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Variational Model Reduction for Non-hydrostatic Stratified Flows in the Mid-latitude and the Equator
(2022)
This thesis studies balance models for a rotating stratified three-dimensional fluid on a tangent plane with full Coriolis force. Derivations are done for two different regions, namely mid-latitude and equator, which we considered separately. Each model is studied via a variational approach which is based on Lagrangian dynamics assuming smallness of the Rossby number and allowing for anisotropy in the horizontal length scales. We assume semigeostrophic scaling, akin to the derivation of the L 1 model by Salmon (1985) for the rotating shallow water equations. Contrary to Salmon’s derivation, we start with an arbitrary change of coordinates and then choose the transformation to fix the degeneracy on the first order of the Lagrangian, L 1, as suggested by Oliver (2006). In our setting, the full projection of the rotation vector of the Earth is considered, so that the horizontal component of the Coriolis vector is taken into account. For each model, conservation laws for the energy and the potential vorticity are valid because of the Hamiltonian structure. Our first model on f-plane is the most general model obtained so far in semi-geostrophic scaling. The other model concerns balance model on the equatorial β-plane. Under the additional assumption of construction of zero-meridional velocity as suggested by the leading order dynamics, an equatorial balance model is obtained.
Optimal balance is a numerical decomposition method of geophysical flows into a balanced and unbalanced components without any asymptotic analysis. It was introduced under optimal potential vorticity (PV) balance by Viúdez and Dritschel (2004) in a special semi-Lagrangian PV-based scheme. The method adiabatically deforms the nonlinear model into its linear form where mode decomposition is exact. It leads to a boundary value problem in time where gravity waves are removed at the linear end and a base-point coordinate is restored at the nonlinear end. This problem is solved by an iterative backward-forward nudging scheme. As global geophysical ocean models use primitive variables, we study optimal balance on an existing f-plane shallow water model in the primitive velocity-height variables. Our model, nevertheless, includes kinematic PV-inversion formulas if the PV is base point.
We, here, systematically investigate our numerical model for several design parameters. We found that optimal balance works with PV-based projectors which are the most robust choice with primitive variable-based projectors which are useful for general domains and global models. The PV-based projectors are the linear oblique projector and the base point PV. The linear oblique projector can be reformulated as a PDE-based projector preserving linear PV. Besides, the height field as a prominent candidate of base point and a linear PDE-based projector support more general cases.
The method returns high-quality balance with rapid convergence of the nudging scheme, but its convergence is, still, an open question. We proved the ''quasi-converge'' of the nudging iterates up to a small termination residual, and this residual is as small as the balance error which is of algebraic order in the time-separation parameter for a lower-dimensional system. Hence, optimal balance is an accurate diagnostic tool in primitive variables and can be implemented on complicated models without fundamental obstacles.
Physical Layer Security (PHYSEC) uses the inherently random and reciprocal nature of physical (wireless) channels as a source for the generation of symmetric keys at the physical layer. The channel measurements of the two users involved in the key agreement, from which the keys are derived, are corrupted by independent noise components. This leads to key discrepancies which need to be reconciled between the two parties involved in the key agreement before the keys can be used for encryption and authentication.
The focus of this thesis is the key reconciliation step of PHYSEC, with particular emphasis on the two main classes of reconciliation schemes: those based on introducing guard bands during the quantization process and those based on error-correcting codes.
To that end, we first investigate the effect that the choice of the quantization method and associated parameters has on the key agreement rate and on the security of the system.
Our findings show that for medium to high SNRs, good reconciliation performance can be achieved with guard-based methods without compromising security. When the legitimate users experience low SNRs, however, we have found guard-based methods to be unsuitable when used as the sole reconciliation method. This is because, in order to achieve the target reconciliation performance at low SNRs, they would require large guard-band widths, which would have a negative impact not only on the efficiency and key generation rate but also on security by providing an advantage to potential eavesdroppers.
We propose a hybrid reconciliation method that combines guard bands with error-correcting codes which we specifically designed to achieve good performance at low SNRs. As a final result, we provide several Low-Density Parity-Check (LDPC) code ensembles with a Multi-Edge-Type (MET) structure, which we have specifically designed for wireless key reconciliation.
This thesis discusses how memory of the source, of disturbances, or of the channel can be efficiently dealt with inside the decoding of LDPC codes. Furthermore, how such codes can be optimized for including source memory is also presented.
At the source, the memory is modeled via a Markov chain. The transition probabilities of the model are used at the decoder to estimate the source symbols. Although computed at the decoder, this information is considered to be a-priori information. The a-priori LLR can be directly incorporated into the Tanner graph, a novel simplified computation which provides equal performance to existing methods is shown. A Turbo-like scheme is also proposed where a BCJR and an LDPC decoder decode the source and received sequences iteratively, each utilizing extrinsic information computed by the other. The Turbo-like scheme performs the best at low SNRs. Subsequently, a code design algorithm is provided for obtaining optimized codes for the decoding model with direct additional links in the Tanner graph. For the optimization, density evolution is used. The optimized codes provide steeper performance curves than non-optimized ones.
Thereafter, impulse noise with memory is investigated, which is modeled by the Middleton Class-A model. A Markov model provides the transition probabilities between background and impulsive noise states. A Viterbi decoder estimates the noise sequence and an LDPC decoder estimates the transmitted symbols. Information is iterated between the decoders to improve the overall correction at the receiver. Possibilities for computing the noise states directly at the decoder are also investigated. However, the noise-memory cannot be directly incorporated into the Tanner graph. Lastly, a method is proposed to mitigate channel memory which causes inter-symbol interference using an LDPC decoder. A decision-feedback equalization like structure is used in which the intermediate LDPC decoder results are used for equalization.
Biological data represent a large, challenging sector of data engineering applications. Biological data are typically complex and poorly standardized. Moreover, high value, rapid growth in volume and advances in acquisition technologies characterize modern environmental and health research data, humbling the classical practices for data transformation and analytics. Furthermore, data in biology make more sense when integrated with usually different data types, or data from different sources or even fields. In addition, the uniqueness of each case and research question call for a deep understanding of data life cycle and for customized solutions. Having a large volume and value, and being produced at a high velocity in a large variety, biological data encourage the investigation of scalable workflows to automate acquisition and integration, closing the gaps in optimizing analytics specially for heterogeneous data.
This thesis aims at exploring and optimizing the state-of-the-art methods for heterogeneous data integration and analysis, of sequence and non-sequence-based data, by identifying four areas of application concerning primary and secondary data from environmental and health research. It presents four challenges in data preparation and transformation for variable selection, and accompanying case studies. Particularly, the thesis investigates knowledge extraction from primary inherently high-dimensional marine sequence data, scalability in handling secondary photosynthetic sequence data, integration and statistical modeling of secondary high-dimensional relational health care claims data for adverse drug event prediction, and integration of heterogeneous primary epidemiological data for childhood obesity investigation. The thesis highlights the importance of data model development for data transformation and integration, and the role of scalable analytics in the foreseen increase in data dimensions.
Owing to the ever-growing volume of mobile traffic and wireless devices as shown in network traffic reports over the last decades, the wireless mobile technology is required and expected to offer continuous improvements on the major communication performance such as data rate and connection density. Besides expanding such communication performance, various application-centric Quality of Service (QoS) requirements have been raised from a wide range of application fields, imposing on the research community the need of diverse wireless solutions to satisfy such heterogeneous QoS requirements.
In light of the above, this dissertation intends to contribute to the aforementioned trend by addressing three essentials in future wireless systems: massive connectivity, low-latency, and reliability, offering the corresponding algorithm design(s) and quantitative analyses to evaluate the performance. Numerical performance assessments via computer simulations are offered to evaluate the aforementioned proposed methods, illustrating their advantages against existing counterparts.
Currently, two-dimensional (2D) fluoroscopy and conventional digital subtraction angiography are the gold standard for the navigation of medical instruments in many minimal-invasive interventions like the endovascular aneurysm repair (EVAR) procedures. However, this requires X-rays, contrast agent is used, and the depth information is missing. A three-dimensional (3D) guidance based on tracking systems does no have these disadvantages. The key hypothesis of the PhD work is that a tracking-based guidance of medical instruments is possible and that it facilitates the navigation in minimal invasive interventions. The evaluated use case will be the navigation of a stent graft during an EVAR procedure.
First, an analysis and optimization of a fiber optical shape sensing (FOSS) model is conducted: The usage of an optical fiber with fiber Bragg gratings (FBGs) allows measuring the shape of a medical tool. Here, methods from literature are analyzed and evaluated in different experiments. The accuracy of the obtained optimized shape sensing model is evaluated with different 3D measurements.
Then, novel tracking-based guidance methods are introduced: The combination of FOSS and EM sensors allows determining the located shape of medical instruments. For this purpose, a spatial calibration method for an optical fiber and EM sensors is introduced. Moreover, the methods for obtaining the located shape using three, two or only one EM sensor (together with preoperative data). The guidance methods have been evaluated in different experiments and compared with an image-based 3D shape localization approach.
In addition, the developed approaches are applied in order to guide a stent graft in EVAR procedures. A spatial calibration between stent graft and tracking systems and a suitable visualization of the guidance information are described. This stent graft guidance method was evaluated by conducting an EVAR procedure on a torso phantom.
Global manufacturing networks and the underlying global supply chains form the centerpiece of automotive production. Over the last decades, original equipment manufacturers established overseas plants in the course of their expansion strategy and employed so-called knocked-down supply chains to ship all parts pre-assembled and arranged in kits to them. The overseas plants have matured into fully-equipped plants by taking over value-adding processes. As a consequence, the global manufacturing networks have shifted their focus away from simplification toward performance. The underlying knocked-down supply chains, however, have not adapted and still feature high inventories, lead times and costs.
Even though knocked-down supply chains play a key role in global manufacturing networks, they have not been integrated. It is not possible to evaluate their fit and to derive the requirements. Despite the intense effort to improve the performance in the factories, there is little research on improvement levers in the context of knocked-down supply chains.
This Thesis intends to explore how knocked-down supply chains can be aligned with global manufacturing networks. It conducts a cross-case study to provide an overview of current knocked-down supply chains and global manufacturing networks. The Thesis develops an integrated framework that matches knocked-down supply chains and global manufacturing networks and identifies weak spots in supply chain performance. The Thesis then applies a two-fold approach. It explores the general working principle of knocked-down supply chains by means of intermodal transportation. Gaining impetus from lean management, the Thesis then identifies improvement levers and subsequently evaluates their effect on knocked-down supply chains. The Thesis shows that the supply chain performance of knocked-down supply chains and thus the fit with the global manufacturing network can be improved.
Implications of Dataset Heterogeneity on Deep Learning Performance in Medical Image Segmentation
(2021)
This thesis is about medical image segmentation using deep learning, with a particular focus on the influence of the training data. The performance of deep learning algorithms is impacted by the training set quality and heterogeneity, here grouped into three categories: technical image quality, reference segmentations and study populations.
Different training strategies are compared for parotid gland segmentation in CT data. All yield robust segmentation results, also in the presence of artifacts, and outperform non-deep learning methods on public data. Typical errors coincide with regions of high inter-observer variability. Training on contours from clinical routine, and on curated contours yield similar accuracy and results.
Bladder, rectum and uterus are segmented in cone-beam CT data, that is noisier and less well-calibrated than CT data. Using CT data for augmenting the anatomical variability is proposed and found to improve the performance. Prior knowledge about the presence of typical artifacts is integrated into the data sampling. Curriculum learning seems promising to increase the robustness to the particular artifact.
The hippocampus is segmented in CT data. A CT-only approach for generating the training contours could facilitate the data collection, but it is found that MRI-based training contours yield significantly higher performance and lower uncertainty.
White matter hyperintensity lesions are an imaging biomarker linked to stroke and cognitive decline. It is shown that a single neural network can segment these lesions in heterogeneous MRI data with varying image quality and lesion loads, and for a wide range of training set compositions, generated by pooling and systematic sampling. A challenge is the co-occurrence of stroke lesions. An approach that uses stroke segmentations for guiding the sampling, but not for optimizing the training loss, is proposed and found to outperform other sampling approaches with respect to false positive detections.
Modeling, Estimating, and Visualizing Spatial and Temporal Uncertainty for Image-Guided Therapy
(2021)
We address different aspects of the problem of uncertainty in image-guided therapies. This is of great interest, because such uncertainty could have a substantial impact on public health. Significant uncertainties can occur in image segmentation and estimating deformations of anatomy. To model the uncertainty in the image segmentation aspect, we propose a novel stationary Gaussian process (GP)-based generative segmentation model. This segmentation model allows us to draw many possible image segmentations, which can be used for estimating and visualizing different aspects of the uncertainty in image-guided therapies. To enable drawing of many image segmentation samples efficiently, we propose a fast method for sampling from stationary GPs. To model the uncertainty in the aspect of estimating deformations of anatomy, we propose a novel spatiotemporal GP model for uncertainty-aware soft-tissue motion estimation using GP regression. The spatiotemporal GP formalism enables the estimation of anatomy displacements at any location, and for any time interval from measured motions that are sparse in space and time. The use of GP regression enables the quantification of uncertainty in the soft-tissue motion estimation result, which allows the amount of uncertainty in some aspects, e.g., registered planning medical images, of image-guided therapies or procedures governing the decisions of medical specialists to be conveyed. To convey the amount of uncertainty in the anatomy motion estimates, we propose novel motion uncertainty visualization methods. To showcase the use of the devised methods, we deploy them in the context of radiotherapy and image-guided soft-tissue intervention navigation. We expect that incorporating estimates of spatial and temporal uncertainty into the processing pipelines of image-guided therapy will eventually enable improved treatments, and thus, improved outcomes.
