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This thesis addresses the problem of terrain classification in unstructured outdoor environments. Terrain classification includes the detection of obstacles and passable areas as well as the analysis of ground surfaces. A 3D laser range finder is used as primary sensor for perceiving the surroundings of the robot. First of all, a grid structure is introduced for data reduction. The chosen data representation allows for multi-sensor integration, e.g., cameras for color and texture information or further laser range finders for improved data density. Subsequently, features are computed for each terrain cell within the grid. Classification is performedrnwith a Markov random field for context-sensitivity and to compensate for sensor noise and varying data density within the grid. A Gibbs sampler is used for optimization and is parallelized on the CPU and GPU in order to achieve real-time performance. Dynamic obstacles are detected and tracked using different state-of-the-art approaches. The resulting information - where other traffic participants move and are going to move to - is used to perform inference in regions where the terrain surface is partially or completely invisible for the sensors. Algorithms are tested and validated on different autonomous robot platforms and the evaluation is carried out with human-annotated ground truth maps of millions of measurements. The terrain classification approach of this thesis proved reliable in all real-time scenarios and domains and yielded new insights. Furthermore, if combined with a path planning algorithm, it enables full autonomy for all kinds of wheeled outdoor robots in natural outdoor environments.

Efficient Cochlear Implant (CI) surgery requires prior knowledge of the cochlea’s size and its characteristics. This information helps to select suitable implants for different patients. Registered and fused images helps doctors by providing more informative image that takes advantages of different modalities. The cochlea’s small size and complex structure, in addition to the different resolutions and head positions during imaging, reveals a big challenge for the automated registration of the different image modalities. To obtain an automatic measurement of the cochlea length and the volume size, a segmentation method of cochlea medical images is needed. The goal of this dissertation is to introduce new practical and automatic algorithms for the human cochlea multi-modal 3D image registration, fusion, segmentation and analysis. Two novel methods for automatic cochlea image registration (ACIR) and automatic cochlea analysis (ACA) are introduced. The proposed methods crop the input images to the cochlea part and then align the cropped images to obtain the optimal transformation. After that, this transformation is used to align the original images. ACIR and ACA use Mattes mutual information as similarity metric, the adaptive stochastic gradient descent (ASGD) or the stochastic limited memory Broyden–Fletcher–Goldfarb–Shanno (s-LBFGS) optimizer to estimate the parameters of 3D rigid transform. The second stage of nonrigid registration estimates B-spline coefficients that are used in an atlas-model-based segmentation to extract cochlea scalae and the relative measurements of the input image. The image which has segmentation is aligned to the input image to obtain the non-rigid transformation. After that the segmentation of the first image, in addition to point-models are transformed to the input image. The detailed transformed segmentation provides the scala volume size. Using the transformed point-models, the A-value, the central scala lengths, the lateral and the organ of corti scala tympani lengths are computed. The methods have been tested using clinical 3D images of total 67 patients: from Germany (41 patients) and Egypt (26 patients). The atients are of different ages and gender. The number of images used in the experiments is 217, which are multi-modal 3D clinical images from CT, CBCT, and MRI scanners. The proposed methods are compared to the state of the arts ptimizers related medical image registration methods e.g. fast adaptive stochastic gradient descent (FASGD) and efficient preconditioned tochastic gradient descent (EPSGD). The comparison used the root mean squared distance (RMSE) between the ground truth landmarks and the resulted landmarks. The landmarks are located manually by two experts to represent the round window and the top of the cochlea. After obtaining the transformation using ACIR, the landmarks of the moving image are transformed using the resulted transformation and RMSE of the transformed landmarks, and at the same time the fixed image landmarks are computed. I also used the active length of the cochlea implant electrodes to compute the error aroused by the image artifact, and I found out an error ranged from 0.5 mm to 1.12 mm. ACIR method’s RMSE average was 0.36 mm with a standard deviation (SD) of 0.17 mm. The total time average required for registration of an image pair using ACIR was 4.62 seconds with SD of 1.19 seconds. All experiments are repeated 3 times for justifications. Comparing the RMSE of ACIR2017 and ACIR2020 using paired T-test shows no significant difference (p-value = 0.17). The total RMSE average of ACA method was 0.61 mm with a SD of 0.22 mm. The total time average required for analysing an image was 5.21 seconds with SD of 0.93 seconds. The statistical tests show that there is no difference between the results from automatic A-value method and the manual A-value method (p-value = 0.42). There is no difference also between length’s measurements of the left and the right ear sides (p-value > 0.16). Comparing the results from German and Egypt dataset shows there is no difference when using manual or automatic A-value methods (p-value > 0.20). However, there is a significant difference when using ACA2000 method between the German and the Egyptian results (p-value < 0.001). The average time to obtain the segmentation and all measurements was 5.21 second per image. The cochlea scala tympani volume size ranged from 38.98 mm3 to 57.67 mm3 . The combined scala media and scala vestibuli volume size ranged from 34.98 mm 3 to 49.3 mm 3 . The overall volume size of the cochlea should range from 73.96 mm 3 to 106.97 mm 3 . The lateral wall length of scala tympani ranged from 42.93 mm to 47.19 mm. The organ-of-Corti length of scala tympani ranged from 31.11 mm to 34.08 mm. Using the A-value method, the lateral length of scala tympani ranged from 36.69 mm to 45.91 mm. The organ-of-Corti length of scala tympani ranged from 29.12 mm to 39.05 mm. The length from ACA2020 method can be visualised and has a well-defined endpoints. The ACA2020 method works on different modalities and different images despite the noise level or the resolution. In the other hand, the A-value method works neither on MRI nor noisy images. Hence, ACA2020 method may provide more reliable and accurate measurement than the A-value method. The source-code and the datasets are made publicly available to help reproduction and validation of my result.

Reactive local algorithms are distributed algorithms which suit the needs of battery-powered, large-scale wireless ad hoc and sensor networks particularly well. By avoiding both unnecessary wireless transmissions and proactive maintenance of neighborhood tables (i.e., beaconing), such algorithms minimize communication load and overhead, and scale well with increasing network size. This way, resources such as bandwidth and energy are saved, and the probability of message collisions is reduced, which leads to an increase in the packet reception ratio and a decrease of latencies.
Currently, the two main application areas of this algorithm type are geographic routing and topology control, in particular the construction of a node's adjacency in a connected, planar representation of the network graph. Geographic routing enables wireless multi-hop communication in the absence of any network infrastructure, based on geographic node positions. The construction of planar topologies is a requirement for efficient, local solutions for a variety of algorithmic problems.
This thesis contributes to reactive algorithm research in two ways, on an abstract level, as well as by the introduction of novel algorithms:
For the very first time, reactive algorithms are considered as a whole and as an individual research area. A comprehensive survey of the literature is given which lists and classifies known algorithms, techniques, and application domains. Moreover, the mathematical concept of O- and Omega-reactive local topology control is introduced. This concept unambiguously distinguishes reactive from conventional, beacon-based, topology control algorithms, serves as a taxonomy for existing and prospective algorithms of this kind, and facilitates in-depth investigations of the principal power of the reactive approach, beyond analysis of concrete algorithms.
Novel reactive local topology control and geographic routing algorithms are introduced under both the unit disk and quasi unit disk graph model. These algorithms compute a node's local view on connected, planar, constant stretch Euclidean and topological spanners of the underlying network graph and route messages reactively on these spanners while guaranteeing the messages' delivery. All previously known algorithms are either not reactive, or do not provide constant Euclidean and topological stretch properties. A particularly important partial result of this work is that the partial Delaunay triangulation (PDT) is a constant stretch Euclidean spanner for the unit disk graph.
To conclude, this thesis provides a basis for structured and substantial research in this field and shows the reactive approach to be a powerful tool for algorithm design in wireless ad hoc and sensor networking.

Graph-based data formats are flexible in representing data. In particular semantic data models, where the schema is part of the data, gained traction and commercial success in recent years. Semantic data models are also the basis for the Semantic Web - a Web of data governed by open standards in which computer programs can freely access the provided data. This thesis is concerned with the correctness of programs that access semantic data. While the flexibility of semantic data models is one of their biggest strengths, it can easily lead to programmers accidentally not accounting for unintuitive edge cases. Often, such exceptions surface during program execution as run-time errors or unintended side-effects. Depending on the exact condition, a program may run for a long time before the error occurs and the program crashes.
This thesis defines type systems that can detect and avoid such run-time errors based on schema languages available for the Semantic Web. In particular, this thesis uses the Web Ontology Language (OWL) and its theoretic underpinnings, i.e., description logics, as well as the Shapes Constraint Language (SHACL) to define type systems that provide type-safe data access to semantic data graphs. Providing a safe type system is an established methodology for proving the absence of run-time errors in programs without requiring execution. Both schema languages are based on possible world semantics but differ in the treatment of incomplete knowledge. While OWL allows for modelling incomplete knowledge through an open-world semantics, SHACL relies on a fixed domain and closed-world semantics. We provide the formal underpinnings for type systems based on each of the two schema languages. In particular, we base our notion of types on sets of values which allows us to specify a subtype relation based on subset semantics. In case of description logics, subsumption is a routine problem. For
the type system based on SHACL, we are able to translate it into a description
logic subsumption problem.

Empirical studies in software engineering use software repositories as data sources to understand software development. Repository data is either used to answer questions that guide the decision-making in the software development, or to provide tools that help with practical aspects of developers’ everyday work. Studies are classified into the field of Empirical Software Engineering (ESE), and more specifically into Mining Software Repositories (MSR). Studies working with repository data often focus on their results. Results are statements or tools, derived from the data, that help with practical aspects of software development. This thesis focuses on the methods and high order methods used to produce such results. In particular, we focus on incremental methods to scale the processing of repositories, declarative methods to compose a heterogeneous analysis, and high order methods used to reason about threats to methods operating on repositories. We summarize this as technical and methodological improvements. We contribute the improvements to methods and high-order methods in the context of MSR/ESE to produce future empirical results more effectively. We contribute the following improvements. We propose a method to improve the scalability of functions that abstract over repositories with high revision count in a theoretically founded way. We use insights on abstract algebra and program incrementalization to define a core interface of highorder functions that compute scalable static abstractions of a repository with many revisions. We evaluate the scalability of our method by benchmarks, comparing a prototype with available competitors in MSR/ESE. We propose a method to improve the definition of functions that abstract over a repository with a heterogeneous technology stack, by using concepts from declarative logic programming and combining them with ideas on megamodeling and linguistic architecture. We reproduce existing ideas on declarative logic programming with languages close to Datalog, coming from architecture recovery, source code querying, and static program analysis, and transfer them from the analysis of a homogeneous to a heterogeneous technology stack. We provide a prove-of-concept of such method in a case study. We propose a high-order method to improve the disambiguation of threats to methods used in MSR/ESE. We focus on a better disambiguation of threats, operationalizing reasoning about them, and making the implications to a valid data analysis methodology explicit, by using simulations. We encourage researchers to accomplish their work by implementing ‘fake’ simulations of their MSR/ESE scenarios, to operationalize relevant insights about alternative plausible results, negative results, potential threats and the used data analysis methodologies. We prove that such way of simulation based testing contributes to the disambiguation of threats in published MSR/ESE research.

The goal of this PhD thesis is to investigate possibilities of using symbol elimination for solving problems over complex theories and analyze the applicability of such uniform approaches in different areas of application, such as verification, knowledge representation and graph theory. In the thesis we propose an approach to symbol elimination in complex theories that follows the general idea of combining hierarchical reasoning with symbol elimination in standard theories. We analyze how this general approach can be specialized and used in different areas of application.
In the verification of parametric systems it is important to prove that certain safety properties hold. This can be done by showing that a property is an inductive invariant of the system, i.e. it holds in the initial state of the system and is invariant under updates of the system. Sometimes this is not the case for the condition itself, but for a stronger condition it is. In this thesis we propose a method for goal-directed invariant strengthening.
In knowledge representation we often have to deal with huge ontologies. Combining two ontologies usually leads to new consequences, some of which may be false or undesired. We are interested in finding explanations for such unwanted consequences. For this we propose a method for computing interpolants in the description logics EL and EL⁺, based on a translation to the theory of semilattices with monotone operators and a certain form of interpolation in this theory.
In wireless network theory one often deals with classes of geometric graphs in which the existence or non-existence of an edge between two vertices in a graph relies on properties on their distances to other nodes. One possibility to prove properties of those graphs or to analyze relations between the graph classes is to prove or disprove that one graph class is contained in the other. In this thesis we propose a method for checking inclusions between geometric graph classes.