Bachelor-, Diplom- und Masterarbeiten

Simulating “Kommunaler Finanzausgleich”

How much a municipality or city receives in its annual budget through the federal equalization mechanism depends on a huge number of factors, the interaction of which is difficult for out- and insiders to understand. For example, it is not only the municipality’s own tax revenue that is decisive, but also indirectly the population in the other municipalities. The aim of the project is to provide a tool with which the calculations can be carried out automatically and, if possible, presented in a graphically appealing way. In addition to finding and entering raw data, the difficulties of the project are the sometimes changing legal regulations over time. Nevertheless the main scientific focus will be on how sensitive the system is to the parameter of the “Grundsteuer Hebesatz”, which can be set by each local authority.

Note: In terms of content, this project is very much geared towards dual students of the tax office, as a great deal of specialized knowledge will be required. Nevertheless, the topic is of course open to all students.

Inquiries: Tobias Hille

To be (distributive) or not to be: Distributivity of Real World Data

In this work, we propose a series of experiments aimed at exploring some structural properties of non-distributive lattices on real-world datasets. Our primary objective is to implement and evaluate methods that measure how far a given lattice deviates from being distributive. These methods will provide a quantitative understanding of non-distributivity . The effectiveness of these techniques will be tested on real datasets from various domains, allowing us to assess their practical applicability.

Inquiries: Mohammad Abdulla

Formalizing Results of Formal Concept Analysis

Formalization of a large number of definitions and theorems in Algebra, Number Theory and Analysis in the lean prover brings the field of formal theorem proving to the forefront of mathematical research. However, mathematical notions and results from the field of Formal Concept Analysis are not yet included. Thus the goal of this project (or thesis) is to formally prove the “Basic Theorem on Concept Lattices” (or a comparable result) in order to provide a stepping stone in this direction. Essentially, this involves building core definitions and necessary preliminary results by extending existing ones. We will aim to build a lean blueprint and if you are only interested in a small project, we will find a reasonable partial realization to stop at.

Inquiries: Tobias Hille

Implementierung von Algorithmen für die Ordnungsdimension

Es gibt diverse Algorithmen zur Berechnung der Ordnungsdimension. In diesem Projekt implementieren Sie diese und evaluieren ihre Qualität im Hinblick auf Laufzeit und Speicherplatzbedarf.

Informationen: Dominik Dürrschnabel

Temporal Ordinal Motifs in Topic Models

Topic models are, often, dimension reduction techniques for large corpora of textual documents. A central aspect to these models is that they allow for text based explanations of the dimensions in the reduced space. A novel technique, called ordinal motifs, interpret and visualize these dimension hierarchically with respect to (ordinal) substructures of standard shape. With your work, you extent this technique towards ordinal motifs over time, develop visualization techniques, and show their applicability in a practical setting.

Informationen: Johannes Hirth

Ordinal Motifs in Hierarchical Topic Models

Topic models are, often, dimension reduction techniques for large corpora of textual documents. A central aspect to these models is that they allow for text based explanations of the dimensions in the reduced space. A novel technique, called ordinal motifs, interpret and visualize these dimension hierarchically with respect to (ordinal) substructures of standard shape. With your work, you extent this technique towards hierarchical topic models, define hierarchical motif structures, develop visualization techniques, and show their applicability in a practical setting.

Informationen: Johannes Hirth

Network Motifs in Topic Flow Networks

In scientometrics, scientific collaboration is often analyzed by means of co-authorships. An aspect which is often overlooked and more difficult to quantify is the flow of expertise between authors from different research topics, which is an important part of scientific progress. With the Topic Flow Network (TFN) a graph structure for the analysis of research topic flows between scientific authors and their respective research fields was proposed. With your work, you identify and interpret substructures that are integral to this network.

Informationen: Johannes Hirth

Formal Concept Analysis mit Attribut und Objektordnungen

In dieser Arbeit untersuchen Sie, inwiefern sich die Theorie der formalen Begriffsanalyse auf den Fall übertragen lässt, dass wir eine lineare Ordnung auf den Attributen und den Objekten vorliegen haben.

Das Ziel ist es, die in der FCA üblichen Ideen (Begriffe, Implikationen etc.) auf solche Datensätze zu übertragen und die Theorie mit Echtwelt-Datensätzen zu evaluieren.

Informationen: Dominik Dürrschnabel

Tag Combination and Synthesis in OpenStreetMap

The geographically organised objects in OpenStreetMap are usually tagged with a large number of tags. A side effect of the wiki ethos, however, is that tags are not used consistently and there is a lot of duplication and overlap. Building on previous work analysing tags, we will now look for tags that that have similar meanings or serve the same purpose. A demonstration application is to be developed for the project, which will give suggestions for combining or changing the current tags assigned to an object.
Most (if not all) of the programming will be done in Python.

Inquiries: Tobias Hille

Detecting Graphs in Images

The project aims to develop a machine learning model that can detect (simple) graphs in images. This involves not only an extensive literature review but also gathering useful training data. Moreover we need to train the model to recognize and segment images containing graphs. The project will use image classification algorithms and techniques to achieve this goal. Completing individual parts may already be enough for a successful conclusion. You will build upon work done by previous participants.
Most (if not all) of the programming will be done in Python.

Inquiries: Tobias Hille