A Matlab toolbox for the regularization of descriptor systems arising from generalized realization procedures

In this report we introduce a Matlab toolbox for the regularization of descriptor systems. We apply it, in particular, for systems resulting from the generalized realization procedure of [16], which generates, via rational interpolation techniques, a linear descriptor system from interpolation data. The resulting system needs to be regularized to make it feasible for the use in simulation, optimization, and control. This process is called regularization.DFG, SFB 1029, Substantial efficiency increase in gas turbines through direct use of coupled unsteady combustion and flow dynamic

On Matrix Nearness Problems: Distance to Delocalization

This paper introduces two new matrix nearness problems that are intended to generalize the distance to instability and the distance to stability. They are named the distance to delocalization and the distance to localization due to their applicability in analyzing the robustness of eigenvalues with respect to arbitrary localization sets (domains) in the complex plane. For the open left-half plane or the unit circle, the distance to the nearest unstable/stable matrix is obtained as a special case. Then, following the theoretical framework of Hermitian functions and the Lyapunov-type localization approach, we present a new Newton-type algorithm for the distance to delocalization (D2D) and study its implementations using both an explicit and an implicit computation of the desired singular values. Since our investigations are motivated by several practical applications, we will illustrate our approach on some of them. Furthermore, in the special case when the distance to delocalization becomes the distance to instability, we will validate our algorithms against the state of the art computational method

Hypothalamic FTO is associated with the regulation of energy intake not feeding reward

<p>Abstract</p> <p>Background</p> <p>Polymorphism in the FTO gene is strongly associated with obesity, but little is known about the molecular bases of this relationship. We investigated whether hypothalamic FTO is involved in energy-dependent overconsumption of food. We determined FTO mRNA levels in rodent models of short- and long-term intake of palatable fat or sugar, deprivation, diet-induced increase in body weight, baseline preference for fat versus sugar as well as in same-weight animals differing in the inherent propensity to eat calories especially upon availability of diverse diets, using quantitative PCR. FTO gene expression was also studied in organotypic hypothalamic cultures treated with anorexigenic amino acid, leucine. In situ hybridization (ISH) was utilized to study FTO signal in reward- and hunger-related sites, colocalization with anorexigenic oxytocin, and c-Fos immunoreactivity in FTO cells at initiation and termination of a meal.</p> <p>Results</p> <p>Deprivation upregulated FTO mRNA, while leucine downregulated it. Consumption of palatable diets or macronutrient preference did not affect FTO expression. However, the propensity to ingest more energy without an effect on body weight was associated with lower FTO mRNA levels. We found that 4-fold higher number of FTO cells displayed c-Fos at meal termination as compared to initiation in the paraventricular and arcuate nuclei of re-fed mice. Moreover, ISH showed that FTO is present mainly in hunger-related sites and it shows a high degree of colocalization with anorexigenic oxytocin.</p> <p>Conclusion</p> <p>We conclude that FTO mRNA is present mainly in sites related to hunger/satiation control; changes in hypothalamic FTO expression are associated with cues related to energy intake rather than feeding reward. In line with that, neurons involved in feeding termination express FTO. Interestingly, baseline FTO expression appears linked not only with energy intake but also energy metabolism.</p

Flexible Krylov-type Methods for Electronic Structure Eigenvalue Computations

Determing excited states in quantum physics or calculating the number of valence electrons in the Density Functional Theory (DFT) involve solving eigenvalue problems of very large dimensions. Moreover, very often the interesting features of these complex systems go beyond information contained in the extreme eigenpairs. For this reason, it is important to consider iterative solvers developed to compute a large amount of eigenpairs in the middle of the spectrum of large Hermitian and non-Hermitian matrices. In this talk, we present a newly developed Krylov-type methods and compare them with the well-established techniques in electronic structure calculations. We demonstrate their efficiency and robustness through various numerical examples.Non UBCUnreviewedAuthor affiliation: University of Kansas​Researche

Inexakte Adaptive Finite Elemente Methoden für elliptische PDE Eigenwertprobleme

Seit Jahrzehnten führen technische Anwendungen, wie z.B. Strukturschwingungen, die Modellierung von photonische Bandlücke Materialien, Analyse von hydrodynamischer Stabilität oder die Berechnung von Energieleveln in der Quantenmechanik, auf PDE Eigenwertprobleme. Zur Zeit konzentriert sich die Forschung auf sogenannte Adaptive Finite Elemente Methoden (AFEM). In den meisten AFEM Ansätzen wird angenommen, dass das resultierende endlichdimensionale algebraische Problem (lineares Gleichungssystem oder Eigenwertproblem) exakt gelöst wird und der Berechnungsaufwand, sowie die Tatsache, dass die Lösungen nur in endlicher Genauigkeit vorliegen, wird vernachlässigt. Ziel dieser Arbeit ist es, den Einfluss der Genauigket der algebraischen Approximation auf den adaptiven Prozess zu analysieren. Effiziente und verlässliche adaptive Algorithmen sollen betrachtet werden, d.h. nicht nur die Diskretisierungsfehler sondern auch die Iterationsfehler und insbesondere die Kondition der Eigenwerte für unsymmetrische Probleme müssen berücksichtigt werden. Unser neuer AFEMLA Algorithmus erweitert die üblichen AFEM Ansätze durch Berücksichtigung des Approximationsfehlers im adaptiven Prozess. Desweiteren zeigen wir, dass die adaptive Gitterverfeinerung durch den diskreten Residuenvektor gesteuert werden kann, z.B. wenn das Problem in diskreter Form gegeben ist und nur die zugrundeliegenden Matrizen und Gitter verfügbar sind. Wir zeigen, wie der Berechnungsaufwand des iterativen Lösers durch Anpassung der Dimension des Krylov-Unterraums reduziert werden kann. Mit Hilfe von klassischen Störungsresultaten beweisen wir obere Schranken für den Fehler in den Eigenwerten und Eigenfunktionen. Ähnliche Resultate werden für Konvektions-Diffusions Probleme angegeben. Wir betrachten funktionale Störungsresultate für PDE Eigenwertprobleme, d.h. funktionale Rückwärtsfehler und funktionale Konditionzahl. Diese Resultate werden verwendet um einen gemeinsamen a posteriori Fehlerschätzer zu entwickeln, der Diskretisierungs- und Approximationsfehler berücksichtigt. Basierend auf bekannten Störungsresultaten in der H^{1}- und H^{-1}-Norm und den residuenbasierten a posteriori Fehlerschätzern wurde ein balancierter AFEM Algorithmus entwickelt. Das Abbruchkriterium des Eigenwertlösers basiert auf Gleichgewichtsstrategien, d.h. die Iteration erfolgt so lange wie der diskrete Anteil des Fehlerschätzers den kontinuierlichen Anteil dominiert. Ein neuer Ansatz, der die Adaptive Finite Elemente Methode mit Homotopie verbindet, wird vorgestellt, um den Eigenwert des Konvektions-Diffusions Problems zu berechnen. Die entwickelte adaptive Homotopie hebt die Notwendigkeit von mehrfacher Adaptivität hervor, d.h. basierend auf den Homotopie-, Diskretisierungs- und Iterationsfehlern. Alle unsere Ergebnisse werden mit verschiedenen numerischen Beispielen illustriert.Since decades modern technological applications lead to challenging PDE eigenvalue problems, e.g., vibrations of structures, modeling of photonic gap materials, analysis of the hydrodynamic stability, or calculations of energy levels in quantum mechanics. Recently, a lot of research is devoted to the so-called Adaptive Finite Element Methods (AFEM). In most AFEM approaches it is assumed that the resulting finite dimensional algebraic problem (linear system or eigenvalue problem) is solved exactly and computational costs for this part of the method as well as the fact that they are solved in the finite precision arithmetic are typically ignored. The goal of this work is to analyze the influence of the accuracy of the algebraic approximation on the adaptivity process. Efficient and reliable adaptive algorithms should take into consideration not only discretization errors, but also iteration errors and especially for non-symmetric problems the conditioning of eigenvalues. Our new AFEMLA algorithm extends the standard AFEM approach to incorporate approximation errors into the adaptation process. Furthermore, we show that the adaptive mesh refinement may be steered by the discrete residual vector, e.g., when the problem is stated in a discrete formulation where only the underlying matrices and meshes are available. Moreover, we discuss how to reduce the computational effort of the iterative solver by adapting the size of the Krylov subspace. With classical perturbation results we prove upper bounds of the eigenvalue and the eigenfunction error. Under certain assumptions similar results are obtained for convection-diffusion problems. We introduce functional perturbation results for PDE eigenvalue problems including the functional backward error and the functional condition number. These results are used to establish a combined a posteriori error estimator embodying the discretization and the approximation error. Based on known perturbation results in H^{1}- and H^{−1}-norm and a standard residual a posteriori error estimator a balancing AFEM algorithm is proposed. The eigensolver stopping criterion is based on the equilibrating strategy, i.e., iterations proceed as long as the discrete part of the error estimator dominates the continuous part. A completely new approach combining the adaptive finite element method with the homotopy method is introduced to determine the particular eigenvalue of the convection-diffusion problem. The adaptive homotopy approach derived here emphasizes the need of the multi-way adaptation based on three different errors, the homotopy, the discretization and the iteration error. All our statements are illustrated with several numerical examples

Analysis of Outcomes in Ischemic vs Nonischemic Cardiomyopathy in Patients With Atrial Fibrillation A Report From the GARFIELD-AF Registry

IMPORTANCE Congestive heart failure (CHF) is commonly associated with nonvalvular atrial fibrillation (AF), and their combination may affect treatment strategies and outcomes