In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically—showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the 1-dimensional Weisfeiler-Leman graph isomorphism heuristic (1-WL). We show that GNNs have the same expressiveness as the 1-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called k-dimensional GNNs (k-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.

The PAMONO-sensor (plasmon assisted microscopy of nano-objects) demonstrated an ability to detect and quantify individual viruses and virus-like particles. However, another group of biological vesicles—microvesicles (100–1000 nm)—also attracts growing interest as biomarkers of different pathologies and needs development of novel techniques for characterization. This work shows the applicability of a PAMONO-sensor for selective detection of microvesicles in aquatic samples. The sensor permits comparison of relative concentrations of microvesicles between samples. We also study a possibility of repeated use of a sensor chip after elution of the microvesicle capturing layer. Moreover, we improve the detection features of the PAMONO-sensor. The detection process utilizes novel machine learning techniques on the sensor image data to estimate particle size distributions of nano-particles in polydisperse samples. Altogether, our findings expand analytical features and the application field of the PAMONO-sensor. They can also serve for a maturation of diagnostic tools based on the PAMONO-sensor platform.

In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically -- showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the $1$-dimensional Weisfeiler-Leman graph isomorphism heuristic ($1$-WL). We show that GNNs have the same expressiveness as the $1$-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called $k$-dimensional GNNs ($k$-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.

A mobile system that can detect viruses in real time is urgently needed, due to the combination of virus emergence and evolution with increasing global travel and transport. A biosensor called PAMONO (for Plasmon Assisted Microscopy of Nano-sized Objects) represents a viable technology for mobile real-time detection of viruses and virus-like particles. It could be used for fast and reliable diagnoses in hospitals, airports, the open air, or other settings. For analysis of the images provided by the sensor, state-of-the-art methods based on convolutional neural networks (CNNs) can achieve high accuracy. However, such computationally intensive methods may not be suitable on most mobile systems. In this work, we propose nanoparticle classification approaches based on frequency domain analysis, which are less resource-intensive. We observe that on average the classification takes 29 $\mathsf{\mu }$ s per image for the Fourier features and 17 $\mathsf{\mu }$ s for the Haar wavelet features. Although the CNN-based method scores 1–2.5 percentage points higher in classification accuracy, it takes 3370 $\mathsf{\mu }$ s per image on the same platform. With these results, we identify and explore the trade-off between resource efficiency and classification performance for nanoparticle classification of images provided by the PAMONO sensor.

In our recent work, the plasmon assisted microscopy of nano-objects (PAMONO) was successfully employed for the detection and quantification of individual viruses and virus-like particles in aquatic samples (Shpacovitch et al., 2015).