S. Huber

Elias Reich, Saverio Messineo, Stefan Huber

Discrete automated processes in industrial and cyber-physical systems often exhibit a repetitive structure in which successive repetitions follow a common trajectory while differing in duration, amplitude, and fine-scale dynamics. Such \emph{approximately periodic} behavior poses a challenge for Gaussian Processes (GP) modeling: strictly periodic models suppress inter-repetition variability, while non-periodic models fail to capture the strong structural regularities required for generation. In this work, we propose a stochastic generative model for approximately periodic time series. The model is based on a GP whose posterior is modulated by a novel kernel. Our approach decouples intra-repetition structure from inter-repetition variability through a two-stage construction which yields a generative distribution with a identical mean function across repetitions, while allowing smooth variation between repetitions. The modeling choices are supported by an implementation in which realistic synthetic trajectories are generated from toy datasets.

Johannes Ferner, Stefan Huber, Saverio Messineo et al.

The Hough transform is a popular and classical technique in computer vision for the detection of lines (or more general objects). It maps a pixel into a dual space -- the Hough space: each pixel is mapped to the set of lines through this pixel, which forms a curve in Hough space. The detection of lines then becomes a voting process to find those lines that received many votes by pixels. However, this voting is done by thresholding, which is susceptible to noise and other artifacts. In this work, we present an alternative voting technique to detect peaks in the Hough space based on persistent homology, which very naturally addresses limitations of simple thresholding. Experiments on synthetic data show that our method significantly outperforms the original method, while also demonstrating enhanced robustness. This work seeks to inspire future research in two key directions. First, we highlight the untapped potential of Topological Data Analysis techniques and advocate for their broader integration into existing methods, including well-established ones. Secondly, we initiate a discussion on the mathematical stability of the Hough transform, encouraging exploration of mathematically grounded improvements to enhance its robustness.

Jonas Thiergart, Stefan Huber, Thomas Übellacker

Providing computer systems with the ability to understand and generate natural language has long been a challenge of engineers. Recent progress in natural language processing (NLP), like the GPT-3 language model released by OpenAI, has made both possible to an extent. In this paper, we explore the possibility of rationalising email communication using GPT-3. First, we demonstrate the technical feasibility of understanding incoming emails and generating responses, drawing on literature from the disciplines of software engineering as well as data science. Second, we apply knowledge from both business studies and, again, software engineering to identify ways to tackle challenges we encountered. Third, we argue for the economic viability of such a solution by analysing costs and market demand. We conclude that applying GPT-3 to rationalising email communication is feasible both technically and economically.