From circular paths to elliptic orbits: A geometric approach to Kepler's motion

The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.Comment: 9 pages, 4 figure

Quantisation without Gauge Fixing: Avoiding Gribov Ambiguities through the Physical Projector

The quantisation of gauge invariant systems usually proceeds through some gauge fixing procedure of one type or another. Typically for most cases, such gauge fixings are plagued by Gribov ambiguities, while it is only for an admissible gauge fixing that the correct dynamical description of the system is represented, especially with regards to non perturbative phenomena. However, any gauge fixing procedure whatsoever may be avoided altogether, by using rather a recently proposed new approach based on the projection operator onto physical gauge invariant states only, which is necessarily free on any such issues. These different aspects of gauge invariant systems are explicitely analysed within a solvable U(1) gauge invariant quantum mechanical model related to the dimensional reduction of Yang-Mills theory.Comment: 22 pages, no figures, plain LaTeX fil

Extreme flood response to short-duration convective rainfall in South-West Germany

The 2 June 2008 flood-producing storm on the Starzel river basin in South-West Germany is examined as a prototype for organized convective systems that dominate the upper tail of the precipitation frequency distribution and are likely responsible for the flash flood peaks in Central Europe. The availability of high-resolution rainfall estimates from radar observations and a rain gauge network, together with indirect peak discharge estimates from a detailed post-event survey, provided the opportunity to study in detail the hydrometeorological and hydrological mechanisms associated with this extreme storm and the ensuing flood. Radar-derived rainfall, streamgauge data and indirect estimates of peak discharges are used along with a distributed hydrologic model to reconstruct hydrographs at multiple locations. Observations and model results are combined to examine two main questions, (i) assessment of the distribution of the runoff ratio for the 2008 flash flood and how it compares with other less severe floods; and (ii) analysis of how the spatial and temporal distribution of the extreme rainfall, and more specifically storm motion, controls the flood response. It is shown that small runoff ratios (less than 20 %) characterized the runoff response and that these values are in the range of other, less extreme, flood events. The influence of storm structure, evolution and motion on the modeled flood hydrograph is examined by using the “spatial moments of catchment rainfall”. It is shown that downbasin storm motion (in the range of 0.7–0.9ms−1) had a noticeable impact on flood response by increasing the modeled flood peak by 13 %

Imaging Active Infection in vivo Using D-Amino Acid Derived PET Radiotracers.

Occult bacterial infections represent a worldwide health problem. Differentiating active bacterial infection from sterile inflammation can be difficult using current imaging tools. Present clinically viable methodologies either detect morphologic changes (CT/ MR), recruitment of immune cells (111In-WBC SPECT), or enhanced glycolytic flux seen in inflammatory cells (18F-FDG PET). However, these strategies are often inadequate to detect bacterial infection and are not specific for living bacteria. Recent approaches have taken advantage of key metabolic differences between prokaryotic and eukaryotic organisms, allowing easier distinction between bacteria and their host. In this report, we exploited one key difference, bacterial cell wall biosynthesis, to detect living bacteria using a positron-labeled D-amino acid. After screening several 14C D-amino acids for their incorporation into E. coli in culture, we identified D-methionine as a probe with outstanding radiopharmaceutical potential. Based on an analogous procedure to that used for L-[methyl-11C]methionine ([11C] L-Met), we developed an enhanced asymmetric synthesis of D-[methyl-11C]methionine ([11C] D-Met), and showed that it can rapidly and selectively differentiate both E. coli and S. aureus infections from sterile inflammation in vivo. We believe that the ease of [11C] D-Met radiosynthesis, coupled with its rapid and specific in vivo bacterial accumulation, make it an attractive radiotracer for infection imaging in clinical practice

Sensitivity analysis of uncertain dynamic systems using set-valued integration

We present an extension of set-valued integration to enable efficient sensitivity analysis of parameter-dependent ordinary differential equation (ODE) systems, using both the forward and adjoint methods. The focus is on continuous-time set-valued integration, whereby auxiliary ODE systems are derived whose solutions describe high-order inclusions of the parametric trajectories in the form of polynomial models. The forward and adjoint auxiliary ODE systems treat the parameterization error of the original differential variables as a time-varying uncertainty, and propagate the sensitivity bounds forward and backward in time, respectively. This construction enables building on the sensitivity analysis capabilities of state-of-the-art solvers, such as CVODES in the SUNDIALS suite. Several numerical case studies are presented to assess the performance and accuracy of these set-valued sensitivity integrators

Development and validation of the ACE tool: Assessing medical trainees' competency in evidence based medicine

BACKGROUND: While a variety of instruments have been developed to assess knowledge and skills in evidence based medicine (EBM), few assess all aspects of EBM - including knowledge, skills attitudes and behaviour - or have been psychometrically evaluated. The aim of this study was to develop and validate an instrument that evaluates medical trainees’ competency in EBM across knowledge, skills and attitude. METHODS: The ‘Assessing Competency in EBM’ (ACE) tool was developed by the authors, with content and face validity assessed by expert opinion. A cross-sectional sample of 342 medical trainees representing ‘novice’, ‘intermediate’ and ‘advanced’ EBM trainees were recruited to complete the ACE tool. Construct validity, item difficulty, internal reliability and item discrimination were analysed. RESULTS: We recruited 98 EBM-novice, 108 EBM-intermediate and 136 EBM-advanced participants. A statistically significant difference in the total ACE score was observed and corresponded to the level of training: on a 0-15-point test, the mean ACE scores were 8.6 for EBM-novice; 9.5 for EBM-intermediate; and 10.4 for EBM-advanced (p < 0.0001). Individual item discrimination was excellent (Item Discrimination Index ranging from 0.37 to 0.84), with internal reliability consistent across all but three items (Item Total Correlations were all positive ranging from 0.14 to 0.20). CONCLUSION: The 15-item ACE tool is a reliable and valid instrument to assess medical trainees’ competency in EBM. The ACE tool provides a novel assessment that measures user performance across the four main steps of EBM. To provide a complete suite of instruments to assess EBM competency across various patient scenarios, future refinement of the ACE instrument should include further scenarios across harm, diagnosis and prognosis

Characterization of wood-laden flows in rivers

Inorganic sediment is not the only solid‐fraction component of river flows; flows may also carry significant amounts of large organic material (i.e., large wood), but the characteristics of these wood‐laden flows (WLF) are not well understood yet. With the aim to shed light on these relatively unexamined phenomena, we collected home videos showing natural flows with wood as the main solid component. Analyses of these videos as well as the watersheds and streams where the videos were recorded allowed us to define for the first time WLF, describe the main characteristics of these flows and broaden the definition of wood transport regimes (adding a new regime called here hypercongested wood transport). According to our results, WLF may occur repeatedly, in a large range of catchment sizes, generally in steep, highly confined single thread channels in mountain areas. WLF are typically highly unsteady and the log motion is non‐uniform, as described for other inorganic sediment‐laden flows (e.g., debris flows). The conceptual integration of wood into our understanding of flow phenomena is illustrated by a novel classification defining the transition from clear water to hypercongested, wood and sediment‐laden flows, according to the composition of the mixture (sediment, wood, and water). We define the relevant metrics for the quantification and modelling of WLF, including an exhaustive discussion of different modelling approaches (i.e., Voellmy, Bingham and Manning) and provide a first attempt to simulate WLF. We draw attention to WLF phenomena to encourage further field, theoretical, and experimental investigations that may contribute to a better understanding of flows river basins, leading to more accurate predictions, and better hazard mitigation and management strategies

Joint system quantum descriptions arising from local quantumness

Bipartite correlations generated by non-signalling physical systems that admit a finite-dimensional local quantum description cannot exceed the quantum limits, i.e., they can always be interpreted as distant measurements of a bipartite quantum state. Here we consider the effect of dropping the assumption of finite dimensionality. Remarkably, we find that the same result holds provided that we relax the tensor structure of space-like separated measurements to mere commutativity. We argue why an extension of this result to tensor representations seems unlikely