Kustaanheimo–Stiefel transformation with an arbitrary defining vector

Kustaanheimo–Stiefel (KS) transformation depends on the choice of some preferred direction in the Cartesian 3D space. This choice, seldom explicitly mentioned, amounts typically to the direction of the first or the third coordinate axis in Celestial Mechanics and atomic physics, respectively. The present work develops a canonical KS transformation with an arbitrary preferred direction, indicated by what we call a defining vector. Using a mix of vector and quaternion algebra, we formulate the transformation in a reference frame independent manner. The link between the oscillator and Keplerian first integrals is given. As an example of the present formulation, the Keplerian motion in a rotating frame is re-investigated.     

Traffic transformer: Capturing the continuity and periodicity of time series for traffic forecasting

Traffic forecasting is a challenging problem due to the complexity of jointly modeling spatio‐temporal dependencies at different scales. Recently, several hybrid deep learning models have been developed to capture such dependencies. These approaches typically utilize convolutional neural networks or graph neural networks (GNNs) to model spatial dependency and leverage recurrent neural networks (RNNs) to learn temporal dependency. However, RNNs are only able to capture sequential information in the time series, while being incapable of modeling their periodicity (e.g., weekly patterns). Moreover, RNNs are difficult to parallelize, making training and prediction less efficient. In this work we propose a novel deep learning architecture called Traffic Transformer to capture the continuity and periodicity of time series and to model spatial dependency. Our work takes inspiration from Google’s Transformer framework for machine translation. We conduct extensive experiments on two real‐world traffic data sets, and the results demonstrate that our model outperforms baseline models by a substantial margin.     

Deeply integrating Linked Data with Geographic Information Systems

The realization that knowledge often forms a densely interconnected graph has fueled the development of graph databases, Web‐scale knowledge graphs and query languages for them, novel visualization and query paradigms, as well as new machine learning methods tailored to graphs as data structures. One such example is the densely connected and global Linked Data cloud that contains billions of statements about numerous domains, including life science and geography. While Linked Data has found its way into everyday applications such as search engines and question answering systems, there is a growing disconnect between the classical ways in which Geographic Information Systems (GIS) are still used today and the open‐ended, exploratory approaches used to retrieve and consume data from knowledge graphs such as Linked Data. In this work, we conceptualize and prototypically implement a Linked Data connector framework as a set of toolboxes for Esri's ArcGIS to close this gap and enable the retrieval, integration, and analysis of Linked Data from within GIS. We discuss how to connect to Linked Data endpoints, how to use ontologies to probe data and derive appropriate GIS representations on the fly, how to make use of reasoning, how to derive data that are ready for spatial analysis out of RDF triples, and, most importantly, how to utilize the link structure of Linked Data to enable analysis. The proposed Linked Data connector framework can also be regarded as the first step toward a guided geographic question answering system over geographic knowledge graphs.     

Computing and querying strict,approximate, and metrically refined topological relations in linked geographic data

Geographic entities and the information associated with them play a major role in Web‐scale knowledge graphs such as Linked Data. Interestingly, almost all major datasets represent places and even entire regions as point coordinates. There are two key reasons for this. First, complex geometries are difficult to store and query using the current Linked Data technology stack to a degree where many queries take minutes to return or will simply time out. Second, the absence of complex geometries confirms a common suspicion among GIScientists, namely that for many everyday queries place‐based relational knowledge is more relevant than raw geometries alone. To give an illustrative example, the statement that the White House is in Washington, DC is more important for gaining an understating of the city than the exact geometries of both entities. This does not imply that complex geometries are unimportant but that (topological) relations should also be extracted from them. As Egenhofer and Mark (1995b) put it in their landmark paper on naive geography, topology matters, metric refines. In this work we demonstrate how to compute and utilize strict, approximate, and metrically refined topological relations between several geographic feature types in DBpedia and compare our results to approaches that compute result sets for topological queries on the fly.     

Making direction a first‐class citizen of Tobler's first law of geography

Waldo Tobler frequently reminded us that the law named after him was nothing more than calling for exceptions. This article discusses one of these exceptions. Spatial relations between points are frequently modeled as vectors in which both distance and direction are of equal prominence. However, in Tobler's first law of geography, such a relation is described only from the perspective of distance by relating the decreasing similarity of observations in some attribute space to their increasing distance in geographic space. Although anisotropic versions of many geographic analysis techniques, such as directional semivariograms, anisotropy clustering, and anisotropic point pattern analysis, have been developed over the years, direction remains on the level of an afterthought. We argue that, compared to distance, directional information is still under‐explored and anisotropic techniques are substantially less frequently applied in everyday GIS analysis. Commonly, when classical spatial autocorrelation indicators, such as Moran's I, are used to understand a spatial pattern, the weight matrix is only built from distance, without direction being considered. Similarly, GIS operations, such as buffering, do not take direction into account either, with distance in all directions being treated equally. In reality, meanwhile, particularly in urban structures and when processes are driven by the underlying physical geography, direction plays an essential role. In this article we ask whether the development of early GIS, data (sample) sparsity, and Tobler's law lead to a theory‐induced blindness for the role of direction. If so, is it possible to envision direction becoming a first‐class citizen of equal importance to distance instead of being an afterthought only considered when the deviation from a perfect circle becomes too obvious to be ignored?     

Distribution of compact object mergers around galaxies

Compact object mergers are one of the currently favoured models for the origin of gamma-ray bursts (GRBs). The discovery of optical afterglows and identification of the nearest, presumably host, galaxies allow the analysis of the distribution of burst sites with respect to these galaxies. Using a model of stellar binary evolution we synthesize a population of compact binary systems which merge within the Hubble time. We include the kicks in the supernovae explosions and calculate orbits of these binaries in galactic gravitational potentials. We present the resulting distribution of merger sites and discuss the results in the framework of the observed GRB afterglows.     

Review of Image Quality Measures for Solar Imaging

Observations of the solar photosphere from the ground encounter significant problems caused by Earth’s turbulent atmosphere. Before image reconstruction techniques can be applied, the frames obtained in the most favorable atmospheric conditions (the so-called lucky frames) have to be carefully selected. However, estimating the quality of images containing complex photospheric structures is not a trivial task, and the standard routines applied in nighttime lucky imaging observations are not applicable. In this paper we evaluate 36 methods dedicated to the assessment of image quality, which were presented in the literature over the past 40 years. We compare their effectiveness on simulated solar observations of both active regions and granulation patches, using reference data obtained by the Solar Optical Telescope on the Hinode satellite. To create images that are affected by a known degree of atmospheric degradation, we employed the random wave vector method, which faithfully models all the seeing characteristics. The results provide useful information about the method performances, depending on the average seeing conditions expressed by the ratio of the telescope’s aperture to the Fried parameter, \(D/r_{0}\). The comparison identifies three methods for consideration by observers: Helmli and Scherer’s mean, the median filter gradient similarity, and the discrete cosine transform energy ratio. While the first method requires less computational effort and can be used effectively in virtually any atmospheric conditions, the second method shows its superiority at good seeing (\(D/r_{0}<4\)). The third method should mainly be considered for the post-processing of strongly blurred images.     

Influence of a Multipurpose Retention Reservoir on Extreme River Flows,a Case Study of the Nielisz Reservoir on the Wieprz River (Eastern Poland)

Water Resources - The objective of this paper is the assessment of the effect of a multifunctional mid-size retention reservoir on the occurrence of floods and low flows. The study object was...     

SE‐KGE: A location‐aware Knowledge Graph Embedding model for Geographic Question Answering and Spatial Semantic Lifting

Learning knowledge graph (KG) embeddings is an emerging technique for a variety of downstream tasks such as summarization, link prediction, information retrieval, and question answering. However, most existing KG embedding models neglect space and, therefore, do not perform well when applied to (geo)spatial data and tasks. Most models that do consider space primarily rely on some notions of distance. These models suffer from higher computational complexity during training while still losing information beyond the relative distance between entities. In this work, we propose a location‐aware KG embedding model called SE‐KGE. It directly encodes spatial information such as point coordinates or bounding boxes of geographic entities into the KG embedding space. The resulting model is capable of handling different types of spatial reasoning. We also construct a geographic knowledge graph as well as a set of geographic query–answer pairs called DBGeo to evaluate the performance of SE‐KGE in comparison to multiple baselines. Evaluation results show that SE‐KGE outperforms these baselines on the DBGeo data set for the geographic logic query answering task. This demonstrates the effectiveness of our spatially‐explicit model and the importance of considering the scale of different geographic entities. Finally, we introduce a novel downstream task called spatial semantic lifting which links an arbitrary location in the study area to entities in the KG via some relations. Evaluation on DBGeo shows that our model outperforms the baseline by a substantial margin.     

A spatially explicit reinforcement learning model for geographic knowledge graph summarization

Web‐scale knowledge graphs such as the global Linked Data cloud consist of billions of individual statements about millions of entities. In recent years, this has fueled the interest in knowledge graph summarization techniques that compute representative subgraphs for a given collection of nodes. In addition, many of the most densely connected entities in knowledge graphs are places and regions, often characterized by thousands of incoming and outgoing relationships to other places, actors, events, and objects. In this article, we propose a novel summarization method that incorporates spatially explicit components into a reinforcement learning framework in order to help summarize geographic knowledge graphs, a topic that has not been considered in previous work. Our model considers the intrinsic graph structure as well as the extrinsic information to gain a more comprehensive and holistic view of the summarization task. By collecting a standard data set and evaluating our proposed models, we demonstrate that the spatially explicit model yields better results than non‐spatial models, thereby demonstrating that spatial is indeed special as far as summarization is concerned.