Academic literature on the topic 'Polygonal space vector structures'

N-ary relational knowledge base (KBs) embedding aims to map binary and beyond-binary facts into low-dimensional vector space simultaneously. Existing approaches typically decompose n-ary relational facts into subtuples (entity pairs, triples or quintuples, etc.), and they generally model n-ary relational KBs in Euclidean space. However, n-ary relational facts are semantically and structurally intact, decomposition leads to the loss of global information and undermines the semantical and structural integrity. Moreover, compared to the binary relational KBs, n-ary ones are characterized by more abundant and complicated hierarchy structures, which could not be well expressed in Euclidean space. To address the issues, we propose a gyro-polygon embedding approach to realize n-ary fact integrity keeping and hierarchy capturing, termed as PolygonE. Specifically, n-ary relational facts are modeled as gyro-polygons in the hyperbolic space, where we denote entities in facts as vertexes of gyro-polygons and relations as entity translocation operations. Importantly, we design a fact plausibility measuring strategy based on the vertex-gyrocentroid geodesic to optimize the relation-adjusted gyro-polygon. Extensive experiments demonstrate that PolygonE shows SOTA performance on all benchmark datasets, generalizability to binary data, and applicability to arbitrary arity fact. Finally, we also visualize the embedding to help comprehend PolygonE's awareness of hierarchies.

Abstract Traverses (polygons) from two caves have been tested: Wielka Śnieżna Cave System (2858 vectors) and Śnieżna Studnia cave (742). The box counting technique was applied to evaluate the fractal analysis of spatial orientation of traverses. The polygonal survey of Wielka Śnieżna Cave, Śnieżna Studnia and both caves merged together have a fractal geometry. It may be concluded that these caves are close to the full recognition of passages forming by a hydrological system and they could have close relation with geological structures. The usual explanation of fractal dimension D higher than 1 indicates that caves with such dimension fill more space than those with ideal dimension of 1.00 (for example a straight line), and the geological constraints limit the dimension to be lower than 2 (Verbovsek 2007). It may suggest that systems can be developped into more complicated passages in future. The fact that both caves merged together also have showed fractal geometry indicates that they are belonging to the same hydrological system. It was noticed that D-value of merged caves is slightly larger than individual cave. It can be explained by “occupying” more space in rock mass.

Aim. The purpose of the work is to process archival cartographic materials and remote sensing data for the interpretation of objects of historical and cultural heritage (OHCH) of Cherkasy, including those that have not been preserved. Method. One of the possible technological schemes for research is offered. According to her, the first step was to analyze the input data of the study, among which were: a map of Cherkasy in 1895 at a scale of 1:42000; German aerial image of 1944; a fragment of a space image of Cherkasy obtained from the GeoEye-1 satellite in 2018. Geometric correction of the input materials was performed in the Mercator projection and the WGS84 coordinate system, in which the transformed image was obtained. The next step was to vectorize the objects of historical and cultural heritage of Cherkasy, according to the list obtained on the city’s website. There are two types of objects: point and polygonal. When vectorizing polygonal objects, the historical boundaries were specified with the help of archival maps and aerial images. Special symbols have been developed for each of the types of historical and cultural heritage sites, according to the proposed classification. In addition, an attributive database of these objects was created, which had the following structure: number of the passport of object, the name of the object, the address of the OHCH, the number of the decision to take under protection, information about the OHCH. Also, the obtained vector data was exported to the exchange format with the extension kmz and an online version of the thematic map was created on the basis of the free GISFile resource. Results. As a result of the conducted researches, the thematic GIS of the objects of historical and cultural heritage of Cherkasy was created, which are plotted on the space image of high spatial resolution, obtained in 2018. An on-line version of the GIS of Cherkasy historical and cultural heritage sites has been created on the basis of the free GISFile cartographic service, with the possibility of analyzing the location of these objects and building optimal tourist routes. Scientific novelty. Possible algorithms for creating offline and on-line versions of thematic GIS are proposed. Practical value. The obtained results of mapping the objects of historical and cultural heritage of Cherkasy can be used by the structures of protection of objects of historical and cultural heritage of Cherkasy at the Ministry of Culture.

It may be supposed that the development of an algorithm capable of automatically generating boundary lines among parts for designing IC diagrams and automatic recognition of intervals among parts as well as mapping is widely desired in different industrial sectors. The most basic, effective solution conceivable will be image analysis using an ITV camera. The authors, however, tried to develop an algorithm capable of automatically generating boundary lines which would not interfere with one another using a great number of profiles comprising, in principle, polygons based on vector input data. It is not that this enables every boundary line between graphics to be automatically generated with good precision, but a result has been obtained which can appropriately be applied to roughly calculating the living space in a floor plan, and dividing structures for land use status drawing on a scale of about 1 to 2500. It can also be used for designing wiring drawings among parts. It is conceivable that the utilization of the results of this research will enable the algorithm to be used for graphic recognition by image processing. The following are the proposed problem, definitions, and a detailed description of the algorithm leading to a solution.

For a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r < R(K) define satellite structures, or local knotting. We explore knotting within these tubes both theoretically and numerically. We provide bounds on perturbation radii for which one can obtain small trefoil and figure-eight summands and use Monte Carlo simulations to estimate the relative probabilities of these structures as a function of the number of edges.

Abstract. Accurate and timely maps of urban underlying land properties at the national scale are of significance in improving habitat environment and achieving sustainable development goals. Urban impervious surface (UIS) and urban green space (UGS) are two core components for characterizing urban underlying environments. However, the UIS and UGS are often mosaicked in the urban landscape with complex structures and composites. The “hard classification” or binary single type cannot be used effectively to delineate spatially explicit urban land surface property. Although six mainstream datasets on global or national urban land use and land cover products with a 30 m spatial resolution have been developed, they only provide the binary pattern or dynamic of a single urban land type, which cannot effectively delineate the quantitative components or structure of intra-urban land cover. Here we propose a new mapping strategy to acquire the multitemporal and fractional information of the essential urban land cover types at a national scale through synergizing the advantage of both big data processing and human interpretation with the aid of geoknowledge. Firstly, the vector polygons of urban boundaries in 2000, 2005, 2010, 2015 and 2018 were extracted from China's Land Use/cover Dataset (CLUD) derived from Landsat images. Secondly, the national settlement and vegetation percentages were retrieved using a sub-pixel decomposition method through a random forest algorithm using the Google Earth Engine (GEE) platform. Finally, the products of China's UIS and UGS fractions (CLUD-Urban) at a 30 m resolution were developed in 2000, 2005, 2010, 2015 and 2018. We also compared our products with six existing mainstream datasets in terms of quality and accuracy. The assessment results showed that the CLUD-Urban product has higher accuracies in urban-boundary and urban-expansion detection than other products and in addition that the accurate UIS and UGS fractions were developed in each period. The overall accuracy of urban boundaries in 2000–2018 are over 92.65 %; and the correlation coefficient (R) and root mean square errors (RMSEs) of UIS and UGS fractions are 0.91 and 0.10 (UIS) and 0.89 and 0.11 (UGS), respectively. Our result indicates that 71 % of pixels of urban land were mosaicked by the UIS and UGS within cities in 2018; a single UIS classification may highly increase the mapping uncertainty. The high spatial heterogeneity of urban underlying covers was exhibited with average fractions of 68.21 % for UIS and 22.30 % for UGS in 2018 at a national scale. The UIS and UGS increased unprecedentedly with annual rates of 1605.56 and 627.78 km2 yr−1 in 2000–2018, driven by fast urbanization. The CLUD-Urban mapping can fill the knowledge gap in understanding impacts of the UIS and UGS patterns on ecosystem services and habitat environments and is valuable for detecting the hotspots of waterlogging and improving urban greening for planning and management practices. The datasets can be downloaded from https://doi.org/10.5281/zenodo.4034161 (Kuang et al., 2020a).

Abstract Biopolymers, like chromatin, are often confined in small volumes. Confinement has a great effect on polymer conformations, including polymer entanglement. Polymer chains and other filamentous structures can be represented by polygonal curves in three-space. In this manuscript, we examine the topological complexity of polygonal chains in three-space and in confinement as a function of their length. We model polygonal chains by equilateral random walks in three-space and by uniform random walks (URWs) in confinement. For the topological characterization, we use the second Vassiliev measure. This is an integer topological invariant for polygons and a continuous functions over the real numbers, as a function of the chain coordinates for open polygonal chains. For URWs in confined space, we prove that the average value of the Vassiliev measure in the space of configurations increases as O(n 2) with the length of the walks or polygons. We verify this result numerically and our numerical results also show that the mean value of the second Vassiliev measure of equilateral random walks in three-space increases as O(n). These results reveal the rate at which knotting of open curves and not simply entanglement are affected by confinement.