Low-rank Linear Fluid-structure Interaction Discretizations

Fluid-structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid-structure interaction model for different solids and different fluids. For instance, a shipping company wants to know how the material, a ship's hull is made of, interacts with fluids at different Reynolds and Strouhal numbers before the building process takes place. Also, the behavior of such models for solids with different properties is considered before the prototype phase. A parameter-dependent linear fluid-structure interaction discretization provides approximations for a bundle of different parameters at one step. Such a discretization with respect to different material parameters leads to a big block-diagonal system matrix that is equivalent to a matrix equation as discussed in [KressnerTobler 2011]. The unknown is then a matrix which can be approximated using a low-rank approach that represents the iterate by a tensor. This paper discusses a low-rank GMRES variant and a truncated variant of the Chebyshev iteration. Bounds for the error resulting from the truncation operations are derived. Numerical experiments show that such truncated methods applied to parameter-dependent discretizations provide approximations with relative residual norms smaller than $10^{-8}$ within a twentieth of the time used by individual standard approaches.Comment: 30 pages, 7 figure

Real-World Modelling to Increase Mathematical Creativity

Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners\u27 creativity, first, we combined cognitive and creative spirals and mathematical modelling cycles. Then, in a case study, we tested this combination of cognitive and creative spirals and mathematical modelling cycles in a secondary school and teacher education. Applying the combination of cognitive and creative spirals and mathematical modelling cycles, we discovered that it could be collaboration among learners and technological knowledge and skills of learners that determine whether knowledge can be acquired in mathematical modelling

Retrospective Analysis of Prescription Drug Claims, with Applications to Risk Score Construction and Treatment of Heart Failure in End Stage Renal Disease

University of Minnesota Ph.D. dissertation. May 2015. Major: Epidemiology. Advisor: Sue Duval. 1 computer file (PDF); v, 176 pages.There are more than 450,000 patients receiving chronic dialysis in the US. Patients with end stage renal disease are statutorily eligible for Medicare, regardless of age. Due to high prevalence of poverty, many are dually enrolled in Medicare and Medicaid and are automatically enrolled in Part D (prescription drug insurance). This dissertation comprises 3 studies involving prescription drug claims in dialysis patients. In the first study, I constructed and validated risk scores based on Part D claims in incident and prevalent dialysis patients. Comorbidity indices derived from administrative data are typically based on diagnosed diseases, but the middling sensitivity of diagnosis codes limits the accuracy of these indices. In contrast, prescription drug claims are bona fide evidence of medication dispensation. I investigated aspects of newly developed scores and compared their performance in predicting risk with older scores based on diseases. In the second study, I assessed the efficacy and safety of pharmacologic inhibition of the renin-angiotensin system in dialysis patients with congestive heart failure. ACE inhibitors and ARBs are recommended for the treatment of heart failure with reduced ejection fraction. However, pivotal clinical trials all excluded patients on dialysis. I used propensity score matching to identify matched controls for treated patients that were newly dispensed an ACE inhibitor or ARB shortly after discharge from hospitalization for heart failure. I described the relative hazards of mortality and morbidity with treatment. In the third study, I assessed relative hazards of death and hospitalization associated with 4 ACE inhibitors and 2 ARBs in dialysis patients with congestive heart failure. The existence of class effects is generally presumed, but not necessarily supported by evidence regarding clinical outcomes. I showed that the most widely used agent (lisinopril) in this patient population is not necessarily associated with best outcomes

Towards Flipped Learning in Upper Secondary Mathematics Education

Challenges for students in the 21st century, such as acquiring technology, problem-solving, and cooperation skills, also necessitate changes in mathematics education to be able to respond to changing educational needs. One way to respond to these challenges is by utilizing recent educational innovations in schools, for instance, among others are flipped learning (FL) approaches. In this paper, we outline our explorative educational experiment that investigates vital elements of mathematics learning in FL approaches in upper secondary education. We describe the methodologies and findings of our qualitative study based on design-based research to discover key elements of FL approaches in upper secondary education. Analyzing the oral and written data collected over ten months using grounded theory approaches suggested categories (a) confidence when learning; (b) learning by working, and, and (c) flexibility when learning could be essential to understand FL approaches practices in mathematics classrooms. These categories indicate that when using FL approaches in mathematics learning, it could be essential for students to acquire knowledge in a confident and adaptable environment actively

GENDER DIFFERENCES IN TIBIAL ACCELERATION IN PRE-SEASON YOUTH SOCCER PLAYERS

In soccer, the players need to be able to change direction quickly, meaning the players need the ability to rapidly accelerate and decelerate. Females at a young age have a higher risk of sustaining injuries that can be caused by rapidly accelerating compared to males. The purpose was to investigate the gender differences in acceleration in youth soccer players. 30 youth soccer players engaged in the following drills: a jog, the M drill, 5-10-5 drill, and a single leg triple jump. This data was collected using inertial measurement units. The peak accelerations in the M drill on the left side was the only statistically significant drill (p=0.006, females: 590.9 ± 275.9 m/s2, males: 882.1 ± 263.4 m/s2). There is support to add load management strategies to current training programs and that individualized programs may be the most effective

A Low-rank Method for Parameter-dependent Fluid-structure Interaction Discretizations With Hyperelasticity

In aerospace engineering and boat building, fluid-structure interaction models are considered to investigate prototypes before they are physically assembled. How a material interacts with different fluids at different Reynold numbers has to be studied before it is passed over to the manufacturing process. In addition, examining the same model not only for different fluids but also for different solids allows to optimize the choice of materials for construction even better. A possible answer on this demand is parameter-dependent discretization. Furthermore, low-rank techniques can reduce the complexity needed to compute approximations to parameter-dependent fluid-structure interaction discretizations. Low-rank methods have been applied to parameter-dependent linear fluid-structure interaction discretizations. The linearity of the operators involved allows to translate the resulting equations to a single matrix equation. The solution is approximated by a low-rank method. In this paper, we propose a new method that extends this framework to nonlinear parameter-dependent fluid-structure interaction problems by means of the Newton iteration. The parameter set is split into disjoint subsets. On each subset, the Newton approximation of the problem related to the upper median parameter is computed and serves as initial guess for one Newton step on the whole subset. This Newton step yields a matrix equation whose solution can be approximated by a low-rank method. The resulting method requires a smaller number of Newton steps if compared with a direct approach that applies the Newton iteration to the separate problems consecutively. In the experiments considered, the proposed method allowed to compute a low-rank approximation within a twentieth of the time used by the direct approach.Comment: 20 pages, 6 figure

Carbon source dependent promoters in yeasts

Budding yeasts are important expression hosts for the production of recombinant proteins. The choice of the right promoter is a crucial point for efficient gene expression, as most regulations take place at the transcriptional level. A wide and constantly increasing range of inducible, derepressed and constitutive promoters have been applied for gene expression in yeasts in the past; their different behaviours were a reflection of the different needs of individual processes. Within this review we summarize the majority of the large available set of carbon source dependent promoters for protein expression in yeasts, either induced or derepressed by the particular carbon source provided. We examined the most common derepressed promoters for Saccharomyces cerevisiae and other yeasts, and described carbon source inducible promoters and promoters induced by non-sugar carbon sources. A special focus is given to promoters that are activated as soon as glucose is depleted, since such promoters can be very effective and offer an uncomplicated and scalable cultivation procedure

Analyse der Grundzüge der DDR-Pädagogik anhand zweier Videoaufnahmen zum schulpsychologischen Gespräch aus dem Jahre 1977

Die vorliegende Diplomarbeit wurde im Fachbereich der Bildungswissenschaft im Arbeitsbereich der Bildungstheorie und Bildungsforschung unter der Leitung von Prof. Dr. H., verfasst. Neben der theoretischen Bearbeitung liegen der behandelten Thematik methodische Überlegungen zu Grunde, die teilweise neu formuliert und exemplarisch ausgetestet wurden. In der Auseinandersetzung mit der Deutschen Demokratischen Republik und ihrem Bildungswesen, gilt die Forschung dieser Arbeit der Widmung historisch pädagogischer Videoaufnahmen aus dem Jahre 1977. Mittels zweier Videoaufnahmen zum schulpsychologischen Gespräch soll sich mit der Thematik der postulierten Bildungs- und Erziehungsziele und die Umsetzung derselben innerhalb der aufgezeichneten Gespräche auseinandergesetzt werden. Außerdem sollen die Aufzeichnungen im Speziellen analysiert werden, wobei hier die verbale und nonverbale Ebene in Betracht gezogen werden. Wesentliche inhaltliche Elemente sind die Analyse der historischen Entwicklung der DDR, die Persönlichkeitsbildung des sozialistischen Ideals, die schulpsychologische Bewegung und Ausbildung zu DDR-Zeiten und schließlich die Analyse der Gesprächsführung der auf den Videos sichtbaren Psychologin mit ihren Gesprächspartnern in der methodischen Anwendung. Es soll herausgefunden werden, ob und inwiefern die aufgezeichneten Gespräche eine Beeinflussung durch die verbalen Äußerungen der Psychologin auf die Reaktionen ihrer Gesprächspartner, darstellen. Der vorliegenden Diplomarbeit ist eine DVD mit den beiden verwendeten Videoaufnahmen beigelegt, welche allerdings aus datenschutzrechtlichen Gründen nicht frei zugänglich ist.This diploma thesis was written for the School of Education in the field of education theory and research under the direction of Dr. H. In addition to the theoretical argument, there are the underlying considerations of the treated theme, which were partially newly formulated and exemplarily tested. In examination of the German Democratic Republic (GDR) and its educational system, the research of this work stems from the application of historical, pedagogical video recordings from 1977. Using video recordings of two sessions, one should grapple with the idea of the postulated educational and rearing goals and the realization thereof in the recorded conversations. Furthermore, in particular, the videos themselves should be analyzed so that the verbal and non-verbal components can also be considered. The essential, substantial elements of this work are the analysis of the historical development of the GDR, the formation of socialist ideals, the school psychology movement, education in GDR times, and finally the systematic analysis of the recordings showing the psychologist with her subject during a session. The goal then is to discover, if and in what way the the verbal statements of the psychologist affected the reaction of her subject. This diploma thesis is attached a DVD with the two contained video recordings, which is not accessible for the public domain regarding data protection regulations

Die Verebnung der Welt

Die folgende Arbeit setzt sich mit dem fächerübergreifenden Unterricht der Unterrichtsgegenstände Mathematik sowie Geographie und Wirtschaftskunde auseinander. Das erste Kapitel soll die Vorteile und Vorzüge des fächerübergreifenden Unterrichts hervor streichen, jedoch auch die Herausforderungen beleuchten, welche damit verbunden sind. Es wird hierin beschrieben, welchen Mehrwert die schulische Behandlung eines konkreten Problems hat, wenn man sich jenem aus unterschiedlichen Richtungen nähert. Das zweite Kapitel soll das Vorurteil brechen, dass Mathematik nur in Verbindung mit Physik oder Chemie fächerübergreifend unterrichtet werden kann. Meines Erachtens ist es möglich, dass man jedes Unterrichtsfach in Verbindung mit Mathematik fächerübergreifend lehrt – was am Beispiel der Geographie und Wirtschaftskunde gezeigt wird. Den Kern dieserArbeit bildet das Kapitel drei. Darin soll gezeigt werden, welche Teile der nichteuklidischen Geometrie mit den Schülerinnen und Schülern behandelt werden könnten und dass diese gewissen Aspekte jenes Teilgebiets der Mathematik auch selbständig erarbeitet werden können. Weiters soll verdeutlicht werden, dass die Möglichkeiten, ein reales Problem mathematisch darzustellen, begrenzt ist und dass man hiervon öfter im Alltag betroffen ist als man unter Umständen glaubt. Die Hauptaufgabe der „Kartographie in Wahlpflichtfach Mathematik“ ist jedoch den Schülerinnen und Schülern das mathematische Argumentieren und Schlussfolgern näher zu bringen und somit die Lernenden in die mathematische Denkweise einzuführen. Der letzte Abschnitt dieser Arbeit soll zeigen, wie einfach man die Geographie und Wirtschaftskunde in den Mathematikunterricht integrieren und jenen dadurch mit noch mehr Leben füllen kann

Effects of Gait Speed of Femoroacetabular Joint Forces

Alterations in hip joint loading have been associated with diseases such as arthritis and osteoporosis. Understanding the relationship between gait speed and hip joint loading in healthy hips may illuminate changes in gait mechanics as walking speed deviates from preferred. The purpose of this study was to quantify hip joint loading during the gait cycle and identify differences with varying speed using musculo skeletal modeling. Ten, healthy, physically active individuals performed walking trials at their preferred speed, 10% faster, and 10% slower. Kinematic, kinetic, and electromyographic data were collected and used to estimate hip joint force via a musculoskeletal model. Vertical ground reaction forces, hip joint force planar components, and the resultant hip joint force were compared between speeds. There were significant increases in vertical ground reaction forces and hip joint forces as walking speed increased. Furthermore, the musculoskeletal modeling approach employed yielded hip joint forces that were comparable to previous simulation studies and in vivo measurements and was able to detect changes in hip loading due to small deviations in gait speed. Applying this approach to pathological and aging populations could identify specific areas within the gait cycle where force discrepancies may occur which could help focus management of care