Open Access

In this paper we describe methods to approximate functions and differential operators on adaptive sparse (dyadic) grids. We distinguish between several representations of a function on the sparse grid and we describe how finite difference (FD) operators can be applied to these representations. For general variable coefficient equations on sparse grids, genuine finite element (FE) discretizations are not feasible and FD operators allow an easier operator evaluation than the adapted FE operators. However, the structure of the FD operators is complex. With the aim to construct an efficient multigrid procedure, we analyze the structure of the discrete Laplacian in its hierarchical representation and show the relation between the full and the sparse grid case. The rather complex relations, that are expressed by scaling matrices for each separate coordinate direction, make us doubt about the possibility of constructing efficient preconditioners that show spectral equivalence. Hence, we question the possibility of constructing a natural multigrid algorithm with optimal O(N) efficiency. We conjecture that for the efficient solution of a general class of adaptive grid problems it is better to accept an additional condition for the dyadic grids (condition L) and to apply adaptive hp-discretization.

The paper presents a comprehensive model of a banking system that integrates network effects, bankruptcy costs, fire sales, and cross-holdings. For the integrated financial market we prove the existence of a price-payment equilibrium and design an algorithm for the computation of the greatest and the least equilibrium. The number of defaults corresponding to the greatest price-payment equilibrium is analyzed in several comparative case studies. These illustrate the individual and joint impact of interbank liabilities, bankruptcy costs, fire sales and cross-holdings on systemic risk. We study policy implications and regulatory instruments, including central bank guarantees and quantitative easing, the significance of last wills of financial institutions, and capital requirements.

Die Arbeit untersucht die Anwendung von maschinellem Lernen zur Erkennung von Aktivitäten von Schiffen anhand von AIS-Signalen. Das Automatic Identification System (AIS) wird von Schiffen genutzt, um Informationen über ihren Status in regelmäßigen Intervallen zu übertragen. Auf Basis der Daten wurden mithilfe von Machine Learning-Algorithmen aus der Gruppe der überwachten Klassifikationsalgorithmen Modelle gelernt, die in der Lage sind zu erkennen, welcher Aktivität ein Schiff zu einem Zeitpunkt nachgeht. Da das erfolgreiche Lernen eines Modells von einer sorgfältigen Datenvorbereitung abhängt, wurden verschiedene Verfahren zur Datenvorbereitung verwendet. Anschließend wurden verschiedene Algorithmen eingesetzt, darunter der Random Forest und k-NN, um Modelle zu lernen. Die Ergebnisse zeigen, dass die Aktivitäten mit einer Genauigkeit von bis zu 99% erkannt werden konnten, wenn in der Datenvorbereitung geeignete Verfahren gewählt wurden.

In the last years generative models have gained large public attention due to their high level of quality in generated images. In short, generative models learn a distribution from a finite number of samples and are able then to generate infinite other samples. This can be applied to image data. In the past generative models have not been able to generate realistic images, but nowadays the results are almost indistinguishable from real images. This work provides a comparative study of three generative models: Variational Autoencoder (VAE), Generative Adversarial Network (GAN) and Diffusion Models (DM). The goal is not to provide a definitive ranking indicating which one of them is the best, but to qualitatively and where possible quantitively decide which model is good with respect to a given criterion. Such criteria include realism, generalization and diversity, sampling, training difficulty, parameter efficiency, interpolating and inpainting capabilities, semantic editing as well as implementation difficulty. After a brief introduction of how each model works on the inside, they are compared against each other. The provided images help to see the differences among the models with respect to each criterion. To give a short outlook on the results of the comparison of the three models, DMs generate most realistic images. They seem to generalize best and have a high variation among the generated images. However, they are based on an iterative process, which makes them the slowest of the three models in terms of sample generation time. On the other hand, GANs and VAEs generate their samples using one single forward-pass. The images generated by GANs are comparable to the DM and the images from VAEs are blurry, which makes them less desirable in comparison to GANs or DMs. However, both the VAE and the GAN, stand out from the DMs with respect to the interpolations and semantic editing, as they have a latent space, which makes space-walks possible and the changes are not as chaotic as in the case of DMs. Furthermore, concept-vectors can be found, which transform a given image along a given feature while leaving other features and structures mostly unchanged, which is difficult to archive with DMs.

Im Rahmen dieser Bachelorarbeit werden zwei Skelettierungsalgorithmen für Baum-Punktwolken implementiert und miteinander verglichen. Darüber hinaus werden zwei Erweiterungen für einen der beiden Algorithmen präsentiert.

During the Corona-Pandemic, information (e.g. from the analysis of balance sheets and payment behavior) traditionally used for corporate credit risk analysis became less valuable because it represents only past circumstances. Therefore, the use of currently published data from social media platforms, which have shown to contain valuable information regarding the financial stability of companies, should be evaluated. In this data e. g. additional information from disappointed employees or customers can be present. In order to analyze in how far this data can improve the information base for corporate credit risk assessment, Twitter data regarding the ten greatest insolvencies of German companies in 2020 and solvent counterparts is analyzed in this paper. The results from t-tests show, that sentiment before the insolvencies is significantly worse than in the comparison group which is in alignment with previously conducted research endeavors. Furthermore, companies can be classified as prospectively solvent or insolvent with up to 70% accuracy by applying the k-nearest-neighbor algorithm to monthly aggregated sentiment scores. No significant differences in the number of Tweets for both groups can be proven, which is in contrast to findings from studies which were conducted before the Corona-Pandemic. The results can be utilized by practitioners and scientists in order to improve decision support systems in the domain of corporate credit risk analysis. From a scientific point of view, the results show, that the information asymmetry between lenders and borrowers in credit relationships, which are principals and agents according to the principal-agent-theory, can be reduced based on user generated content from social media platforms. In future studies, it should be evaluated in how far the data can be integrated in established processes for credit decision making. Furthermore, additional social media platforms as well as samples of companies should be analyzed. Lastly, the authenticity of user generated contend should be taken into account in order to ensure, that credit decisions rely on truthful information only.

Unternehmen, die sich ernsthaft mit Nachhaltigkeit beschäftigen, müssen den Nachweis erbringen, dass sie positive Effekte für die Gesellschaft erzielen. Damit ist eine ganzheitliche Wirkungsmessung unabdingbar. Sozialunternehmen sollten als Vorbild für eine solche Wirkungsmessung dienen. Eine wissenschaftliche Studie auf Basis der sog. „Ergebnispyramide“ kommt jedoch zu dem Schluss, dass selbst diese ihre Wirkung bisher kaum ganzheitlich messen.

Music streaming platforms offer music listeners an overwhelming choice of music. Therefore, users of streaming platforms need the support of music recommendation systems to find music that suits their personal taste. Currently, a new class of recommender systems based on knowledge graph embeddings promises to improve the quality of recommendations, in particular to provide diverse and novel recommendations. This paper investigates how knowledge graph embeddings can improve music recommendations. First, it is shown how a collaborative knowledge graph can be derived from open music data sources. Based on this knowledge graph, the music recommender system EARS (knowledge graph Embedding-based Artist Recommender System) is presented in detail, with particular emphasis on recommendation diversity and explainability. Finally, a comprehensive evaluation with real-world data is conducted, comparing of different embeddings and investigating the influence of different types of knowledge.

The transfer of historically grown monolithic software architectures into modern service-oriented architectures creates a lot of loose coupling points. This can lead to an unforeseen system behavior and can significantly impede those continuous modernization processes, since it is not clear where bottlenecks in a system arise. It is therefore necessary to monitor such modernization processes with an adaptive monitoring concept to be able to correctly record and interpret unpredictable system dynamics. This contribution presents a generic QoS measurement framework for service-based systems. The framework consists of an XML-based specification for the measurement to be performed – the Information Model (IM) – and the QoS System, which provides an execution platform for the IM. The framework will be applied to a standard business process of the German insurance industry, and the concepts of the IM and their mapping to artifacts of the QoS System will be presented. Furtherm ore, design and implementation of the QoS System’s parser and generator module and the generated artifacts are explained in detail, e.g., event model, agents, measurement module and analyzer module.

Even for the more traditional insurance industry, the Microservices Architecture (MSA) style plays an increasingly important role in provisioning insurance services. However, insurance businesses must operate legacy applications, enterprise software, and service-based applications in parallel for a more extended transition period. The ultimate goal of our ongoing research is to design a microservice reference architecture in cooperation with our industry partners from the insurance domain that provides an approach for the integration of applications from different architecture paradigms. In Germany, individual insurance services are classified as part of the critical infrastructure. Therefore, German insurance companies must comply with the Federal Office for Information Security requirements, which the Federal Supervisory Authority enforces. Additionally, insurance companies must comply with relevant laws, regulations, and standards as part of the business’s compliance requirements. Note: Since Germany is seen as relatively ’tough’ with respect to privacy and security demands, fullfilling those demands might well be suitable (if not even ’over-achieving’) for insurances in other countries as well. The question raises thus, of how insurance services can be secured in an application landscape shaped by the MSA style to comply with the architectural and security requirements depicted above. This article highlights the specific regulations, laws, and standards the insurance industry must comply with. We present initial architectural patterns to address authentication and authorization in an MSA tailored to the requirements of our insurance industry partners.