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The Rothman–Woodroofe symmetry test statistic is revisited on the basis of independent but not necessarily identically distributed random variables. The distribution-freeness if the underlying distributions are all symmetric and continuous is obtained. The results are applied for testing symmetry in a meta-analysis random effects model. The consistency of the procedure is discussed in this situation as well. A comparison with an alternative proposal from the literature is conducted via simulations. Real data are analyzed to demonstrate how the new approach works in practice.
We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.
The established Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic is investigated for partly not identically distributed data. Surprisingly, it turns out that the statistic has the well-known distribution-free limiting null distribution of the classical criterion under standard regularity conditions. An application is testing goodness-of-fit for the regression function in a non parametric random effects meta-regression model, where the consistency is obtained as well. Simulations investigate size and power of the approach for small and moderate sample sizes. A real data example based on clinical trials illustrates how the test can be used in applications.
With the variety of toothbrushes on the market, the question arises, which toothbrush is best suited to maintain oral health? This thematic review focuses first on plaque formation mechanisms and then on the plaque removal effectiveness of ultrasonic toothbrushes and their potential in preventing oral diseases like periodontitis, gingivitis, and caries. We overviewed the physical effects that occurred during brushing and tried to address the question of whether ultrasonic toothbrushes effectively reduced the microbial burden by increasing the hydrodynamic forces. The results of published studies show that electric toothbrushes, which combine ultrasonic and sonic (or acoustic and mechanic) actions, may have the most promising effect on good oral health. Existing ultrasonic/sonic toothbrush models do not significantly differ regarding the removal of dental biofilm and the reduction of gingival inflammation compared with other electrically powered toothbrushes, whereas the manual toothbrushes show a lower effectiveness.
LAPS-based monitoring of metabolic responses of bacterial cultures in a paper fermentation broth
(2020)
As an alternative renewable energy source, methane production in biogas plants is gaining more and more attention. Biomass in a bioreactor contains different types of microorganisms, which should be considered in terms of process-stability control. Metabolically inactive microorganisms within the fermentation process can lead to undesirable, time-consuming and cost-intensive interventions. Hence, monitoring of the cellular metabolism of bacterial populations in a fermentation broth is crucial to improve the biogas production, operation efficiency, and sustainability. In this work, the extracellular acidification of bacteria in a paper-fermentation broth is monitored after glucose uptake, utilizing a differential light-addressable potentiometric sensor (LAPS) system. The LAPS system is loaded with three different model microorganisms (Escherichia coli, Corynebacterium glutamicum, and Lactobacillus brevis) and the effect of the fermentation broth at different process stages on the metabolism of these bacteria is studied. In this way, different signal patterns related to the metabolic response of microorganisms can be identified. By means of calibration curves after glucose uptake, the overall extracellular acidification of bacterial populations within the fermentation process can be evaluated.
Superparamagnetic iron oxide nanoparticles (SPION) are extensively used for magnetic resonance imaging (MRI) and magnetic particle imaging (MPI), as well as for magnetic fluid hyperthermia (MFH). We here describe a sequential centrifugation protocol to obtain SPION with well-defined sizes from a polydisperse SPION starting formulation, synthesized using the routinely employed co-precipitation technique. Transmission electron microscopy, dynamic light scattering and nanoparticle tracking analyses show that the SPION fractions obtained upon size-isolation are well-defined and almost monodisperse. MRI, MPI and MFH analyses demonstrate improved imaging and hyperthermia performance for size-isolated SPION as compared to the polydisperse starting mixture, as well as to commercial and clinically used iron oxide nanoparticle formulations, such as Resovist® and Sinerem®. The size-isolation protocol presented here may help to identify SPION with optimal properties for diagnostic, therapeutic and theranostic applications.
Design, evaluation and comparison of endorectal coils for hybrid MR-PET imaging of the prostate
(2020)
Prostate cancer is one of the most common cancers among men and its early detection is critical for its successful treatment. The use of multimodal imaging, such as MR-PET, is most advantageous as it is able to provide detailed information about the prostate. However, as the human prostate is flexible and can move into different positions under external conditions, it is important to localise the focused region-of-interest using both MRI and PET under identical circumstances. In this work, we designed five commonly used linear and quadrature radiofrequency surface coils suitable for hybrid MR-PET use in endorectal applications. Due to the endorectal design and the shielded PET insert, the outer face of the coils investigated was curved and the region to be imaged was outside the volume of the coil. The tilting angles of the coils were varied with respect to the main magnetic field direction. This was done to approximate the various positions from which the prostate could be imaged. The transmit efficiencies and safety excitation efficiencies from simulations, together with the signal-to-noise ratios from the MR images were calculated and analysed. Overall, it was found that the overlapped loops driven in quadrature were superior to the other types of coils we tested. In order to determine the effect of the different coil designs on PET, transmission scans were carried out, and it was observed that the differences between attenuation maps with and without the coils were negligible. The findings of this work can provide useful guidance for the integration of such coil designs into MR-PET hybrid systems in the future.
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970–986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.