We introduce Quantitative Market Situation Embeddings (QMSEs), a pioneering artificial intelligence (AI)-driven methodology for encoding distinct temporal segments of stock markets into high-dimensional contextual embeddings exclusively leveraging quantitative stock data. Building upon prior research, we construe quantitative stock data analogously to Natural Language Processing (NLP) data, thereby adopting Doc2Vec methodologies to effectuate the embedding of stock data similar to document-level representations. We ascertain the efficacy of QMSEs in representing market dynamics by assessing their ability to discern various significant economic downturns post-2000, including but not limited to, the events of 9/11, the Subprime Crisis of 2008, and the Covid-induced market disruption. Moreover, we elucidate the practical utility of QMSEs through their application in employing distance metrics to gauge the rarity of market scenarios, serving as a regularizer in the training of quantitative stock AI models. Subsequently, we proceed to assess the algorithmic identification of analogous market conditions, aiming to elucidate their potential implications for future stock movements. Additionally, we demonstrate the efficacy of QMSEs in reducing data requirements for quantitative stock AI models by leveraging them as condensed representations of stock data.

The vast majority of cardiovascular diseases are avoidable or treatable by preventive measures and early de-tection. To efficiently detect early signs and risk factors, car-diovascular parameters can be monitored continuously with small sensor patches, which improve the comfort of patients. However, processing the sensor data is a challenging task with the demanding needs of robustness, reliability, performance and efficiency. The field of deep learning has tremendous potential to provide a way to analyze cardiovascular sensor data to detect anomalies which alleviates the workload of doctors for more effective data interpretation. In this work, we show the feasibility of applying deep learning for the classification of synchronized electrocardiogram and phonocardiogram recordings under very tight resource constraints. Our model employs an early fusion of data and uses convolutional layers to solve the problem of binary classification of anomalies. Our experiments show that our model matches the accuracy of the current state-of-the-art model on the “training-a” dataset of the Physionet Challenge 2016 database while being more than two orders of magnitude more efficient in memory footprint and compute cost. Further, we demonstrate the applicability of our model on edge devices, such as sensor patches, by estimating processor performance, power consumption, and silicon area.

Since segmentation of surface data is of growing interest, many image segmentation algorithms have already been applied to surfaces. Mesh segmentation can not only be based on color and texture but also on shape properties like curvature. Graph Cuts based methods are very popular and also applicable to mesh data having irregular vertex neighborhoods. However, Graph Cuts suffer from problems such as shortcuts, generation of small regions and sensitivity to variations of the boundary indicator function. Moreover, they are often hard to implement and computationally expensive. Here we show that a quite old approach for image segmentation, a fast and extremely simple greedy algorithm, which we call LexicoGraph Cut, avoids the problems mentioned above. In this paper we use this algorithm to segment triangulated surface meshes and we introduce new boundary indicator functions, which combine color and curvature properties. We show that using these boundary indicator functions the LexicoGraph Cut algorithm produces a globally optimal result regarding a lexicographic optimization criterion.

The problem to reconstruct a surface given a finite set of boundary points is of growing interest, e.g. in the context of laser range images. While a lot of heuristic methods have been published in this context (e.g. the ball-pivoting algorithm), there exist only a few algorithms which guarantee the reconstruction to be homeomorphic to the original surface if a certain sampling density is reached. However, the sampling density mentioned is in most cases much higher than what seems to be sufficient on real data. In this paper we show how recently proved results about homology extraction from surface samples can be adopted to surface reconstruction and we significantly improve the bounds on the sampling density in case of noise-free samplings. This allows us to prove for the first time that the ball-pivoting algorithm reconstructs certain object surfaces without any topological changes and we can give bounds on the reconstruction error regarding both position and normal direction of the boundary.

Digitization is not as easy as it looks. If one digitizes a 3D object even with a dense sampling grid, the reconstructed digital object may have topological distortions and, in general, there exists no upper bound for the Hausdorff distance. This explains why so far no algorithm has been known which guarantees topology preservation. However, as we will show, it is possible to repair the obtained digital image in a locally bounded way so that it is homeomorphic and close to the 3D object. The resulting digital object is always well-composed, which has nice implications for a lot of image analysis problems. Moreover, we will show that the surface of the original object is homeomorphic to the result of the marching cubes algorithm. This is really surprising since it means that the well-known topological problems of the marching cubes reconstruction simply do not occur for digital images of r-regular objects. Based on the trilinear interpolation, we also construct a smooth isosurface from the digital image that has the same topology as the original surface. Finally, we give a surprisingly simple topology preserving reconstruction method by using overlapping balls instead of cubical voxels. This is the first approach of digitizing 3D objects which guarantees topology preservation and gives an upper bound for the geometric distortion. Since the output can be chosen as a pure voxel presentation, a union of balls, a reconstruction by trilinear interpolation, a smooth isosurface, or the piecewise linear marching cubes surface, the results are directly applicable to a huge class of image analysis algorithms. Moreover, we show how one can efficiently estimate the volume and the surface area of 3D objects by looking at their digitizations. Measuring volume and surface area of digital objects are important problems in 3D image analysis. Good estimators should be multigrid convergent, i.e., the error goes to zero with increasing sampling density. We will show that every presented reconstruction method can be used for volume estimation and we will give a solution for the much more difficult problem of multigrid-convergent surface area estimation. Our solution is based on simple counting of voxels and we are the first to be able to give absolute bounds for the surface area.