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Elastic transmission eigenvalues and their computation via the method of fundamental solutions
(2020)
A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach.
There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost.
Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different.
A second-order L-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.
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.
To prevent the reduction of muscle mass and loss of strength coming along with the human aging process, regular training with e.g. a leg press is suitable. However, the risk of training-induced injuries requires the continuous monitoring and controlling of the forces applied to the musculoskeletal system as well as the velocity along the motion trajectory and the range of motion. In this paper, an adaptive norm-optimal iterative learning control algorithm to minimize the knee joint loadings during the leg extension training with an industrial robot is proposed. The response of the algorithm is tested in simulation for patients with varus, normal and valgus alignment of the knee and compared to the results of a higher-order iterative learning control algorithm, a robust iterative learning control and a recently proposed conventional norm-optimal iterative learning control algorithm. Although significant improvements in performance are made compared to the conventional norm-optimal iterative learning control algorithm with a small learning factor, for the developed approach as well as the robust iterative learning control algorithm small steady state errors occur.
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.
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.
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.
Exercise training effectively mitigates aging-induced health and fitness impairments. Traditional training recommendations for the elderly focus separately on relevant physiological fitness domains, such as balance, flexibility, strength and endurance. Thus, a more holistic and functional training framework is needed. The proposed agility training concept integratively tackles spatial orientation, stop and go, balance and strength. The presented protocol aims at introducing a two-armed, one-year randomized controlled trial, evaluating the effects of this concept on neuromuscular, cardiovascular, cognitive and psychosocial health outcomes in healthy older adults. Eighty-five participants were enrolled in this ongoing trial. Seventy-nine participants completed baseline testing and were block-randomized to the agility training group or the inactive control group. All participants undergo pre- and post-testing with interim assessment after six months. The intervention group currently receives supervised, group-based agility training twice a week over one year, with progressively demanding perceptual, cognitive and physical exercises. Knee extension strength, reactive balance, dual task gait speed and the Agility Challenge for the Elderly (ACE) serve as primary endpoints and neuromuscular, cognitive, cardiovascular, and psychosocial meassures serve as surrogate secondary outcomes. Our protocol promotes a comprehensive exercise training concept for older adults, that might facilitate stakeholders in health and exercise to stimulate relevant health outcomes without relying on excessively time-consuming physical activity recommendations.
Bacterial cellulose (BC) is a promising material for biomedical applications due to its unique properties such as high mechanical strength and biocompatibility. This article describes the microbiological synthesis, modification, and characterization of the obtained BC-nanocomposites originating from symbiotic consortium Medusomyces gisevii. Two BC-modifications have been obtained: BC-Ag and BC-calcium phosphate (BC-Ca3(PO4)2). Structure and physicochemical properties of the BC and its modifications were investigated by scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), atomic force microscopy (AFM), and infrared Fourier spectroscopy as well as by measurements of mechanical and water holding/absorbing capacities. Topographic analysis of the surface revealed multicomponent thick fibrils (150–160 nm in diameter and about 15 µm in length) constituted by 50–60 nm nanofibrils weaved into a left-hand helix. Distinctive features of Ca-phosphate-modified BC samples were (a) the presence of 500–700 nm entanglements and (b) inclusions of Ca3(PO4)2 crystals. The samples impregnated with Ag nanoparticles exhibited numerous roundish inclusions, about 110 nm in diameter. The boundaries between the organic and inorganic phases were very distinct in both cases. The Ag-modified samples also showed a prominent waving pattern in the packing of nanofibrils. The obtained BC gel films possessed water-holding capacity of about 62.35 g/g. However, the dried (to a constant mass) BC-films later exhibited a low water absorption capacity (3.82 g/g). It was found that decellularized BC samples had 2.4 times larger Young’s modulus and 2.2 times greater tensile strength as compared to dehydrated native BC films. We presume that this was caused by molecular compaction of the BC structure.
Coronavirus disease 2019 (COVID-19) is a novel human infectious disease provoked by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Currently, no specific vaccines or drugs against COVID-19 are available. Therefore, early diagnosis and treatment are essential in order to slow the virus spread and to contain the disease outbreak. Hence, new diagnostic tests and devices for virus detection in clinical samples that are faster, more accurate and reliable, easier and cost-efficient than existing ones are needed. Due to the small sizes, fast response time, label-free operation without the need for expensive and time-consuming labeling steps, the possibility of real-time and multiplexed measurements, robustness and portability (point-of-care and on-site testing), biosensors based on semiconductor field-effect devices (FEDs) are one of the most attractive platforms for an electrical detection of charged biomolecules and bioparticles by their intrinsic charge. In this review, recent advances and key developments in the field of label-free detection of viruses (including plant viruses) with various types of FEDs are presented. In recent years, however, certain plant viruses have also attracted additional interest for biosensor layouts: Their repetitive protein subunits arranged at nanometric spacing can be employed for coupling functional molecules. If used as adapters on sensor chip surfaces, they allow an efficient immobilization of analyte-specific recognition and detector elements such as antibodies and enzymes at highest surface densities. The display on plant viral bionanoparticles may also lead to long-time stabilization of sensor molecules upon repeated uses and has the potential to increase sensor performance substantially, compared to conventional layouts. This has been demonstrated in different proof-of-concept biosensor devices. Therefore, richly available plant viral particles, non-pathogenic for animals or humans, might gain novel importance if applied in receptor layers of FEDs. These perspectives are explained and discussed with regard to future detection strategies for COVID-19 and related viral diseases.
Muscular activity in terms of surface electromyography (sEMG) is usually normalised to maximal voluntary isometric contractions (MVICs). This study aims to compare two different MVIC-modes in handcycling and examine the effect of moving average window-size. Twelve able-bodied male competitive triathletes performed ten MVICs against manual resistance and four sport-specific trials against fixed cranks. sEMG of ten muscles [M. trapezius (TD); M. pectoralis major (PM); M. deltoideus, Pars clavicularis (DA); M. deltoideus, Pars spinalis (DP); M. biceps brachii (BB); M. triceps brachii (TB); forearm flexors (FC); forearm extensors (EC); M. latissimus dorsi (LD) and M. rectus abdominis (RA)] was recorded and filtered using moving average window-sizes of 150, 200, 250 and 300 ms. Sport-specific MVICs were higher compared to manual resistance for TB, DA, DP and LD, whereas FC, TD, BB and RA demonstrated lower values. PM and EC demonstrated no significant difference between MVIC-modes. Moving average window-size had no effect on MVIC outcomes. MVIC-mode should be taken into account when normalised sEMG data are illustrated in handcycling. Sport-specific MVICs seem to be suitable for some muscles (TB, DA, DP and LD), but should be augmented by MVICs against manual/mechanical resistance for FC, TD, BB and RA.
In this study, we describe the manufacturing and characterization of silk fibroin membranes derived from the silkworm Bombyx mori. To date, the dissolution process used in this study has only been researched to a limited extent, although it entails various potential advantages, such as reduced expenses and the absence of toxic chemicals in comparison to other conventional techniques. Therefore, the aim of this study was to determine the influence of different fibroin concentrations on the process output and resulting membrane properties. Casted membranes were thus characterized with regard to their mechanical, structural and optical assets via tensile testing, SEM, light microscopy and spectrophotometry. Cytotoxicity was evaluated using BrdU, XTT, and LDH assays, followed by live–dead staining. The formic acid (FA) dissolution method was proven to be suitable for the manufacturing of transparent and mechanically stable membranes. The fibroin concentration affects both thickness and transparency of the membranes. The membranes did not exhibit any signs of cytotoxicity. When compared to other current scientific and technical benchmarks, the manufactured membranes displayed promising potential for various biomedical applications. Further research is nevertheless necessary to improve reproducible manufacturing, including a more uniform thickness, less impurity and physiological pH within the membranes.
Electrolyte-insulator-semiconductor (EIS) field-effect sensors belong to a new generation of electronic chips for biochemical sensing, enabling a direct electronic readout. The review gives an overview on recent advances and current trends in the research and development of chemical sensors and biosensors based on the capacitive field-effect EIS structure—the simplest field-effect device, which represents a biochemically sensitive capacitor. Fundamental concepts, physicochemical phenomena underlying the transduction mechanism and application of capacitive EIS sensors for the detection of pH, ion concentrations, and enzymatic reactions, as well as the label-free detection of charged molecules (nucleic acids, proteins, and polyelectrolytes) and nanoparticles, are presented and discussed.
The enantioselective synthesis of α-hydroxy ketones and vicinal diols is an intriguing field because of the broad applicability of these molecules. Although, butandiol dehydrogenases are known to play a key role in the production of 2,3-butandiol, their potential as biocatalysts is still not well studied. Here, we investigate the biocatalytic properties of the meso-butanediol dehydrogenase from Bacillus licheniformis DSM 13T (BlBDH). The encoding gene was cloned with an N-terminal StrepII-tag and recombinantly overexpressed in E. coli. BlBDH is highly active towards several non-physiological diketones and α-hydroxyketones with varying aliphatic chain lengths or even containing phenyl moieties. By adjusting the reaction parameters in biotransformations the formation of either the α-hydroxyketone intermediate or the diol can be controlled.
BACKGROUND: Muscle stretch reflexes are widely used to examine neural muscle function. The knowledge of reflex response in muscles crossing the shoulder is limited. OBJECTIVE: To quantify reflex modulation according to various subject postures and different procedures of muscle pre-activation steering. METHODS: Thirteen healthy male participants performed two sets of external shoulder rotation stretches in various positions and with different procedures of muscle pre-activation steering on an isokinetic dynamometer over a range of two different pre-activation levels. All stretches were applied with a dynamometer acceleration of 104∘/s2 and a velocity of 150∘/s. Electromyographical response was measured via sEMG. RESULTS: Consistent reflexive response was observed in all tested muscles in all experimental conditions. The reflex elicitation rate revealed a significant muscle main effect (F (5,288) = 2.358, ρ= 0.040; η2= 0.039; f= 0.637) and a significant test condition main effect (F (1,288) = 5.884, ρ= 0.016; η2= 0.020; f= 0.143). Reflex latency revealed a significant muscle pre-activation level main effect (F (1,274) = 5.008, ρ= 0.026; η2= 0.018; f= 0.469). CONCLUSION: Muscular reflexive response was more consistent in the primary internal rotators of the shoulder. Supine posture in combination with visual feedback of muscle pre-activation level enhanced the reflex elicitation rate.