@phdthesis{Herrmann2021,
  author    = {Herrmann, Marc},
  title     = {The Total Variation on Surfaces and of Surfaces},
  doi       = {10.25972/OPUS-24073},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-240736},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {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.},
  subject      = {Gestaltoptimierung},
  language  = {en}
}
@phdthesis{Moldovan2021,
  author    = {Moldovan, Christian},
  title     = {Performance Modeling of Mobile Video Streaming},
  issn      = {1432-8801},
  doi       = {10.25972/OPUS-22871},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-228715},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {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.},
  subject      = {Video{\"u}bertragung},
  language  = {en}
}
@phdthesis{Handwerker2002,
  author    = {Handwerker, Michael},
  title     = {Optimierung der Schneidleistung oszillierender Knochens{\"a}gen},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-4018},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2002},
  abstract  = {Grundvoraussetzung einer erfolgreichen zementlosen Endoprothesenverankerungen ist eine hohe Prim{\"a}rstabilit{\"a}t durch formschl{\"u}ssige Implantation. Nach erfolgreicher Prim{\"a}rfixation entscheidet {\"u}ber die Langzeitfunktion neben der Verschleißsituation insbesondere die funktionelle Spannungsverteilung an der Implantatoberfl{\"a}che und im angrenzenden Knochen. Um optimale Bedingungen im Bereich der Grenzfl{\"a}che zwischen Werkstoff und Biosystem zu schaffen, ist die pr{\"a}zise Pr{\"a}paration des Knochens entscheidend. Hierbei spielt neben dem Operateur und der Beschaffenheit des Knochens das verwendete System zur Zerspanung, bestehend aus der S{\"a}ge und dem S{\"a}geblatt, eine wichtige Rolle. Oszillierende S{\"a}gen werden neben der Gipsbehandlung ausschließlich bei der Knochenbearbeitung verwendet, wobei Fragestellungen zu Leistungs- und Qualit{\"a}tssteigerung auftreten. Ansatzpunkt ist unter anderem das S{\"a}geblatt. Die Modellvielfalt der auf dem Markt erh{\"a}ltlichen S{\"a}gebl{\"a}tter erschwert die richtige Auswahl. Bei verschiedenen Modellen und deren unterschiedlichen Ausf{\"u}hrungen ist es schwierig, Vergleiche anzustellen und Verbesserungen einzuf{\"u}hren. Die Charakteristik eines S{\"a}geblattes ist durch die Sch{\"a}rfe beschrieben, um eine schnelle Zerspanung des Knochens zu gew{\"a}hrleisten, und durch die Steifigkeit des Blattes, um eine m{\"o}glichst geringe Abweichung aus der S{\"a}gelinie sicherzustellen. Die Sch{\"a}rfe des S{\"a}geblattes ist von der Zahnform und -geometrie abh{\"a}ngig. Die Steifigkeit ist abh{\"a}ngig von Material, Geometrie, Ausf{\"u}hrung und Eigenschwingung/Eigenform des Blattes. Modifikationen an diesem System f{\"u}hren auch zu einer ver{\"a}nderten Eigenform des S{\"a}geblattes. In der folgender Arbeit wurden verschiedene Ausf{\"u}hrungen von S{\"a}gebl{\"a}ttern hinsichtlich ihrer Eigenform charakterisiert. In einem praktischen Versuch wurde versucht, den Einfluss des S{\"a}geblattes auf die Vibration im Knochen von dem der S{\"a}ge abzugrenzen. Ziel der Studie war daher die Berechnung der Eigenform der S{\"a}gebl{\"a}tter, die experimentelle {\"U}berpr{\"u}fung der Eigenform und die Abgrenzung des Einflusses von S{\"a}geblatt und S{\"a}ge auf die Vibration beim S{\"a}gevorgang. 9 verschiedene S{\"a}gebl{\"a}tter unterschiedlicher Form und Geometrie wurden untersucht. Zun{\"a}chst wurde eine Eigenformberechnung mittels der Finiten Elemente Methode durchgef{\"u}hrt. Anschließend erfolgte die Eigenformbestimmung im Shakerversuch. Um den Einfluss der S{\"a}gebl{\"a}tter auf die Beschleunigung im Knochen von dem der S{\"a}ge abzugrenzen erfolgte die Beschleunigungsmessung in einem S{\"a}gepr{\"u}fstand. Bez{\"u}glich des Eigenschwingungsverhalten konnten die S{\"a}gebl{\"a}tter drei Gruppen zugeordnet werden. Als optimal erweist sich anhand der Eigenformberechnung und -bestimmung ein S{\"a}geblatt mit 2 L{\"o}chern und einer Pr{\"a}gung von 136 bar. Hier zeigte sich eine Reduzierung der Maximal-Amplitude von 15,3 \% und der Minimal-Amplitude von 23,5 \%.},
  language  = {de}
}
@phdthesis{Fleszar2018,
  author    = {Fleszar, Krzysztof},
  title     = {Network-Design Problems in Graphs and on the Plane},
  edition   = {1. Auflage},
  publisher = {W{\"u}rzburg University Press},
  address   = {W{\"u}rzburg},
  isbn      = {978-3-95826-076-4 (Print)},
  doi       = {10.25972/WUP-978-3-95826-077-1},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-154904},
  school      = {W{\"u}rzburg University Press},
  pages     = {xi, 204},
  year      = {2018},
  abstract  = {A network design problem defines an infinite set whose elements, called instances, describe relationships and network constraints. It asks for an algorithm that, given an instance of this set, designs a network that respects the given constraints and at the same time optimizes some given criterion. In my thesis, I develop algorithms whose solutions are optimum or close to an optimum value within some guaranteed bound. I also examine the computational complexity of these problems. Problems from two vast areas are considered: graphs and the Euclidean plane. In the Maximum Edge Disjoint Paths problem, we are given a graph and a subset of vertex pairs that are called terminal pairs. We are asked for a set of paths where the endpoints of each path form a terminal pair. The constraint is that any two paths share at most one inner vertex. The optimization criterion is to maximize the cardinality of the set. In the hard-capacitated k-Facility Location problem, we are given an integer k and a complete graph where the distances obey a given metric and where each node has two numerical values: a capacity and an opening cost. We are asked for a subset of k nodes, called facilities, and an assignment of all the nodes, called clients, to the facilities. The constraint is that the number of clients assigned to a facility cannot exceed the facility's capacity value. The optimization criterion is to minimize the total cost which consists of the total opening cost of the facilities and the total distance between the clients and the facilities they are assigned to. In the Stabbing problem, we are given a set of axis-aligned rectangles in the plane. We are asked for a set of horizontal line segments such that, for every rectangle, there is a line segment crossing its left and right edge. The optimization criterion is to minimize the total length of the line segments. In the k-Colored Non-Crossing Euclidean Steiner Forest problem, we are given an integer k and a finite set of points in the plane where each point has one of k colors. For every color, we are asked for a drawing that connects all the points of the same color. The constraint is that drawings of different colors are not allowed to cross each other. The optimization criterion is to minimize the total length of the drawings. In the Minimum Rectilinear Polygon for Given Angle Sequence problem, we are given an angle sequence of left (+90°) turns and right (-90°) turns. We are asked for an axis-parallel simple polygon where the angles of the vertices yield the given sequence when walking around the polygon in counter-clockwise manner. The optimization criteria considered are to minimize the perimeter, the area, and the size of the axis-parallel bounding box of the polygon.},
  subject      = {Euklidische Ebene},
  language  = {en}
}
@phdthesis{Klug2006,
  author    = {Klug, Andreas},
  title     = {Affine-Scaling Methods for Nonlinear Minimization Problems and Nonlinear Systems of Equations with Bound Constraints},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-18851},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {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.},
  subject      = {Skalierungsfunktion},
  language  = {en}
}