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- viscoelastic modeling (1)
- viscosity model (1)
- visual structure (1)
- voltage sensitive dye (1)
- vortex seperation (1)
- waveguides (1)
- wavelength multiplex (1)
- wear (1)
- weighing (1)
- weighted finite-state transducers (1)
- well-posedness (1)
- wheel side-slip estimation (1)
- whole genome microarray analysis (1)
- wireless communications system (1)
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- wireless sensor network (1)
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- worst-case scenario (1)
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Faculty / Organisational entity
- Fachbereich Mathematik (219)
- Fachbereich Informatik (139)
- Fachbereich Maschinenbau und Verfahrenstechnik (95)
- Fachbereich Chemie (58)
- Fachbereich Elektrotechnik und Informationstechnik (45)
- Fachbereich Biologie (27)
- Fachbereich Sozialwissenschaften (15)
- Fachbereich Wirtschaftswissenschaften (8)
- Fachbereich Physik (6)
- Fachbereich ARUBI (5)
In this dissertation we apply financial mathematical modelling to electricity markets. Electricity is different from any other underlying of financial contracts: it is not storable. This means that electrical energy in one time point cannot be transferred to another. As a consequence, power contracts with disjoint delivery time spans basically have a different underlying. The main idea throughout this thesis is exactly this two-dimensionality of time: every electricity contract is not only characterized by its trading time but also by its delivery time.
The basis of this dissertation are four scientific papers corresponding to the Chapters 3 to 6, two of which have already been published in peer-reviewed journals. Throughout this thesis two model classes play a significant role: factor models and structural models. All ideas are applied to or supported by these two model classes. All empirical studies in this dissertation are conducted on electricity price data from the German market and Chapter 4 in particular studies an intraday derivative unique to the German market. Therefore, electricity market design is introduced by the example of Germany in Chapter 1. Subsequently, Chapter 2 introduces the general mathematical theory necessary for modelling electricity prices, such as Lévy processes and the Esscher transform. This chapter is the mathematical basis of the Chapters 3 to 6.
Chapter 3 studies factor models applied to the German day-ahead spot prices. We introduce a qualitative measure for seasonality functions based on three requirements. Furthermore, we introduce a relation of factor models to ARMA processes, which induces a new method to estimate the mean reversion speed.
Chapter 4 conducts a theoretical and empirical study of a pricing method for a new electricity derivative: the German intraday cap and floor futures. We introduce the general theory of derivative pricing and propose a method based on the Hull-White model of interest rate modelling, which is a one-factor model. We include week futures prices to generate a price forward curve (PFC), which is then used instead of a fixed deterministic seasonality function. The idea that we can combine all market prices, and in particular futures prices, to improve the model quality also plays the major role in Chapter 5 and Chapter 6.
In Chapter 5 we develop a Heath-Jarrow-Morton (HJM) framework that models intraday, day-ahead, and futures prices. This approach is based on two stochastic processes motivated by economic interpretations and separates the stochastic dynamics in trading and delivery time. Furthermore, this framework allows for the use of classical day-ahead spot price models such as the ones of Schwartz and Smith (2000), Lucia and Schwartz (2002) and includes many model classes such as structural models and factor models.
Chapter 6 unifies the classical theory of storage and the concept of a risk premium through the introduction of an unobservable intrinsic electricity price. Since all tradable electricity contracts are derivatives of this actual intrinsic price, their prices should all be derived as conditional expectation under the risk-neutral measure. Through the intrinsic electricity price we develop a framework, which also includes many existing modelling approaches, such as the HJM framework of Chapter 5.
The main focus of the research lies in the interpretation and application of results and correlations of soil properties from in situ testing and subsequent use in terramechanical applications. The empirical correlations and current procedures were mainly developed for medium to large depths, and therefore they were re-evaluated and adjusted herein to reflect the current state of knowledge for the assessment of near-surface soil. For testing technologies, a field investigation to a moon analogue site was carried out. Focus was placed in the assessment of the near surface soil properties. Samples were collected for subsequent analysis in laboratory conditions. Further laboratory experiments in extraterrestrial soil simulants and other terrestrial soils were conducted and correlations with relative density and shear strength parameters were attempted. The correlations from the small scale laboratory experiments, and the new re-evaluated correlation for relative density were checked against the data from the field investigation. Additionally, single tire-soil tests were carried out, which enable the investigation of the localized soil response in order to advance current wheel designs and subsequently the vehicle’s mobility. Furthermore, numerical simulations were done to aid the investigation of the tire-soil interaction. Summing up, current relationships for estimating relative density of near surface soil were re-evaluated, and subsequently correlated to shear strength parameters that are the main input to model soil in numerical analyses. Single tire-soil tests were carried out and were used as a reference to calibrate the interaction of the tire and the soil and subsequently were utilized to model rolling scenarios which enable the assessment of soil trafficability and vehicle’s mobility.
Planar force or pressure is a fundamental physical aspect during any people-vs-people and people-vs-environment activities and interactions. It is as significant as the more established linear and angular acceleration (usually acquired by inertial measurement units). There have been several studies involving planar pressure in the discipline of activity recognition, as reviewed in the first chapter. These studies have shown that planar pressure is a promising sensing modality for activity recognition. However, they still take a niche part in the entire discipline, using ad hoc systems and data analysis methods. Mostly these studies were not followed by further elaborative works. The situation calls for a general framework that can help push planar pressure sensing into the mainstream.
This dissertation systematically investigates using planar pressure distribution sensing technology for ubiquitous and wearable activity recognition purposes. We propose a generic Textile Pressure Mapping (TPM) Framework, which encapsulates (1) design knowledge and guidelines, (2) a multi-layered tool including hardware, software and algorithms, and (3) an ensemble of empirical study examples. Through validation with various empirical studies, the unified TPM framework covers the full scope of application recognition, including the ambient, object, and wearable subspaces.
The hardware part constructs a general architecture and implementations in the large-scale and mobile directions separately. The software toolkit consists of four heterogeneous tiers: driver, data processing, machine learning, visualization/feedback. The algorithm chapter describes generic data processing techniques and a unified TPM feature set. The TPM framework offers a universal solution for other researchers and developers to evaluate TPM sensing modality in their application scenarios.
The significant findings from the empirical studies have shown that TPM is a versatile sensing modality. Specifically, in the ambient subspace, a sports mat or carpet with TPM sensors embedded underneath can distinguish different sports activities or different people's gait based on the dynamic change of body-print; a pressure sensitive tablecloth can detect various dining actions by the force propagated from the cutlery through the plates to the tabletop. In the object subspace, swirl office chairs with TPM sensors under the cover can be used to detect the seater's real-time posture; TPM can be used to detect emotion-related touch interactions for smart objects, toys or robots. In the wearable subspace, TPM sensors can be used to perform pressure-based mechanomyography to detect muscle and body movement; it can also be tailored to cover the surface of a soccer shoe to distinguish different kicking angles and intensities.
All the empirical evaluations have resulted in accuracies well-above the chance level of the corresponding number of classes, e.g., the `swirl chair' study has classification accuracy of 79.5% out of 10 posture classes and in the `soccer shoe' study the accuracy is 98.8% among 17 combinations of angle and intensity.
Topological insulators (TI) are a fascinating new state of matter. Like usual insulators, their band structure possesses a band gap, such that they cannot conduct current in their bulk. However, they are able to conduct current along their edges and surfaces, due to edge states that cross the band gap. What makes TIs so interesting and potentially useful are these robust unidirectional edge currents. They are immune to significant defects and disorder, which means that they provide scattering-free transport.
In photonics, using topological protection has a huge potential for applications, e.g. for robust optical data transfer [1-3] – even on the quantum level [4, 5] – or to make devices more stable and robust [6, 7]. Therefore, the field of topological insulators has spread to optics to create the new and active research field of topological photonics [8-10].
Well-defined and controllable model systems can help to provide deeper insight into the mechanisms of topologically protected transport. These model systems provide a vast control over parameters. For example, arbitrary lattice types without defects can be examined, and single lattice sites can be manipulated. Furthermore, they allow for the observation of effects that usually happen at extremely short time-scales in solids. Model systems based on photonic waveguides are ideal candidates for this.
They consist of optical waveguides arranged on a lattice. Due to evanescent coupling, light that is inserted into one waveguide spreads along the lattice. This coupling of light between waveguides can be seen as an analogue to electrons hopping/tunneling between atomic lattice sites in a solid.
The theoretical basis for this analogy is given by the mathematical equivalence between Schrödinger and paraxial Helmholtz equation. This means that in these waveguide systems, the role of time is assigned to a spatial axis. The field evolution along the waveguides' propagation axis z thus models the temporal evolution of an electron's wave-function in solid states. Electric and magnetic fields acting on electrons in solids need to be incorporated into the photonic platform by introducing artificial fields. These artificial gauge fields need to act on photons in the same way that their electro-magnetic counterparts act on electrons. E.g., to create a photonic analogue of a topological insulator the waveguides are bent helically along their propagation axis to model the effect of a magnetic field [3]. This means that the fabrication of these waveguide arrays needs to be done in 3D.
In this thesis, a new method to 3D micro-print waveguides is introduced. The inverse structure is fabricated via direct laser writing, and subsequently infiltrated with a material with higher refractive index contrast. We will use these model systems of evanescently coupled waveguides to look at different effects in topological systems, in particular at Floquet topological systems.
We will start with a topologically trivial system, consisting of two waveguide arrays with different artificial gauge fields. There, we observe that an interface between these trivial gauge fields has a profound impact on the wave vector of the light traveling across it. We deduce an analog to Snell's law and verify it experimentally.
Then we will move on to Floquet topological systems, consisting of helical waveguides. At the interface between two Floquet topological insulators with opposite helicity of the waveguides, we find additional trivial interface modes that trap the light. This allows to investigate the interaction between trivial and topological modes in the lattice.
Furthermore, we address the question if topological edge states are robust under the influence of time-dependent defects. In a one-dimensional topological model (the Su-Schrieffer-Heeger model [11]) we apply periodic temporal modulations to an edge wave-guide. We find Floquet copies of the edge state, that couple to the bulk in a certain frequency window and thus depopulate the edge state.
In the two-dimensional Floquet topological insulator, we introduce single defects at the edge. When these defects share the temporal periodicity of the helical bulk waveguides, they have no influence on a topological edge mode. Then, the light moves around/through the defect without being scattered into the bulk. Defects with different periodicity, however, can – likewise to the defects in the SSH model – induce scattering of the edge state into the bulk.
In the end we will briefly highlight a newly emerging method for the fabrication of waveguides with low refractive index contrast. Moreover, we will introduce new ways to create artificial gauge fields by the use of orbital angular momentum states in waveguides.
Under the notion of Cyber-Physical Systems an increasingly important research area has
evolved with the aim of improving the connectivity and interoperability of previously
separate system functions. Today, the advanced networking and processing capabilities
of embedded systems make it possible to establish strongly distributed, heterogeneous
systems of systems. In such configurations, the system boundary does not necessarily
end with the hardware, but can also take into account the wider context such as people
and environmental factors. In addition to being open and adaptive to other networked
systems at integration time, such systems need to be able to adapt themselves in accordance
with dynamic changes in their application environments. Considering that many
of the potential application domains are inherently safety-critical, it has to be ensured
that the necessary modifications in the individual system behavior are safe. However,
currently available state-of-the-practice and state-of-the-art approaches for safety assurance
and certification are not applicable to this context.
To provide a feasible solution approach, this thesis introduces a framework that allows
“just-in-time” safety certification for the dynamic adaptation behavior of networked
systems. Dynamic safety contracts (DSCs) are presented as the core solution concept
for monitoring and synthesis of decentralized safety knowledge. Ultimately, this opens
up a path towards standardized service provision concepts as a set of safety-related runtime
evidences. DSCs enable the modular specification of relevant safety features in
networked applications as a series of formalized demand-guarantee dependencies. The
specified safety features can be hierarchically integrated and linked to an interpretation
level for accessing the scope of possible safe behavioral adaptations. In this way, the networked
adaptation behavior can be conditionally certified with respect to the fulfilled
DSC safety features during operation. As long as the continuous evaluation process
provides safe adaptation behavior for a networked application context, safety can be
guaranteed for a networked system mode at runtime. Significant safety-related changes
in the application context, however, can lead to situations in which no safe adaptation
behavior is available for the current system state. In such cases, the remaining DSC
guarantees can be utilized to determine optimal degradation concepts for the dynamic
applications.
For the operationalization of the DSCs approach, suitable specification elements and
mechanisms have been defined. Based on a dedicated GUI-engineering framework it is
shown how DSCs can be systematically developed and transformed into appropriate runtime
representations. Furthermore, a safety engineering backbone is outlined to support
the DSC modeling process in concrete application scenarios. The conducted validation
activities show the feasibility and adequacy of the proposed DSCs approach. In parallel,
limitations and areas of future improvement are pointed out.
Many loads acting on a vehicle depend on the condition and quality of roads
traveled as well as on the driving style of the motorist. Thus, during vehicle development,
good knowledge on these further operations conditions is advantageous.
For that purpose, usage models for different kinds of vehicles are considered. Based
on these mathematical descriptions, representative routes for multiple user
types can be simulated in a predefined geographical region. The obtained individual
driving schedules consist of coordinates of starting and target points and can
thus be routed on the true road network. Additionally, different factors, like the
topography, can be evaluated along the track.
Available statistics resulting from travel survey are integrated to guarantee reasonable
trip length. Population figures are used to estimate the number of vehicles in
contained administrative units. The creation of thousands of those geo-referenced
trips then allows the determination of realistic measures of the durability loads.
Private as well as commercial use of vehicles is modeled. For the former, commuters
are modeled as the main user group conducting daily drives to work and
additional leisure time a shopping trip during workweek. For the latter, taxis as
example for users of passenger cars are considered. The model of light-duty commercial
vehicles is split into two types of driving patterns, stars and tours, and in
the common traffic classes of long-distance, local and city traffic.
Algorithms to simulate reasonable target points based on geographical and statistical
data are presented in detail. Examples for the evaluation of routes based
on topographical factors and speed profiles comparing the influence of the driving
style are included.
In computer graphics, realistic rendering of virtual scenes is a computationally complex problem. State-of-the-art rendering technology must become more scalable to
meet the performance requirements for demanding real-time applications.
This dissertation is concerned with core algorithms for rendering, focusing on the
ray tracing method in particular, to support and saturate recent massively parallel computer systems, i.e., to distribute the complex computations very efficiently
among a large number of processing elements. More specifically, the three targeted
main contributions are:
1. Collaboration framework for large-scale distributed memory computers
The purpose of the collaboration framework is to enable scalable rendering
in real-time on a distributed memory computer. As an infrastructure layer it
manages the explicit communication within a network of distributed memory
nodes transparently for the rendering application. The research is focused on
designing a communication protocol resilient against delays and negligible in
overhead, relying exclusively on one-sided and asynchronous data transfers.
The hypothesis is that a loosely coupled system like this is able to scale linearly
with the number of nodes, which is tested by directly measuring all possible
communication-induced delays as well as the overall rendering throughput.
2. Ray tracing algorithms designed for vector processing
Vector processors are to be efficiently utilized for improved ray tracing performance. This requires the basic, scalar traversal algorithm to be reformulated
in order to expose a high degree of fine-grained data parallelism. Two approaches are investigated: traversing multiple rays simultaneously, and performing
multiple traversal steps at once. Efficiently establishing coherence in a group
of rays as well as avoiding sorting of the nodes in a multi-traversal step are the
defining research goals.
3. Multi-threaded schedule and memory management for the ray tracing acceleration structure
Construction times of high-quality acceleration structures are to be reduced by
improvements to multi-threaded scalability and utilization of vector processors. Research is directed at eliminating the following scalability bottlenecks:
dynamic memory growth caused by the primitive splits required for high-
quality structures, and top-level hierarchy construction where simple task par-
allelism is not readily available. Additional research addresses how to expose
scatter/gather-free data-parallelism for efficient vector processing.
Together, these contributions form a scalable, high-performance basis for real-time,
ray tracing-based rendering, and a prototype path tracing application implemented
on top of this basis serves as a demonstration.
The key insight driving this dissertation is that the computational power necessary
for realistic light transport for real-time rendering applications demands massively
parallel computers, which in turn require highly scalable algorithms. Therefore this
dissertation provides important research along the path towards virtual reality.
While the design step should be free from computational related constraints and operations due to its artistic aspect, the modeling phase has to prepare the model for the later stages of the pipeline.
This dissertation is concerned with the design and implementation of a framework for local remeshing and optimization. Based on the experience gathered, a full study about mesh quality criteria is also part of this work.
The contributions can be highlighted as: (1) a local meshing technique based on a completely novel approach constrained to the preservation of the mesh of non interesting areas. With this concept, designers can work on the design details of specific regions of the model without introducing more polygons elsewhere; (2) a tool capable of recovering the shape of a refined area to its decimated version, enabling details on optimized meshes of detailed models; (3) the integration of novel techniques into a single framework for meshing and smoothing which is constrained to surface structure; (4) the development of a mesh quality criteria priority structure, being able to classify and prioritize according to the application of the mesh.
Although efficient meshing techniques have been proposed along the years, most of them lack the possibility to mesh smaller regions of the base mesh, preserving the mesh quality and density of outer areas.
Considering this limitation, this dissertation seeks answers to the following research questions:
1. Given that mesh quality is relative to the application it is intended for, is it possible to design a general mesh evaluation plan?
2. How to prioritize specific mesh criteria over others?
3. Given an optimized mesh and its original design, how to improve the representation of single regions of the first, without degrading the mesh quality elsewhere?
Four main achievements came from the respective answers:
1. The Application Driven Mesh Quality Criteria Structure: Due to high variation in mesh standards because of various computer aided operations performed for different applications, e.g. animation or stress simulation, a structure for better visualization of mesh quality criteria is proposed. The criteria can be used to guide the mesh optimization, making the task consistent and reliable. This dissertation also proposes a methodology to optimize the criteria values, which is adaptable to the needs of a specific application.
2. Curvature Driven Meshing Algorithm: A novel approach, a local meshing technique, which works on a desired area of the mesh while preserving its boundaries as well as the rest of the topology. It causes a slow growth in the overall amount of polygons by making only small regions denser. The method can also be used to recover the details of a reference mesh to its decimated version while refining it. Moreover, it employs a geometric fast and easy to implement approach representing surface features as simple circles, being used to guide the meshing. It also generates quad-dominant meshes, with triangle count directly dependent on the size of the boundary.
3. Curvature-based Method for Anisotropic Mesh Smoothing: A geometric-based method is extended to 3D space to be able to produce anisotropic elements where needed. It is made possible by mapping the original space to another which embeds the surface curvature. This methodology is used to enhance the smoothing algorithm by making the nearly regularized elements follow the surface features, preserving the original design. The mesh optimization method also preserves mesh topology, while resizing elements according to the local mesh resolution, effectively enhancing the design aspects intended.
4. Framework for Local Restructure of Meshed Surfaces: The combination of both methods creates a complete tool for recovering surface details through mesh refinement and curvature aware mesh smoothing.
In this thesis we consider the directional analysis of stationary point processes. We focus on three non-parametric methods based on second order analysis which we have defined as Integral method, Ellipsoid method, and Projection method. We present the methods in a general setting and then focus on their application in the 2D and 3D case of a particular type of anisotropy mechanism called geometric anisotropy. We mainly consider regular point patterns motivated by our application to real 3D data coming from glaciology. Note that directional analysis of 3D data is not so prominent in the literature.
We compare the performance of the methods, which depends on the relative parameters, in a simulation study both in 2D and 3D. Based on the results we give recommendations on how to choose the methods´ parameters in practice.
We apply the directional analysis to the 3D data coming from glaciology, which consist in the locations of air-bubbles in polar ice cores. The aim of this study is to provide information about the deformation rate in the ice and the corresponding thinning of ice layers at different depths. This information is substantial for the glaciologists in order to build ice dating models and consequently to give a correct interpretation of the climate information which can be found by analyzing ice cores. In this thesis we consider data coming from three different ice cores: the Talos Dome core, the EDML core and the Renland core.
Motivated by the ice application, we study how isotropic and stationary noise influences the directional analysis. In fact, due to the relaxation of the ice after drilling, noise bubbles can form within the ice samples. In this context we take two classification algorithms into consideration, which aim to classify points in a superposition of a regular isotropic and stationary point process with Poisson noise.
We introduce two methods to visualize anisotropy, which are particularly useful in 3D and apply them to the ice data. Finally, we consider the problem of testing anisotropy and the limiting behavior of the geometric anisotropy transform.
In this thesis, we consider the problem of processing similarity queries over a dataset of top-k rankings and class constrained objects. Top-k rankings are the most natural and widely used technique to compress a large amount of information into a concise form. Spearman’s Footrule distance is used to compute the similarity between rankings, considering how well rankings agree on the positions (ranks) of ranked items. This setup allows the application of metric distance-based pruning strategies, and, alternatively, enables the use of traditional inverted indices for retrieving rankings that overlap in items. Although both techniques can be individually applied, we hypothesize that blending these two would lead to better performance. First, we formulate theoretical bounds over the rankings, based on Spearman's Footrule distance, which are essential for adapting existing, inverted index based techniques to the setting of top-k rankings. Further, we propose a hybrid indexing strategy, designed for efficiently processing similarity range queries, which incorporates inverted indices and metric space indices, such as M- or BK-trees, resulting in a structure that resembles both indexing methods with tunable emphasis on one or the other. Moreover, optimizations to the inverted index component are presented, for early termination and minimizing bookkeeping. As vast amounts of data are being generated on a daily bases, we further present a distributed, highly tunable, approach, implemented in Apache Spark, for efficiently processing similarity join queries over top-k rankings. To combine distance-based filtering with inverted indices, the algorithm works in several phases. The partial results are joined for the computation of the final result set. As the last contribution of the thesis, we consider processing k-nearest-neighbor (k-NN) queries over class-constrained objects, with the additional requirement that the result objects are of a specific type. We introduce the MISP index, which first indexes the objects by their (combination of) class belonging, followed by a similarity search sub index for each subset of objects. The number of such subsets can combinatorially explode, thus, we provide a cost model that analyzes the performance of the MISP index structure under different configurations, with the aim of finding the most efficient one for the dataset being searched.