Abstract:
Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a continuous time generalisation of what is known as weakly constrained four dimensional variational assimilation (WC--4DVAR) in the geosciences. The technique allows to assimilate trajectories in the case of partial observations and in the presence of model error. Several mathematical aspects of the approach are studied. Computationally, it amounts to solving a two point boundary value problem. For imperfect models, the trade off between small dynamical error (i.e. the trajectory obeys the model dynamics) and small observational error (i.e. the trajectory closely follows the observations) is investigated. For (nearly) perfect models, this trade off turns out to be (nearly) trivial in some sense, yet allowing for some dynamical error is shown to have positive effects even in this situation. The presented formalism is dynamical in character; no assumptions need to be made about the presence (or absence) of dynamical or observational noise, let alone about their statistics.

Abstract:
Scoring rules are an important tool for evaluating the performance of probabilistic forecasting schemes. In the binary case, scoring rules (which are strictly proper) allow for a decomposition into terms related to the resolution and to the reliability of the forecast. This fact is particularly well known for the Brier Score. In this paper, this result is extended to forecasts for finite--valued targets. Both resolution and reliability are shown to have a positive effect on the score. It is demonstrated that resolution and reliability are directly related to forecast attributes which are desirable on grounds independent of the notion of scores. This finding can be considered an epistemological justification of measuring forecast quality by proper scores. A link is provided to the original work of DeGroot et al (1982), extending their concepts of sufficiency and refinement. The relation to the conjectured sharpness principle of Gneiting et al (2005a) is elucidated.

Abstract:
Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio equal to a linear combination of the inputs. As any statistical model, logistic models will suffer from over-fitting if the number of inputs is comparable to the number of forecast instances. Computational approaches to avoid over-fitting by regularisation are discussed, and efficient approaches for model assessment and selection are presented. A logit version of the so called lasso, which is originally a linear tool, is discussed. In lasso models, less important inputs are identified and discarded, thereby providing an efficient and automatic model reduction procedure. For this reason, lasso models are particularly appealing for diagnostic purposes.

Abstract:
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among the f-divergences. It is shown that every f-divergence is bounded from below by a monotonous function of the total variation. Under appropriate regularity conditions, this function is shown to be monotonous. Remark: The proof of the main proposition is relatively easy, whence it is highly likely that the result is known. The author would be very grateful for any information regarding references or related work.

Abstract:
Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time--tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established which allows to calculate the latter under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, aka synchronisation. Numerical examples demonstrate the feasibility of the approach.

Abstract:
During a dive peregrine falcons can reach velocities of more than 320 km/h and makes themselves the fastest animals in the world. The aerodynamic mechanisms involved are not fully understood yet and the search for a conclusive answer to this fact motivates the three-dimensional (3-D) flow study. Especially the cupped wing configuration which is a unique feature of the wing shape in falcon peregrine dive is our focus herein. In particular, the flow in the gap between the main body and the cupped wing is studied to understand how this flow interacts with the body and to what extend it affects the integral forces of lift and drag. Characteristic shapes of the wings while diving are studied with regard to their aerodynamics using computational fluid dynamics (CFD). The results of the numerical simulations via ICEM CFD and OpenFOAM show predominant flow structures around the body surface and in the wake of the falcon model such as a pair of body vortices and tip vortices. The drag for the cupped wing profile is reduced in relation to the configuration of opened wings (without cupped-like profile) while lift is increased. The purpose of this study is primarily the basic research of the aerodynamic mechanisms during the falcon’s diving flight. The results could be important for maintaining good maneuverability at high speeds in the aviation sector.

Abstract:
Based on our preceding studies on the aerodynamics of a falcoperegrinus in diving flight along a vertical dam it is known that even when the body shape of the bird is rather streamlined in V-shape some feathers tips may elevate in certain regions of the body. These regions were identified in wind tunnel tests for typical diving flight conditions as regions of locally separated flow. A life-size model in V-shape of a falcoperegrinus with artificial feathers fixed along the body was studied in a wind tunnel to focus on the fluid-structure interaction of feathers located in this sector. The distal ends of the feathers show flow-induced vibrations at typical flight conditions which grow linear in amplitude with increasing angle of incidence until incipient separation. In light of the proven existence of vibration-sensitive mechanoreceptors in the follicles of secondary feathers in birds it is hypothesized that this linear amplitude response offers the bird to sense the angle of incidence during the diving flight using the vibration magnitude as sensory stimulus. Thus the bird in streamlined shape has still a good measure to control its attitude to be in the narrow window of safe angle of incidence. This might have implications also for other birds or technical applications of airfoil sensors regarding incipient separation detection.

Abstract:
Background Methicillin-resistant Staphylococcus aureus (MRSA) may cause prolonged outbreaks of infections in neonatal intensive care units (NICUs). While the specific factors favouring MRSA spread on neonatal wards are not well understood, colonized infants, their relatives, or health-care workers may all be sources for MRSA transmission. Whole-genome sequencing may provide a new tool for elucidating transmission pathways of MRSA at a local scale. Methods and Findings We applied whole-genome sequencing to trace MRSA spread in a NICU and performed a case-control study to identify risk factors for MRSA transmission. MRSA genomes had accumulated sequence variation sufficiently fast to reflect epidemiological linkage among individual patients, between infants and their mothers, and between infants and staff members, such that the relevance of individual nurses’ nasal MRSA colonization for prolonged transmission could be evaluated. In addition to confirming previously reported risk factors, we identified an increased risk of transmission from infants with as yet unknown MRSA colonisation, in contrast to known MRSA-positive infants. Conclusions The integration of epidemiological (temporal, spatial) and genomic data enabled the phylogenetic testing of several hypotheses on specific MRSA transmission routes within a neonatal intensive-care unit. The pronounced risk of transmission emanating from undetected MRSA carriers suggested that increasing the frequency or speed of microbiological diagnostics could help to reduce transmission of MRSA.

Abstract:
Reliability analysis of probabilistic forecasts, in particular through the rank histogram or Talagrand diagram, is revisited. Two shortcomings are pointed out: Firstly, a uniform rank histogram is but a necessary condition for reliability. Secondly, if the forecast is assumed to be reliable, an indication is needed how far a histogram is expected to deviate from uniformity merely due to randomness. Concerning the first shortcoming, it is suggested that forecasts be grouped or stratified along suitable criteria, and that reliability is analyzed individually for each forecast stratum. A reliable forecast should have uniform histograms for all individual forecast strata, not only for all forecasts as a whole. As to the second shortcoming, instead of the observed frequencies, the probability of the observed frequency is plotted, providing and indication of the likelihood of the result under the hypothesis that the forecast is reliable. Furthermore, a Goodness-Of-Fit statistic is discussed which is essentially the reliability term of the Ignorance score. The discussed tools are applied to medium range forecasts for 2 m-temperature anomalies at several locations and lead times. The forecasts are stratified along the expected ranked probability score. Those forecasts which feature a high expected score turn out to be particularly unreliable.

Abstract:
A biomimetic approach is used to generate a directed transversal transportation of micron-sized particles in liquids based on the principle of cilia-type arrays in coordinated motion. Rows of flaps mimicking planar cilia are positioned off-centre along an array of cavities covered with membranes that support the flaps. These membranes are deflected from a concave to a convex shape and vice versa by pneumatic actuation applying positive and negative pressures (relative to the ambient) inside the cavities. As a result, the flap on top of the membrane tilts to the left or right within such a pressure cycle, performing a beat stroke. Since each cavity can be addressed in the device individually and in rapid succession, waves of coordinated flap motion can be run along the wall. Such metachronal waves are generated and transport of particles along the cilia surface is achieved in both symplectic and antiplectic direction. It is shown that the initial tilt of the flaps relative to the wall-normal determines the direction of transport.