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Blockchains in public administration : a RADIUS on blockchain framework for public administration
(2023)
The emergence of blockchain technology has generated a great deal of attention, as reflected in numerous scientific and journalistic articles. However, the implementation of blockchain for public administrations in Germany has encountered a setback owing to unsuccessful initiatives. Initial enthusiasm was followed by disillusionment. Nevertheless, technology continues to evolve. This paper examines whether the use of a blockchain can still optimize the processes of public administrations. Not only the failed projects are analysed, but also more current applications of the technology and their potential relevance for the administration, especially in the state of Hesse.
To answer if blockchains are promising to administrations, a Design Science Research (DSR) research approach is chosen. The DSR method is a research-based approach that aims to create new and innovative solutions to real-world problems through the development and evaluation of artefacts such as models, methods, or prototypes. For this work, the implementation of a framework to realize an Authentication, Authorization, and Accounting (AAA) system on the blockchain was identified as profitable. The framework aims to implement the aforementioned AAA tasks using a blockchain. The Remote Authentication Dial-In User Service (RADIUS) protocol has been identified as a potential protocol of the AAA system. The goal is to create a way to implement the system either entirely on a blockchain or as a hybrid system. Various blockchain technologies will be considered. Suitable for development, the framework AAA-me is named.
The development of AAA-me has shown that the desired framework for implementing RADIUS on the blockchain is possible in various degrees of implementation. Previous work mostly relied on full development. Additionally, it has been shown that AAA-me can be used to perform hybrid integration at different implementation levels. This makes AAA-me stand out from the few hybrid previous approaches. Furthermore, AAA-me was investigated in different laboratory environments. This was to determine the expected resilience against Single Point of Failure (SPOF). The results of the lab investigation indicated that a RADIUS system on top of a blockchain can provide benefits in terms of security and performance. In the lab environment, times were measured within which a series of authorization requests were processed. In addition, it was illustrated how a RADIUS system implemented using blockchain can protect itself against Man-in-the-Middle (MITM) attacks.
Finally, in collaboration with the Hessian Central Office for Data Processing (German: Hessische Zentrale für Datenverarbeitung) (HZD), another test lab demonstrated how a RADIUS system on the blockchain can integrate with the existing IT systems of the German state of Hesse. Based on these findings, this work reevaluated the applicability of blockchain technology for public administration processes.
The work has thus shown that the use of a blockchain can still be purposeful. However, it has also been shown that an implementation can bring many problems with it. The small number of blockchain developers and engineers also poses the risk of finding people to develop and maintain a system. In addition, one faces the problem of determining an architecture now that will be applied to many projects in the future. However, each project can, in turn, have an impact on the choice of architecture. Once one has solved this problem and a blockchain infrastructure is available, it can be established quickly and be more SPOF resistant, for example, for Public Key Infrastructure (PKI) systems.
AAA-me was only applied in lab and test environments. As a result, no real data ran over its own infrastructure. This allowed the necessary flexibility for development. However, system-related properties could appear in real situations that are not detectable here in this way. Furthermore, the initial stage of AAA-me’s development is still in its infancy. Many manual adjustments need to be made in order for this to integrate with an existing RADIUS system. Also, no system security effort in and of itself has been carried out in the lab environments. Thus, vulnerabilities can quickly open up on web servers due to misconfigurations and missing updates. For the above reasons, productive use should be discouraged unless major developments are carried out.
This dissertation is concerned with the task of map-based self-localization, using images of the ground recorded with a downward-facing camera. In this context, map-based (self-)localization is the task of determining the position and orientation of a query image that is to be localized. The map used for this purpose consists of a set of reference images with known positions and orientations in a common coordinate system. For localization, the considered methods determine correspondences between features of the query image and those of the reference images.
In comparison with localization approaches that use images of the surrounding environment, we expect that using images of the ground has the advantage that, unlike the surrounding, the visual appearance of the ground is often long-term stable. Also, by using active lighting of the ground, localization becomes independent of external lighting conditions.
This dissertation includes content of several published contributions, which present research on the development and testing of methods for feature-based localization of ground images. Our first contribution examines methods for the extraction of image features that have not been designed to be used on ground images. This survey shows that, with appropriate parametrization, several of these methods are well suited for the task.
Based on this insight, we develop and examine methods for various subtasks of map-based localization in the following contributions. We examine global localization, where all reference images have to be considered, as well as local localization, where an approximation of the query image position is already known, which allows for disregarding reference images with a large distance to this position.
In our second contribution, we present the first systematic comparison of state-of-the-art methods for ground texture based localization. Furthermore, we present a method, which is characterized by its usage of our novel feature matching technique. This technique is called identity matching, as it matches only those features with identical descriptors, in contrast to the state-of-the-art that also matches features with similar descriptors. We show that our method is well suited for global and local localization, as it has favorable scaling with the number of reference images considered during the localization process. In another contribution, we develop a variant of our localization method that is significantly faster to compute, as it applies a sampling approach to determine the image positions at which local features are extracted, instead of using classical feature detectors.
Two further contributions are concerned with global localization. The first one introduces a prediction model for the global localization performance, based on an evaluation of the local localization performance. This allows us to quickly evaluate any considered parameter settings of global localization methods. The second contribution introduces a learning-based method that computes compact descriptors of ground images. This descriptor can be used to retrieve the overlapping reference images of a query image from a large set of reference images with little computational effort.
The most recent contribution included in this dissertation presents a new ground image database, which was recorded with a dedicated platform using a downward-facing camera. In addition to the data, we also explain our guidelines for the construction of the platform. In comparison with existing databases, our database contains more images and presents a larger variety of ground textures. Furthermore, this database enables us to perform the first systematic evaluation of how localization performance is affected by the time interval between the point in time at which the reference images are recorded and the point in time at which the query image is recorded. We find out that for outdoor areas all ground texture based localization methods have reliability issues, if the time interval between the recording of the query and reference images is large, and also if there are different weather conditions. These findings point to remaining challenges in ground texture base localization that should be addressed in future work.
Matroids are combinatorial objects that generalize linear independence. A matroid can be represented geometrically by its Bergman fan and we compare the symmetries of these two objects. Sometimes, the Bergman fan has additional automorphisms, which are related to Cremona transformations in projective space. Their existence depends on a combinatorial property of the matroid, as has been shown by Shaw and Werner, and we study the consequences for the structure of such matroids. This allows us to gain a better understanding of the so-called Cremona group of a matroid and we apply our results to root system matroids.
Das adaptive Immunsystem schützt den Menschen vor extra- wie auch intrakorporal auftretenden Pathogenen und Krebszellen. Die Funktionalität dieses Prozesses geht hierbei auf die Interaktion und Kooperation einer Vielzahl verschiedener Zelltypen des Körpers zurück und ist vorwiegend innerhalb der Lymphknoten lokalisiert. Ist auch nur ein Bestandteil dieses sensiblen Prozesses gestört, kann dies zu einem teilweisen oder vollständigen Verlust der immunologischen Fitness des Menschen führen. Daher war es das Ziel dieser Arbeit, solche Aberrationen des humanen Lymphknotengewebes umfassend digital-pathologisch zu detektieren und zu definieren.
Hierfür wurde zunächst eine digitale Gewebedatenbank etabliert. Diese basiert auf dem im Rahmen dieser Arbeit implementierten Content-Management-System Digital Tissue Management Suite. Weiterhin wurde die Software Feature analysis in tissue histomorphometry entwickelt, welche die Analyse von zweidimensionalen whole slide images ermöglicht. Hierbei werden Methoden aus dem Bereich Computer Vision und Graphentheorie eingesetzt, um morphologische und distributionale Eigenschaften der Zelltypen des Lymphknotens zu charakterisieren. Darüber hinaus enthält diese Software Plug-ins zur Visualisierung und statistischen Analyse der Daten.
Aufbauend auf der eigens implementierten, digitalen Infrastruktur, in Kombination mit der Software Imaris wurden zweidimensional und dreidimensional gescannte, reaktive und neoplastische Gewebeproben digital phänotypisiert. Hierbei konnten neue mechanische Barrieren zur Kompartimentalisierung der Keimzentren aufgeklärt werden. Weiterhin konnte der Erhalt des quantitativen Verhältnisses einzelner Zellpopulationen innerhalb der Keimzentren beschrieben werden. Ausgehend von den reaktiven Phänotypen des Lymphknotens, wurden pathophysiologische Aberrationen in verschiedenen lymphatischen Neoplasien untersucht. Hierbei konnte gezeigt werden, dass speziell die strukturelle Destruktion häufig mit einer morphologischen Veränderung der fibroblastischen Retikulumzellen einhergeht.
Neben strukturellen Veränderungen sind auch zytologische Veränderungen der Tumormikroumgebung zu verzeichnen. Eine besondere Rolle spielen hierbei sogenannte Tumor-assoziierte Makrophagen. Im Rahmen dieser Arbeit konnte gezeigt werden, dass speziell Makrophagen in der Tumormikroumgebung des diffus großzelligen B-Zell-Lymphoms und der chronisch lymphatischen Leukämie spezifische pathophysiologische Veränderungen aufzeigen. Auch konnte gezeigt werden, dass genetische Änderungen neoplastischer B-Zellen mit einer generellen Reduktion der CD20-Antigendichte einhergehen.
Zusammenfassend ermöglichten die Ergebnisse die Generierung eines umfassenden digital-pathologischen Profils des klassischen Hodgkin-Lymphoms. Hierbei konnten morphologische Veränderungen neoplastischer, CD30-positiver Hodgkin-Reed-Sternberg-Zellen validiert und beschrieben werden. Auch konnten pathologische Veränderungen des Konnektoms und der Tumormikroumgebung dieser Zellen parametrisiert und quantifiziert werden. Abschließend wurde unter Anwendung eines Random forest-Klassifikators die diagnostische Potenz digital-pathologischer Profile evaluiert und validiert.
The single-source shortest-path problem is a fundamental problem in computer science. We consider a generalization of the shortest-path problem, the $k$-shortest path problem. Let $G$ be a directed edge-weighted graph with $n$ nodes and $m$ edges and $s,t$ be two fixed nodes. The goal is to compute $k$ paths $P_1,\dots,P_k$ between two fixed nodes $s$ and $t$ in non-decreasing order of their length such that all other paths between $s$ and $t$ are at least as long as the $k$\nth path $P_k$. We focus on the version of the $k$-shortest path problem where the paths are not allowed to visit nodes multiple times, sometime referred to as $k$-shortest simple path problem.
The probably best known $k$-shortest path algorithm is Yen's algorithm. It has a worst-case time complexity of O(kn\cdot scp(n,m)), where scp(n,m) is the complexity of the single-source shortest-path algorithm used as a subroutine. In case of Dijkstra's algorithm scp(n,m) is O(m + n\log n). One of the more recent improvements of Yen's algorithm is by Feng.
Even though Feng's algorithm is much faster in practice, it has the same worst-case complexity as Yen's algorithm.
The main results presented in this thesis are upper bounds on the average-case of Yen's and Feng's algorithm, as well as practical improvements and a parallel implementation of Yen's and Feng's algorithms including these improvements. The implementation is publicly available under GPLv3 open source license.
We show in our analysis that Yen's algorithm has an average-case complexity of O(k \log(n)\cdot scp(n,m)) on G(n,p) graphs with at least logarithmic average-degree and random edge weights following a distribution with certain properties.
On G(n,p) graphs with constant to logarithmic average-degree and uniform random edge-weights over $[0;1]$, we show an average-case complexity of O(k\cdot\frac{\log^2 n}{np}\cdot scp(n,m)). Feng's algorithm has an even better average-case complexity of O(k\cdot scp(n,m)) on unweighted G(n,p) graphs with logarithmic average-degree and for constant values of $k$. We further provide evidence that the same holds true for G(n,p) graphs with uniform random edge-weights over $[0;1]$.
On the practical side, we suggest new heuristics to prune even more single-source shortest-path computations than Feng's algorithm and evaluate all presented algorithms on G(n,p) and Grid graphs with up to 256 million nodes. We demonstrate speedups by a factor of up to 40 compared to Feng's algorithm.
Finally we discuss two ways to parallelize the suggested algorithms and evaluate them on grid graphs showing speedups by a factor of 2 using 4 threads and by a factor of up to 8 using 16 threads, respectively.
Cyber Physical Systems (CPS) are growing more and more complex due to the availability of cheap hardware, sensors, actuators and communication links. A network of cooperating CPSs (CPN) additionally increases the complexity. This poses challenges as well as it offers chances: the increasing complexity makes it harder to design, operate, optimize and maintain such CPNs. However, on the other side an appropriate use of the increasing resources in computational nodes, sensors, actuators can significantly improve the system performance, reliability and flexibility. Therefore, self-X features like self-organization, self-adaptation and self-healing are key principles for such systems.
Additionally, CPNs are often deployed in dynamic, unpredictable environments and safety-critical domains, such as transportation, energy, and healthcare. In such domains, usually applications of different criticality level exist. In an automotive environment for example, the brake has a higher criticality level regarding safety as the infotainment. As a result of mixed-criticality, applications requiring hard real-time guarantees compete with those requiring soft real-time guarantees and best-effort application for the given resources within the overall system. This leads to the need to accommodate multiple levels of criticality while ensuring safety and reliability, which increases the already high complexity even more.
This thesis deals with the question on how to conveniently, effectively and efficiently handle the management and complexity of mixed-critical CPNs (MC-CPNs). Since this cannot be done by the system developer without the assistance of the system itself any longer, it is essential to develop new approaches and techniques to ensure that such systems can operate under a range of conditions while meeting stringent requirements.
Based on five research hypothesis, this thesis introduces a comprehensive adaptive mixed-criticality supporting middleware for Cyber-Physical Networks (Chameleon), which efficiently and autonomously takes care of the management and complexity of CPNs with regard to the mixed-criticality aspect.
Chameleon contributes to the state-of-art by introducing and combining the following concepts:
- A comprehensive self-adaption mechanism on all levels of the system model is provided.
- This mechanism allows a flexible combination of parametric and structural adaptation actions (relocation, scheduling, tuning, ...) to modify the behavior of the system.
- Real-time constraints of mixed-critical applications (hard real-time, soft real-time, best-effort) are considered in all possible adaptation conditions and actions by the use of the importance parameter.
- CPNs are supported by the introduction of different scopes (local, system, global) for the adaptation conditions and actions. This also enables the combination of different scopes for conditions and actions.
- The realization of the adaptation with a MAPE-K loop instantiated by a distributed LCS allows for real-time capable reasoning of adaptation actions which also works on resource-spare systems.
- The developed rule language Rango offers an intuitive way to specify an initial rule set for LCS in the context of CPS/CPNs and supports the system administrators in the process of rule set generation.
Proteins are biological macromolecules playing essential roles in all living organisms.
Proteins often bind with each other forming complexes to fulfill their function. Such protein complexes assemble along an ordered pathway. An assembled protein complex can often be divided into structural and functional modules. Knowing the order of assembly and the modules of a protein complex is important to understand biological processes and treat diseases related to misassembly.
Typical structures of the Protein Data Bank (PDB) contain two to three subunits and a few thousand atoms. Recent developments have led to large protein complexes being resolved. The increasing number and size of the protein complexes demand for computational assistance for the visualization and analysis. One such large protein complex is respiratory complex I accounting for 45 subunits in Homo sapiens.
Complex I is a well understood protein complex that served as case study to validate our methods.
Our aim was to analyze time-resolved Molecular Dynamics (MD) simulation data, identify modules of a protein complex and generate hypotheses for the assembly pathway of a protein complex. For that purpose, we abstracted the topology of protein complexes to Complex Graphs of the Protein Topology Graph Library (PTGL). The subunits are represented as vertices, and spatial contacts as edges. The edges are weighted with the number of contacts based on a distance threshold. This allowed us to apply graph-theoretic methods to visualize and analyze protein complexes.
We extended the implementations of two methods to achieve a computation of Complex Graphs in feasible runtimes. The first method skipped checks for contacts using the information which residues are sequential neighbors. We extended the method to protein complexes and structures containing ligands. The second method introduced spheres encompassing all atoms of a subunit and skipped the check for contacts if the corresponding spheres do not overlap. Both methods combined allowed skipping up to 93 % of the checks for contacts for sample complexes of 40 subunits compared to up to 10 % of the previous implementation. We showed that the runtime of the combined method scaled linearly with the number of atoms compared to a non-linear scaling of the previous implementation We implemented a third method fixing the assignment of an orientation to secondary structure elements. We placed a three-dimensional vector in each secondary structure element and computed the angle between secondary structure elements to assign an orientation. This method sped up the runtime especially for large structures, such as the capsid of human immunodeficiency virus, for which the runtime decreased from 43 to less than 9 hours.
The feasible runtimes allowed us to investigate two data sets of MD trajectories of respiratory complex I of Thermus thermophilus that we received. The data sets differ only by whether ubiquinone is bound to the complex. We implemented a pipeline, PTGLdynamics, to compute the contacts and Complex Graphs for all time steps of the trajectories. We investigated different methods to track changes of contacts during the simulation and created a heat map put onto the three-dimensional structure visualizing the changes. We also created line plots to visualize the changes of contacts over the course of the simulation. Both visualizations helped spotting outstandingly flexible or rigid regions of the structure or time points of the simulation in which major dynamics occur.
We introduced normalizations of the edge weights of Complex Graphs for identi-fying modules and predicting the assembly pathway. The idea is to normalize the number of contacts for the number of residues of a subunit. We defined five different normalizations.
To identify structural and functional modules, we applied the Leiden graph clustering algorithm to the Complex Graphs of respiratory complex I and the respiratory supercomplex. We examined the results for the different normalizations of the weights of the Complex Graphs. The absolute edge weight produced the best result identifying three of four modules that have been defined in the literature for respiratory complex I.
We applied agglomerative hierarchical clustering to the edges of a Complex Graph to create hypotheses of the assembly pathway. The rationale was that subunits with an extensive interface in the final structure assemble early. We tested our method against two existing methods on a data set of 21 proteins with reported assembly pathways. Our prediction outperformed the other methods and ran in feasible runtimes of a few minutes at most.
We also tested our method on respiratory complex I, the respiratory supercomplex and the respiratory megacomplex. We compared the results for the different normalizations with an assembly pathway of respiratory complex I described in the literature. We transformed the assembly pathways to dendrograms and compared the predictions to the reference using the Robinson-Foulds distance and clustering information distance. We analyzed the landscape of the clustering information distance by generating random dendrograms and showed that our result is far better than expected at random. We showed in a detailed analysis that the assembly prediction using one normalization was able to capture key features of the assembly pathway that has been proposed in the literature.
In conclusion, we presented different applications of graph theory to automatically analyze the topology of protein complexes. Our programs run in feasible runtimes even for large complexes. We showed that graph-theoretic modeling of the protein structure can be used to analyze MD simulation data, identify modules of protein complexes and predict assembly pathways.
This thesis presents a first-of-its-kind phenomenological framework that formally describes the development of acquired epilepsy and the role of the neuro-immune axis in this development. Formulated as a system of nonlinear differential equations, the model describes the interaction of processes such as neuroinflammation, blood- brain barrier disruption, neuronal death, circuit remodeling, and epileptic seizures. The model allows for the simulation of epilepsy development courses caused by a variety of neurological injuries. The simulation results are in agreement with ex- perimental findings from three distinct animal models of epileptogenesis. Simula- tions capture injury-specific temporal patterns of seizure occurrence, neuroinflam- mation, blood-brain barrier leakage, and progression of neuronal death. In addition, the model provides insights into phenomena related to epileptogenesis such as the emergence of paradoxically long time scales of disease development after injury, the dose-dependence of epileptogenesis features on injury severity, and the variability of clinical outcomes in subjects exposed to identical injury. Moreover, the developed framework allows for the simulation of therapeutic interventions, which provides insights into the injury-specificity of prominent intervention strategies. Thus, the model can be used as an in silico tool for the generation of testable predictions, which may aid pre-clinical research for the development of epilepsy treatments.
In the recent past, we are making huge progress in the field of Artificial Intelligence. Since the rise of neural networks, astonishing new frontiers are continuously being discovered. The development is so fast that overall no major technical limits are in sight. Hence, digitization has expanded from the base of academia and industry to such an extent that it is prevalent in the politics, mass media and even popular arts. The DFG-funded project Specialized Information Service for Biodiversity Research and the BMBF-funded project Linked Open Tafsir can be placed exactly in that overall development. Both projects aim to build an intelligent, up-to-date, modern research infrastructure on biodiversity and theological studies for scholars researching in these respective fields of historical science. Starting from digitized German and Arabic historical literature containing so far unavailable valuable knowledge on biodiversity and theological studies, at its core, our dissertation targets to incorporate state-of-the-art Machine Learning methods for analyzing natural language texts of low-resource languages and enabling foundational Natural Language Processing tasks on them, such as Sentence Boundary Detection, Named Entity Recognition, and Topic Modeling. This ultimately leads to paving the way for new scientific discoveries in the historical disciplines of natural science and humanities. By enriching the landscape of historical low-resource languages with valuable annotation data, our work becomes part of the greater movement of digitizing the society, thus allowing people to focus on things which really matter in science and industry.
Die Emergenz digitaler Netzwerke ist auf die ständige Entwicklung und Transformation neuer Informationstechnologien zurückzuführen.
Dieser Strukturwandel führt zu äußerst komplexen Systemen in vielen verschiedenen Lebensbereichen.
Es besteht daher verstärkt die Notwendigkeit, die zugrunde liegenden wesentlichen Eigenschaften von realen Netzwerken zu untersuchen und zu verstehen.
In diesem Zusammenhang wird die Netzwerkanalyse als Mittel für die Untersuchung von Netzwerken herangezogen und stellt beobachtete Strukturen mithilfe mathematischer Modelle dar.
Hierbei, werden in der Regel parametrisierbare Zufallsgraphen verwendet, um eine systematische experimentelle Evaluation von Algorithmen und Datenstrukturen zu ermöglichen.
Angesichts der zunehmenden Menge an Informationen, sind viele Aspekte der Netzwerkanalyse datengesteuert und zur Interpretation auf effiziente Algorithmen angewiesen.
Algorithmische Lösungen müssen daher sowohl die strukturellen Eigenschaften der Eingabe als auch die Besonderheiten der zugrunde liegenden Maschinen, die sie ausführen, sorgfältig berücksichtigen.
Die Generierung und Analyse massiver Netzwerke ist dementsprechend eine anspruchsvolle Aufgabe für sich.
Die vorliegende Arbeit bietet daher algorithmische Lösungen für die Generierung und Analyse massiver Graphen.
Zu diesem Zweck entwickeln wir Algorithmen für das Generieren von Graphen mit vorgegebenen Knotengraden, die Berechnung von Zusammenhangskomponenten massiver Graphen und zertifizierende Grapherkennung für Instanzen, die die Größe des Hauptspeichers überschreiten.
Unsere Algorithmen und Implementierungen sind praktisch effizient für verschiedene Maschinenmodelle und bieten sequentielle, Shared-Memory parallele und/oder I/O-effiziente Lösungen.
Antimicrobial resistant infections arise as a consequential response to evolutionary mechanisms within microbes which cause them to be protected from the effects of antimicrobials. The frequent occurrence of resistant infections poses a global public health threat as their control has become challenging despite many efforts. The dynamics of such infections are driven by processes at multiple levels. For a long time, mathematical models have proved valuable for unravelling complex mechanisms in the dynamics of infections. In this thesis, we focus on mathematical approaches to modelling the development and spread of resistant infections at between-host (population-wide) and within-host (individual) levels.
Within an individual host, switching between treatments has been identified as one of the methods that can be employed for the gradual eradication of resistant strains on the long term. With this as motivation, we study the problem using dynamical systems and notions from control theory. We present a model based on deterministic logistic differential equations which capture the general dynamics of microbial resistance inside an individual host. Fundamentally, this model describes the spread of resistant infections whilst accounting for evolutionary mutations observed in resistant pathogens and capturing them in mutation matrices. We extend this model to explore the implications of therapy switching from a control theoretic perspective by using switched systems and developing control strategies with the goal of reducing the appearance of drug resistant pathogens within the host.
At the between-host level, we use compartmental models to describe the transmission of infection between multiple individuals in a population. In particular, we make a case study of the evolution and spread of the novel coronavirus (SARS-CoV-2) pandemic. So far, vaccination remains a critical component in the eventual solution to this public health crisis. However, as with many other pathogens, vaccine resistant variants of the virus have been a major concern in control efforts by governments and all stakeholders. Using network theory, we investigate the spread and transmission of the disease on social networks by compartmentalising and studying the progression of the disease in each compartment, considering both the original virus strain and one of its highly transmissible vaccine-resistant mutant strains. We investigate these dynamics in the presence of vaccinations and other interventions. Although vaccinations are of absolute importance during viral outbreaks, resistant variants coupled with population hesitancy towards vaccination can lead to further spread of the virus.
We thoroughly study the properties of conically stable polynomials and imaginary projections. A multivariate complex polynomial is called stable if its nonzero whenever all coordinates of the respective argument have a positive imaginary part. In this dissertation we consider the generalized notion of K-stability. A multivariate complex polynomial is called K-stable if its non-zero whenever the imaginary part of the respective argument lies in the relative interior of the cone K. We study connections to various other objects, including imaginary projections as well as preservers and combinatorial criteria for conically stable polynomials.
People can describe spatial scenes with language and, vice versa, create images based on linguistic descriptions. However, current systems do not even come close to matching the complexity of humans when it comes to reconstructing a scene from a given text. Even the ever-advancing development of better and better Transformer-based models has not been able to achieve this so far. This task, the automatic generation of a 3D scene based on an input text, is called text-to-3D scene generation. The key challenge, and focus of this dissertation, now relate to the following topics:
(a) Analyses of how well current language models understand spatial information, how static embeddings compare, and whether they can be improved by anaphora resolution.
(b) Automated resource generation for context expansion and grounding that can help in the creation of realistic scenes.
(c) Creation of a VR-based text-to-3D scene system that can be used as an annotation and active-learning environment, but can also be easily extended in a modular way with additional features to solve more contexts in the future.
(d) Analyze existing practices and tools for digital and virtual teaching, learning, and collaboration, as well as the conditions and strategies in the context of VR.
In the first part of this work, we could show that static word embeddings do not benefit significantly from pronoun substitution. We explain this result by the loss of contextual information, the reduction in the relative occurrence of rare words, and the absence of pronouns to be substituted. But we were able to we have shown that both static and contextualizing language models appear to encode object knowledge, but require a sophisticated apparatus to retrieve it. The models themselves in combination with the measures differ greatly in terms of the amount of knowledge they allow to extract.
Classifier-based variants perform significantly better than the unsupervised methods from bias research, but this is also due to overfitting. The resources generated for this evaluation are later also an important component of point three.
In the second part, we present AffordanceUPT, a modularization of UPT trained on the HICO-DET dataset, which we have extended with Gibsonien/telic annotations. We then show that AffordanceUPT can effectively make the Gibsonian/telic distinction and that the model learns other correlations in the data to make such distinctions (e.g., the presence of hands in the image) that have important implications for grounding images to language.
The third part first presents a VR project to support spatial annotation respectively IsoSpace. The direct spatial visualization and the immediate interaction with the 3D objects should make the labeling more intuitive and thus easier. The project will later be incorporated as part of the Semantic Scene Builder (SeSB). The project itself in turn relies on the Text2SceneVR presented here for generating spatial hypertext, which in turn is based on the VAnnotatoR. Finally, we introduce Semantic Scene Builder (SeSB), a VR-based text-to-3D scene framework using Semantic Annotation Framework (SemAF) as a scheme for annotating semantic relations. It integrates a wide range of tools and resources by utilizing SemAF and UIMA as a unified data structure to generate 3D scenes from textual descriptions and also supports annotations. When evaluating SeSB against another state-of-the-art tool, it was found that our approach not only performed better, but also allowed us to model a wider variety of scenes. The final part reviews existing practices and tools for digital and virtual teaching, learning, and collaboration, as well as the conditions and strategies needed to make the most of technological opportunities in the future.
In the human brain, the incoming light to the retina is transformed into meaningful representations that allow us to interact with the world. In a similar vein, the RGB pixel values are transformed by a deep neural network (DNN) into meaningful representations relevant to solving a computer vision task it was trained for. Therefore, in my research, I aim to reveal insights into the visual representations in the human visual cortex and DNNs solving vision tasks.
In the previous decade, DNNs have emerged as the state-of-the-art models for predicting neural responses in the human and monkey visual cortex. Research has shown that training on a task related to a brain region’s function leads to better predictivity than a randomly initialized network. Based on this observation, we proposed that we can use DNNs trained on different computer vision tasks to identify functional mapping of the human visual cortex.
To validate our proposed idea, we first investigate a brain region occipital place area (OPA) using DNNs trained on scene parsing task and scene classification task. From the previous investigations about OPA’s functions, we knew that it encodes navigational affordances that require spatial information about the scene. Therefore, we hypothesized that OPA’s representation should be closer to a scene parsing model than a scene classification model as the scene parsing task explicitly requires spatial information about the scene. Our results showed that scene parsing models had representation closer to OPA than scene classification models thus validating our approach.
We then selected multiple DNNs performing a wide range of computer vision tasks ranging from low-level tasks such as edge detection, 3D tasks such as surface normals, and semantic tasks such as semantic segmentation. We compared the representations of these DNNs with all the regions in the visual cortex, thus revealing the functional representations of different regions of the visual cortex. Our results highly converged with previous investigations of these brain regions validating the feasibility of the proposed approach in finding functional representations of the human brain. Our results also provided new insights into underinvestigated brain regions that can serve as starting hypotheses and promote further investigation into those brain regions.
We applied the same approach to find representational insights about the DNNs. A DNN usually consists of multiple layers with each layer performing a computation leading to the final layer that performs prediction for a given task. Training on different tasks could lead to very different representations. Therefore, we first investigate at which stage does the representation in DNNs trained on different tasks starts to differ. We further investigate if the DNNs trained on similar tasks lead to similar representations and on dissimilar tasks lead to more dissimilar representations. We selected the same set of DNNs used in the previous work that were trained on the Taskonomy dataset on a diverse range of 2D, 3D and semantic tasks. Then, given a DNN trained on a particular task, we compared the representation of multiple layers to corresponding layers in other DNNs. From this analysis, we aimed to reveal where in the network architecture task-specific representation is prominent. We found that task specificity increases as we go deeper into the DNN architecture and similar tasks start to cluster in groups. We found that the grouping we found using representational similarity was highly correlated with grouping based on transfer learning thus creating an interesting application of the approach to model selection in transfer learning.
During previous works, several new measures were introduced to compare DNN representations. So, we identified the commonalities in different measures and unified different measures into a single framework referred to as duality diagram similarity. This work opens up new possibilities for similarity measures to understand DNN representations. While demonstrating a much higher correlation with transfer learning than previous state-of-the-art measures we extend it to understanding layer-wise representations of models trained on the Imagenet and Places dataset using different tasks and demonstrate its applicability to layer selection for transfer learning.
In all the previous works, we used the task-specific DNN representations to understand the representations in the human visual cortex and other DNNs. We were able to interpret our findings in terms of computer vision tasks such as edge detection, semantic segmentation, depth estimation, etc. however we were not able to map the representations to human interpretable concepts. Therefore in our most recent work, we developed a new method that associates individual artificial neurons with human interpretable concepts.
Overall, the works in this thesis revealed new insights into the representation of the visual cortex and DNNs...
In this thesis, we cover two intimately related objects in combinatorics, namely random constraint satisfaction problems and random matrices. First we solve a classic constraint satisfaction problem, 2-SAT using the graph structure and a message passing algorithm called Belief Propagation. We also explore another message passing algorithm called Warning Propagation and prove a useful result that can be employed to analyze various type of random graphs. In particular, we use this Warning Propagation to study a Bernoulli sparse parity matrix and reveal a unique phase transition regarding replica symmetry. Lastly, we use variational methods and a version of local limit theorem to prove a sufficient condition for a general random matrix to be of full rank.
Ausgangspunkt der Forschungsarbeit ist der Gebrauch von Gesten in mathematischen Interaktionen von Lernenden. Es wird untersucht, inwiefern Gesten Teil des mathematischen Aushandlungsprozesses sind. Damit ist die Rekonstruktion einer potentiell fachlichen Bedeutung des Gestengebrauchs beim Mathematiklernen das zentrale Forschungsanliegen.
Theoretisch gerahmt wird die Arbeit von Erkenntnissen aus der psychologisch-linguistischen Gestenforschung zur systematischen Beschreibung von Gestik im Zusammenspiel mit der gleichzeitig geäußerten Lautsprache (McNeill, 1992; Kendon, 2004). Es werden ebenso ausgewählte Forschungen zur Gestik beim Mathematiklernen beleuchtet (Arzarello, 2006; Wille, 2020; Kiesow, 2016). Die mathematikdidaktische Interaktionstheorie begründet den sozial-konstruktivistischen Lernbegriff (Krummheuer, 1992). Ausgewählte Aspekte der Semiotik nach C. S. Peirce bieten eine theoretische Fundierung des Zeichenbegriffs und des Kerns mathematischen Agierens, verstanden als diagrammatisches Arbeiten (Peirce, 1931, CP 1.54 u. 1932, CP 2.228).
Von besonderer Bedeutung für die vorliegende Forschungsarbeit ist der linguistische Ansatz der Code-Integration und -Manifestation von redebegleitenden Gesten im Sprachsystem nach Fricke (2007, 2012) in Verbindung mit dem Peirce’schen Diagrammbegriff. Diese Perspektive ermöglicht eine theoretische Fundierung der zunächst empirisch beobachtbaren Multimodalität der Ausdrucksweisen von Lernenden beim gemeinsamen Mathematiktreiben. Der Peirce’sche Diagrammbegriff dient hierbei zur Rekonstruktion einer systemischen Relevanz von Gesten für das Betreiben von Mathematik: Bestimmte Gesten sind semiotisch als mathematische Zeichen beschreibbar und haben potentiell konstituierende Funktion für das diagrammatische Arbeiten der Lernenden. Der übergeordnete Forschungsfokus lautet: Wie nutzen Grundschüler*innen Gestik und Lautsprache, insbesondere in deren Zusammenspiel, um ihre mathematischen Ideen in den interaktiven Aushandlungsprozess einzubringen und über den Verlauf der Interaktion aufzugreifen, möglicherweise weiterzuentwickeln oder auch zu verwerfen? In der Ausdifferenzierung wird die Funktion der verwendeten Gesten und die Rekonstruktion von potentiell gemeinsam gebrauchten Gesten der Interagierenden in den Blick genommen.
Methodisch lässt sich die Forschungsarbeit der qualitativen Sozialforschung (Bohnsack, 2008) bzw. der interpretativen mathematikdidaktischen Unterrichtsforschung zuordnen (Krummheuer & Naujok, 1999). Es werden Beispiele aus mathematischen Interaktionssituationen ausgewertet, in denen sich Paare von Zweitklässler*innen mit einem mathematischen Problem aus der Kombinatorik und der Geometrie beschäftigen. Eine eigens theoriekonform entwickelte Transkriptpartitur dient zur Aufarbeitung der Videodaten. Mit der textbasierten Interaktionsanalyse (Krummheuer, 1992) und der grafisch angelegten Semiotischen Analyse (Schreiber, 2010) in einer Weiterentwicklung der Semiotischen Prozess-Karten (Huth, 2014) werden zwei hierarchisch aufeinander aufbauende Analyseverfahren verwendet.
Zentrale Forschungsergebnisse sind 1) die funktionale und gestalterische Flexibilität des Gestengebrauchs beim diagrammatischen Arbeiten der Lernenden, 2) die Rekonstruktion von Modusschnittstellen der Gesten mit anderen Ausdrucksmodi in Funktion, interaktionaler Bedeutungszuschreibung und Chronologie, und 3) die häufige Verwendung der Gesten als Modus der Wahl der Lernenden in mathematischen Interaktionen. Gesten weisen eine unmittelbare und voraussetzungslose Verfügbarkeit auf, eine funktionale und gestalterische Flexibilität in der mathematischen Auseinandersetzung und die Möglichkeit, Funktionen anderer Modi (vorübergehen) zu übernehmen. Es zeigt sich eine konstitutive und fachliche Bedeutung der Gestik für das mathematisch-diagrammatische Agieren der Lernenden. In der Arbeit wird daraus schließlich das doppelte Kontinuum der Gesten für das Mathematiklernen entwickelt. Es zeigt in der Dimension der Funktion des Gestengebrauchs und der Dimension des Objektbezugs der Gestengestalt die Vielfältigkeit der Gestenfunktionen im gemeinsamen diagrammatischen Arbeiten der Lernenden und gibt Einblick in die verwendeten Gestengestalten.
Die Forschungsarbeit offenbart den Bedarf einer Beachtung von Gesten in der fachdidaktischen Planung und Gestaltung von Mathematikunterricht und in der Erforschung und Diagnostik der mathematischen Entwicklung von Lernenden. Es handelt sich bei Gesten in mathematischen Interaktionen nicht um ein reines Beiwerk der Äußerung, sondern um einen fachlich bedeutsamen Modus in Bezug auf das Mathematiklernen. Der Gebrauch von Gestik ermöglicht die Erzeugung von Diagrammen im Handumdrehen und eröffnet perspektivisch eine Erforschung ihrer Bedeutung für mathematische Lehr-Lern-Prozesse.
Die in dieser Zusammenfassung angegebene Literatur findet sich im Literaturverzeichnis der vorgelegten Forschungsarbeit.
The main task of modern large experiments with heavy ions, such as CBM (FAIR), STAR (BNL) and ALICE (CERN) is a detailed study of the phase diagram of quantum chromodynamics (QCD) in the quark-gluon plasma (QGP), the equation of state of matter at extremely high baryonic densities, and the transition from the hadronic phase of matter to the quark-gluon phase.
In the thesis, the missing mass method is developed for the reconstruction of short-lived particles with neutral particles in their decay products, as well as its implementation in the form of fast algorithms and a set of software for prac- tical application in heavy ion physics experiments. Mathematical procedures implementing the method were developed and implemented within the KF Par- ticle Finder package for the future CBM (FAIR) experiment and subsequently adapted and applied for processing and analysis of real data in the STAR (BNL) experiment.
The KF Particle Finder package is designed to reconstruct most signal particles from the physics program of the CBM experiment, including strange particles, strange resonances, hypernuclei, light vector mesons, charm particles and char- monium. The package includes searches for over a hundred decays of short-lived particles. This makes the KF Particle Finder a universal platform for short-lived particle reconstruction and physics analysis both online and offline.
The missing mass method has been proposed to reconstruct decays of short-lived charged particles when one of the daughter particles is neutral and is not regis- tered in the detector system. The implementation of the missing mass method was integrated into the KF Particle Finder package to search for 18 decays with a neutral daughter particle.
Like all other algorithms of the KF Particle Finder package, the missing mass method is implemented with extensive use of vector (SIMD) instructions and is optimized for parallel operation on modern many-core high performance com- puter clusters, which can include both processors and coprocessors. A set of algorithms implementing the method was tested on computers with tens of cores and showed high speed and practically linear scalability with respect to the num- ber of cores involved.
It is extremely important, especially for the initial stage of the CBM experiment, which is planned for 2025, to demonstrate already now on real data the reliability of the developed approach, as well as the high efficiency of the current implemen- tation of both the entire KF Particle Finder package, and its integral part, the missing mass method. Such an opportunity was provided by the FAIR Phase-0 program, motivating the use in the STAR experiment of software packages orig- inally developed for the CBM experiment.
Application of the method to real data of the STAR experiment shows very good results with a high signal-to-background ratio and a large significance value. The results demonstrate the reliability and high efficiency of the missing mass method in the reconstruction of both charged mother particles and their neutral daughter particles. Being an integral part of the KF Particle Finder package, now the main approach for reconstruction and analysis of short-lived particles in the STAR experiment, the missing mass method will continue to be used for the physics analysis in online and offline modes.
The high quality of the results of the express data analysis has led to their status as preliminary physics results with the right to present them at international physics conferences and meetings on behalf of the STAR Collaboration.
Das Projekt anan ist ein Werkzeug zur Fehlersuche in verteilten Hochleistungsrechnern. Die Neuheit des Beitrags besteht darin, dass die bekannten Methoden, die bereits erfolgreich zum Debuggen von Soft- und Hardware eingesetzt werden, auf Hochleistungs-Rechnen übertragen worden sind. Im Rahmen der vorliegenden Arbeit wurde ein Werkzeug namens anan implementiert, das bei der Fehlersuche hilft. Außerdem kann es als dynamischeres Monitoring eingesetzt werden. Beide Einsatzzwecke sind
getestet worden.
Das Werkzeug besteht aus zwei Teilen:
1. aus einem Teil namens anan, der interaktiv vom Nutzer bedient wird
2. und aus einem Teil namens anand, der automatisiert die verlangten Messwerte erhebt und nötigenfalls Befehle ausführt.
Der Teil anan führt Sensoren aus — kleine mustergesteuerte Algorithmen —, deren Ergebnisse per anan zusammengeführt werden. In erster Näherung lässt anan sich als Monitoring beschreiben, welches (1) schnell umkonfiguriert werden (2) komplexere Werte messen kann, die über Korrelationen einfacher Zeitreihen hinausgehen.
In this thesis we discuss the group Out(Gal_K) of outer automorphism of the absolute Galois group Gal_K of a p-adic number field K. Using results about the mapping class group of a surface S, as well as a result by Jannsen--Wingberg on the structure of the absolute Galois group Gal_K, we construct a large subgroup of Out(Gal_K) arising as images of certain Dehn twists on S.
This thesis is concerned with the study of symmetry breaking phenomena for several different semilinear partial differential equations. Roughly speaking, this encompasses equations whose symmetries are not necessarily inherited by their solutions, which is particularly interesting for ground state solutions.
Reactive oxygen species are a class of naturally occurring, highly reactive molecules that change the structure and function of macromolecules. This can often lead to irreversible intracellular damage. Conversely, they can also cause reversible changes through post-translational modification of proteins which are utilized in the cell for signaling. Most of these modifications occur on specific cysteines. Which structural and physicochemical features contribute to the sensitivity of cysteines to redox modification is currently unclear. Here, I investigated the in uence of protein structural and sequence features on the modifiability of proteins and specific cysteines therein using statistical and machine learning methods. I found several strong structural predictors for redox modification, such as a higher accessibility to the cytosol and a high number of positively charged amino acids in the close vicinity. I detected a high frequency of other post-translational modifications, such as phosphorylation and ubiquitination, near modified cysteines. Distribution of secondary structure elements appears to play a major role in the modifiability of proteins. Utilizing these features, I created models to predict the presence of redox modifiable cysteines in proteins, including human mitochondrial complex I, NKG2E natural killer cell receptors and proximal tubule cell proteins, and compared some of these predictions to earlier experimental results.
This thesis concerns three specific constraint satisfaction problems: the k-SAT problem, random linear equations and the Potts model. We investigated a phenomenon called replica symmetry, its consequences and its limitation. For the $k$-SAT problem, we were able to show that replica symmetry holds up to a threshold $d^{*}$. However, after another critical threshold $d^{**}$, we discovered that replica symmetry could not hold anymore, which enabled us to establish the existence of a replica symmetry breaking region. For the random linear problem, a peculiar phenomenon occurs. We observed that a more robust version of replica symmetry (strong replica symmetry) holds up to a threshold $d=e$ and ceases to hold after. This phenomenon is linked to the fact that before the threshold $d=e$, the fraction of frozen variables, i.e. variable forced to take the same value in all solutions, is concentrated around a deterministic value but vacillates between two values with equal probability for $d>e$. Lastly, for the Potts model, we show that a phenomenon called metastability occurs. The latter phenomenon can be understood as a consequence of trivial replica symmetry breaking scheme. This metastability phenomenon further produces slow mixing results for two famous Markov chains, the Glauber and the Swendsen-Wang dynamics.
The relevant field of interest in High Energy Physics experiments is shifting to searching and studying extremely rare particles and phenomena. The search for rare probes requires an increase in the number of available statistics by increasing the particle interaction rate. The structure of the events also becomes more complicated, the multiplicity of particles in each event increases, and a pileup appears. Due to technical limitations, such data flow becomes impossible to store fully on available storage devices. The solution to the problem is the correct triggering of events and real-time data processing.
In this work, the issue of accelerating and improving the algorithms for reconstruction of the charged particles' trajectories based on the Cellular Automaton in the STAR experiment is considered to implement them for track reconstruction in real-time within the High-Level Trigger. This is an important step in the preparation of the CBM experiment as part of the FAIR Phase-0 program. The study of online data processing methods in real conditions at similar interaction energies allows us to study this process and determine the possible weaknesses of the approach.
Two versions of the Cellular Automaton based track reconstruction are discussed, which are used, depending on the detecting systems' features. HFT~CA Track Finder, similar to the tracking algorithm of the CBM experiment, has been accelerated by several hundred times, using both algorithm optimization and data-level parallelism. TPC~CA Track Finder has been upgraded to improve the reconstruction quality while maintaining high calculation speed. The algorithm was tuned to work with the new iTPC geometry and provided an additional module for very low momentum track reconstruction.
The improved track reconstruction algorithm for the TPC detector in the STAR experiment was included in the HLT reconstruction chain and successfully tested in the express production for the online real data analysis. This made it possible to obtain important physical results during the experiment runtime without the full offline data processing. The tracker is also being prepared for integration into a standard offline data processing chain, after which it will become the basic track search algorithm in the STAR experiment.
Monte Carlo methods : barrier option pricing with stable Greeks and multilevel Monte Carlo learning
(2021)
For discretely observed barrier options, there exists no closed solution under the Black-Scholes model. Thus, it is often helpful to use Monte Carlo simulations, which are easily adapted to these models. However, as presented above, the discontinuous payoff may lead to instability in option's sensitivities for Monte Carlo algorithms.
This thesis presents a new Monte Carlo algorithm that can calculate the pathwise sensitivities for discretely monitored barrier options. The idea is based on Glasserman and Staum's one-step survival strategy and the results of Alm et al., with which we can stably determine the option's sensitivities such as Delta and Vega by finite-differences. The basic idea of Glasserman and Staum is to use a truncated normal distribution, which excludes the values above the barrier (e.g.\ for knock-up-out options), instead of sampling from the full normal distribution. This approach avoids the discontinuity generated by any Monte Carlo path crossing the barrier and yields a Lipschitz-continuous payoff function.
The new part will be to develop an extended algorithm that estimates the sensitivities directly, without simulation at multiple parameter values as in finite-difference.
Consider the local volatility model, which is a generalisation of the Black-Scholes model. Although standard Monte Carlo algorithms work well for the pricing of continuously monitored barrier options within this model, they often do not behave stably with respect to numerical differentiation.
To bypass this problem, one would generally either resort to regularised differentiation schemes or derive an algorithm for precise differentiation. Unfortunately, while the widespread solution of using a Brownian bridge approach leads to accurate first derivatives, they are not Lipschitz-continuous. This leads to instability with respect to numerical differentiation for second-order Greeks.
To alleviate this problem - i.e. produce Lipschitz-continuous first-order derivatives - and reduce variance, we generalise the idea of one-step survival to general scalar stochastic differential equations. This approach leads to the new one-step survival Brownian bridge approximation, which allows for stable second-order Greeks calculations.
To show the new approach's numerical efficiency, we present a new respective Monte Carlo pathwise sensitivity estimator for the first-order Greeks and study different methods to compute second-order Greeks stably. Finally, we develop a one-step survival Brownian bridge multilevel Monte Carlo algorithm to reduce the computational cost in practice.
This thesis proves unbiasedness and variance reduction of our new, one-step survival version with respect to the classical, Brownian bridge approach. Furthermore, we will present a new convergence result for the Brownian bridge approach using the Milstein scheme under certain conditions. Overall, these properties imply convergence of the new one-step survival Brownian bridge approach.
In recent years, deep learning has become pervasive in various fields. As a family of machine learning methods it is used in a broad set of applications, such as image processing, voice recognition, email filtering, computer vision. Most modern deep learning algorithms are based on artificial neural networks inspired by the biological neural networks constituting animal brains. Also in computational finance deep learning may be of use: Consider there is no closed-solution available for an option price, Monte Carlo simulations are substantially for estimation. Instead of persistently contributing new price computations arising from an updated volatility term, one could replace these by evaluating a neural network.
If an according neural network is available, the evaluation could lead to substantial savings and be highly efficient. I.e., once trained, a neural network could save further expensive estimations. However, in practice, the challenge is the training process of the neural network.
We study and compare two generic neural network training algorithms' computational complexity. Then, we introduce a new multilevel training algorithm that combines a deep learning algorithm with the idea of multilevel Monte Carlo path simulation. The idea is to train several neural networks with training data computed from the so-called level estimators of the multilevel Monte Carlo approach introduced by Giles. We show that the new method can reduce computational complexity by formulating a complexity theorem.
The thesis is composed of four Chapters.
In the first Chapter, the boundary expression of the one-sided shape derivative of nonlocal Sobolev best constants is derived. As a simple consequence, we obtain the fractional version of the so-called Hadamard formula for the torsional rigidity and the first Dirichlet eigenvalue. An application to the optimal obstacle placement problem for the torsional rigidity and the first eigenvalue of the fractional Laplacian is given.
In the second Chapter, we introduce and prove a new maximum principle for doubly antisymmetric functions. The latter can be seen as the first step towards studying the optimal obstacle placement problem for the second fractional eigenvalue. Using the new maximum principle we derive new symmetry results for odd solutions to semilinear Dirichlet boundary value problems with Lipschitz nonlinearity.
In the third Chapter, we derive new integration by parts formula for the fractional Laplace operator with a general globally Lipschitz vector field and in particular, we obtain a new Pohozaev type identity generalizing the one obtained by X. Ros-Oton and J. Serra. As an application we obtain nonexistence results for semilinear Dirichlet boundary problems in bounded domains that are not necessarly starshaped.
In the last Chapter, we study symmetry properties of second eigenfunctions of annuli. Using results from the first Chapter and the maximum principle in Chpater 2, we extend the result on the optimal obstacle placement problem from the first eigenvalue to the second eigenvalue.
We present new results on nonlocal Dirichlet problems established by means of suitable spectral theoretic and variational methods, taking care of the nonlocal feature of the operators. We mainly address: First, we estimate the Morse index of radially symmetric sign changing bounded weak solutions to a semilinear Dirichlet problem involving the fractional Laplacian. In particular, we derive a conjecture due to Bañuelos and Kulczycki on the geometric structure of the second Dirichlet eigenfunctions. Secondly, we study a small order asymptotics with respect to the parameter s of the Dirichlet eigenvalues problem for the fractional Laplacian. Thirdly, we deal with the logarithmic Schrödinger operator. In particular, we provide an alternative to derive the singular integral representation corresponding to the associated Fourier symbol and introduce tools and functional analytic framework for variational studies. Finaly, we study nonlocal operators of order strictly below one. In particular, we investigate interior regularity properties of weak solutions to the associated Poisson problem depending on the regularity of the right-hand side.
Wir betrachten Algorithmen für strategische Kommunikation mit Commitment Power zwischen zwei rationalen Parteien mit eigenen Interessen. Wenn eine Partei Commitment Power hat, so legt sie sich auf eine Handlungsstrategie fest und veröffentlicht diese und kann nicht mehr davon abweichen.
Beide Parteien haben Grundinformation über den Zustand der Welt. Die erste Partei (S) hat die Möglichkeit, diesen direkt zu beobachten. Die zweite Partei (R) trifft jedoch eine Entscheidung durch die Wahl einer von n Aktionen mit für sie unbekanntem Typ. Dieser Typ bestimmt die möglicherweise verschiedenen, nicht-negativen Nutzwerte für S und R. Durch das Senden von Signalen versucht S, die Wahl von R zu beeinflussen. Wir betrachten zwei Grundszenarien: Bayesian Persuasion und Delegated Search.
In Bayesian Persuasion besitzt S Commitment Power. Hier legt sich S sich auf ein Signalschema φ fest und teilt dieses R mit. Es beschreibt, welches Signal S in welcher Situation sendet. Erst danach erfährt S den wahren Zustand der Welt. Nach Erhalt der durch φ bestimmten Signale wählt R eine der Aktionen. Das Wissen um φ erlaubt R die Annahmen über den Zustand der Welt in Abhängigkeit von den empfangenen Signalen zu aktualisieren. Dies muss S für das Design von φ berücksichtigen, denn R wird Empfehlungen nicht folgen, die S auf Kosten von R übervorteilen. Wir betrachten das Problem aus der Sicht von S und beschreiben Signalschemata, die S einen möglichst großen Nutzen garantieren.
Zuerst betrachten wir den Offline-Fall. Hier erfährt S den kompletten Zustand der Welt und schickt daraufhin ein Signal an R. Wir betrachten ein Szenario mit einer beschränkten Anzahl k ≤ n Signale. Mit nur k Signalen kann S höchstens k verschiedene Aktionen empfehlen. Für verschiedene symmetrische Instanzen beschreiben wir einen Polynomialzeitalgorithmus für die Berechnung eines optimalen Signalschemas mit k Signalen.
Weiterhin betrachten wir eine Teilmenge von Instanzen, in denen die Typen aus bekannten, unabhängigen Verteilungen gezogen werden. Wir beschreiben Polynomialzeitalgorithmen, die ein Signalschema mit k Signalen berechnen, das einen konstanten Approximationsfaktor im Verhältnis zum optimalen Signalschema mit k Signalen garantiert.
Im Online-Fall werden die Aktionstypen einzeln in Runden aufgedeckt. Nach Betrachtung der aktuellen Aktion sendet S ein Signal und R muss sofort durch Wahl oder Ablehnung der Aktion darauf reagieren. Der Prozess endet mit der Wahl einer Aktion. Andernfalls wird der nächste Aktionstyp aufgedeckt und vorherige Aktionen können nicht mehr gewählt werden. Als Richtwert für unsere Online-Signalschemata verwenden wir das beste Offline-Signalschema.
Zuerst betrachten wir ein Szenario mit unabhängigen Verteilungen. Wir zeigen, wie ein optimales Signalschema in Polynomialzeit bestimmt werden kann. Jedoch gibt es Beispiele, bei denen S – anders als im Offline-Fall – im Online-Fall keinen positiven Wert erzielen kann. Wir betrachten daraufhin eine Teilmenge der Instanzen, für die ein einfaches Signalschema einen konstanten Approximationsfaktor garantiert und zeigen dessen Optimalität.
Zusätzlich betrachten wir 16 verschiedene Szenarien mit unterschiedlichem Level an Information für S und R und unterschiedlichen Zielfunktionen für S und R unter der Annahme, dass die Aktionstypen a priori unbekannt sind, aber in uniform zufälliger Reihenfolge aufgedeckt werden. Für 14 Fälle beschreiben wir Signalschemata mit konstantem Approximationsfaktor. Solche Schemata existieren für die verbleibenden beiden Fälle nicht. Zusätzlich zeigen wir für die meistern Fälle, dass die beschriebenen Approximationsgarantien optimal sind.
Im zweiten Teil betrachten wir eine Online-Variante von Delegated Search. Hier besitzt nun R Commitment Power. Die Aktionstypen werden aus bekannten, unabhängigen Verteilungen gezogen. Bevor S die realisierten Typen beobachtet, legt R sich auf ein Akzeptanzschema φ fest. Für jeden Typen gibt φ an, mit welcher Wahrscheinlichkeit R diesen akzeptiert. Folglich versucht S, eine Aktion mit einem guten Typen für sich selbst zu finden, der von R akzeptiert wird. Da der Prozess online abläuft, muss S für jede Aktion einzeln entscheiden, diese vorzuschlagen oder zu verwerfen. Nur empfohlene Aktionen können von R ausgewählt werden.
Für den Offline-Fall sind für identisch verteilte Aktionstypen konstante Approximationsfaktoren im Vergleich zu einer Aktion mit optimalem Wert für R bekannt. Wir zeigen, dass R im Online-Fall im Allgemeinen nur eine Θ(1/n)-Approximation erzielen kann. Der Richtwert ist der erwartete Wert für eine eindimensionale Online-Suche von R.
Da für die Schranke eine exponentielle Diskrepanz in den Werten der Typen für S benötigt wird, betrachten wir parametrisierte Instanzen. Die Parameter beschränken die Werte für S bzw. das Verhältnis der Werte für R und S. Wir zeigen (beinahe) optimale logarithmische Approximationsfaktoren im Bezug auf diese Parameter, die von effizient berechenbaren Schemata garantiert werden.
Machine learning (ML) techniques have evolved rapidly in recent years and have shown impressive capabilities in feature extraction, pattern recognition, and causal inference. There has been an increasing attention to applying ML to medical applications, such as medical diagnosis, drug discovery, personalized medicine, and numerous other medical problems. ML-based methods have the advantage of processing vast amounts of data.
With an ever increasing amount of medical data collection and large, inter-subject variability in the medical data, automated data processing pipelines are very much desirable since it is laborious, expensive, and error-prone to rely solely on human processing. ML methods have the potential to uncover interesting patterns, unravel correlations between complex features, learn patient-specific representations, and make accurate predictions. Motivated by these promising aspects, in this thesis, I present studies where I have implemented deep neural networks for the early diagnosis of epilepsy based on electroencephalography (EEG) data and brain tumor detection based on magnetic resonance spectroscopy (MRS) data.
In the project for early diagnosis of epilepsy, we are dealing with one of the most common neurological disorders, epilepsy, which is characterized by recurrent unprovoked seizures. It can be triggered by a variety of initial brain injuries and manifests itself after a time window which is called the latent period. During this period, a cascade of structural and functional brain alterations takes place leading to an increased seizure susceptibility.
The development and extension of brain tissue capable of generating spontaneous seizures is defined as epileptogenesis (EPG).
Detecting the presence of EPG provides a precious opportunity for targeted early medical interventions and, thus, can slow down or even halt the disease progression. In order to study brain signals in this latent window, animal epilepsy models are used to provide valuable data as it is extremely difficult to obtain this data from human patients. The aim of this study is to discover biomarkers of EPG using animal models and then to find the equivalent and counterparts in human patients' data. However, the EEG features for EPG are not well-understood and there is not a sufficiently large amount of annotated data for ML-based algorithms. To approach this problem, firstly, I utilized the timestamp information of the recorded EEG from an animal epilepsy model where epilepsy is induced by an electrical stimulation. The timestamp serves as a form of weak supervision, i.e., before and after the stimulation. Secondly, I implemented a deep residual neural network and trained it with a binary classification task to distinguish the EEG signals from these two phases. After obtaining a high discriminative ability on the binary classification task, I proposed to divide further the time span after the stimulation for a three-class classification, aiming to detect possible stages of the progression of the latent EPG phase. I have shown that the model can distinguish EEG signals at different stages of EPG with high accuracy and generalization ability. I have also demonstrated that some of the learned features from the network are clinically relevant.
In the task of detecting brain tumors based on MRS data, I first proposed to apply a deep neural network on the MRS data collected from over 400 patients for a binary classification task. To combat the challenge of noisy labeling, I developed a distillation step to filter out relatively ``cleanly'' labeled samples. A mixing-based data augmentation method was also implemented to expand the size of the training set. All the experiments were designed to be conducted with a leave-patient-out scheme to ensure the generalization ability of the model. Averaged across all leave-patient-out cross-validation sets, the proposed method performed on par with human neuroradiologists, while outperforming other baseline methods. I have demonstrated the distillation effect on the MNIST data set with manually-introduced label noise as well as providing visualization of the input influences on the final classification through a class activation map method.
Moreover, I have proposed to aggregate information at the subject level, which could provide more information and insights. This is inspired by the concept of multiple instance learning, where instance-level labels are not required and which is more tolerant to noisy labeling. I have proposed to generate data bags consisting of instances from each patient and also proposed two modules to ensure permutation invariance, i.e., an attention module and a pooling module. I have compared the performance of the network in different cases, i.e., with and without permutation-invariant modules, with and without data augmentation, single-instance-based and multiple-instance-based learning and have shown that neural networks equipped with the proposed attention or pooling modules can outperform human experts.
In the first part of this thesis, we introduce the concept of prospective strict no-arbitrage for discrete-time financial market models with proportional transaction. The prospective strict no-arbitrage condition, which is a variant of strict no-arbitrage, is slightly weaker than the robust no-arbitrage condition. It still implies that the set of portfolios attainable from zero initial endowment is closed in probability. Consequently, prospective strict no-arbitrage implies the existence of consistent prices, which may lie on the boundary of the bid-ask spread. A weak version of prospective strict no-arbitrage turns out to be equivalent to the existence of a consistent price system.
In continuous-time financial market models with proportional transaction costs, efficient friction, i.e., nonvanishing transaction costs, is a standing assumption. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation which usually appear in frictionless financial markets. In the second part of this thesis, we show how models with and without transaction costs can be unified. The bid and the ask price of a risky asset are given by cadlag processes which are locally bounded from below and may coincide at some points. In a first step, we show that if the bid-ask model satisfies no unbounded profit with bounded risk for simple long-only strategies, then there exists a semimartingale lying between the bid and the ask price process.
In a second step, under the additional assumption that the zeros of the bid-ask spread are either starting points of an excursion away from zero or inner points from the right, we show that for every bounded predictable strategy specifying the amount of risky assets, the semimartingale can be used to construct the corresponding self-financing risk-free position in a consistent way. Finally, the set of most general strategies is introduced, which also provides a new view on the frictionless case.
The main topic of the present thesis is scene flow estimation in a monocular camera system. Scene flow describes the joint representation of 3D positions and motions of the scene. A special focus is placed on approaches that combine two kinds of information, deep-learning-based single-view depth estimation and model-based multi-view geometry.
The first part addresses single-view depth estimation focussing on a method that provides single-view depth information in an advantageous form for monocular scene flow estimation methods. A convolutional neural network, called ProbDepthNet, is proposed, which provides pixel-wise well-calibrated depth distributions. The experiments show that different strategies for quantifying the measurement uncertainty provide overconfident estimates due to overfitting effects. Therefore, a novel recalibration technique is integrated as part of the ProbDepthNet, which is validated to improve the calibration of the uncertainty measures. The monocular scene flow methods presented in the subsequent parts confirm that the integration of single-view depth information results in the best performance if the neural network provides depth distributions instead of single depth values and contains a recalibration.
Three methods for monocular scene flow estimation are presented, each one designed to combine multi-view geometry-based optimization with deep learning-based single-view depth estimation such as ProbDepthNet. While the first method, SVD-MSfM, performs the motion and depth estimation as two subsequent steps, the second method, Mono-SF, jointly optimizes the motion estimates and the depth structure. Both methods are tailored to address scenes, where the objects and motions can be represented by a set of rigid bodies. Dynamic traffic scenes are one kind of scenes that essentially fulfill this characteristic. The method, Mono-Stixel, uses an even more specialized scene model for traffic scenes, called stixel world, as underlying scene representation.
The proposed methods provide new state of the art for monocular scene flow estimation with Mono-SF being the first and leading monocular method on the KITTI scene flow benchmark at the time of submission of the present thesis. The experiments validate that both kind of information, the multi-view geometric optimization and the single-view depth estimates, contribute to the monocular scene flow estimates and are necessary to achieve the new state of the art accuracy.
Analysing survival or fixation probabilities for a beneficial allele is a prominent task in the field of theoretical population genetics. Haldane's asymptotics is an approximation for the fixation probability in the case of a single beneficial mutant with small selective advantage in a large population.
In this thesis we analyse the interplay between genetic drift and directional selection and prove Haldane's asymptotics in different settings: For the fixation probability in Cannings models with moderate selection and for the survival probability of a slightly supercritical branching processes in a random environment.
In Chapter 3 we introduce a class of Cannings models with selection that allow for a forward and backward construction. In particular, a Cannings ancestral selection process can be defined for this class of models, which counts the number of potential parents and is in sampling duality to the forward frequency process. By means of this duality the probability of fixation can be expressed through the expectation of the Cannings ancestral selection process in stationarity. A control of this expectation yields that the fixation probability fulfils Haldane's asymptotics in a regime of moderately weak selection (Thm. 8).
In Chapter 4 we study the fixation probability of Cannings models in a regime of moderately strong selection. Here couplings of the frequency process of beneficial individuals with slightly supercritical Galton-Watson processes imply that the fixation probability is given by Haldane's asymptotics (Thm. 9).
Lastly, in Chapter 5 we consider slightly supercritical branching processes in an independent and identically distributed random environment and study the probability of survival as the number of expected offspring tends from above to one. We show that only if variance and expectation of the random offspring mean are of the same order the random environment has a non-trivial influence on the probability of survival, which results in a modification of Haldane's asymptotics. Out of the critical parameter regime the population goes extinct or survives with a probability that fulfils Haldane's asymptotics (Thm. 10).
The proof establishes an expression for the survival probability in terms of the shape function of the random offspring generating functions. This expression exhibits similarities to perpetuities known from a financial context. Consequently, we prove a limiting theorem for perpetuities with vanishing interest rates (Thm. 11).
This work describes development of a comprehensive methodology for analyzing vibro-acoustic and wear mechanisms in transmission systems. The thesis addresses certain gaps present in the fields of structure dynamics and abrasion mechanism and opens new areas for further research.
The paper attempts to understand new and relatively unexplored challenges like influences of wear on the dynamics of drive train. It also focuses on developing new techniques for analyzing the vibration and acoustic behavior of the drive unit structures and surrounding fluids respectively.
The developed methodology meets the requirements of both the complete system and component level modeling by using specially identified combination of different simulation techniques. Based on the created template model, a three-stage spur plus helical gearbox is constructed and simulated as an application example. In addition to the internal mechanical excitation mechanisms, the transmission model also includes the rotational and translational dynamics of the gears, shafts and bearings. It is followed by illustration of wear among the rotating components.
Different kinds of static and dynamic analyses are performed and coupled at various levels depending on the mechanical complexities involved. Furthermore, the structure dynamic vibration of the housing and the associated sound particle radiations are mapped into the surrounding fluid. Additionally, the approach for selection of the potential parameters for optimization is depicted. Final part focuses on the measurements of different system states used for validation of the model. In the end, results obtained from both simulations and experiments are analyzed and assessed for there respective performances.
Machine Learning (ML) is so pervasive in our todays life that we don't even realise that, more often than expected, we are using systems based on it. It is also evolving faster than ever before. When deploying ML systems that make decisions on their own, we need to think about their ignorance of our uncertain world. The uncertainty might arise due to scarcity of the data, the bias of the data or even a mismatch between the real world and the ML-model. Given all these uncertainties, we need to think about how to build systems that are not totally ignorant thereof. Bayesian ML can to some extent deal with these problems. The specification of the model using probabilities provides a convenient way to quantify uncertainties, which can then be included in the decision making process.
In this thesis, we introduce the Bayesian ansatz to modeling and apply Bayesian ML models in finance and economics. Especially, we will dig deeper into Gaussian processes (GP) and Gaussian process latent variable model (GPLVM). Applied to the returns of several assets, GPLVM provides the covariance structure and also a latent space embedding thereof. Several financial applications can be build upon the output of the GPLVM. To demonstrate this, we build an automated asset allocation system, a predictor for missing asset prices and identify other structure in financial data.
It turns out that the GPLVM exhibits a rotational symmetry in the latent space, which makes it harder to fit. Our second publication reports, how to deal with that symmetry. We propose another parameterization of the model using Householder transformations, by which the symmetry is broken. Bayesian models are changed by reparameterization, if the prior is not changed accordingly. We provide the correct prior distribution of the new parameters, such that the model, i.e. the data density, is not changed under the reparameterization. After applying the reparametrization on Bayesian PCA, we show that the symmetry of nonlinear models can also be broken in the same way.
In our last project, we propose a new method for matching quantile observations, which uses order statistics. The use of order statistics as the likelihood, instead of a Gaussian likelihood, has several advantages. We compare these two models and highlight their advantages and disadvantages. To demonstrate our method, we fit quantiled salary data of several European countries. Given several candidate models for the fit, our method also provides a metric to choose the best option.
We hope that this thesis illustrates some benefits of Bayesian modeling (especially Gaussian processes) in finance and economics and its usage when uncertainties are to be quantified.
Within the last thirty years, the contraction method has become an important tool for the distributional analysis of random recursive structures. While it was mainly developed to show weak convergence, the contraction approach can additionally be used to obtain bounds on the rate of convergence in an appropriate metric. Based on ideas of the contraction method, we develop a general framework to bound rates of convergence for sequences of random variables as they mainly arise in the analysis of random trees and divide-and-conquer algorithms. The rates of convergence are bounded in the Zolotarev distances. In essence, we present three different versions of convergence theorems: a general version, an improved version for normal limit laws (providing significantly better bounds in some examples with normal limits) and a third version with a relaxed independence condition. Moreover, concrete applications are given which include parameters of random trees, quantities of stochastic geometry as well as complexity measures of recursive algorithms under either a random input or some randomization within the algorithm.
This thesis presents research which spans three conference papers and one manuscript which has not yet been submitted for peer review.
The topic of 1 is the inherent complexity of maintaining perfect height in B-trees. We consider the setting in which a B-tree of optimal height contains n = (1−ϵ)N elements where N is the number of elements in full B-tree of the same height (the capacity of the tree). We show that the rebalancing cost when updating the tree—while maintaining optimal height—depends on ϵ. Specifically, our analysis gives a lower bound for the rebalancing cost of Ω(1/(ϵB)). We then describe a rebalancing algorithm which has an amortized rebalancing cost with an almost matching upper bound of O(1/(ϵB)⋅log²(min{1/ϵ,B})). We additionally describe a scheme utilizing this algorithm which, given a rebalancing budget f(n), maintains optimal height for decreasing ϵ until the cost exceeds the
budget at which time it maintains optimal height plus one. Given a rebalancing budget of Θ(logn), this scheme maintains optimal height for all but a vanishing fraction of sizes in the intervals between tree capacities.
Manuscript 2 presents empirical analysis of practical randomized external-memory algorithms for computing the connected components of graphs. The best known theoretical results for this problem are essentially all derived from results for minimum spanning tree algorithms. In the realm of randomized external-memory MST algorithms, the best asymptotic result has I/O-complexity O(sort(|E|)) in expectation while an empirically studied practical algorithm has a bound of O(sort(|E|)⋅log(|V|/M)). We implement and evaluate an algorithm for connected components with expected I/O-complexity O(sort(|E|))—a simplification of the MST
algorithm with this asymptotic cost, we show that this approach may also yield good results in practice.
In paper 3, we present a novel approach to simulating large-scale population protocol models. Naive simulation of N interactions of a population protocol with n agents and m states requires Θ(nlogm) bits of memory and Θ(N) time. For
very large n, this is prohibitive both in memory consumption and time, as interesting protocols will typically require N > n interactions for convergence. We describe a histogram-based simulation framework which requires Θ(mlogn) bits of memory instead—an improvement as it is typically the case that
n ≫ m. We analyze, implement, and compare a number of different data structures to perform correct agent sampling in this regime. For this purpose, we develop dynamic alias tables which allow sampling an interaction in expected amortized
constant time. We then show how to use sampling techniques to process agent interactions in batches, giving a simulation approach which uses subconstant time per interaction under reasonable assumptions.
With paper 4, we introduce the new model of fragile complexity for comparison-based algorithms. Within this model, we analyze classical comparison-based problems such as finding the minimum value of a set, selection (or finding the median), and sorting. We prove a number of lower and upper bounds and in particular, we give a number of randomized results which describe trade-offs not achievable by deterministic algorithms.
Um Wissen in einer Form abzulegen, in der es automatisiert verarbeitet werden kann, werden unter anderem Ontologien verwendet. Ontologien erlauben über einen als Inferenz bezeichneten Prozess die Ableitung neuen Wissens. Bei inhaltlichen Überschneidungen werden Ontologien über Ontologie-Alignments miteinander verbunden, die Entitäten aus den verschiedenen Ontologien in Beziehung zueinander setzen. Üblicherweise werden diese Alignments als Mengen von Äquivalenzen formuliert, die beschreiben, welche Konzepte aus einer Ontologie Konzepten aus einer anderen Ontologie entsprechen. Ebenfalls verbreitet sind Ober- und Unterklassenbeziehungen in Alignments.
Diese Ontologie-Alignments werden zum Beispiel in der Biomedizin in Forschungsdatenbanken verwendet, da durch Alignments Informationen aus verschiedenen Bereichen zusammengeführt werden können. Der manuelle Aufwand, um große Ontologien und Alignments zu erstellen, ist sehr hoch. Dementsprechend wäre es wünschenswert, bei einer Veränderung von Ontologien nicht wieder von vorne beginnen und eine neue Ontologie erstellen zu müssen und möglichst viel aus der veränderten Ontologie und den die Ontologie betreffenden Alignments wiederverwenden zu können. Daher sollten möglichst automatisierte Verfahren verwendet werden. Diese Arbeit untersucht vier Ansätze, um die Anpassung von Alignments an Veränderungen in Ontologien zu automatisieren.
Der erste Ansatz bezieht Inferenzen in den Prozess zur Vorhersage von Alignment-Änderungen mit ein. Dazu werden die Inferenzen vor und nach der Änderung der Ontologien berechnet und auf Basis der Unterschiede mit einem regelbasierten Algorithmus bestimmt, wie sich das Alignment ändern soll. Der zweite Ansatz, wie auch die weiteren Ansätze, hat nicht zum Ziel das Alignment direkt anzupassen. Stattdessen soll vorhergesagt werden, welche Teile des Alignments angepasst werden müssen. Dazu werden die Ontologien und das Alignment als Wissensgraph-Embeddings repräsentiert. Diese Embeddings bilden Knoten aus den Ontologien in einen Raum mit 300-1000 Dimensionen so ab, dass in dem Raum auch die Beziehungen zwischen den Entitäten der Ontologien repräsentiert werden können. Diese Embeddings werden dann verwendet, um verschiedene Klassifikationsalgorithmen zu trainieren. Auf diese Weise wird vorhergesagt, welche Teile des Alignments sich verändern werden. Der dritte Ansatz verbindet Embeddings mit einem Veränderungsmodell. Das Veränderungsmodell kategorisiert die an den Ontologien vorgenommenen Veränderungen. Auf diese Kategorisierung und das Embedding werden dann Klassifikationsalgorithmen angewandt. Der vierte Ansatz verwendet eine speziell auf Wissensgraphen ausgerichtete Architektur für neuronale Netze, sogenannte Graph Convolutional Networks, um Veränderungen an Alignments vorher zu sagen.
Diese Ansätze werden auf ihre jeweiligen Vor- und Nachteile untersucht. Dazu werden die Verfahren an zwei Anwendungsfällen untersucht. Der Ansatz zur regelbasierten Einbeziehung von Inferenzen wird anhand eines Anwendungsbeispiels aus dem Bereich der Interweaving Systems betrachtet. In dem Beispiel wird eine allgemeine Methode für Interweaving Systems angewandt um das Selbstmanagement von Ampelsteuerungen zu ermöglichen. Die auf maschinellem Lernen aufbauenden Ansätze werden auf einem Auszug aus der biomedizinischen Forschungsdatenbank UMLS evaluiert.
Dabei konnte festgestellt werden, dass die betrachteten Ansätze grundsätzlich zur Anpassung von Alignments an Ontologie-Veränderungen eingesetzt werden können. Der Ansatz zur regelbasierten Einbeziehung von Inferenzen kann dabei vor allem auf sehr kleinen Datensätzen eingesetzt werden, bei denen alle Gesetzmäßigkeiten der Veränderungen grundsätzlich bekannt sind. Diese Anwendbarkeit ergibt sich aus dem Entwurf der Problemstellung für den ersten Ansatz. Die auf maschinellem Lernen aufbauenden Ansätze eignen sich besonders für große Datensätze und bieten den Vorteil, dass auch ohne ein vollständiges Verständnis des Veränderungsprozesses Vorhersagen getroffen werden können.
Unter den Ansätzen, die maschinelles Lernen einsetzen, zeigte die Einbeziehung von Veränderungsmodellen keine Vorteile gegenüber den anderen Ansätzen. Auf einem etwas
kleineren Datensatz waren die Ergebnisse des Embedding-basierten Ansatzes und der Relational Graph Convolutional Networks vergleichbar, während auf einem größeren Datensatz
die Graph Convolutional Networks etwas bessere Ergebnisse erreichen konnten.
Weitere Ergebnisse dieser Arbeit stellen eine Formalisierung der Problemstellung der Anpassung von Ontologie-Alignments an Veränderungen sowie eine formale Darstellung der Ansätze dar. Ein weiterer Beitrag der Arbeit ist die Vorstellung eines Anwendungsfalls aus dem Bereich der Interweaving Systems für Ontologie-Alignments. Außerdem wurde das Problem der Anpassung von Alignments an Veränderungen so formuliert, dass es mithilfe von
maschinellem Lernen betrachtet werden kann.
Deep learning with neural networks seems to have largely replaced traditional design of computer vision systems. Automated methods to learn a plethora of parameters are now used in favor of previously practiced selection of explicit mathematical operators for a specific task. The entailed promise is that practitioners no longer need to take care of every individual step, but rather focus on gathering big amounts of data for neural network training. As a consequence, both a shift in mindset towards a focus on big datasets, as well as a wave of conceivable applications based exclusively on deep learning can be observed.
This PhD dissertation aims to uncover some of the only implicitly mentioned or overlooked deep learning aspects, highlight unmentioned assumptions, and finally introduce methods to address respective immediate weaknesses. In the author’s humble opinion, these prevalent shortcomings can be tied to the fact that the involved steps in the machine learning workflow are frequently decoupled. Success is predominantly measured based on accuracy measures designed for evaluation with static benchmark test sets. Individual machine learning workflow components are assessed in isolation with respect to available data, choice of neural network architecture, and a particular learning algorithm, rather than viewing the machine learning system as a whole in context of a particular application. Correspondingly, in this dissertation, three key challenges have been identified: 1. Choice and flexibility of a neural network architecture. 2. Identification and rejection of unseen unknown data to avoid false predictions. 3. Continual learning without forgetting of already learned information. These latter challenges have already been crucial topics in older literature, alas, seem to require a renaissance in modern deep learning literature. Initially, it may appear that they pose independent research questions, however, the thesis posits that the aspects are intertwined and require a joint perspective in machine learning based systems. In summary, the essential question is thus how to pick a suitable neural network architecture for a specific task, how to recognize which data inputs belong to this context, which ones originate from potential other tasks, and ultimately how to continuously include such identified novel data in neural network training over time without overwriting existing knowledge.
Thus, the central emphasis of this dissertation is to build on top of existing deep learning strengths, yet also acknowledge mentioned weaknesses, in an effort to establish a deeper understanding of interdependencies and synergies towards the development of unified solution mechanisms. For this purpose, the main portion of the thesis is in cumulative form. The respective publications can be grouped according to the three challenges outlined above. Correspondingly, chapter 1 is focused on choice and extendability of neural network architectures, analyzed in context of popular image classification tasks. An algorithm to automatically determine neural network layer width is introduced and is first contrasted with static architectures found in the literature. The importance of neural architecture design is then further showcased on a real-world application of defect detection in concrete bridges. Chapter 2 is comprised of the complementary ensuing questions of how to identify unknown concepts and subsequently incorporate them into continual learning. A joint central mechanism to distinguish unseen concepts from what is known in classification tasks, while enabling consecutive training without forgetting or revisiting older classes, is proposed. Once more, the role of the chosen neural network architecture is quantitatively reassessed. Finally, chapter 3 culminates in an overarching view, where developed parts are connected. Here, an extensive survey further serves the purpose to embed the gained insights in the broader literature landscape and emphasizes the importance of a common frame of thought. The ultimately presented approach thus reflects the overall thesis’ contribution to advance neural network based machine learning towards a unified solution that ties together choice of neural architecture with the ability to learn continually and the capability to automatically separate known from unknown data.
Studying large discrete systems is of central interest in, non-exclusively, discrete mathematics, computer sciences and statistical physics. The study of phase transitions, e.g. points in the evolution of a large random system in which the behaviour of the system changes drastically, became of interest in the classical field of random graphs, the theory of spin glasses as well as in the analysis of algorithms [78,82, 121].
It turns out that ideas from the statistical physics’ point of view on spin glass systems can be used to study inherently combinatorial problems in discrete mathematics and theoretical computer sciences(for instance, satisfiability) or to analyse phase transitions occurring in inference problems (like the group testing problem) [68, 135, 168]. A mathematical flaw of this approach is that the physical methods only render mathematical conjectures as they are not known to be rigorous.
In this thesis, we will discuss the results of six contributions. For instance, we will explore how the
theory of diluted mean-field models for spin glasses helps studying random constraint satisfaction problems through the example of the random 2−SAT problem. We will derive a formula for the number of satisfying assignments that a random 2−SAT formula typically possesses [2].
Furthermore, we will discuss how ideas from spin glass models (more precisely, from their planted versions) can be used to facilitate inference in the group testing problem. We will answer all major open questions with respect to non-adaptive group testing if the number of infected individuals scales sublinearly in the population size and draw a complete picture of phase transitions with respect to the
complexity and solubility of this inference problem [41, 46].
Subsequently, we study the group testing problem under sparsity constrains and obtain a (not fully understood) phase diagram in which only small regions stay unexplored [88].
In all those cases, we will discover that important results can be achieved if one combines the rich theory of the statistical physics’ approach towards spin glasses and inherent combinatorial properties of the underlying random graph.
Furthermore, based on partial results of Coja-Oghlan, Perkins and Skubch [42] and Coja-Oghlan et al. [49], we introduce a consistent limit theory for discrete probability measures akin to the graph limit theory [31, 32, 128] in [47]. This limit theory involves the extensive study of a special variant of the cut-distance and we obtain a continuous version of a very simple algorithm, the pinning operation, which allows to decompose the phase space of an underlying system into parts such that a probability
measure, restricted to this decomposition, is close to a product measure under the cut-distance. We will see that this pinning lemma can be used to rigorise predictions, at least in some special cases, based on the physical idea of a Bethe state decomposition when applied to the Boltzmann distribution.
Finally, we study sufficient conditions for the existence of perfect matchings, Hamilton cycles and bounded degree trees in randomly perturbed graph models if the underlying deterministic graph is sparse [93].
Netzwerkmodelle spielen in verschiedenen Wissenschaftsdisziplinen eine wichtige Rolle und dienen unter anderem der Beschreibung realistischer Graphen.
Sie werden häufig als Zufallsgraphen formuliert und stellen somit Wahrscheinlichkeitsverteilungen über Graphen dar.
Meist ist die Verteilung dabei parametrisiert und ergibt sich implizit, etwa über eine randomisierten Konstruktionsvorschrift.
Ein früher Vertreter ist das G(n,p) Modell, welches über allen ungerichteten Graphen mit n Knoten definiert ist und jede Kante unabhängig mit Wahrscheinlichkeit p erzeugt.
Ein aus G(n,p) gezogener Graph hat jedoch kaum strukturelle Ähnlichkeiten zu Graphen, die zumeist in Anwendungen beobachtet werden.
Daher sind populäre Modelle so gestaltet, dass sie mit hinreichend hoher Wahrscheinlichkeit gewünschte topologische Eigenschaften erzeugen.
Beispielsweise ist es ein gängiges Ziel die nur unscharf definierte Klasse der sogenannten komplexen Netzwerke nachzubilden, der etwa viele soziale Netze zugeordnet werden.
Unter anderem verfügen diese Graphen in der Regel über eine Gradverteilung mit schweren Rändern (heavy-tailed), einen kleinen Durchmesser, eine dominierende Zusammenhangskomponente, sowie über überdurchschnittlich dichte Teilbereiche, sogenannte Communities.
Die Einsatzmöglichkeiten von Netzwerkmodellen gehen dabei weit über das ursprüngliche Ziel, beobachtete Effekte zu erklären, hinaus.
Ein gängiger Anwendungsfall besteht darin, Daten systematisch zu produzieren.
Solche Daten ermöglichen oder unterstützen experimentelle Untersuchungen, etwa zur empirischen Verifikation theoretischer Vorhersagen oder zur allgemeinen Bewertung von Algorithmen und Datenstrukturen.
Hierbei ergeben sich insbesondere für große Probleminstanzen Vorteile gegenüber beobachteten Netzen.
So sind massive Eingaben, die auf echten Daten beruhen, oft nicht in ausreichender Menge verfügbar, nur aufwendig zu beschaffen und zu verwalten, unterliegen rechtlichen Beschränkungen, oder sind von unklarer Qualität.
In der vorliegenden Arbeit betrachten wir daher algorithmische Aspekte der Generierung massiver Zufallsgraphen.
Um Anwendern Reproduzierbarkeit mit vorhandenen Studien zu ermöglichen, fokussieren wir uns hierbei zumeist auf getreue Implementierungen etablierter Netzwerkmodelle,
etwa Preferential Attachment-Prozesse, LFR, simple Graphen mit vorgeschriebenen Gradsequenzen, oder Graphen mit hyperbolischer (o.Ä.) Einbettung.
Zu diesem Zweck entwickeln wir praktisch sowie analytisch effiziente Generatoren.
Unsere Algorithmen sind dabei jeweils auf ein geeignetes Maschinenmodell hin optimiert.
Hierzu entwerfen wir etwa klassische sequentielle Generatoren für Registermaschinen, Algorithmen für das External Memory Model, und parallele Ansätze für verteilte oder Shared Memory-Maschinen auf CPUs, GPUs, und anderen Rechenbeschleunigern.
Diese Arbeit beschäftigt sich mit linearen inversen Problemen, wie sie in einer Vielzahl an Anwendungen auftreten. Diese Probleme zeichnen sich dadurch aus, dass sie typischerweise schlecht gestellt sind, was in erster Linie die Stabilität betrifft. Selbst kleinste Messfehler haben enorme Konsequenzen für die Rekonstruktion der zu bestimmenden Größe.
Um eine robuste Rekonstruktion zu ermöglichen, muss das Problem regularisiert, dass heißt durch eine ganze Familie abgeänderter, stabiler Approximationen ersetzt werden. Die konkrete Wahl aus der Familie, die sogenannte Parameterwahlstrategie, stützt sich dann auf zusätzliche ad hoc Annahmen über den Messfehler. Typischerweise ist dies im deterministischen Fall die Kenntnis einer oberen Schranke an die Norm des Datenfehlers, oder im stochastischen Fall, die Kenntnis der Verteilung des Fehlers, beziehungsweise die Einschränkung auf eine bestimmte Klasse von Verteilungen, zumeist Gaußsche. In der vorliegenden Arbeit wird untersucht, wie sich diese Informationen unter der Annahme der Wiederholbarkeit der Messung gewinnen lassen. Die Daten werden dabei aus mehreren Messungen gemittelt, welche einer beliebigen, unbekannten Verteilung folgen, wobei die zur Lösung des Problems unweigerlich notwendige Fehlerschranke geschätzt wird. Auf Mittelwert und Schätzer wird dann ein klassisches Regularisierungsverfahren angewandt. Als Regularisierungen werden größtenteils Filter-basierte Verfahren behandelt, die sich auf die Spektralzerlegung des Problems stützen. Als Parameterwahlstrategien werden sowohl einfache a priori-Wahlen betrachtet, als auch das Diskrepanzprinzip als adaptives Verfahren. Es wird Konvergenz für unbekannte beliebige Fehlerverteilungen mit endlicher Varianz sowie für Weißes Rauschen (bezüglich allgemeiner Diskretisierungen) nachgewiesen. Schließlich wird noch die Konvergenz des Diskrepanzprinzips für ein stochastisches Gradientenverfahren gezeigt, als erste rigorose Analyse einer adaptiven Stoppregel für ein solches nicht Filter-basiertes Regularisierungsverfahren.
Diese Arbeit beschäftigt sich mit der theoriegeleiteten Entwicklung eines digitalen Werkzeugs namens MathCityMap (MCM) für das außerschulische Lehren und Lernen von Mathematik.
Den Ausgangspunkt des Projekts bilden die sogenannten Mathtrails. Dies sind Wanderpfade zum Entdecken mathematischer Sachverhalte an realen Objekten in der Umwelt. Eine didaktische, methodische sowie lernpsychologische Analyse konstatiert Mathtrails zahlreiche Potentiale für den Lernprozess wie beispielsweise die Möglichkeit, Primärerfahrungen zu sammeln, das Interesse am Fach Mathematik zu steigern sowie das Lernen aktiv und konstruktiv zu gestalten. Trotz der genannten Vorteile wird deutlich, dass die Vorbereitung und Umsetzung der mathematischen Wanderpfade mit einem immensen Aufwand verbunden sind. Eine weitere Herausforderung für Lernende liegt im offenen Charakter der Mathtrails, die in der Regel in autonomen Kleingruppen abgelaufen werden. Aus der Literatur ist bekannt, dass insbesondere für schwächere Lerner die Gefahr besteht, durch die Anforderungen einer selbstständigen Arbeitsweise überfordert zu werden.
Als Lösungsansatz für die zuvor genannten Probleme wird im Rahmen dieser Arbeit die Entwicklung eines digitalen Werkzeugs für Mathtrails erläutert. Die erste Forschungsfrage beschäftigt sich mit den theoretischen Anforderungen an solch ein Tool:
1. Welchen Anforderungen muss ein digitales Werkzeug genügen, um die Vorzüge der Mathtrails zu erhalten, deren Aufwand zu minimieren und die Gefahren zu kompensieren?
Unter Berücksichtigung der theoretischen Grundlagen digitaler Werkzeuge und des „Mobile Learnings“ werden zunächst Möglichkeiten identifiziert, den Vorbereitungsaufwand zu minimieren. Konkret erscheinen die automatische Datenverarbeitung, das digitale Zusammen-arbeiten sowie das Teilen und Wiederverwenden von digitalen Aufgaben und Trails als theoretisch zielführende Bestandteile von MCM. Weiterhin sollen zur Unterstützung der Lerner bei der eigenständigen Bearbeitung von Mathtrails didaktisch bewährte Konzepte – wie gestufte Hilfestellungen und Feedback – eingesetzt werden.
Vor dem Hintergrund der soeben formulierten Anforderungen bilden der Entwicklungsprozess sowie die Beschreibung des aktuellen Ist-Zustandes des MCM-Systems zentrale Bestand-teile dieser Arbeit. Das System setzt sich aus zwei Komponenten für jeweils unterschiedliche Zielgruppen zusammen: das MCM-Webportal zum Erstellen von Mathtrails und die MCM-App zum Ablaufen selbiger. Die Hauptziele von MCM können in der Minimierung des Vorbereitungsaufwands sowie der Kompensation einer Überforderungsgefahr gesehen werden.
In ersten Feldversuchen konnte MCM bereits in einem frühen Stadium erfolgreich mit Lernenden der Sekundarstufe I getestet werden. Gleichzeitig fiel jedoch auf, dass das implementierte Feedback-System Schwächen aufwies und von Lernenden zum systematischen Erraten von Lösungen genutzt werden konnte. In der Folge wurden Spielelemente (Gamification), denen nicht nur eine motivationssteigernde Wirkung nachgesagt wird, sondern auch das Potential das Verhalten zu beeinflussen, Bestandteil der MCM-App. Die zweite Forschungs-frage dieser Arbeit zielt auf die Auswirkungen der Gamification-Integration ab und lautet:
2. Welchen Einfluss haben Gamification-Elemente auf die Motivation sowie auf das Nutzungs-verhalten des digitalen Werkzeugs von Neuntklässlern bei der Bearbeitung eines Mathtrails?
Zur Beantwortung der zweiten Forschungsfrage wurde eine empirische Studie mit 16 Schulklassen (304 Schülerinnen und Schüler) der neunten Jahrgangsstufe im Sommer 2017 durch-geführt. Die Ergebnisse können wie folgt zusammengefasst werden: Die Implementierung einer Rangliste (Leaderboard) in die MCM-App führte zwar nicht zu einer höheren Motivation, jedoch spornte der Wettbewerb die Teilnehmer an, viele Aufgaben zu bearbeiten. Im Ver-gleich zu der Kontrollgruppe ohne Gamification-Elemente löste die Experimentalgruppe signifikant mehr Aufgaben, legte die doppelte Strecke zurück und nutzte das Feedbacks-System seltener aus, um Lösungen zu erraten. Die Studie konnte empirisch den gewünschten Einfluss von Spielelementen auf die Benutzung eines digitalen Werkzeugs für das außerschulische Lernen von Mathematik aufzeigen.
Die Evaluation der Ziele von MCM erfolgt indirekt über die Analyse der Verbreitung der Mathtrail-Idee ohne MCM und mit MCM. Die dritte Forschungsfrage lautet dementsprechend:
3. Welchen Beitrag hat das digitale Werkzeug zur Verbreitung der Mathtrail-Idee nach 4 Jahren Projektlaufzeit geleistet?
Zur Beantwortung der dritten Forschungsfrage werden wissenschaftliche Publikationen zu Mathtrails analysiert. Es wird insbesondere in Publikationen mit und ohne Stichwort „MathCityMap“ unterschieden, um eine Aussage über den Einfluss des MCM-Projekts auf den wissenschaftlichen Diskurs treffen zu können. Stand August 2020 enthält bereits jede dritte Mathtrail-Publikation einen Bezug zu MCM. Weiterhin wird ein Vergleich zu vorherigen, ähnlichen Bemühungen – gemeint sind Online-Mitmach-Projekte für Mathtrails – gezogen. So existierten im Zeitraum 2000 bis 2010 im anglo-amerikanischen Raum erste Webseiten für mathematische Wanderpfade. Diese boten zusammengenommen 131 Mathtrails an. Im Vergleich hierzu existieren bereits über 2.500 MCM-Mathtrails in 57 Ländern.
Sowohl die Publikationen als auch die Anzahl der erstellten Trails stellen erste Indizien dafür dar, dass mit MCM die Realisation eines theoretischen Konzepts für ein digitales Mathtrail-Werkzeug gelungen ist und die Idee der Mathtrails verbreitet werden konnte.
The $p$-adic section conjecture predicts that for a smooth, proper, hyperbolic curve $X$ over a $p$-adic field $k$, every section of the map of étale fundamental groups $\pi_1(X) \to G_k$ is induced by a unique $k$-rational point of $X$. While this conjecture is still open, the birational variant in which $X$ is replaced by its generic point is known due to Koenigsmann. Generalising an alternative proof of Pop, we extend this result to certain localisations of $X$ at a set of closed points $S$, an intermediate version in between the full section conjecture and its birational variant. As one application, we prove the section conjecture for $X_S$ whenever $S$ is a countable set of closed points.
A Large Ion Collider Experiment (ALICE) is one of the four large experiments at the Large Hadron Collider (LHC) at the European Organization for Particle Physics (CERN). ALICE focuses on the physics of the strong interaction and in particular on the Quark-Gluon Plasma. This is a state of matter in which quarks are de-confined. It is believed that it existed in the earliest moments of the evolution of the universe. The ALICE detector studies the products of the collisions between heavy-nuclei, between protons, and between protons and heavy-nuclei. The sub-detector closest to the interaction point is the Inner Tracking System (ITS), which is used to measure the momentum and trajectory of the particles generated by the collisions and allows reconstructing primary and secondary interaction vertices. The ITS needs to have an accurate spatial resolution, together with a low material budget to limit the effect of multiple scattering on low-energetic particles to precisely reconstruct their trajectory. During the Long Shutdown 2 (2019-2020) of the LHC, the current ITS will be replaced by a completely redesigned sub-detector, which will improve readout rate and particle tracking performance especially at low-momentum.
The ALice PIxel DEtector (ALPIDE) chip was designed to meet the requirements of the upgraded ITS in terms of resolution, material budget, radiation hardness, and readout rate. The ALPIDE chip is a Monolithic Active Pixel Sensor (MAPS) realised in Complementary Metal-Oxide Semiconductor (CMOS) technology. Sensing element, analogue front-end, and its digital readout are integrated into the same silicon die. The readout architecture of the new ITS foresees that data is transmitted via a high-speed serial link directly from the ALPIDE to the off-detector electronics. The data is transmitted off-chip by a so-called Data Transmission Unit (DTU) which needs to be tolerant to Single-Event Effects induced by radiation, in order to guarantee reliable operation. The ALPIDE chip will operate in a radiation field with a High-Energy Hadron peak flux of 7.7·10^5 cm^-2s^-1.
The data are sent by the ALPIDE on copper cables to the readout system, which aggregates them and re-transmits them via optical fibres to the counting room. The position where the readout electronics will be placed is constrained by the maximum transmission distance reasonably achievable by the ALPIDE Data Transmission Unit and mechanical constraints of the ALICE experiment. The radiation field at that location is not negligible for its effects on electronics: the high-energy hadrons flux can reach 10^3 cm^-2s^-1. Static RAM (SRAM)-based Field Programmable Gate Arrays (FPGAs) are favoured over Application Specific Integrated Circuits (ASICs) or Radiation Hard by Design (RHBD) commercial devices because of cost effectiveness. Moreover, SRAM-based FPGAs are re-configurable and provide the data throughput required by the ITS. The main issue with SRAM-based FPGAs, for the intended application, is the susceptibility of their Configuration RAM (CRAM) to Single-Event Upsets: the number of CRAM bits is indeed much higher than the logic they configure. Total Ionizing Dose (TID) at the readout designed position is indeed still acceptable for Component Off The Shelf (COTS), provided that proper verification is carried out.
This dissertation focuses on two parts of the design of the readout system: the Data Transmission Unit of the ALPIDE chip and the design of fundamental modules for the SRAM-based FPGA of the readout electronics. In the first part, a module of the Data Transmission Unit is designed, optimising the trade-off between power consumption, radiation tolerance, and jitter performance. The design was tested and thoroughly characterised, including tests while under irradiation with a 30 MeV protons. Furthermore the Data Transmission Unit performance was validated after the integration into the first prototypes of ITS modules. In the second part, the problem of developing a radiation-tolerant SRAM-based FPGA design is investigated and a solution is provided. First, a general methodology for designing radiation-tolerant Finite State Machines in SRAM-based FPGAs is analysed, implemented, and verified. Later, the radiation-tolerant FPGA design for the ITS readout is described together with the radiation effects mitigation techniques that were selectively applied to the different modules. The design was tested with multiple irradiation tests and the results are stated below.
Space optimizations in deterministic and concurrent call-by-need functional programming languages
(2020)
In this thesis the space consumption and runtime of lazy-evaluating functional programming languages are analyzed.
The typed and extended lambda-calculi LRP and CHF* as core languages for Haskell and Concurrent Haskell are used. For each LRP and CHF* compatible abstract machines are introduced.
Too lower the distortion of space measurement a classical implementable garbage collector is applied after each LRP reduction step. Die size of expressions and the space measure spmax as maximal size of all garbage-free expressions during an LRP-evaluation, are defined.
Program-Transformations are considered as code-to-code transformations. The notions Space Improvement and Space Equivalence as properties of transformations are defined. A Space Improvement does neither change the semantics nor it increases the needed space consumption, for a space equivalence the space consumption is required to remain the same. Several transformations are shown as Space Improvements and Equivalences.
An abstract machine for space measurements is introduced. An implementation of this machine is used for more complex space- and runtime-analyses.
Total Garbage Collection replaces subexpressions by a non-terminating constant with size zero, if the overall termination is not affected. Thereby the notion of improvement is more independent from the used garbage collector.
Analogous to Space Improvements and Equivalences the notions Total Space Improvement and Total Space Equivalence are defined, which use Total Garbage Collection during the space measurement. Several Total Space Improvements and Equivalences are shown.
Space measures for CHF* are defined, that are compatible to the space measure of LRP. An algorithm with sort-complexity is developed, that calculates the required space of independent processes that all start and end together. If a constant amount of synchronization restrictions is added and a constant number of processors is used, the runtime is polynomial, if arbitrary synchronizations are used, then the problem is NP-complete.
Abstract machines for space- and time-analyses in CHF* are developed and implementations of these are used for space and runtime analyses.
Viele Methoden wurden in dieser Arbeit vorgestellt, die sich mit dem Hauptziel der automatischen Dokumentenanalyse auf semantischer Ebene befassen. Um das Hauptziel zu erreichen, mussten wir jedoch zunächst eine solide Basis entwickeln, um das Gesamtbild zu vervollständigen. So wurden verschiedene Methoden und Werkzeuge entwickelt, die verschiedene Aspekte des NLP abdecken. Das Zusammenspiel dieser Methoden ermöglichte es, unser Ziel erfolgreich zu erreichen. Neben der automatischen Dokumentenanalyse legen wir großen Wert auf die drei Prinzipien von Effizienz, Anwendbarkeit und Sprachunabhängigkeit. Dadurch waren die entwickelten Tools für die Anwendungen bereit. Die Größe und Sprache der zu analysierenden Daten ist kein Hindernis mehr, zumindest für die im Bezug auf die von Wikipedia unterstützten Sprachen.
Einen großen Beitrag dazu leistete TextImager, das Framework, dass für die zugrunde liegende Architektur verschiedener Methoden und die gesamte Vorverarbeitung der Texte verantwortlich ist. TextImager ist als Multi-Server und Multi-Instanz-Cluster konzipiert, sodass eine verteilte Verarbeitung von Daten ermöglicht wird. Hierfür werden Cluster-Management-Dienste UIMA-AS und UIMA-DUCC verwendet. Darüber hinaus ermöglicht die Multi-Service-Architektur von TextImager die Integration beliebiger NLP-Tools und deren gemeinsame Ausführung. Zudem bietet der TextImager eine webbasierte Benutzeroberfläche, die eine Reihe von interaktiven Visualisierungen bietet, die die Ergebnisse der Textanalyse darstellen. Das Webinterface erfordert keine Programmierkenntnisse - durch einfaches Auswählen der NLP-Komponenten und der Eingabe des Textes wird die Analyse gestartet und anschließend visualisiert, so dass auch Nicht-Informatiker mit diesen Tools arbeiten können.
Zudem haben wir die Integration des statistischen Frameworks R in die Funktionalität und Architektur von TextImager demonstriert. Hier haben wir die OpenCPU-API verwendet, um R-Pakete auf unserem eigenen R-Server bereitzustellen. Dies ermöglichte die Kombination von R-Paketen mit den modernsten NLP-Komponenten des TextImager. So erhielten die Funktionen der R-Pakete extrahierte Informationen aus dem TextImager, was zu verbesserten Analysen führte.
Darüber hinaus haben wir interaktive Visualisierungen integriert, um die von R abgeleiteten Informationen zu visualisieren.
Einige der im TextImager entwickelten Visualisierungen sind besonders herausragend und haben in vielen Bereichen Anwendung gefunden. Ein Beispiel dafür ist PolyViz, ein interaktives Visualisierungssystem, das die Darstellung eines multipartiten Graphen ermöglicht. Wir haben PolyViz anhand von zwei verschiedenen Anwendungsfällen veranschaulicht.
SemioGraph, eine Visualisierungstechnik zur Darstellung multikodaler Graphen wurde auch vorgestellt. Die visuellen und interaktiven Funktionen von SemioGraph wurden mit einer Anwendung zur Visualisierung von Worteinbettungen vorgestellt. Wir haben gezeigt, dass verschiedene Modelle zu völlig unterschiedlichen Grafiken führen können. So kann Semiograph bei der Suche nach Worteinbettungen für bestimmte NLP-Aufgaben helfen.
Inspiriert von all den Textvisualisierungen im TextImager ist die Idee für text2voronoi geboren. Hier stellten wir einen neuartigen Ansatz zur bildgetriebenen Textklassifizierung vor, der auf einem Voronoi-Diagram linguistischer Merkmale basiert. Dieser Klassifikationsansatz wurde auf die automatische Patientendiagnose angewendet und wir haben gezeigt, dass wir das traditionelle Bag-Of-Words-Modell sogar übertreffen. Dieser Ansatz ermöglicht es, die zugrunde liegenden Merkmale anschließend zu analysieren und damit einen ersten Schritt zur Lösung der Black Box zu machen.
Wir haben text2voronoi auf literarische Werke angewendet und die entstandenen Visualisierungen auf einer webbasierten Oberfläche (LitViz) präsentiert. Hier ermöglichen wir den Vergleich von Voronoi-Diagrammen der verschiedenen Literaturen und damit den visuellen Vergleich der Sprachstile der zugrunde liegenden Autoren.
Mit unserer Kompetenz in der Vorverarbeitung und der Analyse von Texten sind wir unserem Ziel der semantischen Dokumentenanalyse einen Schritt näher gekommen. Als nächstes haben wir die Auflösung der Sinne auf der Wortebene untersucht. Hier stellten wir fastSense vor, ein Disambigierungsframework, das mit großen Datenmengen zurecht kommt. Um dies zu erreichen, haben wir einen Disambiguierungskorpus erstellt, der auf Wikipedias 221965 Disambiguierungsseiten basiert, wobei die sich auf 825179 Sinne beziehen. Daraus resultierten mehr als 50 Millionen Datensätze, die fast 50 GB Speicherplatz benötigten. Wir haben nicht nur gezeigt, dass fastSense eine so große Datenmenge problemlos verarbeiten kann, sondern auch, dass wir mit unseren Wettbewerbern mithalten und sie bei einigen NLP-Aufgaben sogar übertreffen können.
Jetzt, da wir den Wörtern Sinne zuordnen können, sind wir der semantischen Dokumentenanalyse einen weiteren Schritt näher gekommen. Je mehr Informationen wir aus einem Text und seinen Wörtern gewinnen können, desto genauer können wir seinen Inhalt analysieren. Wir stellten zudem einen netzwerktheoretischen Ansatz zur Modellierung der Semantik großer Textnetzwerke am Beispiel der deutschen Wikipedia vor. Zu diesem Zweck haben wir einen Algorithmus namens text2ddc entwickelt, um die thematische Struktur eines Textes zu modellieren. Dabei basiert das Modell auf einem etablierten Klassifikationsschema, nämlich der Dewey Decimal Classification. Mit diesem Modell haben wir gezeigt, wie man aus der Vogelperspektive die Hervorhebung und Verknüpfung von Themen, die sich in Millionen von Dokumenten manifestiert, darstellt. So haben wir eine Möglichkeit geschaffen, die thematische Dynamik von Dokumentnetzwerken automatisch zu visualisieren. Die Trainings- und Testdaten, die wir in diesem Kapitel hatten, bestanden jedoch hauptsächlich aus kurzen Textausschnitten. Zudem haben wir DDC Korpora erstellt, indem wir Informationen aus Wikidata, Wikipedia und der von der Deutschen Nationalbibliothek verwalteten Gemeinsamen Normdatei (GND) vereinigt haben. Auf diese Weise konnten wir nicht nur die Datenmenge erhöhen, sondern auch Datensätze für viele bisher unzugängliche Sprachen erstellen. Wir haben text2ddc so weit optimiert, dass wir einen F-score von 87.4% erzielen für die 98 Klassen der zweiten DDC-Stufe. Die Vorverarbeitung von TextImager und die Disambiguierung durch fastSense hatten einen großen Einfluss darauf. Für jedes Textstück berechnet text2ddc eine Wahrscheinlichkeitsverteilung über die DDC-Klassen berechnen
Der klassifikatorinduzierte semantische Raum von text2ddc wurde auch zur Verbesserung weiterer NLP-Methoden genutzt. Dazu gehört auch text2wiki, ein Framework für automatisches Tagging nach dem Wikipedia-Kategoriensystem. Auch hier haben wir einen klassifikatorinduzierten semantischen Raum, aber diesmal basiert er auf dem Wikipedia-Kategoriensystem. Ein großer Vorteil dieses Modells ist die Präzision und Tiefe der behandelten Themen und das sich ständig weiterentwickelnde Kategoriesystem. Damit sind auch die Kriterien eines offenen Themenmodells erfüllt. Um die Vorteile von text2wiki zu demonstrieren, haben wir anschließend die von text2wiki bereitgestellten Themenvektoren verwendet, um text2ddc zu verbessern, so dass sich beide Systeme gegenseitig verbessern können. Die Synergie zwischen den erstellten Methoden in dieser Dissertation war entscheidend für den Erfolg jeder einzelnen Methode.
The World Wide Web is increasing the number of freely accessible textual data, which has led to an increasing interest in research in the field of computational linguistics (CL). This area of research addresses theoretical research to answer the question of how language and knowledge must be represented in order to understand and produce language. For this purpose, mathematical models are being developed to capture the phenomena at various levels in human languages. Another field of research experiencing an increase in interest that is closely related to CL is Natural Language Processing (NLP), which is primarily concerned with developing effective and efficient data structures and algorithms that implement the mathematical models of CL.
With increasing interest in these areas, NLP tools are rapidly and frequently being developed incorporating different CL models to handle different levels of language. The open source trend has benefited all those in the scientific community who develop and use these tools. Due to yet undefined I/O standards for NLP, however, the rapid growth leads to a heterogeneous NLP landscape in which the specializations of the tools cannot benefit from each other because of interface incompatibility. In addition, the constantly growing amount of freely accessible text data requires a high-performance processing solution. This performance can be achieved by horizontal and vertical scaling of hardware and software. For these reasons the first part of this thesis deals with the homogenization of the NLP tool landscape, which is achieved by a standardized framework called TextImager. It is a cloud computing based multi-service, multi-server, multi-pipeline, multi-database, multi-user, multi-representation and multi-visual framework that already provides a variety of tools for various languages to process various levels of linguistic complexity. This makes it possible to answer research questions that require the processing of a large amount of data at several linguistic levels.
The integrated tools and the homogenized I/O data streams of the TextImager make it possible to combine the built-in tools in two dimensions: (1) the horizontal dimension to achieve NLP task-specific improvement (2) the orthogonal dimension to implement CL models that are based on multiple linguistic levels and thus rely on a combination of different NLP tools. The second part of this thesis therefore deals with the creation of models for the horizontal combination of tools in order to show the possibilities for improvement using the example of the NLP task of Named Entity Recognition (NER). The TextImager offers several tools for each NLP task, most of which have been trained on the same training basis, but can produce different results. This means that each of the tools processes a subset of the data correctly and at the same time makes errors in another subset. In order to process as large a subset of the data as possible correctly, a horizontal combination of tools is therefore required. Machine learning-based voting mechanisms called LSTMVoter and CRFVoter were developed for this purpose, which allow a combination of the outputs of individual NLP tools so that better partial data results can be achieved. In this thesis the benefit of Voter is shown using the example of the NER task, whose results flow
back into the TextImager tool landscape.
The third part of this thesis deals with the orthogonal combination of TextImager tools to accomplish the verb sense disambiguation (VSD). The CL question is investigated, how verb senses should be modelled in order to disambiguate them computatively. Verbsenses have a syntagmatic-paradigmatic relationship with surrounding words. Therefore, preprocessing on several linguistic levels and consequently an orthogonal combination of NLP tools is required to disambiguate verbs on a computational level. With TextImager’s integrated NLP landscape, it is now possible to perform these preprocessing steps to induce the information needed for the VSD. The newly developed NLP tool for the VSD has been integrated into the TextImager tool landscape, enabling the analysis of a further linguistic level.
This thesis presents a framework that homogenizes the NLP tool landscape in a cluster-based way. Methods for combining the integrated tools are implemented to improve the analysis of a specific linguistic level or to develop tools that open up new linguistic levels.