The manifold of essential matrices is equipped with a one-parameter family of (pseudo-)Riemannian metrics. For the whole family, explicit formulas for geodesics are derived. Moreover, specific curves, so-called quasi-geodesics, are studied and a closed form expression for a quasi-geodesic connecting two given essential matrices is obtained.

In this paper, we show an application of spatiotemporal persistence landscapes to real world time series. Spatiotemporal persistence landscapes are a recent extension of persistence landscapes to time series that capture features of the data that are persistent with respect to time and space. We perform our analysis on EEG data to detect absence epileptic seizures. Further, we compare two dimension reduction techniques (DyCA and PCA) with no dimension reduction and show that the combination of DyCA and persistent landscapes yields the best results.

This paper discusses the challenges and methods for source reconstruction of evoked potentials using deep learning in the context of electroencephalography (EEG). We propose the use of deep learning to address known challenges and improve traditional approaches. We explain the creation of a suitable dataset for solving the inverse problem, including the simulation of neural activity and the use of lead field matrices for the forward solution. Furthermore, we undertake a comparative analysis of some initial deep learning models with similar classical methods.

Dynamical Component Analysis (DyCA) and Dynamic Mode Decomposition (DMD), both data-driven dimension reduction methods, are introduced. After application to multivariate simulated signals the techniques of mode selection and the resulting amplitudes are compared with respect to noise robustness and sampling periods. The results indicate that DyCA is a useful alternative to DMD and outperforms DMD under certain conditions. These conditions are based on the underlying dynamics in the terms of differential equations and on the noise ratios of the signals.

This study describes the development of an operation-independent simulation model for an electrified die-casting foundry that uses a smart grid system to meet its energy needs. The model uses real weather and stock exchange electricity price data for the simulation period. The model can be used to determine and compare the cost of electricity for production at a given time (time of day and season) as well as the economics of different PV system and electricity storage options. It is also possible to analyze the share of different energy sources for each configuration. This can be done for sites throughout Germany. In addition, exemplary simulation studies are presented in this paper which demonstrate the wide range of applications of the model. The results provide an initial overview of the potential for savings and optimization. In the future, the model will provide a basis for determining optimum plant layouts and production times by means of simulation-based optimization.

The skilled trade industry is a significant driving force for the development and prosperity of society and constitutes the backbone of the German economy with its small and medium-sized enterprises. Currently, waiting times for craftsmen stand at approximately three months. This trend is on the rise due to the continued and severe shortage of apprentices and skilled workers. Potential trainees are representatives of Generation Z and best reached through social media channels. Consequently, many companies deliberately utilize corporate influencers in employer branding efforts to win young talents. Corporate influencers have the ability to present specifically job-related content and offer more authentic insights into the daily work environment. However, do they genuinely influence the career preferences of potential trainees? The aim of this study is to investigate if and to what extent corporate influencer influence the perception of the skilled trades industry and career preferences of potential applicants. To investigate the impact of corporate influencers on the perception of the skilled trade industry and the respective career preferences of potential applicants, we conducted a study with 66 students from a secondary school in Germany. (1) First, we measured the perception of the skilled trades industry and career preferences of the participants. (2) Then we exposed them to previously selected content of two corporate influencers from the skilled trades sector. (3) After the exposure, we measured the perception of the skilled trades industry and career preferences of the participants again. For the statistical analysis we used regression analyses and T-tests. The findings of the study show that corporate influencer on social media positively influenced both, the perception of the skilled trades industry and the career preferences of potential applicants. Particularly, insights into daily work routines prove to be effective. Simultaneously, the study reveals that the employer attractiveness of the skilled trades industry in general significantly influences the perception of the industry and enhances applicants' interest in craft professions.