Learning content in mathematics, such as vector geometry, is still predominantly taught in an abstract manner, as the visualization and interaction of three-dimensional problems are limited with classical forms of teaching such as blackboard lessons or exercise sheets. This research article proposes the use of augmented reality (AR) in mathematics education. The proposed approach aims at easing the learning process related to vector geometry currently taught in senior mathematics classes by using intuitive visualization. The article introduces the concept of AR and presents the didactic foundations and the influence on the learning process based on an extensive literature review. Although studies see great potential in the use of AR for teaching mathematics, the method has so far hardly been used in schools. This can be mainly explained by the technological entry barrier of AR and the lack of simple, robust AR applications, in particular for vector geometry. To fill this gap, the authors developed “cleARmaths”, a developed android application for augmented reality-based teaching in vector geometry that allows widespread use. As a didactical concept, some example exercises sessions with the app are proposed, demonstrating how the app could be used in a mathematics classroom. Finally, the app was evaluated in a mathematics class and the results analyzed in a detailed study. It was found by the teacher and students to be beneficial and amusing, demonstrating the potential for AR in mathematics classes.

Raman and mid-infrared (MIR) spectroscopy are useful tools for the specific detection of molecules, since both methods are based on the excitation of fundamental vibration modes. In this study, Raman and MIR spectroscopy were applied simultaneously during aerobic yeast fermentations of Saccharomyces cerevisiae. Based on the recorded Raman intensities and MIR absorption spectra, respectively, temporal concentration courses of glucose, ethanol, and biomass were determined. The chemometric methods used to evaluate the analyte concentrations were partial least squares (PLS) regression and multiple linear regression (MLR). In view of potential photometric sensors, MLR models based on two (2D) and four (4D) analyte-specific optical channels were developed. All chemometric models were tested to predict glucose concentrations between 0 and 30 g L⁻¹, ethanol concentrations between 0 and 10 g L⁻¹, and biomass concentrations up to 15 g L⁻¹ in real time during diauxic growth. Root-mean-squared errors of prediction (RMSEP) of 0.68 g L⁻¹, 0.48 g L⁻¹, and 0.37 g L⁻¹ for glucose, ethanol, and biomass were achieved using the MIR setup combined with a PLS model. In the case of Raman spectroscopy, the corresponding RMSEP values were 0.92 g L⁻¹, 0.39 g L⁻¹, and 0.29 g L⁻¹. Nevertheless, the simple 4D MLR models could reach the performance of the more complex PLS evaluation. Consequently, the replacement of spectrometer setups by four-channel sensors were discussed. Moreover, the advantages and disadvantages of Raman and MIR setups are demonstrated with regard to process implementation.

One of the main topics within research activities is the management of research data. Large amounts of data acquired by heterogeneous scientific devices, sensor systems, measuring equipment, and experimental setups have to be processed and ideally be managed by Findable, Accessible, Interoperable, and Reusable (FAIR) data management approaches in order to preserve their intrinsic value to researchers throughout the entire data lifecycle. The symbiosis of heterogeneous measuring devices, FAIR principles, and digital twin technologies is considered to be ideally suited to realize the foundation of reliable, sustainable, and open research data management. This paper contributes a novel architectural approach for gathering and managing research data aligned with the FAIR principles. A reference implementation as well as a subsequent proof of concept is given, leveraging the utilization of digital twins to overcome common data management issues at equipment-intense research institutes. To facilitate implementation, a top-level knowledge graph has been developed to convey metadata from research devices along with the produced data. In addition, a reactive digital twin implementation of a specific measurement device was devised to facilitate reconfigurability and minimized design effort.

Frozen section analysis is a frequently used method for examination of tissue samples, especially for tumour detection. In the majority of cases, the aim is to identify characteristic tissue morphologies or tumour margins. Depending on the type of tissue, a high number of misdiagnoses are associated with this process. In this work, a fast spectroscopic measurement device and workflow was developed that significantly improves the speed of whole frozen tissue section analyses and provides sufficient information to visualize tissue structures and tumour margins, dependent on their lipid and protein molecular vibrations. That optical and non-destructive method is based on selected wavenumbers in the mid-infrared (MIR) range. We present a measuring system that substantially outperforms a commercially available Fourier Transform Infrared (FT-IR) Imaging system, since it enables acquisition of reduced spectral information at a scan field of 1 cm² in 3 s, with a spatial resolution of 20 µm. This allows fast visualization of segmented structure areas with little computational effort. For the first time, this multiphotometric MIR system is applied to biomedical tissue sections. We are referencing our novel MIR scanner on cryopreserved murine sagittal and coronal brain sections, especially focusing on the hippocampus, and show its usability for rapid identification of primary hepatocellular carcinoma (HCC) in mouse liver.

The complex molecular alterations that underlie cancer pathophysiology are studied in depth with omics methods using bulk tissue extracts. For spatially resolved tissue diagnostics using needle biopsy cores, however, histopathological analysis using stained FFPE tissue and the immunohistochemistry (IHC) of a few marker proteins is currently the main clinical focus. Today, spatial omics imaging using MSI or IRI is an emerging diagnostic technology for the identification and classification of various cancer types. However, to conserve tissue-specific metabolomic states, fast, reliable, and precise methods for the preparation of fresh-frozen (FF) tissue sections are crucial. Such methods are often incompatible with clinical practice, since spatial metabolomics and the routine histopathology of needle biopsies currently require two biopsies for FF and FFPE sampling, respectively. Therefore, we developed a device and corresponding laboratory and computational workflows for the multimodal spatial omics analysis of fresh-frozen, longitudinally sectioned needle biopsies to accompany standard FFPE histopathology of the same biopsy core. As a proof-of-concept, we analyzed surgical human liver cancer specimens using IRI and MSI with precise co-registration and, following FFPE processing, by sequential clinical pathology analysis of the same biopsy core. This workflow allowed for a spatial comparison between different spectral profiles and alterations in tissue histology, as well as a direct comparison for histological diagnosis without the need for an extra biopsy.