On separation of a degenerate differential operator in Hilbert space

A coercive estimate for a solution of a degenerate second order di fferential equation is installed, and its applications to spectral problems for the corresponding dif ferential operator is demonstrated. The suffi cient conditions for existence of the solutions of one class of the nonlinear second order diff erential equations on the real axis are obtained.

Machine learning algorithms for spatial data. Case studies: Environmental pollution, natural hazards, renewable resources

This paper presents general problems and approaches for the spatial data analysis using machine learning algorithms. Machine learning is a very powerful approach to adaptive data analysis, modelling and visualisation. The key feature of the machine learning algorithms is that they learn from empirical data and can be used in cases when the modelled environmental phenomena are hidden, nonlinear, noisy and highly variable in space and in time. Most of the machines learning algorithms are universal and adaptive modelling tools developed to solve basic problems of learning from data: classification/pattern recognition, regression/mapping and probability density modelling. In the present report some of the widely used machine learning algorithms, namely artificial neural networks (ANN) of different architectures and Support Vector Machines (SVM), are adapted to the problems of the analysis and modelling of geo-spatial data. Machine learning algorithms have an important advantage over traditional models of spatial statistics when problems are considered in a high dimensional geo-feature spaces, when the dimension of space exceeds 5. Such features are usually generated, for example, from digital elevation models, remote sensing images, etc. An important extension of models concerns considering of real space constrains like geomorphology, networks, and other natural structures. Recent developments in semi-supervised learning can improve modelling of environmental phenomena taking into account on geo-manifolds. An important part of the study deals with the analysis of relevant variables and models' inputs. This problem is approached by using different feature selection/feature extraction nonlinear tools. To demonstrate the application of machine learning algorithms several interesting case studies are considered: digital soil mapping using SVM, automatic mapping of soil and water system pollution using ANN; natural hazards risk analysis (avalanches, landslides), assessments of renewable resources (wind fields) with SVM and ANN models, etc. The dimensionality of spaces considered varies from 2 to more than 30. Figures 1, 2, 3 demonstrate some results of the studies and their outputs. Finally, the results of environmental mapping are discussed and compared with traditional models of geostatistics.

Effects of added dead space on sleep disordered breathing at high altitude

Introduction: Sleep disordered breathing with central apnea or hypopnea frequently occurs during sleep at high altitude. The aim of this study was to assess the effects of added dead space (DS) on sleep disordered breathing and transcutaneous CO2 (PtcCO2) level during sleep at high altitude. Methods: Full night sleep recordings were obtained on 12 unacclimatized mountaineers (11 males, 1 female, mean age 39 ± 12 y.o.) during one of the first 4 nights after arrival in Leh, Ladakh (3500 m). In random order, half of the night was spent with a 500 ml increase in dead space through a custom designed full face mask and the other half without it. PtcCO2 was measured in 3 participants. Results: Baseline recordings reveled two clearly distinct groups: one with severe sleep disordered breathing (n = 5) and the other with mild or no disordered breathing (n = 7). Added dead space markedly improved breathing in the first group (baseline vs DS): apnea hypopnea index (AHI) 70.3 ± 25.8 vs 29.4 ± 6.9 (p = 0.013), oxygen desaturation index (ODI): 72.9 ± 24.1/h vs 42.5 ± 14.4 (p = 0.031), whereas it had no significant effect in the second group. Added dead space did not have a significant effect on mean oxygen saturation level. Respiratory events were almost exclusively central apnea or hypopnea except for one subject. Only a minor increase in mean PtcCO2 (n = 3) was observed: 33.6 ± 1.8 mm Hg at baseline and 35.0 ± 2.62 mm Hg with DS. Sleep quality was preserved under dead space condition, since the microarousal rate remained unchanged (16.8 ± 8.7/h vs 19.4 ± 18.6/h (p = 0.51). Conclusion: In mountaineers with severe sleep disordered breathing at high altitude, a 500 ml increase in dead space through a fitted mask significantly improves nocturnal breathing.

Evaluation of organ-specific peripheral doses after 2-dimensional, 3-dimensional and hybrid intensity modulated radiation therapy for breast cancer based on Monte Carlo and convolution/superposition algorithms: implications for secondary cancer risk assessment.

To make a comprehensive evaluation of organ-specific out-of-field doses using Monte Carlo (MC) simulations for different breast cancer irradiation techniques and to compare results with a commercial treatment planning system (TPS). Three breast radiotherapy techniques using 6MV tangential photon beams were compared: (a) 2DRT (open rectangular fields), (b) 3DCRT (conformal wedged fields), and (c) hybrid IMRT (open conformal+modulated fields). Over 35 organs were contoured in a whole-body CT scan and organ-specific dose distributions were determined with MC and the TPS. Large differences in out-of-field doses were observed between MC and TPS calculations, even for organs close to the target volume such as the heart, the lungs and the contralateral breast (up to 70% difference). MC simulations showed that a large fraction of the out-of-field dose comes from the out-of-field head scatter fluence (>40%) which is not adequately modeled by the TPS. Based on MC simulations, the 3DCRT technique using external wedges yielded significantly higher doses (up to a factor 4-5 in the pelvis) than the 2DRT and the hybrid IMRT techniques which yielded similar out-of-field doses. In sharp contrast to popular belief, the IMRT technique investigated here does not increase the out-of-field dose compared to conventional techniques and may offer the most optimal plan. The 3DCRT technique with external wedges yields the largest out-of-field doses. For accurate out-of-field dose assessment, a commercial TPS should not be used, even for organs near the target volume (contralateral breast, lungs, heart).

Space-time within general relativity : a structural realist understanding

ABSTRACT This dissertation investigates the, nature of space-time as described by the theory of general relativity. It mainly argues that space-time can be naturally interpreted as a physical structure in the precise sense of a network of concrete space-time relations among concrete space-time points that do not possess any intrinsic properties and any intrinsic identity. Such an interpretation is fundamentally based on two related key features of general relativity, namely substantive general covariance and background independence, where substantive general covariance is understood as a gauge-theoretic invariance under active diffeomorphisms and background independence is understood in the sense that the metric (or gravitational) field is dynamical and that, strictly speaking, it cannot be uniquely split into a purely gravitational part and a fixed purely inertial part or background. More broadly, a precise notion of (physical) structure is developed within the framework of a moderate version of structural realism understood as a metaphysical claim about what there is in the world. So, the developement of this moderate structural realism pursues two main aims. The first is purely metaphysical, the aim being to develop a coherent metaphysics of structures and of objects (particular attention is paid to the questions of identity and individuality of these latter within this structural realist framework). The second is to argue that moderate structural realism provides a convincing interpretation of the world as described by fundamental physics and in particular of space-time as described by general relativity. This structuralist interpretation of space-time is discussed within the traditional substantivalist-relationalist debate, which is best understood within the broader framework of the question about the relationship between space-time on the one hand and matter on the other. In particular, it is claimed that space-time structuralism does not constitute a 'tertium quid' in the traditional debate. Some new light on the question of the nature of space-time may be shed from the fundamental foundational issue of space-time singularities. Their possible 'non-local' (or global) feature is discussed in some detail and it is argued that a broad structuralist conception of space-time may provide a physically meaningful understanding of space-time singularities, which is not plagued by the conceptual difficulties of the usual atomsitic framework. Indeed, part of these difficulties may come from the standard differential geometric description of space-time, which encodes to some extent this atomistic framework; it raises the question of the importance of the mathematical formalism for the interpretation of space-time.

Clustering and hot spot detection in socio-economic spatio-temporal data

Distribution of socio-economic features in urban space is an important source of information for land and transportation planning. The metropolization phenomenon has changed the distribution of types of professions in space and has given birth to different spatial patterns that the urban planner must know in order to plan a sustainable city. Such distributions can be discovered by statistical and learning algorithms through different methods. In this paper, an unsupervised classification method and a cluster detection method are discussed and applied to analyze the socio-economic structure of Switzerland. The unsupervised classification method, based on Ward's classification and self-organized maps, is used to classify the municipalities of the country and allows to reduce a highly-dimensional input information to interpret the socio-economic landscape. The cluster detection method, the spatial scan statistics, is used in a more specific manner in order to detect hot spots of certain types of service activities. The method is applied to the distribution services in the agglomeration of Lausanne. Results show the emergence of new centralities and can be analyzed in both transportation and social terms.

Tethyan margins in space and time

Rifting processes, leading to sea-floor spreading, are characterized by a sequence of events: transtensive phase of extension with syn-rift volcanism; simple shear extension accompanied by lithospheric thinning and asthenospheric up-welling and thermal uplift of the rift shoulder and asymmetric volcanism. The simple shear model of extension leads to an asymmetric model of passive margin: a lower plate tilted block margin and an upper plate flexural, ramp-like margin- Both will be affected by thermal contraction and subsidence, starting soon after sea-floor spreading. Based on these actualistic models Tethyan margins are classified as one type or the other. Their evolution from the first transtensional phase of extension to the passive margin stage are analyzed. Four main rifting events are recognized in the Tethyan realm: an episode of lower Paleozoic events leading to the formation of the Paleotethys; a Late Paleozoic event leading to the opening of the Permotethys and East Mediterranean basin: an early Mesozoic event leading to the opening of the Pindos Neotethys and a Jurassic event related to the opening of the Alpine/Atlantic Neotethys. Type margins are given as example of each rifting event: -Northern Iran (Alborz) as a type area for the Late Ordovician to Silurian rifting of Paleotethys. -Northern India and Oman for the Late Carboniferous to early Permian rifting of Permotethys. -The East Mediterranean (Levant, Tunisia) as a Late Carboniferous rifting event. -The Neotethyan rifting phases are separated in two types: an eastern Pindos system found in Turkey and Greece is genetically linked to the Permotethys with a sea-floor spreading delayed until middle Triassic: a western Alpine system directly linked to the opening of the central Atlantic is characterized by a Late Triassic transtensive phase, an early to Middle Liassic break-away phase and. following sea-floor spreading, a thermal subsidence phase starting in Dogger. Problems related to the closure of the Paleozoic oceanic domains are reviewed. A Late Permian, early Triassic phase of `'docking'' between an European accretionary prism (Chios) and a Paleotethyan margin is supported by recent findings in the Mediterranean area. Back-arc rifting within the European active margin led to the formation of marginal seas during Permian and Triassic times and will contribute to the closure of the Paleozoic oceans.

Selective three-dimensional visualization of the coronary arterial lumen using arterial spin tagging.

Conventional coronary magnetic resonance angiography (MRA) techniques display the coronary blood-pool along with the surrounding structures, including the myocardium, the ventricular and atrial blood-pool, and the great vessels. This representation of the coronary lumen is not directly analogous to the information provided by x-ray coronary angiography, in which the coronary lumen displayed by iodinated contrast agent is seen. Analogous "luminographic" data may be obtained using MR arterial spin tagging (projection coronary MRA) techniques. Such an approach was implemented using a 2D selective "pencil" excitation for aortic spin tagging in concert with a 3D interleaved segmented spiral imaging sequence with free-breathing, and real-time navigator technology. This technique allows for selective 3D visualization of the coronary lumen blood-pool, while signal from the surrounding structures is suppressed.

Establishing two-dimensional gels for the analysis of Leishmania proteomes.

Several different sample preparation methods for two-dimensional electrophoresis (2-DE) analysis of Leishmania parasites were compared. From this work, we were able to identify a solubilization method using Nonidet P-40 as detergent, which was simple to follow, and which produced 2-DE gels of high resolution and reproducibility.