Topological Relations Research Articles

Architectural space classification considering topological and 3D visual spatial relations using machine learning techniques

ABSTRACT The paper presents a novel method for classifying architectural spaces in terms of topological and visual relationships required by the functions of the spaces (where spaces such as bedrooms and bathrooms have less visual and physical relationships due to the privacy, while common spaces such as living rooms have higher visual relationship and physical accessibility) through machine learning (ML). The proposed model was applied to single and two-storey residential plans from the leading architects of the 20th century Among the five different ML models whose performances were evaluated comparatively, the best results were obtained with Cascade Forward Neural Networks (CFNN), and the average model success was calculated as 93%. The features affecting the classification models were examined based on SHAP values and revealed that width, control, 3D visibility and 3D natural daylight luminance were among the most influential. The results of five different ML models indicated that the use of topological and 3D visual relationship features in the automated classification of architectural space function can report very high levels of classification accuracy. The findings show that the classification model can be an important part of developing more efficient and adaptive floor plan design, building management and effective reuse strategies.

Topological Recursion Relations from Pixton’s Formula

We prove that every degree-g polynomial in the ψ-classes on M‾g,n can be expressed as a sum of tautological classes supported on the boundary with no κ-classes. Such equations, which we refer to as topological recursion relations, can be used to deduce universal equations for the Gromov–Witten invariants of any target.

An anatomical and connectivity atlas of the marmoset cerebellum

The cerebellum is essential for motor control and cognitive functioning, engaging in bidirectional communication with the cerebral cortex. The common marmoset, a small non-human primate, offers unique advantages for studying cerebello-cerebral circuits. However, the marmoset cerebellum is not well described in published resources. In this study, we present a comprehensive atlas of the marmoset cerebellum comprising (1) fine-detailed anatomical atlases and surface-analysis tools of the cerebellar cortex based on ultra-high-resolution exvivo MRI, (2) functional connectivity and gradient patterns of the cerebellar cortex revealed by awake resting-state fMRI, and (3) structural-connectivity mapping of cerebellar nuclei using high-resolution diffusion MRI tractography. The atlas elucidates the anatomical details of the marmoset cerebellum, reveals distinct gradient patterns of intra-cerebellar and cerebello-cerebral functional connectivity, and maps the topological relationship of cerebellar nuclei in cerebello-cerebral circuits. As version 5 of the Marmoset Brain Mapping project, this atlas is publicly available at https://marmosetbrainmapping.org/MBMv5.html.

Automatic Geographic Information Classification Method Based on SVM for Site Selection of Stretch Field

In tension stringing construction, the site selection of the stretch field is related to the efficiency, safety and cost of the whole wire construction. Surrounding geographic information impacts the site selection extremely seriously. Accurate grasp of the surrounding geographic information along the transmission line is the key to ensure the optimal site selection of the stretch field. Aiming at the geographic image data along the transmission lines collected by the UAV, firstly, the map data is blocked using the image gradient information and the geometric topological relationship in the image; then, the histogram features of the gradient direction are extracted from the blocked data; finally, the support vector machine is used to train the extracted features, and the map data is classified according to the model obtained from the training, and finally the automatic classification and recognition of the geographic information along the transmission lines is obtained. The proposed method can achieve high recognition accuracy by using small samples for training. Through practice, the proposed method can accurately classify map data, thus providing a reliable guarantee for determining the surrounding geographic influences when selecting a site for a stretch field.

Improved adaptive tessellation rendering algorithm.

The human body model in the virtual surgery system is generally nested by multiple complex models and each model has quite complex tangent and curvature change. In actual rendering, if all details of the human body model are rendered with high performance, it may cause the stutter due to insufficient hardware performance. If the human body model is roughly rendered, the details of the model cannot be well represented. In order to realize the real-time rendering of complex models in virtual surgical systems, this paper proposes an improved adaptive tessellation rendering algorithm, which includes offline and online parts. The offline part mainly completes data reading and data structure constructing. The online part performs the surface subdivision operation in-real time for each frame, which includes the subdivision operation of the control points and surface evaluation. The offline part simplifies the subdivision step by recording the surface subdivision hierarchy using a quadtree and using control templates to record control point information. The online part reduces computation time by using a matrix to record topological relationships between vertices and vertex weights. The online part can compress the time complexity of traversing the quadtree of different subdivision levels to O⁢(n⁢log⁡n) by establishing an association with the quadtree of each subdivision level and using the greedy algorithm to complete the traversal of the quadtree. Finally, the adaptive tessellation rendering algorithm proposed in this paper is compared with other commonly used tessellation algorithms. The algorithm has advantages in computational efficiency and graphical display.

A general analysis method of transmission lines faults response with all frequency components under new energy

Nowadays, a large number of photovoltaic power stations have been connected to the grid. As the control algorithm of photovoltaic power generation often uses Maximum Power Point Tracking (MPPT), the electromagnetic transient process generated by frequent regulation process is gathered into the transmission network. And long transmission lines need series compensation which also causes electromagnetic transient process. Since the sampling frequency of the protection device was not high enough in the past, the recorded waveform could not reflect the actual situation. In particular, because some high-frequency harmonics could not be observed, the harm brought by them did not attract enough attention, and the adverse effects gradually increased. In this paper, the transient response of faults in transmission lines can be accurately calculated by a method, which combined with the phase component method and the Laplace transform. According to the topological relationship of transmission lines, a frequency domain model considering the initial energy storage is given. Whether the system parameters are symmetrical or not, the model can accurately calculate the transient response. Besides, various faults are described by modifying the node admittance matrix. And the system response that includes all frequency components in the time domain are obtained by the inverse Laplace transform. In the case of a simple transmission system, the calculation results are compared with those obtained with the ATP/EMTP. Such comparisons validate the effectiveness and accuracy of the method. The method can accurately reflect all transient components at different frequencies caused by faults or disturbances, and it is suitable for both transient studies and steady-state analysis.

Drug-target interaction prediction based on spatial consistency constraint and graph convolutional autoencoder

BackgroundDrug-target interaction (DTI) prediction plays an important role in drug discovery and repositioning. However, most of the computational methods used for identifying relevant DTIs do not consider the invariance of the nearest neighbour relationships between drugs or targets. In other words, they do not take into account the invariance of the topological relationships between nodes during representation learning. It may limit the performance of the DTI prediction methods.ResultsHere, we propose a novel graph convolutional autoencoder-based model, named SDGAE, to predict DTIs. As the graph convolutional network cannot handle isolated nodes in a network, a pre-processing step was applied to reduce the number of isolated nodes in the heterogeneous network and facilitate effective exploitation of the graph convolutional network. By maintaining the graph structure during representation learning, the nearest neighbour relationships between nodes in the embedding space remained as close as possible to the original space.ConclusionsOverall, we demonstrated that SDGAE can automatically learn more informative and robust feature vectors of drugs and targets, thus exhibiting significantly improved predictive accuracy for DTIs.

The Mereotopology of Pregnancy

Consider the following two metaphysical questions about pregnancy: (1) When does a new organism of a certain kind start to exist? (2) What is the mereological and topological relationship between the pregnant organism and with what it is pregnant? Despite assumptions made in the literature, I take these questions to be independent of each other, such that an answer to one does not provide an answer to the other. I argue that the way to connect them is via a maximality principle that prevents one organism being a proper part of another organism of the same kind. That being said, such a maximality principle need not be held, and may not apply in the case of pregnancy. The aims of this paper are thus to distinguish and connect these metaphysical questions, in order to outline a taxonomy of rival mereotopological models of pregnancy that result from the various combinations of their answers.

Elastic beam algorithm for generating circular cartograms

ABSTRACT The circular cartogram, also known as the Dorling map, is a widely used tool for visualizing statistical data. It represents regions as circles with their areas in proportion to the statistical values and requires circle displacement to avoid overlap and maintain spatial relationships. In this paper, we propose a new approach for circular cartogram production that utilizes the elastic beam displacement algorithm in cartographic generalization. First, the initial circles are generated with their areas in proportion to the statistical values. Second, an elastic beam structure is built as a proximity graph based on the spatial relations between the circles. Third, the circles violating the quality requirements are considered to have a force on the nodes of a beam. Fourth, the elastic beam algorithm is applied to assign forces for each node to determine the new positions of the circles. Steps two through four are repeated until a circular cartogram that meets the defined quality requirements is obtained. The experiments indicate that the proposed approach can successfully generate circular cartograms without overlaps while maintaining topology and relative relationships with higher quality than existing approaches. Project website: https://github.com/TrentonWei/DorlingMap

A Nonoverlapping Vision Field Multi-Camera Network for Tracking Human Build Targets

This research presents a procedure for tracking human build targets in a multi-camera network with nonoverlapping vision fields. The proposed approach consists of three main steps: single-camera target detection, single-camera target tracking, and multi-camera target association and continuous tracking. The multi-camera target association includes target characteristic extraction and the establishment of topological relations. Target characteristics are extracted based on the HSV (Hue, Saturation, and Value) values of each human build movement target, and the space-time topological relations of the multi-camera network are established using the obtained target associations. This procedure enables the continuous tracking of human build movement targets in large scenes, overcoming the limitations of monitoring within the narrow field of view of a single camera.

Three-Dimensional Shock Topology Detection Method via Tomographic Reconstruction

Shock waves and shock-shock interaction are typical phenomena in supersonic or hypersonic flows that have significant impacts on aerodynamic performance. To obtain a comprehensive understanding of the mechanism of shock wave interaction, shock wave detection (SWD) methods are required. However, it is often challenging for most current SWD methods to identify the relationship between shock waves (also known as shock topology). To address this issue, this paper proposes a novel three-dimensional shock topology detection method based on the tomographic reconstruction strategy. This method involves extracting parallel slices from the flow field, then utilizing a two-dimensional shock topology recognition algorithm to obtain shock lines. Shock bands are obtained by connecting shock lines for every two adjacent slices, and shock surfaces are generated by assembling shock bands. Interaction lines are also formed by connecting interaction points. The detected shock wave is a structure composed of “point-line-band-surface”, and the topology relationship with other shock waves is obvious. Numerical results show that the shock waves detected by the proposed method can be categorized into families. Moreover, the shock surfaces generated by this method are free of gaps, holes, and un-physical fragments, which is an improvement over existing SWD methods.

Semantic understanding of high spatial resolution remote sensing images using directional geospatial relationships

ABSTRACT Semantic understanding of high spatial resolution remote sensing (RS) images can be divided into object detection, object labelling, identification of geospatial relationships, and semantic description generation. Geographical relations represent the spatial distribution dependencies between geospatial entities such as points, lines, and polygons, and the topologies among them. Geospatial relations play a very important role in describing the relations between geographic objects. These relations can be broadly classified as topological, directional, and proximity relations. These relations describe the adjacency and association relations between geospatial objects. An approach to identify an appropriate directional geospatial relationship between geo-objects present in high spatial resolution RS images is proposed in this paper. Geospatial objects in the form of the closed boundary are taken as input and relationship triplets are generated. Two approaches have been used in the identification of directional relationships and the results of both approaches are compared. The first approach is based on the centroid of the objects and the second considers whole objects while calculating the direction. These relations are then further represented using a knowledge graph, where nodes represent objects and edges represent their relationship. Knowledge graph plays a very important role in overall scene understanding. It shows the association of all objects with each other. These relationships are then represented in the form of descriptions by using template-based sentence generation. Results show that these directional relationships are accurately identified between each pair of objects using both approaches, but relations generated by considering whole objects are closer to human cognition. Semantic understanding of remote sensing images is of great significance in different applications such as urban surveys, urban planning, and management, military intelligence, etc.

Topological reduction approaches for relation decision systems

In this study, we use topological methods to investigate attribute reduction problems for relation decision systems. We propose the notions of topological consistent and inconsistent relation decision systems. Then, we propose the concept of the consistent topological reduction of topological consistent relation decision systems. To enlarge the scope of application, we define the general topological reduction of relation decision systems, which is a further generalization of consistent topological reduction. Moreover, we develop corresponding reduction algorithms for these two types of reductions. To demonstrate that our algorithms cannot be unified by the general reduction algorithm, we discuss the relationship between the consistent topological reducts and the reducts identified by the general reduction algorithm. We conduct numerical experiments on 11 UCI datasets to verify our theoretical results. The experimental results demonstrate that the proposed reduction algorithms are effective and practicable.

Construction and Modification of Topological Tables for Digital Models of Linear Complexes

Building information systems use topological tables to implement the transition from two-dimensional line drawings of the geometry of buildings to digital three-dimensional models of linear complexes. The topological elements of the complex are named and the topological relations of the complex are described by arranging the element names in topological tables. The efficient construction and modification of topological tables for complete buildings is investigated. The topology of a linear complex with nodes, edges, faces, and cells is described with 12 tables. Three of the tables of a complex are independent of each other and form a basis for the construction of the other tables. A highly efficient construction algorithm with complexity O (number of cells) for typical buildings with an approximately constant number of edges per face and faces per cell of is presented. In practice, building designs and their digital models are frequently modified. A modification algorithm is presented, whose complexity equals that of the construction algorithm. Examples illustrate that the efficient algorithms permit the replacement of the conventional focus on the topology of building components by a focus on the topology of the entire building. A set of properties of the original, which are not explicitly described by the topological tables, for example, the orientation of surfaces and multiply connected domains, are analyzed in the paper. An overview of the research dealing with the topological attributes that are not contained in topological tables concludes the paper.

The anatomy of transcriptionally active chromatin loops in Drosophila primary spermatocytes using super-resolution microscopy.

While the biochemistry of gene transcription has been well studied, our understanding of how this process is organised in 3D within the intact nucleus is less well understood. Here we investigate the structure of actively transcribed chromatin and the architecture of its interaction with active RNA polymerase. For this analysis, we have used super-resolution microscopy to image the Drosophila melanogaster Y loops which represent huge, several megabases long, single transcription units. The Y loops provide a particularly amenable model system for transcriptionally active chromatin. We find that, although these transcribed loops are decondensed they are not organised as extended 10nm fibres, but rather they largely consist of chains of nucleosome clusters. The average width of each cluster is around 50nm. We find that foci of active RNA polymerase are generally located off the main fibre axis on the periphery of the nucleosome clusters. Foci of RNA polymerase and nascent transcripts are distributed around the Y loops rather than being clustered in individual transcription factories. However, as the RNA polymerase foci are considerably less prevalent than the nucleosome clusters, the organisation of this active chromatin into chains of nucleosome clusters is unlikely to be determined by the activity of the polymerases transcribing the Y loops. These results provide a foundation for understanding the topological relationship between chromatin and the process of gene transcription.

Global Topology Concept Neighborhood Graph and Its Application in Topological Similarity Measurement

A topological relationship is a key factor in the spatial data processing. Aiming at the problem of topological similarity measurement when the dimension of spatial objects changes in the process of map generalization, this paper proposes a topological similarity measurement method based on the global topological concept neighborhood graph. Firstly, all the topological relationships that can be described by the nine intersection model are abstracted, generalized, and classified, and the classified point/point, point/line, point/polygon, line/line, line/polygon, and polygon/polygon local topological concept neighborhood graphs are established. Then, according to the map generalization rules, the mapping between different types of topological concept neighborhood graphs is established, and the global topological concept neighborhood graph is obtained, Finally, the similarity of the topological relationship between different morphological objects is measured. The experimental results show that the proposed method can better meet the topological similarity measurement when the shape of spatial objects changes.

EANet: A Point Cloud Registration Network Based on EdgeConv with Dual Attention Mechanism

In machine vision, point cloud registration is one of the core elements, which has been applied to many fields such as robot localisation, medical image processing, and autonomous driving. The main problem solved by point cloud registration is to solve the rotation matrix and translation vectors from one point cloud to another. This paper proposes a point cloud registration network based on EdgeConv with spatial attention mechanism. EdgeConv can dynamically construct graph structure and build topological relationships within the point cloud, so that each point can obtain multi-level feature representation; the attention mechanism can capture contextual information and improve the accuracy of the registration. Experimental results show that EANet has higher registration accuracy, stronger generalisation ability and robustness compared to ICP, Go ICP, FGR, PCRNet and PointNetLK.

Developing a Model to Express Spatial Relationships on Omnidirectional Images for Indoor Space Representation to Provide Location-Based Services

The unavailability and fragmentation of spatial data are challenges in creating realistic representations of objects and environments in the real world, especially indoors. Among the numerous methods for representing indoor space, the existing research has shown the efficiency and effectiveness of using omnidirectional images. However, they lack information on spatial relationships, so spatial datasets such as the Node-Relation Structure (NRS) must be used to provide location-based services (LBS). This study proposes a method for embedding topological relationships on omnidirectional images, and correspondingly extracting NRS data to enable the expression of these relationships on the images. These relationships include the connectivity of relations among the indoor subunits, and the containment of relations between the spaces and indoor facilities on the image data. This model allows for the construction of an image-based indoor space representation for providing LBS. This paper also demonstrates an approach to utilizing these datasets through an image-based platform that enables the direct performance of spatial analysis relevant to LBS on the images, and provides the accurate visualization and expression of the spaces and indoor points of interest data representing indoor facilities. This paper also includes an experimental implementation to demonstrate the potential of our model for providing an efficient space representation and the handling of basic spatial queries for indoor space applications.

GCN-ONLSTM: Process Next Event Prediction Method based on Spatio-Temporal Feature Fusion

The task of predicting the next event of a process is the focus of research in the field of predictive process monitoring. Most of the existing methods to achieve this task only process the event log trace as a one-dimensional sequence or regular two-dimensional image data, without considering the simultaneous internal synchronization of the event log. It contains temporal and spatial feature information. In addition, existing studiesignore that trace data is a non-Euclidean structure with topological relationships. In order to solve the above problems and further improve the accuracy of model prediction, this paper constructs a GCN-ONLSTM network that fuses temporal and spatial dimension features, constructs the spatial relationship between events through a two-layer graph convolution network, and improves the feature expression ability of data. And combined with ONLSTM (Ordered Neurons LSTM) network to process the hierarchical structure of trace sequence, to further solve the long-term dependency problem. The ablation experiments and comparison experiments are carried out through 6 BPI public event log data. The results show that the proposed method has significantly improved prediction accuracy in each event log compared with other existing deep learning methods, and the highest is higher than the traditional LSTM (Long Short-term Memory) increased by 8.63%, it can be considered that this method has better performance for the next event prediction task of the process.

Boron Substructures in Inorganic Borides: Network Topology and Free Space

We have analyzed polymeric boron substructures in all 1154 robust inorganic borides from the Inorganic Crystal Structure Database using topological and geometrical models as implemented in the ToposPro program package. We have classified all boron substructures into 63 topological types of atomic networks depending on the method of connection and discriminated them by periodicity into molecular, chain, layer, or framework motifs. We have revealed topological relations between boron motifs of different topologies and periodicities and found the boron substructures that can serve as templates for assembling motifs of a more complicated topology and/or a higher periodicity. We have applied the natural tiling approach to find all cages in a particular boron substructure and estimated the size of these cages with Voronoi polyhedra. The sizes of all metal atoms, which occur in the inorganic borides, have also been calculated in the same way. As a result, we have explained the composition of some borides and showed that the combined geometrical–topological approach helps one to estimate the feasibility of possible new boride structures and to refine the conditions for the synthesis or to prepare initial structural data for the subsequent predictive modeling.