5,791 research outputs found
Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE
In an effort to increase the versatility of finite element codes, we explore
the possibility of automatically creating the Jacobian matrix necessary for the
gradient-based solution of nonlinear systems of equations. Particularly, we aim
to assess the feasibility of employing the automatic differentiation tool
TAPENADE for this purpose on a large Fortran codebase that is the result of
many years of continuous development. As a starting point we will describe the
special structure of finite element codes and the implications that this code
design carries for an efficient calculation of the Jacobian matrix. We will
also propose a first approach towards improving the efficiency of such a
method. Finally, we will present a functioning method for the automatic
implementation of the Jacobian calculation in a finite element software, but
will also point out important shortcomings that will have to be addressed in
the future.Comment: 17 pages, 9 figure
Extraoral Osseous Choristoma in the Head and Neck Region: Case Report and Literature Review
An osseous choristoma is a benign tumor consisting of regular bone tissue in an irregular localization. Choristomas in the head
and neck region are rare. Most frequently, they are found in the region of the tongue or oral mucosa. There are also very few
reports on osseous choristomas in the submandibular region. We present the case of a woman with a large, caudal osseous
choristoma within the lateral cervical triangle. Literature review is given about all of the reported cases in the region of the neck.
The pathogenesis is yet unexplained. Our case supports the theory that the development of an osseous choristoma is a reaction to a
former trauma. Cervical osseous choristomas are seldom, but they represent an important differential diagnosis when dealing with
a cervical tumo
Approximate inference in astronomy
This thesis utilizes the rules of probability theory and Bayesian reasoning to perform inference about astrophysical quantities from observational data, with a main focus on the inference of dynamical systems extended in space and time. The necessary assumptions to successfully solve such inference problems in practice are discussed and the resulting methods are applied to real world data. These assumptions range from the simplifying prior assumptions that enter the inference process up to the development of a novel approximation
method for resulting posterior distributions.
The prior models developed in this work follow a maximum entropy principle by solely constraining those physical properties of a system that appear most relevant to inference, while remaining uninformative regarding all other properties. To this end, prior models that only constrain the statistically homogeneous space-time correlation structure of a physical observable are developed. The constraints placed on these correlations are based on generic physical principles, which makes the resulting models quite flexible and allows for a wide range of applications. This flexibility is verified and explored using multiple numerical examples, as well as an application to data provided by the Event Horizon
Telescope about the center of the galaxy M87. Furthermore, as an advanced and extended form of application, a variant of these priors is utilized within the context of simulating partial differential equations. Here, the prior is used in order to quantify the physical plausibility of an associated numerical solution, which in turn improves the accuracy of the simulation. The applicability and implications of this probabilistic approach to simulation are discussed and studied using numerical examples.
Finally, utilizing such prior models paired with the vast amount of observational data provided by modern telescopes, results in Bayesian inference problems that are typically too complex to be fully solvable analytically. Specifically, most resulting posterior probability distributions become too complex, and therefore require a numerical approximation via a simplified distribution. To improve upon existing methods, this work proposes a novel approximation method for posterior probability distributions: the geometric Variational Inference (geoVI) method. The approximation capacities of geoVI are theoretically established and demonstrated using numerous numerical examples. These results suggest a broad range of applicability as the method provides a decrease in approximation errors compared to state of the art methods at a moderate level of computational costs.Diese Dissertation verwendet die Regeln der Wahrscheinlichkeitstheorie und Bayes’scher Logik, um astrophysikalische Größen aus Beobachtungsdaten zu rekonstruieren, mit einem Schwerpunkt auf der Rekonstruktion von dynamischen Systemen, die in Raum und Zeit definiert sind. Es werden die Annahmen, die notwendig sind um solche Inferenz-Probleme in der Praxis erfolgreich zu lösen, diskutiert, und die resultierenden Methoden auf reale Daten angewendet. Diese Annahmen reichen von vereinfachenden Prior-Annahmen, die in den Inferenzprozess eingehen, bis hin zur Entwicklung eines neuartigen Approximationsverfahrens für resultierende Posterior-Verteilungen.
Die in dieser Arbeit entwickelten Prior-Modelle folgen einem Prinzip der maximalen Entropie, indem sie nur die physikalischen Eigenschaften eines Systems einschränken, die für die Inferenz am relevantesten erscheinen, während sie bezüglich aller anderen Eigenschaften agnostisch bleiben. Zu diesem Zweck werden Prior-Modelle entwickelt, die nur die statistisch homogene Raum-Zeit-Korrelationsstruktur einer physikalischen Observablen einschränken. Die gewählten Bedingungen an diese Korrelationen basieren auf generischen
physikalischen Prinzipien, was die resultierenden Modelle sehr flexibel macht und ein breites Anwendungsspektrum ermöglicht. Dies wird anhand mehrerer numerischer Beispiele sowie einer Anwendung auf Daten des Event Horizon Telescope über das Zentrum der Galaxie M87 verifiziert und erforscht. Darüber hinaus wird als erweiterte Anwendungsform eine Variante dieser Modelle zur Simulation partieller Differentialgleichungen verwendet. Hier wird der Prior als Vorwissen benutzt, um die physikalische Plausibilität einer zugehörigen numerischen Lösung zu quantifizieren, was wiederum die Genauigkeit der Simulation verbessert. Die Anwendbarkeit und Implikationen dieses probabilistischen
Simulationsansatzes werden diskutiert und anhand von numerischen Beispielen untersucht.
Die Verwendung solcher Prior-Modelle, gepaart mit der riesigen Menge an Beobachtungsdaten moderner Teleskope, führt typischerweise zu Inferenzproblemen die zu komplex sind um vollständig analytisch lösbar zu sein. Insbesondere ist für die meisten resultierenden Posterior-Wahrscheinlichkeitsverteilungen eine numerische Näherung durch eine vereinfachte Verteilung notwendig. Um bestehende Methoden zu verbessern, schlägt diese Arbeit eine neuartige Näherungsmethode für Wahrscheinlichkeitsverteilungen vor: Geometric Variational Inference (geoVI). Die Approximationsfähigkeiten von geoVI werden theoretisch
ermittelt und anhand numerischer Beispiele demonstriert. Diese Ergebnisse legen einen breiten Anwendungsbereich nahe, da das Verfahren bei moderaten Rechenkosten eine Verringerung des Näherungsfehlers im Vergleich zum Stand der Technik liefert
Does a large quantum Fisher information imply Bell correlations?
The quantum Fisher information (QFI) of certain multipartite entangled
quantum states is larger than what is reachable by separable states, providing
a metrological advantage. Are these nonclassical correlations strong enough to
potentially violate a Bell inequality? Here, we present evidence from two
examples. First, we discuss a Bell inequality designed for spin-squeezed states
which is violated only by quantum states with a large QFI. Second, we relax a
well-known lower bound on the QFI to find the Mermin Bell inequality as a
special case. However, a fully general link between QFI and Bell correlations
is still open.Comment: 4 pages, minor edit
Maximum antichains in posets of quiver representations
We study maximum antichains in two posets related to quiver representations. Firstly, we consider the set of isomorphism classes of indecomposable representations ordered by inclusion. For various orientations of the Dynkin diagram of type A we construct a maximum antichain in the poset. Secondly, we consider the set of subrepresentations of a given quiver representation, again ordered by inclusion. It is a finite set if we restrict to linear representations over finite fields or to representations with values in the category of pointed sets. For particular situations we prove that this poset is Sperner
Learning Multiple Defaults for Machine Learning Algorithms
The performance of modern machine learning methods highly depends on their
hyperparameter configurations. One simple way of selecting a configuration is
to use default settings, often proposed along with the publication and
implementation of a new algorithm. Those default values are usually chosen in
an ad-hoc manner to work good enough on a wide variety of datasets. To address
this problem, different automatic hyperparameter configuration algorithms have
been proposed, which select an optimal configuration per dataset. This
principled approach usually improves performance, but adds additional
algorithmic complexity and computational costs to the training procedure. As an
alternative to this, we propose learning a set of complementary default values
from a large database of prior empirical results. Selecting an appropriate
configuration on a new dataset then requires only a simple, efficient and
embarrassingly parallel search over this set. We demonstrate the effectiveness
and efficiency of the approach we propose in comparison to random search and
Bayesian Optimization
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