Relevant bibliographies by topics / Topological data structure

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Academic literature on the topic 'Topological data structure'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 February 2022

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Journal articles on the topic "Topological data structure"

1

Salleh, Syahiirah, Uznir Ujang, Suhaibah Azri, and Tan Liat Choon. "3D Topological Validation of Compact Abstract Cell Complexes (CACC) Data Structure for Buildings in CityGML." International Journal of Built Environment and Sustainability 7, no. 2 (2020): 25–32. http://dx.doi.org/10.11113/ijbes.v7.n2.457.

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3D models without the preservation of 3D topological information hinders the ability of 3D models to serve its full potential in terms of 3D analyses. The support of 3D topology is crucial for analyses that requires information regarding adjacencies and connectivity. One of the ways to maintain topological information is by implementing a topological data structure such as the Compact Abstract Cell Complexes (CACC) topological data structure. This paper demonstrates the topological validation for the implementation of the CACC topological data structure implemented for buildings in LoD2 CityGML. Directed graphs and adjacency matrices were constructed for the test datasets of buildings in CityGML. The in-degree and out-degree for all vertices were calculated based on the adjacency matrices. Based on the “Hand-shaking” theorem, the number of α₀-cycles of the CACC topological data structure which connects points to form 1D topological links was compared to the number of directed edges of the constructed directed graphs. Therefore, the implementation of the CACC topological data structure for buildings in LoD2 CityGML was found to be topologically sound.
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Fan, Jun. "Computer Data Structure for Geological Entities Modelling Based on OO-Solid Model." Advanced Materials Research 383-390 (November 2011): 2484–91. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.2484.

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In the long evolution of the earth formation often form a complex geological structure, modeling for these complex geological entities (such as thinning-out, bifurcation, reverse, etc.) still require in-depth 3D modeling study. Because of discontinuity, complexity and uncertainty of distribution of 3D geo-objects, some models only are suitable for regular, continuous and relatively simple spatial objects, and some are suitable for discontinue, complex and uncertain geo-objects, but some improvements on these models, such as, updating of model, maintenance of topological and seamless integration between models, are still to be made. OO-Solid model, put forward by writer in 2002, is an object- oriented topological model based on sections. The OO-Solid Model is an object-oriented 3D topologic data model based on component for geology modeling with fully considering the topological relations between geological objects and its geometric primitives, Comparatively, it accords with the actual requirements of three-dimensional geological modeling . The key issue of 3D geology modeling is the 3D data model. Some data models are suitable for discontinue, complex and uncertain geo-objects, but the OO-Solid model is an object-oriented 3D topologic data model based on component for geology modeling with fully considering the topological relations between geological objects and its geometric primitives. OO-Solid model and data structure are designed. At last, 3D complex geological entities modeling based on OO-Solid are studied in this paper. These study is important and one of the core techniques for the 3DGM.
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3

Ujang, Uznir, Francesc Anton Castro, and Suhaibah Azri. "Abstract Topological Data Structure for 3D Spatial Objects." ISPRS International Journal of Geo-Information 8, no. 3 (2019): 102. http://dx.doi.org/10.3390/ijgi8030102.

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In spatial science, the relationship between spatial objects is considered to be a vital element. Currently, 3D objects are often used for visual aids, improving human insight, spatial observations, and spatial planning. This scenario involves 3D geometrical data handling without the need for topological information. Nevertheless, in the near future, users will shift to more complex queries corresponding to the existing 2D spatial approaches. Therefore, having 3D spatial objects without having these relationships or topology is impractical for 3D spatial analysis queries. In this paper, we present a new method for creating topological information that we call the Compact Abstract Cell Complexes (CACC) data structure for 3D spatial objects. The idea is to express in the most compact way the topology of a model in 3D (or more generally in nD) without requiring the topological space to be discrete or geometric. This is achieved by storing all the atomic cycles through the models (null combinatorial homotopy classes). The main idea here is to store the atomic paths through the models as an ant experiences topology: each time the ant perceives a previous trace of pheromone, it knows it has completed a cycle. The main advantage of this combinatorial topological data structure over abstract simplicial complexes is that the storage size of the abstract cell cycles required to represent the geometric topology of a model is far lower than that for any of the existing topological data structures (including abstract simplicial cell cycles) required to represent the geometric decomposition of the same model into abstract simplicial cells. We provide a thorough comparative analysis of the storage sizes for the different topological data structures to sustain this.
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4

Zhang, Ling Ling, Yun Fei Shi, and Chang Lin Mi. "Survey of Research Progress on Three Dimensional Topological Data Structure." Applied Mechanics and Materials 303-306 (February 2013): 1129–33. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.1129.

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Topology is one of the mechanisms to describe relationships between spatial objects and it is the basis for many spatial operations. The paper gives a survey of current main three dimensional topological data structures. Three dimensional topological data structures can be divided into manifold data structure and non-manifold data structure. Manifold data structure includes Winged-edge data structure, Half-edge data structure, Quad-edge data structure and so on. Non-manifold data structure includes facet-edge data structure, radial edge data structure and so on. The paper gives on overview of fundamental principles of these data structure. On this basis, advantages and disadvantages of these models are compared from more aspects. Through this research, we can provide theoretical basis and technical support for 3D building modeling, 3D cadastre modeling and other 3D fields.
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5

Baudot, Pierre, Monica Tapia, Daniel Bennequin, and Jean-Marc Goaillard. "Topological Information Data Analysis." Entropy 21, no. 9 (2019): 869. http://dx.doi.org/10.3390/e21090869.

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This paper presents methods that quantify the structure of statistical interactions within a given data set, and were applied in a previous article. It establishes new results on the k-multivariate mutual-information ( I k ) inspired by the topological formulation of Information introduced in a serie of studies. In particular, we show that the vanishing of all I k for 2 ≤ k ≤ n of n random variables is equivalent to their statistical independence. Pursuing the work of Hu Kuo Ting and Te Sun Han, we show that information functions provide co-ordinates for binary variables, and that they are analytically independent from the probability simplex for any set of finite variables. The maximal positive I k identifies the variables that co-vary the most in the population, whereas the minimal negative I k identifies synergistic clusters and the variables that differentiate–segregate the most in the population. Finite data size effects and estimation biases severely constrain the effective computation of the information topology on data, and we provide simple statistical tests for the undersampling bias and the k-dependences. We give an example of application of these methods to genetic expression and unsupervised cell-type classification. The methods unravel biologically relevant subtypes, with a sample size of 41 genes and with few errors. It establishes generic basic methods to quantify the epigenetic information storage and a unified epigenetic unsupervised learning formalism. We propose that higher-order statistical interactions and non-identically distributed variables are constitutive characteristics of biological systems that should be estimated in order to unravel their significant statistical structure and diversity. The topological information data analysis presented here allows for precisely estimating this higher-order structure characteristic of biological systems.
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6

Salleh, S., U. Ujang, S. Azri, and T. L. Choon. "SPATIAL ADJACENCY ANALYSIS OF CITYGML BUILDINGS VIA 3D TOPOLOGICAL DATA STRUCTURE." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W16 (October 1, 2019): 573–79. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w16-573-2019.

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Abstract. Adjacencies between objects provides the most basic connectivity information of objects. This connectivity information provides support for more complex 3D spatial analysis such as 3D navigation, nearest neighbour and others. In 3D models, the connectivity information is maintained by building a comprehensive 3D topology. As the international standard for 3D city models, CityGML employs a simple XML links mechanism that references related entities to each other as a means of maintaining topological information. This method fulfils the purpose of relating connected entities but, it does not describe how the entities are related or in other words its adjacencies. In this study, a 3D topological data structure was utilised to preserve topological primitives and maintain connectivity information for CityGML datasets of buildings in LoD2. The adjacencies tested in this study were based on the topological links maintained by the Compact Abstract Cell Complexes 3D topological data structure. Four types of adjacencies were tested which are Point-to-Line, Line-to-Surface, Surface-to-Surface and Volume-to-Volume adjacency. As a result, all adjacencies were able to be executed for both datasets which consisted of two connected buildings and disjointed buildings. It was found that the ability of the 3D topological data structure to preserve topological primitives and build topological links supported the maintenance of connectivity information between buildings. The maintenance of connectivity information was also not limited to objects of the same dimension and could extend to connectivity between building elements in different dimensions.
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7

Pries, A. R., T. W. Secomb, and P. Gaehtgens. "Relationship between structural and hemodynamic heterogeneity in microvascular networks." American Journal of Physiology-Heart and Circulatory Physiology 270, no. 2 (1996): H545—H553. http://dx.doi.org/10.1152/ajpheart.1996.270.2.h545.

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The relationship between structural and hemodynamic heterogeneity of microvascular networks is examined by analyzing the effects of topological and geometric irregularities on network hemodynamics. Microscopic observations of a network in the rat mesentery provided data on length, diameter, and interconnection of all 913 segments. Two idealized network structures were derived from the observed network. In one, the topological structure was made symmetric; in another a further idealization was made by assigning equal lengths and diameters to all segments with topologically equivalent positions in the network. Blood flow through these three networks was simulated with a mathematical model based on experimental information on blood rheology. Overall network conductance and pressure distribution within the network were found to depend strongly on topological heterogeneity and less on geometric heterogeneity. In contrast, mean capillary hematocrit was sensitive to geometric heterogeneity but not to topological heterogeneity. Geometric and topological heterogeneity contributed equally to the dispersion of arteriovenous transit time. Hemodynamic characteristics of heterogeneous microvascular networks can only be adequately described if both topological and geometric variability in network structure are taken into account.
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8

Kim, San, Eunjung Joo, Jusung Ha, and Jaekwang Kim. "Generalization and Processing method of Topological Data Using Sentence Data Structure." Journal of Korean Institute of Intelligent Systems 30, no. 2 (2020): 100–105. http://dx.doi.org/10.5391/jkiis.2020.30.2.100.

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9

Bailor, Maximillian H., Xiaoyan Sun, and Hashim M. Al-Hashimi. "Topology Links RNA Secondary Structure with Global Conformation, Dynamics, and Adaptation." Science 327, no. 5962 (2010): 202–6. http://dx.doi.org/10.1126/science.1181085.

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Thermodynamic rules that link RNA sequences to secondary structure are well established, but the link between secondary structure and three-dimensional global conformation remains poorly understood. We constructed comprehensive three-dimensional maps depicting the orientation of A-form helices across RNA junctions in the Protein Data Bank and rationalized our findings with modeling and nuclear magnetic resonance spectroscopy. We show that the secondary structures of junctions encode readily computable topological constraints that accurately predict the three-dimensional orientation of helices across all two-way junctions. Our results suggest that RNA global conformation is largely defined by topological constraints encoded at the secondary structural level and that tertiary contacts and intermolecular interactions serve to stabilize specific conformers within the topologically allowed ensemble.
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10

Zulkifli, N. A., A. Abdul Rahman, and M. I. Hassan. "DESIGN OF 3D TOPOLOGICAL DATA STRUCTURE FOR 3D CADASTRE OBJECTS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W1 (September 30, 2016): 325–27. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w1-325-2016.

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This paper describes the design of 3D modelling and topological data structure for cadastre objects based on Land Administration Domain Model (LADM) specifications. Tetrahedral Network (TEN) is selected as a 3D topological data structure for this project. Data modelling is based on the LADM standard and it is used five classes (i.e. point, boundary face string, boundary face, tetrahedron and spatial unit). This research aims to enhance the current cadastral system by incorporating 3D topology model based on LADM standard.
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