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This work is concerned with the numerical approximation of solutions to models that are used to describe atmospheric or oceanographic flows. In particular, this work concen- trates on the approximation of the Shallow Water equations with bottom topography and the compressible Euler equations with a gravitational potential. Numerous methods have been developed to approximate solutions of these models. Of specific interest here are the approximations of near equilibrium solutions and, in the case of the Euler equations, the low Mach number flow regime. It is inherent in most of the numerical methods that the quality of the approximation increases with the number of degrees of freedom that are used. Therefore, these schemes are often run in parallel on big computers to achieve the best pos- sible approximation. However, even on those big machines, the desired accuracy can not be achieved by the given maximal number of degrees of freedom that these machines allow. The main focus in this work therefore lies in the development of numerical schemes that give better resolution of the resulting dynamics on the same number of degrees of freedom, compared to classical schemes.
This work is the result of a cooperation of Prof. Klingenberg of the Institute of Mathe- matics in Wu¨rzburg and Prof. R¨opke of the Astrophysical Institute in Wu¨rzburg. The aim of this collaboration is the development of methods to compute stellar atmospheres. Two main challenges are tackled in this work. First, the accurate treatment of source terms in the numerical scheme. This leads to the so called well-balanced schemes. They allow for an accurate approximation of near equilibrium dynamics. The second challenge is the approx- imation of flows in the low Mach number regime. It is known that the compressible Euler equations tend towards the incompressible Euler equations when the Mach number tends to zero. Classical schemes often show excessive diffusion in that flow regime. The here devel- oped scheme falls into the category of an asymptotic preserving scheme, i.e. the numerical scheme reflects the behavior that is computed on the continuous equations. Moreover, it is shown that the diffusion of the numerical scheme is independent of the Mach number.
In chapter 3, an HLL-type approximate Riemann solver is adapted for simulations of the Shallow Water equations with bottom topography to develop a well-balanced scheme. In the literature, most schemes only tackle the equilibria when the fluid is at rest, the so called Lake at rest solutions. Here a scheme is developed to accurately capture all the equilibria of the Shallow Water equations. Moreover, in contrast to other works, a second order extension is proposed, that does not rely on an iterative scheme inside the reconstruction procedure, leading to a more efficient scheme.
In chapter 4, a Suliciu relaxation scheme is adapted for the resolution of hydrostatic equilibria of the Euler equations with a gravitational potential. The hydrostatic relations are underdetermined and therefore the solutions to that equations are not unique. However, the scheme is shown to be well-balanced for a wide class of hydrostatic equilibria. For specific classes, some quadrature rules are computed to ensure the exact well-balanced property. Moreover, the scheme is shown to be robust, i.e. it preserves the positivity of mass and energy, and stable with respect to the entropy. Numerical results are presented in order to investigate the impact of the different quadrature rules on the well-balanced property.
In chapter 5, a Suliciu relaxation scheme is adapted for the simulations of low Mach number flows. The scheme is shown to be asymptotic preserving and not suffering from excessive diffusion in the low Mach number regime. Moreover, it is shown to be robust under certain parameter combinations and to be stable from an Chapman-Enskog analysis.
Numerical results are presented in order to show the advantages of the new approach.
In chapter 6, the schemes developed in the chapters 4 and 5 are combined in order to investigate the performance of the numerical scheme in the low Mach number regime in a gravitational stratified atmosphere. The scheme is shown the be well-balanced, robust and stable with respect to a Chapman-Enskog analysis. Numerical tests are presented to show the advantage of the newly proposed method over the classical scheme.
In chapter 7, some remarks on an alternative way to tackle multidimensional simulations are presented. However no numerical simulations are performed and it is shown why further research on the suggested approach is necessary.
This dissertation focuses on the performance evaluation of all components of Software Defined Networking (SDN) networks and covers whole their architecture. First, the isolation between virtual networks sharing the same physical resources is investigated with SDN switches of several vendors. Then, influence factors on the isolation are identified and evaluated. Second, the impact of control mechanisms on the performance of the data plane is examined through the flow rule installation time of SDN switches with different controllers. It is shown that both hardware-specific and controller instance have a specific influence on the installation time. Finally, several traffic flow monitoring methods of an SDN controller are investigated and a new monitoring approach is developed and evaluated. It is confirmed that the proposed method allows monitoring of particular flows as well as consumes fewer resources than the standard approach. Based on findings in this thesis, on the one hand, controller developers can refer to the work related to the control plane, such as flow monitoring or flow rule installation, to improve the performance of their applications. On the other hand, network administrators can apply the presented methods to select a suitable combination of controller and switches in their SDN networks, based on their performance requirements
Background:
The compound eyes of insects allow them to catch photons and convert the energy into electric signals. All compound eyes consist of numerous ommatidia, each comprising a fixed number of photoreceptors. Different ommatidial types are characterized by a specific set of photoreceptors differing in spectral sensitivity. In honey bees, males and females possess different ommatidial types forming distinct retinal mosaics. However, data are lacking on retinal ontogeny and the mechanisms by which the eyes are patterned. In this study, we investigated the intrinsic temporal and circadian expression patterns of the opsins that give rise to the ultraviolet, blue and green sensitive photoreceptors, as well as the morphological maturation of the retina during pupal development of honey bees.
Results:
qPCR and histological labeling revealed that temporal opsin mRNA expression differs between sexes and correlates with rhabdom elongation during photoreceptor development. In the first half of the pupal stage, when the rhabdoms of the photoreceptors are still short, worker and (dorsal) drone retinae exhibit similar expression patterns with relatively high levels of UV (UVop) and only marginal levels of blue (BLop) and green (Lop1) opsin mRNA. In the second half of pupation, when photoreceptors and rhabdoms elongate, opsin expression in workers becomes dominated by Lop1 mRNA. In contrast, the dorsal drone eye shows high expression levels of UVop and BLop mRNA, whereas Lop1 mRNA level decreases. Interestingly, opsin expression levels increase up to 22-fold during early adult life. We also found evidence that opsin expression in adult bees is under the control of the endogenous clock.
Conclusions:
Our data indicate that the formation of the sex-specific retinal composition of photoreceptors takes place during the second half of the pupal development, and that opsin mRNA expression levels continue to increase in young bees, which stands in contrast to Drosophila, where the highest expression levels are found during the late pupal stage and remain constant in adults. From an evolutionary perspective, we hypothesize that the delayed retinal maturation during the early adult phase is linked to the delayed transition from indoor to outdoor activities in bees, when vision becomes important.
The diffraction contrast modalities accessible by X-ray grating interferometers are not imaged directly but have to be inferred from sine-like signal variations occurring in a series of images acquired at varying relative positions of the interferometer’s gratings. The absolute spatial translations involved in the acquisition of these phase stepping series usually lie in the range of only a few hundred nanometers, wherefore positioning errors as small as 10 nm will already translate into signal uncertainties of 1–10% in the final images if not accounted for. Classically, the relative grating positions in the phase stepping series are considered input parameters to the analysis and are, for the Fast Fourier Transform that is typically employed, required to be equidistantly distributed over multiples of the gratings’ period. In the following, a fast converging optimization scheme is presented simultaneously determining the phase stepping curves’ parameters as well as the actually performed motions of the stepped grating, including also erroneous rotational motions which are commonly neglected. While the correction of solely the translational errors along the stepping direction is found to be sufficient with regard to the reduction of image artifacts, the possibility to also detect minute rotations about all axes proves to be a valuable tool for system calibration and monitoring. The simplicity of the provided algorithm, in particular when only considering translational errors, makes it well suitable as a standard evaluation procedure also for large image series.
Background
The impact of risk factors on poor outcome after ischemic stroke is well known, but estimating the amount of poor outcome attributable to single factors is challenging in presence of multimorbidity. We aim to compare population attributable risk estimates obtained from different statistical approaches regarding their consistency. We use a real-life data set from the PROSCIS study to identify predictors for mortality and functional impairment one year after first-ever ischemic stroke and quantify their contribution to poor outcome using population attributable risks.
Methods
The PROSpective Cohort with Incident Stroke (PROSCIS) is a prospective observational hospital-based cohort study of patients after first-ever stroke conducted independently in Berlin (PROSCIS-B) and Munich (PROSCIS-M). The association of baseline factors with poor outcome one year after stroke in PROSCIS-B was analysed using multiple logistic regression analysis and population attributable risks were calculated, which were estimated using sequential population attributable risk based on a multiple generalized additive regression model, doubly robust estimation, as well as using average sequential population attributable risk. Findings were reproduced in an independent validation sample from PROSCIS-M.
Results
Out of 507 patients with available outcome information after 12 months in PROSCIS-B, 20.5% suffered from poor outcome. Factors associated with poor outcome were age, pre-stroke physical disability, stroke severity (NIHSS), education, and diabetes mellitus. The order of risk factors ranked by magnitudes of population attributable risk was almost similar for all methods, but population attributable risk estimates varied markedly between the methods. In PROSCIS-M, incidence of poor outcome and distribution of baseline parameters were comparable. The multiple logistic regression model could be reproduced for all predictors, except pre-stroke physical disability. Similar to PROSCIS-B, the order of risk factors ranked by magnitudes of population attributable risk was almost similar for all methods, but magnitudes of population attributable risk differed markedly between the methods.
Conclusions
Ranking of risk factors by population impact is not affected by the different statistical approaches. Thus, for a rational decision on which risk factor to target in disease interventions, population attributable risk is a supportive tool. However, population attributable risk estimates are difficult to interpret and are not comparable when they origin from studies applying different methodology. The predictors for poor outcome identified in PROSCIS-B have a relevant impact on mortality and functional impairment one year after first-ever ischemic stroke.
Overwintering temperature and body condition shift emergence dates of spring-emerging solitary bees
(2018)
Solitary bees in seasonal environments must align their life-cycles with favorable environmental conditions and resources; the timing of their emergence is highly fitness relevant. In several bee species, overwintering temperature influences both emergence date and body weight at emergence. High variability in emergence dates among specimens overwintering at the same temperatures suggests that the timing of emergence also depends on individual body conditions. However, possible causes for this variability, such as individual differences in body size or weight, have been rarely studied. In a climate chamber experiment using two spring-emerging mason bees (Osmia cornuta and O. bicornis), we investigated the relationship between temperature, emergence date, body weight, and body size, the last of which is not affected by overwintering temperature. Our study showed that body weight declined during hibernation more strongly in warm than in cold overwintering temperatures. Although bees emerged earlier in warm than in cold overwintering temperatures, at the time of emergence, bees in warm overwintering temperatures had lower body weights than bees in cold overwintering temperatures (exception of male O. cornuta). Among specimens that experienced the same overwintering temperatures, small and light bees emerged later than their larger and heavier conspecifics. Using a simple mechanistic model we demonstrated that spring-emerging solitary bees use a strategic approach and emerge at a date that is most promising for their individual fitness expectations. Our results suggest that warmer overwintering temperatures reduce bee fitness by causing a decrease in body weight at emergence. We showed furthermore that in order to adjust their emergence dates, bees use not only temperature but also their individual body condition as triggers. This may explain differing responses to climate warming within and among bee populations and may have consequences for bee-plant interactions as well as for the persistence of bee populations under climate change.
Recently, our research group identified in a study novel proalgesic targets in acute and chronic inflammatory pain: oxidized phospholipids (OxPL). OxPL, endogenous chemical irritants, are generated in inflamed tissue and mediate their pain-inducing function by activating the transient receptor potential channels TRPA1 and TRPV1. Both channels are sensors for chemical stimuli on primary afferent nociceptors and are involved in nociception. Here, with the help of calcium imaging and whole cell patch clamp recording techniques, it was found that OxPL metabolites acutely activate TRPA1 and TRPV1 ion channels to excite DRG neurons. OxPL species act predominantly via TRPA1 ion channels and mediate long- lasting non-selective inward currents. Notably, one pure OxPL compound, PGPC, activated a TRPA1 mutant lacking the binding site for electrophilic agonists, suggesting that OxPL activate TRP ion channels by an indirect mechanical mechanism. Next, it was investigated how OxPL influence the excitability of primary sensory neurons. Acute stimulation and fast calcium imaging revealed that OxPL elicit repetitive, spike-like calcium transients in small- diameter DRG neurons, which were fully blocked by antagonists against TRPA1/V1 and N- type voltage-gated calcium channels.
In search of a mechanism that drives repetitive spiking of DRG neurons, it was asked whether NaV1.9, a voltage-gated sodium channel involved in subthreshold excitability and nociception, is needed to trigger OxPL-induced calcium spikes and action potential firing. In electrophysiological recordings, both the combination of local application of OxPL and current injection were required to efficiently increase the action potential (AP) frequency of small-diameter sensory neurons. However, no difference was monitored in the resting membrane potential or OxPL-induced AP firing rate between wt and NaV1.9-deficient small diameter DRG neurons. To see whether NaV1.9 needs inflammatory conditions to be integrated in the OxPL-induced excitation cascade, sensory neurons were pretreated with a mixture of inflammatory mediators before OxPL application. Under inflammatory conditions both the AP and the calcium-spike frequency were drastically enhanced in response to an acute OxPL stimulus. Notably, this potentiation of OxPL stimuli was entirely lost in NaV1.9 deficient sensory neurons. Under inflammatory conditions, the resting membrane potential of NaV1.9-deficient neurons was more negative compared to wt neurons, suggesting that NaV1.9 shows resting activity only under inflammatory conditions.
In conclusion, OxPL are endogenous irritants that induce excitability in small-diameter DRG
neurons, a cellular model of nociceptors, via TRP activation. This effect is potentiated under inflammatory conditions. Under these conditions, NaV1.9 functions as essential mediator as it eases the initiation of excitability after OxPL stimulation.
As mutants in the human NaV1.9 mediate an enhanced or painless perception, this study provides new insight into the mechanism on how NaV1.9 amplifies stimuli of endogenous irritants under inflammatory conditions.
Purpose:
The prescribing of oral chemotherapy agents has introduced the new challenge of ensuring patients’ adherence to therapy. Aspects of a close patient–doctor relationship are reported to be correlated with adherence to oral anticancer drugs, but data on capecitabine are scarce.
Patients and methods:
Sixty-four outpatients with a diagnosis of cancer and prescribed capecitabine were recruited from a German Comprehensive Cancer Center. We used the Patient–Doctor Relationship Questionnaire (PDRQ-9), the Medical Adherence Rating Scale (MARS), the Beliefs about Medicines Questionnaire (BMQ), and the Satisfaction with Information about Medicines Scale (SIMS) to assess patients’ perceptions and behavior. Medical data were extracted from the charts.
Results:
Non-adherence was reported by 20% of the 64 participants. The perceived quality of the patient–doctor relationship was high in general, but it did not emerge as a predictor of adherence in our survey (odds ratio [OR]=0.915, P=0.162, 95% CI=0.808–1.036). However, beliefs about medicine (OR=1.268, P<0.002; 95% CI=1.090–1.475) as well as satisfaction with information about medicine (OR=1.252, P<0.040, 95% CI=1.010–1.551) were predictors of adherence and the quality of the patient–doctor relationship was correlated with both variables (r=0.373, P=0.002 for SIMS sum score; r=0.263, P=0.036 for BMQ necessity/concern difference). Overall, adherence to capecitabine was high with a conviction that the therapy is necessary. However, concerns were expressed regarding the long-term effect of capecitabine use. Patients have unmet information needs regarding interactions of capecitabine with other medicines and the impairment of their intimate life.
Conclusions:
In order to ensure adherence to capecitabine, our results seem to encourage the default use of modern and perhaps more impersonal means of information brokerage (eg, email, internet). However, the contents of some of patients’ informational needs as well as the associations of patients’ beliefs and satisfaction about the information received suggest a benefit from a trustful patient–doctor relationship.
Increasing evidence indicates that forest disturbances are changing in response to global change, yet local variability in disturbance remains high. We quantified this considerable variability and analyzed whether recent disturbance episodes around the globe were consistently driven by climate, and if human influence modulates patterns of forest disturbance. We combined remote sensing data on recent (2001–2014) disturbances with in-depth local information for 50 protected landscapes and their surroundings across the temperate biome. Disturbance patterns are highly variable, and shaped by variation in disturbance agents and traits of prevailing tree species. However, high disturbance activity is consistently linked to warmer and drier than average conditions across the globe. Disturbances in protected areas are smaller and more complex in shape compared to their surroundings affected by human land use. This signal disappears in areas with high recent natural disturbance activity, underlining the potential of climate-mediated disturbance to transform forest landscapes.
Fanconi anaemia (FA) is an inherited disease with bone marrow failure, variable congenital and developmental abnormalities, and cancer predisposition. With improved survival, non-haematological manifestations of FA become increasingly important for long-term management. While renal abnormalities are recognized, detailed data on patterns and frequency and implications for long-term management are sparse. We reviewed clinical course and imaging findings of FA patients with respect to renal complications in our centre over a 25-year period to formulate some practical suggestions for guidelines for management of renal problems associated with FA. Thirty patients including four sibling sets were reviewed. On imaging, 14 had evidence of anatomical abnormalities of the kidneys. Two cases with severe phenotype, including renal abnormalities, had chronic kidney disease (CKD) at diagnosis. Haematopoietic stem cell transplantation was complicated by significant acute kidney injury (AKI) in three cases. In three patients, there was CKD at long-term follow-up. All patients had normal blood pressure. Evaluation of renal anatomy with ultrasound imaging is important at diagnostic workup of FA. While CKD is uncommon at diagnosis, our data suggests that the incidence of CKD increases with age, in particular after haematopoietic stem cell transplantation. Monitoring of renal function is essential for management of FA. Based on these long-term clinical observations, we formulate some practical guidelines for assessment and management of renal abnormalities in FA.