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The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Additionally, it can be shown numerically that the ratio between the maximal/minimal value inside the domain and its maximal/minimal value on the boundary can be larger than 1 + 10− 3. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.
Stretch-shortening type actions are characterized by lengthening of the pre-activated muscle-tendon unit (MTU) in the eccentric phase immediately followed by muscle shortening. Under 1 g, pre-activity before and muscle activity after ground contact, scale muscle stiffness, which is crucial for the recoil properties of the MTU in the subsequent push-off. This study aimed to examine the neuro-mechanical coupling of the stretch-shortening cycle in response to gravity levels ranging from 0.1 to 2 g. During parabolic flights, 17 subjects performed drop jumps while electromyography (EMG) of the lower limb muscles was combined with ultrasound images of the gastrocnemius medialis, 2D kinematics and kinetics to depict changes in energy management and performance. Neuro-mechanical coupling in 1 g was characterized by high magnitudes of pre-activity and eccentric muscle activity allowing an isometric muscle behavior during ground contact. EMG during pre-activity and the concentric phase systematically increased from 0.1 to 1 g. Below 1 g the EMG in the eccentric phase was diminished, leading to muscle lengthening and reduced MTU stretches. Kinetic energy at take-off and performance were decreased compared to 1 g. Above 1 g, reduced EMG in the eccentric phase was accompanied by large MTU and muscle stretch, increased joint flexion amplitudes, energy loss and reduced performance. The energy outcome function established by linear mixed model reveals that the central nervous system regulates the extensor muscles phase- and load-specifically. In conclusion, neuro-mechanical coupling appears to be optimized in 1 g. Below 1 g, the energy outcome is compromised by reduced muscle stiffness. Above 1 g, loading progressively induces muscle lengthening, thus facilitating energy dissipation.
Test-retest reliability of the internal shoulder rotator muscles' stretch reflex in healthy men
(2021)
Until now the reproducibility of the short latency stretch reflex of the internal rotator muscles of the glenohumeral joint has not been identified. Twenty-three healthy male participants performed three sets of external shoulder rotation stretches with various pre-activation levels on two different dates of measurement to assess test-retest reliability. All stretches were applied with a dynamometer acceleration of 104°/s2 and a velocity of 150°/s. Electromyographical response was measured via surface EMG. Reflex latencies showed a pre-activation effect (ƞ2 = 0,355). ICC ranged from 0,735 to 0,909 indicating an overall “good” relative reliability. SRD 95% lay between ±7,0 to ±12,3 ms.. The reflex gain showed overall poor test-retest reproducibility. The chosen methodological approach presented a suitable test protocol for shoulder muscles stretch reflex latency evaluation. A proof-of-concept study to validate the presented methodical approach in shoulder involvement including subjects with clinically relevant conditions is recommended.
In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.
The treatment method to deactivate viable microorganisms from objects or products is termed sterilization. There are multiple forms of sterilization, each intended to be applied for a specific target, which depends on—but not limited to—the thermal, physical, and chemical stability of that target. Herein, an overview on the currently used sterilization processes in the global market is provided. Different sterilization techniques are grouped under a category that describes the method of treatment: radiation (gamma, electron beam, X-ray, and ultraviolet), thermal (dry and moist heat), and chemical (ethylene oxide, ozone, chlorine dioxide, and hydrogen peroxide). For each sterilization process, the typical process parameters as defined by regulations and the mode of antimicrobial activity are summarized. Finally, the recommended microorganisms that are used as biological indicators to validate sterilization processes in accordance with the rules that are established by various regulatory agencies are summarized.
Achilles tendon rupture (ATR) patients have persistent functional deficits in the triceps surae muscle–tendon unit (MTU). The complex remodeling of the MTU accompanying these deficits remains poorly understood. The purpose of the present study was to associate in vivo and in silico data to investigate the relations between changes inMTU properties and strength deficits inATR patients. Methods: Elevenmale subjects who had undergone surgical repair of complete unilateral ATR were examined 4.6 ± 2.0 (mean ± SD) yr after rupture. Gastrocnemius medialis (GM) tendon stiffness, morphology, and muscle architecture were determined using ultrasonography. The force–length relation of the plantar flexor muscles was assessed at five ankle joint angles. In addition, simulations (OpenSim) of the GM MTU force–length properties were performed with various iterations of MTU properties found between the unaffected and the affected side. Results: The affected side of the patients displayed a longer, larger, and stiffer GM tendon (13% ± 10%, 105% ± 28%, and 54% ± 24%, respectively) compared with the unaffected side. The GM muscle fascicles of the affected side were shorter (32% ± 12%) and with greater pennation angles (31% ± 26%). A mean deficit in plantarflexion moment of 31% ± 10% was measured. Simulations indicate that pairing an intact muscle with a longer tendon shifts the optimal angular range of peak force outside physiological angular ranges, whereas the shorter muscle fascicles and tendon stiffening seen in the affected side decrease this shift, albeit incompletely. Conclusions: These results suggest that the substantial changes in MTU properties found in ATR patients may partly result from compensatory remodeling, although this process appears insufficient to fully restore muscle function.