Journal articles: 'Topological data structure'

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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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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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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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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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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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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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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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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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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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Sciamarella, Denisse, and G. B. Mindlin. "Topological Structure of Chaotic Flows from Human Speech Data." Physical Review Letters 82, no. 7 (1999): 1450–53. http://dx.doi.org/10.1103/physrevlett.82.1450.

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Vitalis, Stelios, Ken Ohori, and Jantien Stoter. "Incorporating Topological Representation in 3D City Models." ISPRS International Journal of Geo-Information 8, no. 8 (2019): 347. http://dx.doi.org/10.3390/ijgi8080347.

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3D city models are being extensively used in applications such as evacuation scenarios and energy consumption estimation. The main standard for 3D city models is the CityGML data model which can be encoded through the CityJSON data format. CityGML and CityJSON use polygonal modelling in order to represent geometries. True topological data structures have proven to be more computationally efficient for geometric analysis compared to polygonal modelling. In a previous study, we have introduced a method to topologically reconstruct CityGML models while maintaining the semantic information of the dataset, based solely on the combinatorial map (C-Map) data structure. As a result of the limitations of C-Map’s semantic representation mechanism, the resulting datasets could suffer either from semantic information loss or the redundant repetition of them. In this article, we propose a solution for a more efficient representation of geometry, topology and semantics by incorporating the C-Map data structure into the CityGML data model and implementing a CityJSON extension to encode the C-Map data. In addition, we provide an algorithm for the topological reconstruction of CityJSON datasets to append them according to this extension. Finally, we apply our methodology to three open datasets in order to validate our approach when applied to real-world data. Our results show that the proposed CityJSON extension can represent all geometric information of a city model in a lossless way, providing additional topological information for the objects of the model.

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Zhu, Jianning, Minjie Wang, Zhaocheng Wei, and Bin Cao. "An Efficient Data Structure for Representing Trilateral/Quadrilateral Subdivision Surfaces." Cybernetics and Information Technologies 13, no. 3 (2013): 26–40. http://dx.doi.org/10.2478/cait-2013-0023.

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Abstract With the increase of subdivision depths, some problems of common data structures for representing the subdivision surfaces appear, such as excessive computer memory consumption and low efficiency of the data query which restrict the popularization and application of subdivision surfaces in more fields. By utilizing the topological characteristics of the subdivision surface, a two-layer data structure named CELL is presented in order to better realize the piecewise representation of trilateral/quadrilateral subdivision surfaces. The inner structure of CELL represents the subdivision surface patch by using arrays, and the outer structure of CELL represents the topological relations between the subdivision surface patches. Based on Catmull-Clark subdivision scheme, the structural compositions of CELL and the realization mechanism of the subdivision algorithm are proposed. Additionally, sharp and semi-sharp features are constructed, and a primary study on amalgamation of the image/Z-map model and subdivision surface is presented. The results of the experimental and theoretical analysis show the superior performance of CELL with relation to computer memory consumption, data query, subdivision surface computation and algorithm development.

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Zhang, J. L., S. J. Zhang, H. M. Weng, et al. "Pressure-induced superconductivity in topological parent compound Bi2Te3." Proceedings of the National Academy of Sciences 108, no. 1 (2010): 24–28. http://dx.doi.org/10.1073/pnas.1014085108.

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We report a successful observation of pressure-induced superconductivity in a topological compound Bi2Te3 with Tc of ∼3 K between 3 to 6 GPa. The combined high-pressure structure investigations with synchrotron radiation indicated that the superconductivity occurred at the ambient phase without crystal structure phase transition. The Hall effects measurements indicated the hole-type carrier in the pressure-induced superconducting Bi2Te3 single crystal. Consequently, the first-principles calculations based on the structural data obtained by the Rietveld refinement of X-ray diffraction patterns at high pressure showed that the electronic structure under pressure remained topologically nontrivial. The results suggested that topological superconductivity can be realized in Bi2Te3 due to the proximity effect between superconducting bulk states and Dirac-type surface states. We also discuss the possibility that the bulk state could be a topological superconductor.

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Liu, Xu, Zheng Xie, and Dongyun Yi. "A fast algorithm for constructing topological structure in large data." Homology, Homotopy and Applications 14, no. 1 (2012): 221–38. http://dx.doi.org/10.4310/hha.2012.v14.n1.a11.

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Jin, L., X. M. Zhang, X. F. Dai, L. Y. Wang, H. Y. Liu, and G. D. Liu. "Screening topological materials with a CsCl-type structure in crystallographic databases." IUCrJ 6, no. 4 (2019): 688–94. http://dx.doi.org/10.1107/s2052252519007383.

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CsCl-type materials have many outstanding characteristics, i.e. simple in structure, ease of synthesis and good stability at room temperature, thus are an excellent choice for designing functional materials. Using high-throughput first-principles calculations, a large number of topological semimetals/metals (TMs) were designed from CsCl-type materials found in crystallographic databases and their crystal and electronic structures have been studied. The CsCl-type TMs in this work show rich topological character, ranging from triple nodal points, type-I nodal lines and critical-type nodal lines, to hybrid nodal lines. The TMs identified show clean topological band structures near the Fermi level, which are suitable for experimental investigations and future applications. This work provides a rich data set of TMs with a CsCl-type structure.

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Rajeswari, V., and T. Nithiya. "CONSTRUCTING TRI-TOPOLOGICAL NETWORK SPACE MODEL USING CONNECTED COMPONENT GRAPH THEORY (T3-C2G) BASED ON HOMOTOPY ALGEBRAIC INVARIANCE MODEL." Advances in Mathematics: Scientific Journal 10, no. 5 (2021): 2433–47. http://dx.doi.org/10.37418/amsj.10.5.11.

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The complex network contains non-deterministic topological spaces under an invariance structural approach to create failures on a continual link during communication. The non-lineardynamic topological structure leads to problematic threading links on network nodes due to a non-identical path to route the data. To resolve this problem, we propose atri-logical algebraic mathematical construction model called homotopy based tri-topological network spa- ce using connected component graph $(T^3-C^2G)$ under network nonlinear structure,The Algebraic Invariance Linear Queuing Theory (HA/I/LQT) is used to resolve the link failure route propagation to make improved communication performance. This homotopy reduction to reduce the complex nature to make continual link based on Quillen topological structure space under the covariance tri-topological structure. Further, this makes tri-logical structure resembles the sequence of triangle structured route space to make the nearest point of node adjustment from the nearest path. This balances the M/M/G-$T^3$-Max queuing theory on triangular weightage in routing schemes to specify the dynamic homotopy topological structure to make continuous routing links to reduce the complex nature of network routing.

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Zhang, Yingzhong, Xiaofang Luo, and Jia Jia. "A Compact Face-Based Topological Data Structure for Triangle Mesh Representation." Computer-Aided Design and Applications 16, no. 3 (2018): 539–57. http://dx.doi.org/10.14733/cadaps.2019.539-557.

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Hu, Jiming, and Yin Zhang. "Structure and patterns of cross-national Big Data research collaborations." Journal of Documentation 73, no. 6 (2017): 1119–36. http://dx.doi.org/10.1108/jd-12-2016-0146.

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Purpose The purpose of this paper is to reveal the structure and patterns of cross-national collaborations in Big Data research through application of various social network analysis and geographical visualization methods. Design/methodology/approach The sample includes articles containing Big Data research, covering all years, in the Web of Science Core Collection as of December 2015. First, co-occurrence data representing collaborations among nations were extracted from author affiliations. Second, the descriptive statistics, network indicators of collaborations, and research communities were calculated. Third, topological network maps, geographical maps integrated with topological network projections, and proportional maps were produced for visualization. Findings The results show that the scope of international collaborations in Big Data research is broad, but the distribution among nations is unbalanced and fragmented. The USA, China, and the UK were identified as the major contributors to this research area. Five research communities are identified, led by the USA, China, Italy, South Korea, and Brazil. Collaborations within each community vary, reflecting different levels of research development. The visualizations show that nations advance in Big Data research are centralized in North America, Europe, and Asia-Pacific. Originality/value This study applied various informetric methods and tools to reveal the collaboration structure and patterns among nations in Big Data research. Visualized maps help shed new light on global research efforts.

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Yang, Zhi Guo, Dong Fei Liu, and Yu Gao. "Design and Implementation of Topology Management Based on EPON Network Management System." Advanced Materials Research 989-994 (July 2014): 4723–26. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.4723.

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The network bandwidth has been expanded after EPON(Ethernet Passive Optical Network ) came.So a topology management for EPON System is needed.In this paper, methods of topological data collection is analyzed, the form of topological data structure object is designed , and topological structure is displayed in the terminal by coding. With introducing in improved memory object and caching techniques, system performance was significantly improved through experiments.

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Shin, Kilho, and Dave Shepard. "Morphism-Based Learning for Structured Data." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 5767–75. http://dx.doi.org/10.1609/aaai.v34i04.6033.

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In mathematics, morphism is a term that indicates structure-preserving mappings between mathematical structures of the same type. Linear transformations for linear spaces, homomorphisms for algebraic structures and continuous functions for topological spaces are examples. Many data researched in machine learning, on the other hand, can include mathematical structures in them. Strings are totally ordered sets, and trees can be understood not only as graphs but also as partially ordered sets with respect to an ancestor-to-descendent order and semigroups with respect to the binary operation to determine nearest common ancestor. In this paper, we propose a generic and theoretic framework to investigate similarity of structured data through structure-preserving one-to-one partial mappings, which we call morphisms. Through morphisms, useful and important methods studied in the literature can be abstracted into common concepts, although they have been studied separately. When we study new structures of data, we will be able to extend the legacy methods for the purpose of studying the new structure, if we can define morphisms properly. Also, this view reveals hidden relations between methods known in the literature and can let us understand them more clearly. For example, we see that the center star algorithm, which was originally developed to compute sequential multiple alignments, can be abstracted so that it not only applies to data structures other than strings but also can be used to solve problems of pattern extraction. The methods that we study in this paper include edit distance, multiple alignment, pattern extraction and kernel, but it is sure that there exist much more methods that can be abstracted within our framework.

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Hajij, Mustafa, and Paul Rosen. "An Efficient Data Retrieval Parallel Reeb Graph Algorithm." Algorithms 13, no. 10 (2020): 258. http://dx.doi.org/10.3390/a13100258.

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The Reeb graph of a scalar function that is defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer graphics, and computational topology. The demand for analyzing large data sets has increased in the last decade. Hence, the parallelization of topological computations needs to be more fully considered. We propose a parallel augmented Reeb graph algorithm on triangulated meshes with and without a boundary. That is, in addition to our parallel algorithm for computing a Reeb graph, we describe a method for extracting the original manifold data from the Reeb graph structure. We demonstrate the running time of our algorithm on standard datasets. As an application, we show how our algorithm can be utilized in mesh segmentation algorithms.

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Ellis, Cameron T., Michael Lesnick, Gregory Henselman-Petrusek, Bryn Keller, and Jonathan D. Cohen. "Feasibility of topological data analysis for event-related fMRI." Network Neuroscience 3, no. 3 (2019): 695–706. http://dx.doi.org/10.1162/netn_a_00095.

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Recent fMRI research shows that perceptual and cognitive representations are instantiated in high-dimensional multivoxel patterns in the brain. However, the methods for detecting these representations are limited. Topological data analysis (TDA) is a new approach, based on the mathematical field of topology, that can detect unique types of geometric features in patterns of data. Several recent studies have successfully applied TDA to study various forms of neural data; however, to our knowledge, TDA has not been successfully applied to data from event-related fMRI designs. Event-related fMRI is very common but limited in terms of the number of events that can be run within a practical time frame and the effect size that can be expected. Here, we investigate whether persistent homology—a popular TDA tool that identifies topological features in data and quantifies their robustness—can identify known signals given these constraints. We use fmrisim, a Python-based simulator of realistic fMRI data, to assess the plausibility of recovering a simple topological representation under a variety of conditions. Our results suggest that persistent homology can be used under certain circumstances to recover topological structure embedded in realistic fMRI data simulations.

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MADOKORO, Hirokazu, and Kazuhito SATO. "Adaptive Mapping Networks for Visualizing Topological Structure of Data on Category Maps." Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 26, no. 6 (2014): 903–12. http://dx.doi.org/10.3156/jsoft.26.903.

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FUJISHIMA, Satoshi, and Yoshimasa TAKAHASHI. "Topological Fragment Spectra (TFS) Peak Identification System for Chemical Structure Data Mining." Journal of Computer Chemistry, Japan 3, no. 2 (2004): 49–58. http://dx.doi.org/10.2477/jccj.3.49.

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Contreras, M. L., M. Deliz, and R. Rozas. "Personal microcomputer based system of chemical information with topological structure data elaboration." Journal of Chemical Information and Modeling 27, no. 4 (1987): 163–67. http://dx.doi.org/10.1021/ci00056a004.

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Celes, Waldemar, Glaucio H. Paulino, and Rodrigo Espinha. "A compact adjacency-based topological data structure for finite element mesh representation." International Journal for Numerical Methods in Engineering 64, no. 11 (2005): 1529–56. http://dx.doi.org/10.1002/nme.1440.

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Gu, Weisi, Mei-e. Fang, and Lizhuang Ma. "High-quality topological structure extraction of volumetric data on C2-continuous framework." Computer Aided Geometric Design 35-36 (May 2015): 215–24. http://dx.doi.org/10.1016/j.cagd.2015.03.004.

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Kalay, Y. E. "The hybrid edge: a topological data structure for vertically integrated geometric modelling." Computer-Aided Design 21, no. 3 (1989): 130–40. http://dx.doi.org/10.1016/0010-4485(89)90067-5.

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Cramer Pedersen, Martin, Vanessa Robins, Kell Mortensen, and Jacob J. K. Kirkensgaard. "Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2241 (2020): 20200170. http://dx.doi.org/10.1098/rspa.2020.0170.

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Using methods from the field of topological data analysis, we investigate the self-assembly and emergence of three-dimensional quasi-crystalline structures in a single-component colloidal system. Combining molecular dynamics and persistent homology, we analyse the time evolution of persistence diagrams and particular local structural motifs. Our analysis reveals the formation and dissipation of specific particle constellations in these trajectories, and shows that the persistence diagrams are sensitive to nucleation and convergence to a final structure. Identification of local motifs allows quantification of the similarities between the final structures in a topological sense. This analysis reveals a continuous variation with density between crystalline clathrate, quasi-crystalline, and disordered phases quantified by ‘topological proximity’, a visualization of the Wasserstein distances between persistence diagrams. From a topological perspective, there is a subtle, but direct connection between quasi-crystalline, crystalline and disordered states. Our results demonstrate that topological data analysis provides detailed insights into molecular self-assembly.

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Pshenay-Severin, Dmitry A., and Alexander T. Burkov. "Electronic Structure of B20 (FeSi-Type) Transition-Metal Monosilicides." Materials 12, no. 17 (2019): 2710. http://dx.doi.org/10.3390/ma12172710.

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Monosilicides of transition metals crystallizing in a B20 (FeSi-type) structure (space group P2 1 3, #198) possess a wide range of specific properties. Among them are semiconductors, metals, and paramagnetic, diamagnetic, and ferromagnetic compounds. Some of them were studied as promising thermoelectric materials. Recently, B20 monosilicides have attracted attention as a new class of topological semimetals with topological charge greater than unity. In the present work, we analyze the electronic structures of B20-type monosilicides of the fourth, fifth, and sixth periods of the Periodic Table in order to reveal their common features and peculiarities. To make this analysis more consistent, we performed a density-functional study of the electronic structures of the monosilicides in a unified manner. We reviewed the results of previous calculations and the available experimental data, comparing them with our results. The band structures of ReSi and TcSi not found in the literature were calculated and analyzed as well. The topological properties of these materials and of some isostructural germanides and stannides were investigated. Analysis reveals the current understanding of electronic structures and properties of this compound group.

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Hong, Sungryong, Donghui Jeong, Ho Seong Hwang, et al. "Constraining cosmology with big data statistics of cosmological graphs." Monthly Notices of the Royal Astronomical Society 493, no. 4 (2020): 5972–86. http://dx.doi.org/10.1093/mnras/staa566.

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ABSTRACT By utilizing large-scale graph analytic tools implemented in the modern big data platform, apache spark, we investigate the topological structure of gravitational clustering in five different universes produced by cosmological N-body simulations with varying parameters: (1) a WMAP 5-yr compatible ΛCDM cosmology, (2) two different dark energy equation of state variants, and (3) two different cosmic matter density variants. For the big data calculations, we use a custom build of standalone Spark/Hadoop cluster at Korea Institute for Advanced Study and Dataproc Compute Engine in Google Cloud Platform with sample sizes ranging from 7 to 200 million. We find that among the many possible graph-topological measures, three simple ones: (1) the average of number of neighbours (the so-called average vertex degree) α, (2) closed-to-connected triple fraction (the so-called transitivity) $\tau _\Delta$, and (3) the cumulative number density ns ≥ 5 of subgraphs with connected component size s ≥ 5, can effectively discriminate among the five model universes. Since these graph-topological measures are directly related with the usual n-points correlation functions of the cosmic density field, graph-topological statistics powered by big data computational infrastructure opens a new, intuitive, and computationally efficient window into the dark Universe.

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Presnell, S. R., and F. E. Cohen. "Topological distribution of four-alpha-helix bundles." Proceedings of the National Academy of Sciences 86, no. 17 (1989): 6592–96. http://dx.doi.org/10.1073/pnas.86.17.6592.

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The four-alpha-helix bundle, a common structural motif in globular proteins, provides an excellent forum for the examination of predictive constraints for protein backbone topology. An exhaustive examination of the Brookhaven Crystallographic Protein Data Bank and other literature sources has lead to the discovery of 20 putative four-alpha-helix bundles. Application of an analytical method that examines the difference between solvent-accessible surface areas in packed and partially unpacked bundles reduced the number of structures to 16. Angular requirements further reduced the list of bundles to 13. In 12 of these bundles, all pairs of neighboring helices were oriented in an anti-parallel fashion. This distribution is in accordance with structure types expected if the helix macro dipole effect makes a substantial contribution to the stability of the native structure. The characterizations and classifications made in this study prompt a reevaluation of constraints used in structure prediction efforts.

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Hu, Pingbo, Bisheng Yang, Zhen Dong, et al. "Towards Reconstructing 3D Buildings from ALS Data Based on Gestalt Laws." Remote Sensing 10, no. 7 (2018): 1127. http://dx.doi.org/10.3390/rs10071127.

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3D building models are an essential data infrastructure for various applications in a smart city system, since they facilitate spatial queries, spatial analysis, and interactive visualization. Due to the highly complex nature of building structures, automatically reconstructing 3D buildings from point clouds remains a challenging task. In this paper, a Roof Attribute Graph (RAG) method is proposed to describe the decomposition and topological relations within a complicated roof structure. Furthermore, top-down decomposition and bottom-up refinement processes are proposed to reconstruct roof parts according to the Gestalt laws, generating a complete structural model with a hierarchical topological tree. Two LiDAR datasets from Guangdong (China) and Vaihingen (Germany) with different point densities were used in our study. Experimental results, including the assessment on Vaihingen standardized by the International Society for Photogrammetry and Remote Sensing (ISPRS), show that the proposed method can be used to model 3D building roofs with high quality results as demonstrated by the completeness and correctness metrics presented in this paper.

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Sørensen, Søren S., Christophe A. N. Biscio, Mathieu Bauchy, Lisbeth Fajstrup, and Morten M. Smedskjaer. "Revealing hidden medium-range order in amorphous materials using topological data analysis." Science Advances 6, no. 37 (2020): eabc2320. http://dx.doi.org/10.1126/sciadv.abc2320.

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Despite the numerous technological applications of amorphous materials, such as glasses, the understanding of their medium-range order (MRO) structure—and particularly the origin of the first sharp diffraction peak (FSDP) in the structure factor—remains elusive. Here, we use persistent homology, an emergent type of topological data analysis, to understand MRO structure in sodium silicate glasses. To enable this analysis, we introduce a self-consistent categorization of rings with rigorous geometrical definitions of the structural entities. Furthermore, we enable quantitative comparison of the persistence diagrams by computing the cumulative sum of all points weighted by their lifetime. On the basis of these analysis methods, we show that the approach can be used to deconvolute the contributions of various MRO features to the FSDP. More generally, the developed methodology can be applied to analyze and categorize molecular dynamics data and understand MRO structure in any class of amorphous solids.

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Karacay, Timur. "Searching Big Data via cyclic groups." Global Journal of Computer Sciences: Theory and Research 6, no. 2 (2017): 47–53. http://dx.doi.org/10.18844/gjcs.v6i2.1475.

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We look up for a certain information in big data. To achieve this task we first endow the big data with a group structure and partition it to it’s cyclic subgroups. We devise a method to search the whole big data starting from the smallest subroup through the largest one. Our method eventually exhausts the whole big data. Keywords: BigData, topological groups, dual groups, linear search.

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Sizemore, Ann E., Jennifer E. Phillips-Cremins, Robert Ghrist, and Danielle S. Bassett. "The importance of the whole: Topological data analysis for the network neuroscientist." Network Neuroscience 3, no. 3 (2019): 656–73. http://dx.doi.org/10.1162/netn_a_00073.

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Data analysis techniques from network science have fundamentally improved our understanding of neural systems and the complex behaviors that they support. Yet the restriction of network techniques to the study of pairwise interactions prevents us from taking into account intrinsic topological features such as cavities that may be crucial for system function. To detect and quantify these topological features, we must turn to algebro-topological methods that encode data as a simplicial complex built from sets of interacting nodes called simplices. We then use the relations between simplices to expose cavities within the complex, thereby summarizing its topological features. Here we provide an introduction to persistent homology, a fundamental method from applied topology that builds a global descriptor of system structure by chronicling the evolution of cavities as we move through a combinatorial object such as a weighted network. We detail the mathematics and perform demonstrative calculations on the mouse structural connectome, synapses in C. elegans, and genomic interaction data. Finally, we suggest avenues for future work and highlight new advances in mathematics ready for use in neural systems.

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Scoville, Nicholas A., and Karthik Yegnesh. "A persistent homological analysis of network data flow malfunctions." Journal of Complex Networks 5, no. 6 (2017): 884–92. http://dx.doi.org/10.1093/comnet/cnx038.

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Abstract Persistent homology has recently emerged as a powerful technique in topological data analysis for analysing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. In this article, we develop an application of ideas from the theory of persistent homology and persistence diagrams to the study of data flow malfunctions in networks with a certain hierarchical structure. In particular, we formulate an algorithmic construction of persistence diagrams that parameterize network data flow errors, thus enabling novel applications of statistical methods that are traditionally used to assess the stability of persistence diagrams corresponding to homological data to the study of data flow malfunctions. We conclude with an application to network packet delivery systems.

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Lee, Sang Hun, and Kunwoo Lee. "Partial Entity Structure: A Compact Boundary Representation for Non-Manifold Geometric Modeling." Journal of Computing and Information Science in Engineering 1, no. 4 (2001): 356–65. http://dx.doi.org/10.1115/1.1433486.

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Non-manifold boundary representations have become very popular in recent years and various representation schemes have been proposed, as they represent a wider range of objects, for various applications, than conventional manifold representations. As these schemes mainly focus on describing sufficient adjacency relationships of topological entities, the models represented in these schemes occupy storage space redundantly, although they are very efficient in answering queries on topological adjacency relationships. To solve this problem, in this paper, we propose a compact as well as fast non-manifold boundary representation, called the partial entity structure. This representation reduces the storage size to half that of the radial edge structure, which is one of the most popular and efficient of existing data structures, while allowing full topological adjacency relationships to be derived without loss of efficiency. In order to verify the time and storage efficiency of the partial entity structure, the time complexity of basic query procedures and the storage requirement for typical geometric models are derived and compared with those of existing schemes.

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Liu, Xiaoyu, and Weinong Fu. "Finite-Element Method With Topological Data Structure Mesh for Optimization of Electrical Devices." IEEE Transactions on Magnetics 54, no. 11 (2018): 1–4. http://dx.doi.org/10.1109/tmag.2018.2857850.

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Eremeev, S. V., D. E. Andrianov, and V. S. Titov. "An algorithm for matching spatial objects of different-scale maps based on topological data analysis." Computer Optics 43, no. 6 (2019): 1021–29. http://dx.doi.org/10.18287/2412-6179-2019-43-6-1021-1029.

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A problem of automatic comparison of spatial objects on maps with different scales for the same locality is considered in the article. It is proposed that this problem should be solved using methods of topological data analysis. The initial data of the algorithm are spatial objects that can be obtained from maps with different scales and subjected to deformations and distortions. Persistent homology allows us to identify the general structure of such objects in the form of topological features. The main topological features in the study are the connectivity components and holes in objects. The paper gives a mathematical description of the persistent homology method for representing spatial objects. A definition of a barcode for spatial data, which contains a description of the object in the form of topological features is given. An algorithm for comparing feature barcodes was developed. It allows us to find the general structure of objects. The algorithm is based on the analysis of data from the barcode. An index of objects similarity in terms of topological features is introduced. Results of the research of the algorithm for comparing maps of natural and municipal objects with different scales, generalization and deformation are shown. The experiments confirm the high quality of the proposed algorithm. The percentage of similarity in the comparison of natural objects, while taking into account the scale and deformation, is in the range from 85 to 92, and for municipal objects, after stretching and distortion of their parts, was from 74 to 87. Advantages of the proposed approach over analogues for the comparison of objects with significant deformation at different scales and after distortion are demonstrated.

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Bonilla, Luis L., Ana Carpio, and Carolina Trenado. "Tracking collective cell motion by topological data analysis." PLOS Computational Biology 16, no. 12 (2020): e1008407. http://dx.doi.org/10.1371/journal.pcbi.1008407.

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By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments in the literature, the spreading test exhibits formation of fingers in the moving interfaces, there appear swirls in the velocity field, and the polar order parameter and the correlation and swirl lengths increase with time. Numerical simulations show that cells inside the tissue have smaller area than those at the interface, which has been observed in recent experiments. In the antagonistic migration assay, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce the experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to results of our numerical simulations. We use time series of data generated by numerical simulations to automatically group, track and classify the advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These techniques of topological data analysis are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.

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Dabrowski-Tumanski, Pawel, and Joanna I. Sulkowska. "Topological knots and links in proteins." Proceedings of the National Academy of Sciences 114, no. 13 (2017): 3415–20. http://dx.doi.org/10.1073/pnas.1615862114.

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Twenty years after their discovery, knots in proteins are now quite well understood. They are believed to be functionally advantageous and provide extra stability to protein chains. In this work, we go one step further and search for links—entangled structures, more complex than knots, which consist of several components. We derive conditions that proteins need to meet to be able to form links. We search through the entire Protein Data Bank and identify several sequentially nonhomologous chains that form a Hopf link and a Solomon link. We relate topological properties of these proteins to their function and stability and show that the link topology is characteristic of eukaryotes only. We also explain how the presence of links affects the folding pathways of proteins. Finally, we define necessary conditions to form Borromean rings in proteins and show that no structure in the Protein Data Bank forms a link of this type.

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Park, Sung Hee, and Keun Ho Ryu. "A Method of Structure Comparison Using Spatial Topological Patterns." Key Engineering Materials 277-279 (January 2005): 272–77. http://dx.doi.org/10.4028/www.scientific.net/kem.277-279.272.

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The problem of comparison of structural similarity has been complex and computationally expensive. The first step to solve comparison of structural similarity in 3D structure databases is to develop fast methods for structural similarity. Therefore, we propose a new method of comparing structural similarity in protein structure databases by using topological patterns of proteins. In our approach, the geometry of secondary structure elements in 3D space is represented by spatial data types and is indexed using Rtrees. Topological patterns are discovered by spatial topology relations based on the Rtree index join. An algorithm for a similarity search compares topological patterns of a query protein with those of proteins in structure databases by the intersection frequency of SSEs. Our experimental results show that the execution time of our method is three times faster than the generally known method DALITE. Our method can generate small candidate sets for more accurate alignment tools such as DALI and SSAP.

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Erofeev, Kirill Yurevich, Mansur Tagirovich Ziiatdinov, and Evgenii Vladimirovich Mokshin. "Persistent Homology: Application To Monitoring Hydraulic Fracturing." Russian Digital Libraries Journal 23, no. 6 (2020): 1192–212. http://dx.doi.org/10.26907/1562-5419-2020-23-6-1192-1212.

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Persistent homology is a topological data analysis tool which is reflecting changes in topological structure of data along its scale. Application of persistent homology to monitoring hydraulic fracturing which is allowing researchers to consider prior information in a natural way is given in the article

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Perera, Supun S., Michael G. H. Bell, Mahendrarajah Piraveenan, Dharshana Kasthurirathna, and Mamata Parhi. "Topological Structure of Manufacturing Industry Supply Chain Networks." Complexity 2018 (October 3, 2018): 1–23. http://dx.doi.org/10.1155/2018/3924361.

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Empirical analyses of supply chain networks (SCNs) in extant literature have been rare due to scarcity of data. As a result, theoretical research have relied on arbitrary growth models to generate network topologies supposedly representative of real-world SCNs. Our study is aimed at filling the above gap by systematically analysing a set of manufacturing sector SCNs to establish their topological characteristics. In particular, we compare the differences in topologies of undirected contractual relationships (UCR) and directed material flow (DMF) SCNs. The DMF SCNs are different from the typical UCR SCNs since they are characterised by a strictly tiered and an acyclic structure which does not permit clustering. Additionally, we investigate the SCNs for any self-organized topological features. We find that most SCNs indicate disassortative mixing and power law distribution in terms of interfirm connections. Furthermore, compared to randomised ensembles, self-organized topological features were evident in some SCNs in the form of either overrepresented regimes of moderate betweenness firms or underrepresented regimes of low betweenness firms. Finally, we introduce a simple and intuitive method for estimating the robustness of DMF SCNs, considering the loss of demand due to firm disruptions. Our work could be used as a benchmark for any future analyses of SCNs.

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Karim, Hairi, Alias Abdul Rahman, and Pawel Boguslawski. "GENERALIZATION TECHNIQUE FOR 2D+SCALE DHE DATA MODEL." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-2/W1 (October 26, 2016): 61–67. http://dx.doi.org/10.5194/isprs-archives-xlii-2-w1-61-2016.

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Different users or applications need different scale model especially in computer application such as game visualization and GIS modelling. Some issues has been raised on fulfilling GIS requirement of retaining the details while minimizing the redundancy of the scale datasets. Previous researchers suggested and attempted to add another dimension such as scale or/and time into a 3D model, but the implementation of scale dimension faces some problems due to the limitations and availability of data structures and data models. Nowadays, various data structures and data models have been proposed to support variety of applications and dimensionality but lack research works has been conducted in terms of supporting scale dimension. Generally, the Dual Half Edge (DHE) data structure was designed to work with any perfect 3D spatial object such as buildings. In this paper, we attempt to expand the capability of the DHE data structure toward integration with scale dimension. The description of the concept and implementation of generating 3D-scale (2D spatial + scale dimension) for the DHE data structure forms the major discussion of this paper. We strongly believed some advantages such as local modification and topological element (navigation, query and semantic information) in scale dimension could be used for the future 3D-scale applications.

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Frahi, Tarek, Antonio Falco, Baptiste Vinh Mau, Jean Louis Duval, and Francisco Chinesta. "Empowering Advanced Parametric Modes Clustering from Topological Data Analysis." Applied Sciences 11, no. 14 (2021): 6554. http://dx.doi.org/10.3390/app11146554.

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Modal analysis is widely used for addressing NVH—Noise, Vibration, and Hardness—in automotive engineering. The so-called principal modes constitute an orthogonal basis, obtained from the eigenvectors related to the dynamical problem. When this basis is used for expressing the displacement field of a dynamical problem, the model equations become uncoupled. Moreover, a reduced basis can be defined according to the eigenvalues magnitude, leading to an uncoupled reduced model, especially appealing when solving large dynamical systems. However, engineering looks for optimal designs and therefore it focuses on parametric designs needing the efficient solution of parametric dynamical models. Solving parametrized eigenproblems remains a tricky issue, and, therefore, nonintrusive approaches are privileged. In that framework, a reduced basis consisting of the most significant eigenmodes is retained for each choice of the model parameters under consideration. Then, one is tempted to create a parametric reduced basis, by simply expressing the reduced basis parametrically by using an appropriate regression technique. However, an issue remains that limits the direct application of the just referred approach, the one related to the basis ordering. In order to order the modes before interpolating them, different techniques were proposed in the past, being the Modal Assurance Criterion—MAC—one of the most widely used. In the present paper, we proposed an alternative technique that, instead of operating at the eigenmodes level, classify the modes with respect to the deformed structure shapes that the eigenmodes induce, by invoking the so-called Topological Data Analysis—TDA—that ensures the invariance properties that topology ensure.

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Trifunovic, Milan, Milos Stojkovic, Dragan Misic, Miroslav Trajanovic, and Miodrag Manic. "Recognizing Topological Analogy in Semantic Network." International Journal on Artificial Intelligence Tools 24, no. 03 (2015): 1550006. http://dx.doi.org/10.1142/s0218213015500062.

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Recognizing topological analogy between the parts of semantic network seems to be very important step in the process of semantic categorization and interpretation of data that are embedded into the semantic network. Considering the semantic network as a set of graphs, recognition of topological analogy between the parts of semantic network can be treated as maximum common subgraph problem which falls in the group of exact graph matching problems. In this paper authors propose a new algorithm for maximum common subgraph detection aimed to a specific semantic network called Active Semantic Model (ASM). This semantic network can be represented as the set of labeled directed multigraphs with unique node labels. The structure of these graphs is specific because associations or edges are labeled with several attributes and some of them are related to nodes connected by edge. That kind of association-oriented structure enables associations or edges to play key role in the process of semantic categorization and interpretation of data. Furthermore, this kind of structure enables modeling semantic contexts in a form of semantically designated graphs (of associations). Proposed algorithm is capable of recognizing simultaneously maximum common subgraph of input graph and each of the graphs representing different contexts in ASM semantic network.

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Cao, Zhen Zhou, Man Chun Li, and Liang Cheng. "Progressive Transmission of Vector Curve Data over the Internet." Applied Mechanics and Materials 380-384 (August 2013): 2395–98. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.2395.

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This paper proposes a method for multi-scale representation of curve and elaborates the process of progressive transmission of curve data over the internet based on this method. Firstly, the importance degree of nodes and the information about public constrain points and monotone chains are stored in a monotonous linear BLG tree structure, and then the multi-scale curve is generated in real time based on this structure and the topological relationship is maintained by an optimized monotone chains intersection algorithm. Finally, the method was used in the experiment of progressive transmission of river network over the internet and verified its effectiveness.

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Journal articles on the topic 'Topological data structure'

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