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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.
Interior transmission eigenvalue problems for the Helmholtz equation play an important role in inverse wave scattering. Some distribution properties of those eigenvalues in the complex plane are reviewed. Further, a new scattering model for the interior transmission eigenvalue problem with mixed boundary conditions is described and an efficient algorithm for computing the interior transmission eigenvalues is proposed. Finally, extensive numerical results for a variety of two-dimensional scatterers are presented to show the validity of the proposed scheme.
We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues.
Kyphoplasty of Osteoporotic Fractured Vertebrae: A Finite Element Analysis about Two Types of Cement
(2019)
Heating efficiency of magnetic nanoparticles decreases with gradual immobilization in hydrogels
(2019)
Monitoring the cellular metabolism of bacteria in (bio)fermentation processes is crucial to control and steer them, and to prevent undesired disturbances linked to metabolically inactive microorganisms. In this context, cell-based biosensors can play an important role to improve the quality and increase the yield of such processes. This work describes the simultaneous analysis of the metabolic behavior of three different types of bacteria by means of a differential light-addressable potentiometric sensor (LAPS) set-up. The study includes Lactobacillus brevis, Corynebacterium glutamicum, and Escherichia coli, which are often applied in fermentation processes in bioreactors. Differential measurements were carried out to compensate undesirable influences such as sensor signal drift, and pH value variation during the measurements. Furthermore, calibration curves of the cellular metabolism were established as a function of the glucose concentration or cell number variation with all three model microorganisms. In this context, simultaneous (bio)sensing with the multi-organism LAPS-based set-up can open new possibilities for a cost-effective, rapid detection of the extracellular acidification of bacteria on a single sensor chip. It can be applied to evaluate the metabolic response of bacteria populations in a (bio)fermentation process, for instance, in the biogas fermentation process.
Enzyme-catalyzed reactions have been designed to mimic various Boolean logic gates in the general framework of unconventional biomolecular computing. While some of the logic gates, particularly OR, AND, are easy to realize with biocatalytic reactions and have been reported in numerous publications, some other, like NXOR, are very challenging and have not been realized yet with enzyme reactions. The paper reports on a novel approach to mimicking the NXOR logic gate using the bell-shaped enzyme activity dependent on pH values. Shifting pH from the optimum value to the acidic or basic values by using acid or base inputs (meaning 1,0 and 0,1 inputs) inhibits the enzyme reaction, while keeping the optimum pH (assuming 0,0 and 1,1 input combinations) preserves a high enzyme activity. The challenging part of the present approach is the selection of an enzyme with a well-demonstrated bell-shape activity dependence on the pH value. While many enzymes can satisfy this condition, we selected pyrroloquinoline quinone (PQQ)-dependent glucose dehydrogenase as this enzyme has the optimum pH center-located on the pH scale allowing the enzyme activity change by the acidic and basic pH shift from the optimum value corresponding to the highest activity. The present NXOR gate is added to the biomolecular “toolbox” as a new example of Boolean logic gates based on enzyme reactions.