Refine
Has Fulltext
- yes (5)
Is part of the Bibliography
- yes (5)
Document Type
- Doctoral Thesis (5) (remove)
Keywords
- optimization (5) (remove)
Institute
This thesis is concerned with applying the total variation (TV) regularizer to surfaces and different types of shape optimization problems. The resulting problems are challenging since they suffer from the non-differentiability of the TV-seminorm, but unlike most other priors it favors piecewise constant solutions, which results in piecewise flat geometries for shape optimization problems.The first part of this thesis deals with an analogue of the TV image reconstruction approach [Rudin, Osher, Fatemi (Physica D, 1992)] for images on smooth surfaces. A rigorous analytical framework is developed for this model and its Fenchel predual, which is a quadratic optimization problem with pointwise inequality constraints on the surface. A function space interior point method is proposed to solve it. Afterwards, a discrete variant (DTV) based on a nodal quadrature formula is defined for piecewise polynomial, globally discontinuous and continuous finite element functions on triangulated surface meshes. DTV has favorable properties, which include a convenient dual representation. Next, an analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. Its analysis is based on a differential geometric setting in which the unit normal vector is viewed as an element of the two-dimensional sphere manifold. Shape calculus is used to characterize the relevant derivatives and an variant of the split Bregman method for manifold valued functions is proposed. This is followed by an extension of the total variation prior for the normal vector field for piecewise flat surfaces and the previous variant of split Bregman method is adapted. Numerical experiments confirm that the new prior favours polyhedral shapes.
In the past two decades, there has been a trend to move from traditional television to Internet-based video services. With video streaming becoming one of the most popular applications in the Internet and the current state of the art in media consumption, quality expectations of consumers are increasing. Low quality videos are no longer considered acceptable in contrast to some years ago due to the increased sizes and resolution of devices. If the high expectations of the users are not met and a video is delivered in poor quality, they often abandon the service. Therefore, Internet Service Providers (ISPs) and video service providers are facing the challenge of providing seamless multimedia delivery in high quality. Currently, during peak hours, video streaming causes almost 58\% of the downstream traffic on the Internet. With higher mobile bandwidth, mobile video streaming has also become commonplace. According to the 2019 Cisco Visual Networking Index, in 2022 79% of mobile traffic will be video traffic and, according to Ericsson, by 2025 video is forecasted to make up 76% of total Internet traffic. Ericsson further predicts that in 2024 over 1.4 billion devices will be subscribed to 5G, which will offer a downlink data rate of 100 Mbit/s in dense urban environments.
One of the most important goals of ISPs and video service providers is for their users to have a high Quality of Experience (QoE). The QoE describes the degree of delight or annoyance a user experiences when using a service or application. In video streaming the QoE depends on how seamless a video is played and whether there are stalling events or quality degradations. These characteristics of a transmitted video are described as the application layer Quality of Service (QoS). In general, the QoS is defined as "the totality of characteristics of a telecommunications service that bear on its ability to satisfy stated and implied needs of the user of the service" by the ITU. The network layer QoS describes the performance of the network and is decisive for the application layer QoS.
In Internet video, typically a buffer is used to store downloaded video segments to compensate for network fluctuations. If the buffer runs empty, stalling occurs. If the available bandwidth decreases temporarily, the video can still be played out from the buffer without interruption. There are different policies and parameters that determine how large the buffer is, at what buffer level to start the video, and at what buffer level to resume playout after stalling. These have to be finely tuned to achieve the highest QoE for the user. If the bandwidth decreases for a longer time period, a limited buffer will deplete and stalling can not be avoided. An important research question is how to configure the buffer optimally for different users and situations. In this work, we tackle this question using analytic models and measurement studies. With HTTP Adaptive Streaming (HAS), the video players have the capability to adapt the video bit rate at the client side according to the available network capacity. This way the depletion of the video buffer and thus stalling can be avoided. In HAS, the quality in which the video is played and the number of quality switches also has an impact on the QoE. Thus, an important problem is the adaptation of video streaming so that these parameters are optimized. In a shared WiFi multiple video users share a single bottleneck link and compete for bandwidth. In such a scenario, it is important that resources are allocated to users in a way that all can have a similar QoE. In this work, we therefore investigate the possible fairness gain when moving from network fairness towards application-layer QoS fairness. In mobile scenarios, the energy and data consumption of the user device are limited resources and they must be managed besides the QoE. Therefore, it is also necessary, to investigate solutions, that conserve these resources in mobile devices. But how can resources be conserved without sacrificing application layer QoS? As an example for such a solution, this work presents a new probabilistic adaptation algorithm that uses abandonment statistics for ts decision making, aiming at minimizing the resource consumption while maintaining high QoS.
With current protocol developments such as 5G, bandwidths are increasing, latencies are decreasing and networks are becoming more stable, leading to higher QoS. This allows for new real time data intensive applications such as cloud gaming, virtual reality and augmented reality applications to become feasible on mobile devices which pose completely new research questions. The high energy consumption of such applications still remains an issue as the energy capacity of devices is currently not increasing as quickly as the available data rates. In this work we compare the optimal performance of different strategies for adaptive 360-degree video streaming.
Given points in the plane, connect them using minimum ink. Though the task seems simple, it turns out to be very time consuming. In fact, scientists believe that computers cannot efficiently solve it. So, do we have to resign? This book examines such NP-hard network-design problems, from connectivity problems in graphs to polygonal drawing problems on the plane. First, we observe why it is so hard to optimally solve these problems. Then, we go over to attack them anyway. We develop fast algorithms that find approximate solutions that are very close to the optimal ones. Hence, connecting points with slightly more ink is not hard.
In this thesis affine-scaling-methods for two different types of mathematical problems are considered. The first type of problems are nonlinear optimization problems subject to bound constraints. A class of new affine-scaling Newton-type methods is introduced. The methods are shown to be locally quadratically convergent without assuming strict complementarity of the solution. The new methods differ from previous ones mainly in the choice of the scaling matrix. The second type of problems are semismooth system of equations with bound constraints. A new affine-scaling trust-region method for these problems is developed. The method is shown to have strong global and local convergence properties under suitable assumptions. Numerical results are presented for a number of problems arising from different areas.
Grundvoraussetzung einer erfolgreichen zementlosen Endoprothesenverankerungen ist eine hohe Primärstabilität durch formschlüssige Implantation. Nach erfolgreicher Primärfixation entscheidet über die Langzeitfunktion neben der Verschleißsituation insbesondere die funktionelle Spannungsverteilung an der Implantatoberfläche und im angrenzenden Knochen. Um optimale Bedingungen im Bereich der Grenzfläche zwischen Werkstoff und Biosystem zu schaffen, ist die präzise Präparation des Knochens entscheidend. Hierbei spielt neben dem Operateur und der Beschaffenheit des Knochens das verwendete System zur Zerspanung, bestehend aus der Säge und dem Sägeblatt, eine wichtige Rolle. Oszillierende Sägen werden neben der Gipsbehandlung ausschließlich bei der Knochenbearbeitung verwendet, wobei Fragestellungen zu Leistungs- und Qualitätssteigerung auftreten. Ansatzpunkt ist unter anderem das Sägeblatt. Die Modellvielfalt der auf dem Markt erhältlichen Sägeblätter erschwert die richtige Auswahl. Bei verschiedenen Modellen und deren unterschiedlichen Ausführungen ist es schwierig, Vergleiche anzustellen und Verbesserungen einzuführen. Die Charakteristik eines Sägeblattes ist durch die Schärfe beschrieben, um eine schnelle Zerspanung des Knochens zu gewährleisten, und durch die Steifigkeit des Blattes, um eine möglichst geringe Abweichung aus der Sägelinie sicherzustellen. Die Schärfe des Sägeblattes ist von der Zahnform und -geometrie abhängig. Die Steifigkeit ist abhängig von Material, Geometrie, Ausführung und Eigenschwingung/Eigenform des Blattes. Modifikationen an diesem System führen auch zu einer veränderten Eigenform des Sägeblattes. In der folgender Arbeit wurden verschiedene Ausführungen von Sägeblättern hinsichtlich ihrer Eigenform charakterisiert. In einem praktischen Versuch wurde versucht, den Einfluss des Sägeblattes auf die Vibration im Knochen von dem der Säge abzugrenzen. Ziel der Studie war daher die Berechnung der Eigenform der Sägeblätter, die experimentelle Überprüfung der Eigenform und die Abgrenzung des Einflusses von Sägeblatt und Säge auf die Vibration beim Sägevorgang. 9 verschiedene Sägeblätter unterschiedlicher Form und Geometrie wurden untersucht. Zunächst wurde eine Eigenformberechnung mittels der Finiten Elemente Methode durchgeführt. Anschließend erfolgte die Eigenformbestimmung im Shakerversuch. Um den Einfluss der Sägeblätter auf die Beschleunigung im Knochen von dem der Säge abzugrenzen erfolgte die Beschleunigungsmessung in einem Sägeprüfstand. Bezüglich des Eigenschwingungsverhalten konnten die Sägeblätter drei Gruppen zugeordnet werden. Als optimal erweist sich anhand der Eigenformberechnung und -bestimmung ein Sägeblatt mit 2 Löchern und einer Prägung von 136 bar. Hier zeigte sich eine Reduzierung der Maximal-Amplitude von 15,3 % und der Minimal-Amplitude von 23,5 %.