Our conditions are formulated in terms of the ultralimit of X. As applications, we obtain (1) constraints on the behavior of quasi-isometries between tocally compact CAT(0)-spaces, (2) constraints on the possible non-positively curved Riemannian metrics supported by certain manifolds, and (3) a correspondence between metric splittings of a complete, simply connected, non-positively curved Riemannian manifold and the metric splittings of its asymptotic cones. Furthermore, combining our results with the Ballmann, Burns-Spatzier rigidity theorem and the classical Mostow rigidity theorem, we also obtain (4) a new proof of Gromov's rigidity theorem for higher rank locally symmetric spaces.Comment: 21 pages. This article is a substantially improved version of our earlier preprint arXiv:0801.3636. It features more general results, with shorter, cleaner proofs. Applications remain the sam

Quantitative Models and Implicit Complexity

We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by one of us), Light Affine Logic and Soft Affine Logic. The proofs are based on a common semantical framework which is merely instantiated in four different ways. The framework consists of an innovative modification of realizability which allows us to use resource-bounded computations as realisers as opposed to including all Turing computable functions as is usually the case in realizability constructions. For example, all realisers in the model for LFPL are polynomially bounded computations whence soundness holds by construction of the model. The work then lies in being able to interpret all the required constructs in the model. While being the first entirely semantical proof of polytime soundness for light logi cs, our proof also provides a notable simplification of the original already semantical proof of polytime soundness for LFPL. A new result made possible by the semantic framework is the addition of polymorphism and a modality to LFPL thus allowing for an internal definition of inductive datatypes.Comment: 29 page

Integrating ASCAT surface soil moisture and GEOV1 leaf area index into the SURFEX modelling platform: a land data assimilation application over France

The land monitoring service of the European Copernicus programme has developed a set of satellite-based biogeophysical products, including surface soil moisture (SSM) and leaf area index (LAI). This study investigates the impact of joint assimilation of remotely sensed SSM derived from Advanced Scatterometer (ASCAT) backscatter data and the Copernicus Global Land GEOV1 satellite-based LAI product into the the vegetation growth version of the Interactions between Soil Biosphere Atmosphere (ISBA-A-gs) land surface model within the the externalised surface model (SURFEX) modelling platform of Météo-France. The ASCAT data were bias corrected with respect to the model climatology by using a seasonal-based CDF (Cumulative Distribution Function) matching technique. A multivariate multi-scale land data assimilation system (LDAS) based on the extended Kalman Filter (EKF) is used for monitoring the soil moisture, terrestrial vegetation, surface carbon and energy fluxes across the domain of France at a spatial resolution of 8 km. Each model grid box is divided into a number of land covers, each having its own set of prognostic variables. The filter algorithm is designed to provide a distinct analysis for each land cover while using one observation per grid box. The updated values are aggregated by computing a weighted average. <br><br> In this study, it is demonstrated that the assimilation scheme works effectively within the ISBA-A-gs model over a four-year period (2008–2011). The EKF is able to extract useful information from the data signal at the grid scale and distribute the root-zone soil moisture and LAI increments throughout the mosaic structure of the model. The impact of the assimilation on the vegetation phenology and on the water and carbon fluxes varies from one season to another. The spring drought of 2011 is an interesting case study of the potential of the assimilation to improve drought monitoring. A comparison between simulated and in situ soil moisture gathered at the twelve SMOSMANIA (Soil Moisture Observing System–Meteorological Automatic Network Integrated Application) stations shows improved anomaly correlations for eight stations

Generalised Compositional Theories and Diagrammatic Reasoning

This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.Comment: To appear as a Springer book chapter chapter, edited by G. Chirabella, R. Spekken

Use of a stimulated echo sequence in the MRI study of the brain and spine

We describe in this paper how the STEAM sequence can be an efficient tool to obtain images free of flow artifacts in anatomical situation where the spin echo failed. The simplest way to eliminate flow artifacts is to exploit the dephasing induced by motion in magnetic field gradients and to reduce to zero the signal from moving tissues. This can be achieve by increasing the time elapsed between the spin excitation and the signal observed. Because of T2 relaxation, such an increase results in a signal decrease when the spin echo sequence is used. The STEAM sequence has the unique property that the time elapsed between observation and excitation can be increased without change in T2 value and so allows a good suppression of signals from the moving spins with short TE. Our results demonstrate that, although the stimulated echo intensity is only half that of a spin echo taken at the same read out time, the advantages of STEAM imaging can compensate for this partial loss in signal to noise in some particular clinical situations. The influence of mixing time on contrast has been evaluated using thoracic spine imaging and it has been shown that contrast between spine and CSF can be significantly improved (+ 60%) when TM is increased (from 17 ms to 50 ms). In the same time, the contrast between spine and fat issue decreases (40%). This last effect facilitates the adjustment of contrast window. Suppression of motion artifacts has first been evaluated with thoracic spine imaging, using a whole body coil. Suppression of artifacts was better than that obtained with a flow compensated spin echo sequence, especially in the case of kyphotic patients when a presaturation band was inefficient. In a second step suppression of motion artifacts has been evaluated from posterior fossa examination after injection of a paramagnetic contrast agent. The images obtained with the stimulated echo sequence show a dramatic reduction of signal from blood in the lateral sinus, and therefore an increase of quality by elimination of motion artifacts