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We give theorems about asymptotic normality of general additive functionals on patricia tries, derived from results on tries. These theorems are applied to show asymptotic normality of the distribution of random fringe trees in patricia tries. Formulas for asymptotic mean and variance are given. The proportion of fringe trees with 𝑘 keys is asymptotically, ignoring oscillations, given by (1−𝜌(𝑘))/(𝐻 +𝐽)𝑘(𝑘−1) with the source entropy 𝐻, an entropy-like constant 𝐽, that is 𝐻 in the binary case, and an exponentially decreasing function 𝜌(𝑘). Another application gives asymptotic normality of the independence number and the number of 𝑘-protected nodes.
Caroline Ungher-Sabatier wird heute meist mit dem Altsolo bei der Uraufführung der 9. Symphonie Ludwig van Beethovens in Verbindung gebracht. Ihre größten Erfolge konnte sie jedoch mit der italienischen Oper in den 1830er Jahren feiern. Bisher fand ihre sängerische Laufbahn und ihre Kontakte in Wien – abgesehen von Franz Schubert und Beethoven – kaum Beachtung. Deswegen beschäftigt sich diese Masterarbeit eingehend mit der Künstlerin und Sängerin Caroline Ungher-Sabatier, deren Lebensweg mit der Stadt Wien verknüpft ist. Sie genoss dort ihre musikalische Ausbildung, kehrte, nach ihren großen Erfolgen in Italien, 1839 und 1840 für Gastspiele an das Kärntnertortheater zurück und hielt lebenslang ein Netzwerk zu berühmten und bekannten Persönlichkeiten in Wien aufrecht. Nach ihrem Bühnenabschied war Ungher-Sabatier als Gesangspädagogin tätig und setzte sich auch in Wien für ihre Schülerinnen ein.
Neben ihrer erfolgreichen Karriere in der italienischen Oper pflegte Ungher-Sabatier das deutsche Liedrepertoire und komponierte eigene Lieder.
Ihr Werdegang und ihre Rezeption in Wien werden anhand von zeitgenössischen Artikeln aus Zeitungen und Zeitschriften untersucht. Um einen tieferen Einblick in Caroline Ungher-Sabatiers Wiener Netzwerk nach ihrer Opernkarriere zu ermöglichen, wurden ihr Stammbuch und über hundert Briefe ausgewertet.
AI-based computer vision systems play a crucial role in the environment perception for autonomous driving. Although the development of self-driving systems has been pursued for multiple decades, it is only recently that breakthroughs in Deep Neural Networks (DNNs) have led to their widespread application in perception pipelines, which are getting more and more sophisticated. However, with this rising trend comes the need for a systematic safety analysis to evaluate the DNN's behavior in difficult scenarios as well as to identify the various factors that cause misbehavior in such systems. This work aims to deliver a crucial contribution to the lacking literature on the systematic analysis of Performance Limiting Factors (PLFs) for DNNs by investigating the task of pedestrian detection in urban traffic from a monocular camera mounted on an autonomous vehicle. To investigate the common factors that lead to DNN misbehavior, six commonly used state-of-the-art object detection architectures and three detection tasks are studied using a new large-scale synthetic dataset and a smaller real-world dataset for pedestrian detection. The systematic analysis includes 17 factors from the literature and four novel factors that are introduced as part of this work. Each of the 21 factors is assessed based on its influence on the detection performance and whether it can be considered a Performance Limiting Factor (PLF). In order to support the evaluation of the detection performance, a novel and task-oriented Pedestrian Detection Safety Metric (PDSM) is introduced, which is specifically designed to aid in the identification of individual factors that contribute to DNN failure. This work further introduces a training approach for F1-Score maximization whose purpose is to ensure that the DNNs are assessed at their highest performance. Moreover, a new occlusion estimation model is introduced to replace the missing pedestrian occlusion annotations in the real-world dataset. Based on a qualitative analysis of the correlation graphs that visualize the correlation between the PLFs and the detection performance, this study identified 16 of the initial 21 factors as being PLFs for DNNs out of which the entropy, the occlusion ratio, the boundary edge strength, and the bounding box aspect ratio turned out to be most severely affecting the detection performance. The findings of this study highlight some of the most serious shortcomings of current DNNs and pave the way for future research to address these issues.
Die Arbeit befasst sich mit einer Vereinfachung des von Devroye (1999) geprägten Begriffs der random split trees und verallgemeinert diesen im Sinne von Janson (2019) auf unbeschränkten Verzweigungsgrad. Diese Verallgemeinerung deckt auch preferential attachment trees mit linearen Gewichten ab, wofür ein Beweis von Janson (2019) aufbereitet wird. Zusätzlich bleiben die von Devroye (1999) nachgewiesenen Eigenschaften über die Tiefe der hinzugefügten Knoten erhalten.
Statistical shape models learn to capture the most characteristic geometric variations of anatomical structures given samples from their population. Accordingly, shape models have become an essential tool for many medical applications and are used in, for example, shape generation, reconstruction, and classification tasks. However, established statistical shape models require precomputed dense correspondence between shapes, often lack robustness, and ignore the global surface topology. This thesis presents a novel neural flow-based shape model that does not require any precomputed correspondence. The proposed model relies on continuous flows of a neural ordinary differential equation to model shapes as deformations of a template. To increase the expressivity of the neural flow and disentangle global, low-frequency deformations from the generation of local, high- frequency details, we propose to apply a hierarchy of flows. We evaluate the performance of our model on two anatomical structures, liver, and distal femur. Our model outperforms state-of-the-art methods in providing an expressive and robust shape prior, as indicated by its generalization ability and specificity. More so, we demonstrate the effectiveness of our shape model on shape reconstruction tasks and find anatomically plausible solutions. Finally, we assess the quality of the emerging shape representation in an unsupervised setting and discriminate healthy from pathological shapes.
Electron identification with a likelihood method and measurements of di-electrons for the CBM-TRD
(2017)
In this work a likelihood method has been implemented and investigated as particle identification algorithm for the CBM-TRD.
The creation of the probability distributions for the likelihood method via V0-topologies seems to be feasible and the purity of the obtained samples is sufficient for the usage in the likelihood method.
The comparison between the ANN and the likelihood method shows no differences in the identification performance. The pion suppression factor reaches the same values for the same electron identification efficiencies and the yields of the resulting di-lepton signals are comparable. The signal-to-background ratios for both methods have the same values and show a value of about 10−2 in the invariant mass range of minv = 1.5 - 2.5 GeV/c2, which is expected to be sufficient to provide access to the thermal in-medium and QGP radiation.
The investigation of a detector system without a TRD shows no pion suppression for a momentum above p = 6 GeV/c. Therefore, the background contributions increase drastically and the signal-to-background ratio decreases at all invariant masses, but especially in the invariant mass range of minv = 1.5 - 2.5 GeV/c2.
The background contributions in the invariant mass range of minv = 1.5 - 2.5 GeV/c 2 are also influenced by the selected electron identification efficiency of the TRD, which significantly shifts the fraction of the eπ contributions relative to the total number of pairs.
Anisotropic collective flow of protons resulting from non-central heavy ion collisions is a unique hadronic observable providing information about the early stage of the nuclear collision. The analysis of collective flow in the energy regime between 1-2 AGeV enables the study of the phase diagram of hadronic matter at a high baryochemical potential µb, as well as the analysis of the equation of state at densities up to the threefold of the ground state density ρ0.
The algorithms of the standard event plane method and the scalar product method are used to analyse directed and elliptic flow of protons in a centrality range of 0-40 % most central events.
Prior to the analysis of experimental data, the respective influence of the reconstruction procedure on the algorithms is examined using Monte Carlo simulations based on the Ultra relativistic Quantum Molecular Dynamics (UrQMD) model.
Subsequently, experimental data measured in April 2012 with the High Acceptance DiElectron Spectrometer (HADES) is analysed using both methods. About 7.3 · 109 Au+Au events at a kinetic beam energy of 1.23 AGeV, equivalent to a centre of mass energy of √sNN = 2.42 GeV were recorded. A multi-differential analysis is feasible as the HADES detector provides a good transverse momentum and rapidity coverage.
Both algorithms result in identical values for directed and elliptic flow across all centrality classes within the observable phase space of protons. The calculated integrated value of v2 at mid rapidity is in good agreement with world data.
In April and May 2012 data on Au+Au collisions at beam energies of Ekin = 1.23A GeV were collected with the High Acceptance Di-Electron Spectrometer (HADES) at the GSI Helmholtzzentrum für Schwerionenforschung facility in Darmstadt, Germany. In this thesis, the production of deuterons in this collision system is investigated.
A total number of 2.1 × 109 Au+Au events is selected, containing the most central 0-40% of events. After particle identification, based on a mass determination via time-of-flight and momentum and on a measurement of the energy loss, the transverse mass spectra of the deuteron candidates are extracted for various rapidities and subsequently corrected for acceptance and efficiency.
The inverse slope parameter of a Boltzmann fit applied to the transverse mass spectra at midrapidity, which is referred to as the effective temperature, is extracted. For a static thermal source, this parameter corresponds to the kinetic freeze-out temperature Tkin and is therefore expected to be smaller or equal to the chemical freeze-out temperature Tchem. The extracted effective temperature of Tef f = (190 ± 10) MeV however exceeds the chemical freeze-out temperature that was obtained by a statistical model fit to different particle yields. The effective temperatures of various particle species, obtained in previous analyses, suggest a systematic rise with increasing particle mass, which is confirmed by the deuteron results.
An explanation can be the influence of a collective expansion with a radial expansion velocity βr. By fitting a Siemens-Rasmussen function to the transverse mass spectra, the global temperature of T = (100 ± 8) MeV and radial expansion velocity βr = 0.37 ± 0.01 are obtained. This temperature is still very high and only takes into account the production of deuteron nuclei.
The simultaneous fit of a blast-wave function to the transverse mass spectra of deuterons and other particles, as obtained by previous analyses, considers a velocity profile for the radial expansion velocity and takes into account the production of various particle species. The resulting global temperature Tkin = (68 ± 1) MeV and average transverse expansion velocity hβri = 0.341 ± 0.003 are within the expected range for the collision energy.
The Siemens-Rasmussen fits are also used to extrapolate the transverse mass spectra into unmeasured regions, to integrate them and obtain a rapidity-dependent count rate. This count rate exhibits a thermal shape for central events and shows increasing spectator contributions for more peripheral events.
The invariant yield spectra of the deuterons are compared to those of protons, as obtained by a previous analysis, in the context of a nucleon coalescence model. The hereby extracted nucleon coalescence factor B2 = (4.6 ± 0.1) × 10−3 agrees with the expected result for the beam energy that was studied.
Ziel der Simulationsstudien in dieser Arbeit war es, die Leistungsfähigkeit des Transition Radiation Detectors zur Identifikation von leichten Kernen und Hyperkernen im CBM-Experiment zu untersuchen. Die Trennung von Helium und Deuterium
mithilfe ihres spezifischen Energieverlustes im TRD ist zentral, um eine Rekonstruktion des seltenen Hyperkerns 6 ΛΛHe mit einem hohen Signal-zu-Untergrund-Verhältnisse zu leisten. Zur Erfüllung der Anforderungen, die sich aus dem CBM-Forschungsprogramm ergeben, wird eine Auflösung des Energieverlustes dEdx von Helium von höchstens 30 % verlangt...
Das CBM-Experiment konzentriert sich auf die Untersuchung der Eigenschaften des Quark-Gluon-Plasmas bei hohen Netto-Baryonendichten und moderaten Temperaturen. An der zukünftigen Beschleunigeranlage FAIR an der GSI findet das Experiment, neben vielen anderen Experimenten, ihren Platz. Der TRD ist, neben dem RICH, STS und TOF, einer der zentralen Detektoren im CBM-Experiment. Der TRD nutzt dabei den physikalischen Effekt der Übergangsstrahlung, die durch ein geladenes Teilchen beim Durchqueren einer Grenze zweier Medien mit unterschiedlichen Dielektrizitätskonstanten mit einer gewissen Wahrscheinlichkeit entsteht, um Elektronen von Pionen trennen zu können. Im Jahr 2017 wurde an der DESY 4 TRD-Prototypen in einer Teststrahlzeit getestet. Dabei handelt es sich um große TRD-Module mit den Maßen 95 · 95 cm2 , was dem finalen Design sehr nahe kommt. Die Untersuchung der DESY-Daten in Kapitel 5 brachte große Problematiken in den Daten zum Vorschein. Die Hauptprobleme der DESY-Daten sind: 1) Bug des SPADIC-Chips 2.0, bei der FN-Trigger zeitlich verschoben wurden; 2) schwache und suboptimale Trigger-Bedingung, wodurch sehr viel Rauschen aufgenommen wurde. Die Daten müssen für weitere Auswertung aufbereitet werden, wobei sehr viel Information und Statistik verloren geht, da einige Daten durch diverse Probleme nicht mehr rekonstruierbar sind. Kapitel 6 beschäftigt sich mit der Simulation der Detektorantwort und geht genauer auf die einzelnen Schritte, die zur Simulation des vom SPADIC erzeugten Pulses benötigt werden, ein. Am Ende werden Ergebnisse aus beiden Datensätzen miteinander verglichen. Um einen optimalen Vergleich zu gewähren, wird die Simulation bestmöglich an die Einstellungen in der Teststrahlzeit angepasst. Hauptsächlich geht es um die Erhöhung des Gasgains und der Verschiebung der Peaking-Zeit des Pulses. Im Allgemeinen können wir in der Simulation einige Effekte, die auch in den DESY-Daten vorkommen, nachsimulieren. Wir erhalten zum Teil sehr unterschiedliche Ergebnisse in der Simulation, deren Richtigkeit nicht verifiziert werden kann, da die Daten aufgrund der Probleme unzuverlässig werden. Durch die Analyse der DESY-Daten konnten wir die Problematik in den Daten besser verstehen. Eine sinnvolle Anpassung der Simulation wird durch die Unzuverlässigkeit der DESY-Daten unmöglich. Für die Optimierung der Simulation müsste man einen Vergleich mit neueren, zuverlässigeren Daten aus zukünftigen Teststrahlzeiten nehmen.