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Journal articles on the topic 'Hyperbolic visualization'
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Qiu, Chongyang, Xinfei Li, Jianhua Pang, and Peichang Ouyang. "Visualization of Escher-like Spiral Patterns in Hyperbolic Space." Symmetry 14, no. 1 (2022): 134. http://dx.doi.org/10.3390/sym14010134.
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Spirals, tilings, and hyperbolic geometry are important mathematical topics with outstanding aesthetic elements. Nonetheless, research on their aesthetic visualization is extremely limited. In this paper, we give a simple method for creating Escher-like hyperbolic spiral patterns. To this end, we first present a fast algorithm to construct Euclidean spiral tilings with cyclic symmetry. Then, based on a one-to-one mapping between Euclidean and hyperbolic spaces, we establish two simple approaches for constructing spiral tilings in hyperbolic models. Finally, we use wallpaper templates to render such tilings, which results in the desired Escher-like hyperbolic spiral patterns. The method proposed is able to generate a great variety of visually appealing patterns.
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Marić, Filip. "Formalization, Automatization and Visualization of Hyperbolic Geometry." Electronic Proceedings in Theoretical Computer Science 398 (January 20, 2024): 2. http://dx.doi.org/10.4204/eptcs.398.2.
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Urribarri, Dana, Silvia Castro, and Sergio Martig. "Gyrolayout: A Hyperbolic Level-of-Detail Tree Layout." JUCS - Journal of Universal Computer Science 19, no. (1) (2013): 132–56. https://doi.org/10.3217/jucs-019-01-0132.
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Many large datasets can be represented as hierarchical structures,introducing not only the necessity of specialized tree visualization techniques, but also the requirements of handling large amounts of data and offering the user a useful insightinto them. Many two-dimensional techniques have been developed, but 3-dimensional ones, together with navigational interactions, present a promising appropriate tool todeal with large trees. In this paper we present a hyperbolic tree layout extended to support different level-of-detail techniques and suitable for large tree representation and visualization. This layout permits the visualization of large trees with different level of detail in anenclosed 3-dimensional volume. As a significant part of the layout, we also present a Weighted Spherical Centroidal Voronoi Tessellation, an extension of planar Weighted Centroidal Voronoi Tessellations, in order to find an appropriate distribution of nodes on a spherical surface.
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Rangkuti, Rizki Kurniawan, Siti Khabibah, and Rooselyna Ekawati. "Spatial reasoning of mathematics education students: an analysis of differences in solving hyperbola problems based on level of geometry ability." Perspectives of science and Education 72, no. 6 (2025): 248–60. https://doi.org/10.32744/pse.2024.6.16.
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Introduction. The facts show that students at the school level still have low spatial reasoning abilities at the school level, but the spatial reasoning abilities of students at the university level are not yet known. The results of students' spatial reasoning abilities are not yet known, so it is necessary to carry out detailed research so that it can be understood more widely. The purpose of this research is to analyze how hyperbolic problem solving differs based on the level of student ability, so that students with high, medium and low ability can be described more specifically at each step of problem solving. Study participants and methods. The subjects in this research were undergraduate students in the mathematics education study program at the Institut Pendidikan Tapanuli Selatan, Indonesia, who were determined using purposive sampling on the condition that they had taken analytical geometry courses. The research subjects selected were 3 students, each of whom had high ability with a score of 95, medium ability with a score of 85 and low ability with a score of 73 who were tested with a geometric ability test. The results of solving hyperbolic problems refer to indicators of spatial reasoning. Hyperbola problem solving data is analyzed based on the level of geometric ability with stages of data reduction, data presentation, and drawing conclusions. This research method is a qualitative descriptive research method with a single case design. Results. First, subjects with high geometric abilities based on analysis of spatial reasoning indicators, namely spatial visualization, mental rotation, and spatial orientation, have good problem-solving skills with an average achievement of 92.4.In spatial reasoning on hyperbolic objects, starting from the steps to understand the problem and planning a solution based on the problem, as well as carrying out the solution and evaluating the solution, there is no difficulty in solving the hyperbolic problem. Second, subjects with moderate geometric abilities based on analysis of spatial visualization abilities, mental rotation, and spatial orientation have good learning achievements, which are also shown based on spatial reasoning indicators. It is known that the average problem-solving ability for moderate geometry is 84.83. Third, subjects with low geometric ability based on analysis of spatial visualization ability, mental rotation, and spatial orientation showed poor performance, with the average achievement of problem solving with low geometric ability being 73.2. Conclusion. This research describes how the ability to solve hyperbola problems differs based on the level of geometric ability. The results of this research provide a basic description that can be used to show differences in hyperbola problem solving abilities from the four steps based on high, medium and low geometric abilities.
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Celińska, Dorota, and Eryk Kopczyński. "Programming Languages in GitHub: A Visualization in Hyperbolic Plane." Proceedings of the International AAAI Conference on Web and Social Media 11, no. 1 (2017): 727–28. http://dx.doi.org/10.1609/icwsm.v11i1.14862.
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GitHub is nowadays the largest software repository hosting service that incorporates social media functionalities to writing and assessing source code. We visualize the weighted network of programming languages used by the registered users of GitHub as of December 2016. There is an edge in the graph between language A and B if and only if A and B are both used by the same user in any of her repositories. The weight depends on the number of times such edge appears. Our visualization utilizes hyperbolic geometry, which is intrinsic to networks based on similarity and popularity. RogueViz, a novel tool, based on the Open Source game HyperRogue, is used to map the network and navigate the hyperbolic graph.
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Zheng, Wenhu, and Xia He. "Dynamic Application of Matlab in Teaching of Hyperbolic Paraboloid." Advances in Engineering Technology Research 2, no. 1 (2022): 565. http://dx.doi.org/10.56028/aetr.2.1.565.
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In teaching of hyperbolic paraboloid, this paper breaks through the traditional teaching method. Through its theoretical analysis, combined with graphic visualization of MATLAB software, this paper shows two formation processes and notch transformation processes of hyperbolic paraboloid, so as to enhance students' learning interest, cultivate students' spatial imagination and improve teachers' teaching effect, so as to further promote the modernization of basic course teaching methods.
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Ouyang, Peichang, Dongsheng Cheng, Yanhua Cao, and Xiaogen Zhan. "The visualization of hyperbolic patterns from invariant mapping method." Computers & Graphics 36, no. 2 (2012): 92–100. http://dx.doi.org/10.1016/j.cag.2011.12.005.
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Lam, Ho-Ching, and Ivo D. Dinov. "Hyperbolic Wheel: A Novel Hyperbolic Space Graph Viewer for Hierarchical Information Content." ISRN Computer Graphics 2012 (October 31, 2012): 1–10. http://dx.doi.org/10.5402/2012/609234.
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Tree and graph structures have been widely used to present hierarchical and linked data. Hyperbolic trees are special types of graphs composed of nodes (points or vertices) and edges (connecting lines), which are visualized on a non-Euclidean space. In traditional Euclidean space graph visualization, distances between nodes are measured by straight lines. Displays of large graphs in Euclidean spaces may not utilize efficiently the available space and may impose limitations on the number of graph nodes. The special hyperbolic space rendering of tree-graphs enables adaptive and efficient use of the available space and facilitates the display of large hierarchical structures. In this paper we report on a newly developed advanced hyperbolic graph viewer, Hyperbolic Wheel, which enables the navigation, traversal, discovery and interactive manipulation of information stored in large hierarchical structures. Examples of such structures include personnel records, disc directory structures, ontological constructs, web-pages and other nested partitions. The Hyperbolic Wheel framework provides an intuitive and dynamic graphical interface to explore and retrieve information about individual nodes (data objects) and their relationships (data associations). The Hyperbolic Wheel is freely available online for educational and research purposes.
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Saalbach, Axel, Jörg Ontrup, Helge Ritter, and Tim W. Nattkemper. "Image Fusion Based on Topographic Mappings Using the Hyperbolic Space." Information Visualization 4, no. 4 (2005): 266–75. http://dx.doi.org/10.1057/palgrave.ivs.9500106.
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The analysis of multivariate image data is a field of research that is becoming increasingly important in a broad range of applications from remote sensing to medical imaging. While traditional scientific visualization techniques are often not suitable for the analysis of this kind of data, methods of image fusion have evolved as a promising approach for synergistic data integration. In this paper, a new approach for the analysis of multivariate image data by means of image fusion is presented, which employs topographic mapping techniques based on non-Euclidean geometry. The hyperbolic self-organizing map (HSOM) facilitates the exploration of high-dimensional data and provides an interface in the tradition of distortion-oriented presentation techniques. For the analysis of hidden patterns and spatial relationships, the HSOM gives rise to an intuitive and efficient framework for the dynamic visualization of multivariate image data by means of color. In an application, the hyperbolic data explorer (HyDE) is employed for the visualization of image data from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Using 12 image sequences from breast cancer research, the method is introduced by different visual representations of the data and is also quantitatively analyzed. The HSOM is compared to different standard classifiers and evaluated with respect to topology preservation.
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Yahya, Arnasli, and Jenő Szirmai. "Visualization of Sphere and Horosphere Packings Related to Coxeter Tilings by Simply Truncated Orthoschemes with Parallel Faces." KoG, no. 25 (2021): 64–71. http://dx.doi.org/10.31896/k.25.7.
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In this paper we describe and visualize the densest ball and horoball packing configurations to the simply truncated 3-dimensional hyperbolic Coxeter orthoschemes with parallel faces, using the results of [24]. These beautiful packing arrangements describe and show the very interesting structure of the mentioned orthoschemes and the corresponding Coxeter reflection group. We use the Beltrami-Cayley-Klein ball model of 3-dimensional hyperbolic space H^3, the images were made by the Python programming language.
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Ruffner, John W., Nina P. Deibler, Christine L. Holiday, Timothy H. Isenberg, and Angela J. Hutten. "The Hyperbolic Brower as a Tool for Information Visualization, Discovery, and Retrieval on the Web and Enterprise Intranets." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 53, no. 15 (2009): 945–49. http://dx.doi.org/10.1177/154193120905301502.
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Knowledge workers frequently need to locate task-relevant information quickly and efficiently through the Internet or their enterprise intranets. The ability to visualize how information is structured and organized is often a key to timely and efficient information discovery and retrieval. The traditional interface used for browsing Web sites has been a hierarchical, tree-like presentation, such as the Windows Explorer file/folder browser. From a user interface design standpoint, an attractive alternative to this type of browser is the hyperbolic browser, which is a focus + context technique for visualizing and browsing large amounts of hierarchical inter-related information. A hyperbolic view display efficiently represents hierarchical and associative information in a static or dynamic visual format using a relatively small display space. This paper discusses the characteristics of the hyperbolic browser, provides a real-life use case scenario to illustrate its application, and suggests avenues for future research and development.
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Wang, Xiao, Yiding Zhang, and Chuan Shi. "Hyperbolic Heterogeneous Information Network Embedding." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 5337–44. http://dx.doi.org/10.1609/aaai.v33i01.33015337.
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Heterogeneous information network (HIN) embedding, aiming to project HIN into a low-dimensional space, has attracted considerable research attention. Most of the exiting HIN embedding methods focus on preserving the inherent network structure and semantic correlations in Euclidean spaces. However, one fundamental problem is that whether the Euclidean spaces are the appropriate or intrinsic isometric spaces of HIN? Recent researches argue that the complex network may have the hyperbolic geometry underneath, because the underlying hyperbolic geometry can naturally reflect some properties of complex network, e.g., hierarchical and power-law structure. In this paper, we make the first effort toward HIN embedding in hyperbolic spaces. We analyze the structures of two real-world HINs and discover some properties, e.g., the power-law distribution, also exist in HIN. Therefore, we propose a novel hyperbolic heterogeneous information network embedding model. Specifically, to capture the structure and semantic relations between nodes, we employ the meta-path guided random walk to sample the sequences for each node. Then we exploit the distance in hyperbolic spaces as the proximity measurement. The hyperbolic distance is able to meet the triangle inequality and well preserve the transitivity in HIN. Our model enables the nodes and their neighborhoods have small hyperbolic distances. We further derive the effective optimization strategy to update the hyperbolic embeddings iteratively. The experimental results, in comparison with the state-of-the-art, demonstrate that our proposed model not only has superior performance on network reconstruction and link prediction tasks but also shows its ability of capture hierarchy structure in HIN via visualization.
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Mavares Ferrer, Pablo José. "Visualization of the Chaos Game for non-hyperbolic iterated function system." REVISTA ODIGOS 1, no. 2 (2020): 9–20. http://dx.doi.org/10.35290/ro.v1n2.2020.302.
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The chaos game is a random algorithm generally applied to contracting (hyperbolic) iterated function system (IFS) which makes it possible to obtain the unique attractor of the dynamic system. However, when applied to non-contractive IFS extremely interesting results can be obtained that are not only important from a theoretical and application point of view, but can also be part of a mathematical didactics that seeks to modernize teaching. In this sense, this research present some results related to the application of the chaos game to non-contracting IFS are presented.
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Lazutkin, V. F. "Existence and visualization of a hyperbolic structure in area-preserving maps." Chaos, Solitons & Fractals 11, no. 1-3 (2000): 237–40. http://dx.doi.org/10.1016/s0960-0779(98)00288-4.
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Mork, Leah K., and Darin J. Ulness. "Visualization of Mandelbrot and Julia Sets of Möbius Transformations." Fractal and Fractional 5, no. 3 (2021): 73. http://dx.doi.org/10.3390/fractalfract5030073.
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This work reports on a study of the Mandelbrot set and Julia set for a generalization of the well-explored function η(z)=z2+λ. The generalization consists of composing with a fixed Möbius transformation at each iteration step. In particular, affine and inverse Möbius transformations are explored. This work offers a new way of visualizing the Mandelbrot and filled-in Julia sets. An interesting and unexpected appearance of hyperbolic triangles occurs in the structure of the Mandelbrot sets for the case of inverse Möbius transforms. Several lemmas and theorems associated with these types of fractal sets are presented.
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Shneiderman, Ben, Cody Dunne, Puneet Sharma, and Ping Wang. "Innovation trajectories for information visualizations: Comparing treemaps, cone trees, and hyperbolic trees." Information Visualization 11, no. 2 (2011): 87–105. http://dx.doi.org/10.1177/1473871611424815.
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This paper reviews the trajectory of three information visualization innovations: treemaps, cone trees, and hyperbolic trees. These three ideas were first published around the same time in the early 1990s, so we are able to track academic publications, patents, and trade press articles over almost two decades. We describe the early history of each approach, problems with data collection from differing sources, appropriate metrics, and strategies for visualizing these longitudinal data sets. This paper makes two contributions: (1) it offers the information visualization community a history of how certain ideas evolved, influenced others, and were adopted for widespread use and (2) it provides an example of how such scientometric trajectories of innovations can be gathered and visualized. Guidance for designers is offered, but these conjectures may also be useful to researchers, research managers, science policy analysts, and venture capitalists.
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Jeong, Yun-Seok, and Ro-Hae Myung. "An Effective Information Visualization Technique for Intrusion Detection: Hyperbolic View Intrusion Visualizer." Journal of the Ergonomics Society of Korea 30, no. 2 (2011): 319–30. http://dx.doi.org/10.5143/jesk.2011.30.2.319.
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Fanyaev, I. A., Sh Hao, J. Wang, J. Li, and S. A. Khakhomov. "Controlled Hyperbolic Structure of Metamaterial for Subdiffraction Visualization in the Terahertz Range." Crystallography Reports 68, no. 7 (2023): 1215–21. http://dx.doi.org/10.1134/s1063774523600837.
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Latuamury, Bokiraiya, Gun Mardiatmoko, and Agustinus Kastanya. "MASTER RECESSION CURVE VISUALIZATION USING SEVEN BASEFLOW RECESSION MODELS IN PAIRED WATERSHEDS." Jurnal Teknosains 14, no. 1 (2024): 1. https://doi.org/10.22146/teknosains.90705.
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River flow recession analysis plays a crucial role in understanding how watersheds release water during dry periods. Consequently, modeling baseflow recession is closely related to the characteristics of unconfined aquifers, storage behavior, and the discharge properties of the watershed. While several theories exist on modeling recession curves, limited research has compared different approaches regarding baseflow recession characteristics. This study aims to model seven baseflow recession equations in paired watersheds in Ambon City. The research methodology involves calibrating seven baseflow recession models using the Recession Curve (RC) 4.0 Hydro Office software. The tested models include Linear Reservoir, Exponential Reservoir, Double Exponential Horton, Dupuit-Boussinesq Aquifer Storage, Depression Storage, Turbulent Flow Model, and Hyperbolic Function Model. The calibration results yield optimal combinations of recession parameters. The parameterization order from highest to lowest is as follows: Depression Storage, followed by the Hyperbolic Function, Exponential Reservoir, Turbulent Flow Model, Double Exponential Horton, Linear Reservoir, and Dupuit-Boussinesq Aquifer Storage. Quantifying baseflow recession constants and coefficients is essential for understanding baseflow behavior. Visualizing the slope of the Recession Curve (MRC) reveals that models with high recession constants tend to have gradual MRCs, while low recession constants result in steep MRCs. The MRC slope further describes the relationship between storage conditions and discharge from the watershed. The advantage of creating MRCs from discontinuous recession segments lies in their ability to appropriately describe the MRC process and provide quantitative parameters relevant to drainage mechanisms. MRCs also serve as an optimal automated computational tool.
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Şentürk, Gülsüm Yeliz, and Nurten Gürses. "Dual quaternion theory over HGC numbers." Journal of Discrete Mathematical Sciences & Cryptography 27, no. 1 (2024): 117–42. http://dx.doi.org/10.47974/jdmsc-1611.
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Knowing the applications of quaternions in various fields, such as robotics, navigation, computer visualization and animation, in this study, we give the theory of dual quaternions considering Hyperbolic-Generalized Complex (HGC) numbers as coefficients via generalized complex and hyperbolic numbers. We account for how HGC number theory can extend dual quaternions to HGC dual quaternions. Some related theoretical results with HGC Fibonacci/Lucas numbers are established, including their dual quaternions. Given HGC Fibonacci/Lucas numbers, their special matrix correspondences have been identified and these are carried out to HGC Fibonacci/Lucas dual quaternions. Furthermore, we provide a more accurate way to quickly calculate HGC Fibonacci numbers and associate this with HGC generalized Fibonacci numbers. For implementation, we produce an algorithm in Maple. Lastly, we put the theory into practice.
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Gurina, R. V., E. V. Morozova, and V. V. Kosheva. "Rank analysis in evaluating the validity of olympiad tasks." Professional education in the modern world 10, no. 4 (2021): 4302–9. http://dx.doi.org/10.20913/2618-7515-2020-4-14.
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The rank analysis (cenological approach) based on a strict mathematical apparatus allows diagnosing the state of educational systems and processes on a scientific objective basis. The rank analysis base is applying the law of hyperbolic rank distribution of objects in systems-cenoses, which is a refined Pareto law 20/80 (Pareto-Kudrin law). Using of rank analysis to evaluate the validity of the olympiad tasks of the all-Russian Multidisciplinary Engineering Olympiad «Star», the authors demonstrate the necessity of implementing rank analysis in the practice of education quality management. They show that this law is important and appropriate to apply in the education quality management. Optimization of educational systems and processes using rank analysis consists in eliminating anomalous deviations from the hyperbolic law, which is possible only with graphical visualization of the rank distribution and its approximation. The rank distribution graph provides visibility and insight into the nature of the rank decrease. Shortcomings in the content of olympiad tasks (as well as tests), leading to a deterioration of their validity and reliability, are shown the form of distortions of the hyperbolic graph (humps, depressions, tails, degeneration of the hyperbola into other dependencies). The rank analysis allows identifying objectively several levels of validity of olympiad or test tasks carrying on a scientific basis. The paper demonstrates graphs of run distributions illustrating examples of high (natural science) and below the average (history) validity of olympiad tasks. Educational systems are cenoses, ranking objects in them are students, classes, schools, etc., and their ranked parameters are academic performance, rating in points, performance indicators, etc. Using simple mathematical tools of rank analysis and computer software bring the technologies to assess the education quality to a higher level meeting the challenges of the time.
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Tai, Chang-Yu, Ming-Yao Li, and Lun-Wei Ku. "Hyperbolic Disentangled Representation for Fine-Grained Aspect Extraction." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 10 (2022): 11358–66. http://dx.doi.org/10.1609/aaai.v36i10.21387.
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Automatic identification of salient aspects from user reviews is especially useful for opinion analysis. There has been significant progress in utilizing weakly supervised approaches, which require only a small set of seed words for training aspect classifiers. However, there is always room for improvement. First, no weakly supervised approaches fully utilize latent hierarchies between words. Second, each seed word’s representation should have different latent semantics and be distinct when it represents a different aspect. In this paper we propose HDAE, a hyperbolic disentangled aspect extractor in which a hyperbolic aspect classifier captures words’ latent hierarchies, and an aspect-disentangled representation models the distinct latent semantics of each seed word. Compared to previous baselines, HDAE achieves average F1 performance gains of 18.2% and 24.1% on Amazon product review and restaurant review datasets, respectively. In addition, the embedding visualization experience demonstrates that HDAE is a more effective approach to leveraging seed words. An ablation study and a case study further attest the effectiveness of the proposed components.
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FOMENKO, A. T. "COMPUTERS AND VISUALIZATION IN HYPERBOLIC THREE-DIMENSIONAL GEOMETRY AND TOPOLOGY: SOME OPEN PROBLEMS." International Journal of Shape Modeling 01, no. 01 (1994): 41–62. http://dx.doi.org/10.1142/s0218654394000050.
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Martin, Christian, Naryttza N. Diaz, Jörg Ontrup, and Tim W. Nattkemper. "Hyperbolic SOM-based clustering of DNA fragment features for taxonomic visualization and classification." Bioinformatics 24, no. 14 (2008): 1568–74. http://dx.doi.org/10.1093/bioinformatics/btn257.
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Tuan, Nguyen Minh, Sanoe Koonprasert, Sekson Sirisubtawee, Phayung Meesad, and Nattawut Khansai. "New Solutions of Benney-Luke Equation Using The (G’/G,1/G) Method." WSEAS TRANSACTIONS ON MATHEMATICS 23 (April 24, 2024): 267–75. http://dx.doi.org/10.37394/23206.2024.23.29.
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The Benney-Luke equation has contributed to studying the propagation of the water wave surfaces. This paper illustrates the (G’/G,1/G)-method to obtain the solutions of the Benney-Luke equation and an extension of the Benney-Luke equation. The new types of solutions are also constructed to gather the performance and visualization in three dimensions for observing the behaviors. The solutions are found in the expressions of hyperbolic functions giving the general performance by selecting arbitrary constants.
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Piotto, Stefano, and Reinhard Nesper. "CURVIS: a program to study and analyse crystallographic structures and phase transitions." Journal of Applied Crystallography 38, no. 1 (2005): 223–27. http://dx.doi.org/10.1107/s0021889804027311.
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The visualization of scientific data is, nowadays, of extreme importance. Phase transitions, the topology of a crystallographic system, the electron density distribution inside a lattice or the changes in crystal structure during phase transitions cannot be fully investigated without the help of proper visualization. The programCURVIS(downloadable free of charge upon request) was developed as a tool for investigating crystal structures and occurring transitions. In this tool, some features are implemented to analyse, display and manage the three-dimensional structure of crystals and single molecules. More importantly,CURVIScan generate and handle hyperbolic surfaces in three dimensions, and provide specific routines to perform calculations of curvature and energy of such surfaces. The most important features are (i) file format conversion (with assignment of the atom types and atomic charges), (ii) surface calculation and (iii) curvature and surface-energy analysis.
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Afzal, Muhammad, and Hermann Maurer. "Expertise Recommender System for Scientific Community." JUCS - Journal of Universal Computer Science 17, no. (11) (2011): 1529–49. https://doi.org/10.3217/jucs-017-11-1529.
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Finding experts in academics as well as in enterprises is an important practical problem. Both manual and automated approaches are employed and have their own pros and cons. On one hand, the manual approaches need extensive human efforts but the quality of data is good, on the other hand, the automated approaches normally do not need human efforts but the quality of service is not as good as in the manual approaches. Furthermore, the automated approaches normally use only one metric to measure the expertise of an individual. For example, for finding experts in academia, the number of publications of an individual is used to discover and rank experts. This paper illustrates both manual and automated approaches for finding experts and subsequently proposes and implements an automated approach for measuring expertise profile in academia. The proposed approach incorporates multiple metrics for measuring an overall expertise level. To visualize a rank list of experts, an extended hyperbolic visualization technique is proposed and implemented. Furthermore, the discovered experts are pushed to users based on their local context. The research has been implemented for Journal of Universal Computer Science (J. UCS) and is available online for the users of J.UCS.
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Walter, Jörg A. "H-MDS: a new approach for interactive visualization with multidimensional scaling in the hyperbolic space." Information Systems 29, no. 4 (2004): 273–92. http://dx.doi.org/10.1016/j.is.2003.10.002.
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Luo, H., J. Fan, S. Satoh, J. Yang, and W. Ribarsky. "Integrating multi-modal content analysis and hyperbolic visualization for large-scale news video retrieval and exploration." Signal Processing: Image Communication 23, no. 7 (2008): 538–53. http://dx.doi.org/10.1016/j.image.2008.04.014.
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Buynevich, Ilya. "Non-invasive (georadar) investigation of groundhog (Marmota monax) burrows, Pennsylvania, USA." Theriologia Ukrainica 2023, no. 26 (2023): 159–66. http://dx.doi.org/10.53452/tu2614.
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Zoogenic impact plays a critical role in stream processes, especially bank stability and resulting channel dynamics. This study focuses on bioturbation by groundhogs (Marmota monax) along the riparian zone of Mill Creek (Bucks County, Pennsylvania, USA). Several complexes comprising at least 32 active burrows (average diameter: 25.9 cm) were geolocated, with morphometric measurements obtained at selected sites. Two networks were imaged using high-frequency 800 MHz ground-penetrating radar (GPR) and included: 1) a grid of parallel 3-m-long transects on the south bank, and 2) an 11-m-long profile on the north bank. Post-processed electromagnetic signal traces (A-scans) comprising 2D radargrams (B-scans) revealed voids as reverse-polarity anomalies (hollow inclined shafts and tunnels), allowing for a general assessment of burrow depth and orientation. At the southern cutbank site, a large burrow had an entrance diameter of 0.3 m and a westerly dip. A sloping tunnel section was detected at ~0.5 m depth, based on the geometry of point-source (transverse) hyperbolic diffractions corresponding to the roof and a floor ‘pull-up’. The second locality traversed three open burrow entrances adjacent to large tree roots. This survey along a tributary channel shows multiple hyperbolics below adjacent openings, with the latter showing the characteristic signal ‘breakout’. GPR data show hyperbolic signatures ~0.3–0.4 m below the ground surface. Along this transect, burrowing activity appears to increase with proximity to the northern bank of Mill Creek. An example of a depth slice (bedding-plane view) from a nearby riverbank demonstrates the potential for 3D visualization (C-scans) of burrow networks using a grid of closely spaced GPR profiles. Groundhog burrows constrain maximum long-term level of the groundwater table and serve as important zoogeomorphic structures in diverse ecotones, including developed landscapes. Abundant evidence of bank slumping, incision, and treefall suggests that burrowing activity likely weakens root systems and enhances groundwater flow, thereby initiating or accelerating geomorphic cascades leading to slope failure.
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Porsani, Jorge Luís, and William A. Sauck. "Ground-penetrating radar profiles over multiple steel tanks: Artifact removal through effective data processing." GEOPHYSICS 72, no. 6 (2007): J77—J83. http://dx.doi.org/10.1190/1.2783412.
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This paper describes some ground-penetrating radar (GPR) results to characterize steel tanks buried in the subsoil of an urban center. Tanks were installed in the first Brazilian geophysical test site located at the Institute of Astronomy, Geophysics, and Atmospheric Science (IAG) of the University of São Paulo (USP). This paper also presents an effec-tive procedure for removal of hyperbolic artifacts associated with GPR reflections between multiple steel tanks. One hundred sixty-five GPR profiles of [Formula: see text], [Formula: see text], and [Formula: see text] (shielded bistatic antennae) were measured. The work was done in two distinct places: on the geophysical test site of the IAG/USP in the city of São Paulo, Brazil, and in an area formerly occupied by a truck cleaning, refueling, and maintenance facility, located in Oscoda, northeastern Michigan, USA. Predictive deconvolution and Kirchhoff migration were first used to improve vertical and lateral resolution. To minimize the hyperbolic artifacts caused by reflections between tanks, high-pass filtering was applied to data. Then, Hilbert transforms emphasize the location of the steel tanks in an energy cross-section form. Further GPR processing, such as vertical and depth slices, were very important to improve visualization and localization of steel tanks and pipes in the subsurface.
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Zhang, Xianhong, and Chunrui Zhang. "CELLULAR NEURAL NETWORK IMAGE EDGE DETECTION BASED ON HYPERBOLIC TANGENT FUNCTION - FROM PHOTOGRAPHIC IMAGE TO FLOW VISUALIZATION." Journal of Flow Visualization and Image Processing 22, no. 1-3 (2015): 151–63. http://dx.doi.org/10.1615/jflowvisimageproc.2016017209.
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Kulterbaev, Khusen P., Lyalusya A. Baragunova, Maryana M. Shogenova, and Maryana A. Shardanova. "The Solution of a Spectral Task on Variable Section Compressed Beams Vibrations by Numerical Methods." Materials Science Forum 974 (December 2019): 704–10. http://dx.doi.org/10.4028/www.scientific.net/msf.974.704.
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Free flexural free vibrations of variable section are considered. The vibrations mathematical model represents the boundary value problem consisting of the hyperbolic type and boundary conditions main equation. By means of separation method of variables the task at the beginning comes to homogeneous differential equation of the fourth order for fundamental function with the corresponding boundary conditions. The grid area of an argument change and fundamental function in it are applied. That leads to an algebraic problem of eigenvalues. Multimodal non-negative function which null values match its eigenvalues is designed. The finite differences methods and coordinate descent in combination with the specified function sections graphic visualization at a small amount of descents with an adequate accuracy for eigenvalues practice are given. The known ways to define fundamental functions are applied.
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De Marchi, Luca, Alessandro Ceruti, Alessandro Marzani, and Alfredo Liverani. "Augmented Reality to Support On-Field Post-Impact Maintenance Operations on Thin Structures." Journal of Sensors 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/619570.
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This paper proposes an augmented reality (AR) strategy in which a Lamb waves based impact detection methodology dynamically interacts with a head portable visualization device allowing the inspector to see the estimated impact position (with its uncertainty) and impact energy directly on the plate-like structure. The impact detection methodology uses a network of piezosensors bonded on the structure to be monitored and a signal processing algorithm (the Warped Frequency Transform) able to compensate for dispersion the acquired waveforms. The compensated waveforms yield to a robust estimation of Lamb waves difference in distance of propagation (DDOP), used to feed hyperbolic algorithms for impact location determination, and allow an estimation of the uncertainty of the impact positioning as well as of the impact energy. The outputs of the impact methodology are passed to a visualization technology that yielding their representation in Augmented Reality (AR) is meant to support the inspector during the on-field inspection/diagnosis as well as the maintenance operations. The inspector, in fact, can see interactively in real time the impact data directly on the surface of the structure. To validate the proposed approach, tests on an aluminum plate are presented. Results confirm the feasibility of the method and its exploitability in maintenance practice.
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Alyobi, Sultan, Mohammed Alharthi, Yasser Alrashedi, and Imran Khan. "Kink phenomena of the time-space fractional Sharma-Tasso-Olver (STO) equation." Physica Scripta 99, no. 9 (2024): 095265. http://dx.doi.org/10.1088/1402-4896/ad6f4c.
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Abstract This paper aims to obtain exact solutions of solitary waves for the conformable fractional Sharma-Tasso-Olver (STO) equation which plays an important role in nuclear physics to describe the physical occurrences such as the fission and fusion processes. Solitary waves operate central parts in different areas of study such as electromagnetism, atomic quantum theory, as well as special relativity. By means of sub-ode approach with the aid of the modified fractional Riccati-Bernoulli equation, the exact forms of generalized solitary solution of the fractional (STO) equation are found and specified in hyperbolic, trigonometric, and rational functions. This makes the visualization of the fractional effects and the dynamic behaviors of these solutions in 3D and 2D help in establishing practicality for application of the results. The novel analytical results benefit general engineering and mathematical physics in demonstrating that the proposed employment of the given technique allows solving nonlinear problem analytically. These findings are significant for the progress of wave proceedings in the number of applications.
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Majid, Sheikh Zain, Waqas Ali Faridi, Muhammad Imran Asjad, Magda Abd El-Rahman, and Sayed M. Eldin. "Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration." Fractal and Fractional 7, no. 2 (2023): 102. http://dx.doi.org/10.3390/fractalfract7020102.
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The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to the Riemann wave equation using the new extended direct algebraic method. As a result, the soliton patterns of the Riemann wave equation have been successfully illustrated, with exact solutions offered by the plane solution, trigonometry solution, mixed hyperbolic solution, mixed periodic and periodic solutions, shock solution, mixed singular solution, mixed trigonometric solution, mixed shock single solution, complex soliton shock solution, singular solution, and shock wave solutions. Graphical visualization is provided of the results with suitable values of the involved parameters by Mathematica. It was visualized that the velocity of the soliton and the wave number controls the behavior of the soliton. We are confident that our research will assist physicists in predicting new notions in mathematical physics.
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Gandarias, Maria Luz, Nauman Raza, Muhammad Umair, and Yahya Almalki. "Dynamical Visualization and Qualitative Analysis of the (4+1)-Dimensional KdV-CBS Equation Using Lie Symmetry Analysis." Mathematics 13, no. 1 (2024): 89. https://doi.org/10.3390/math13010089.
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This study investigates novel optical solitons within the intriguing (4+1)-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff (KdV-CBS) equation, which integrates features from both the Korteweg–de Vries and the Calogero–Bogoyavlenskii–Schiff equations. Firstly, all possible symmetry generators are found by applying Lie symmetry analysis. By using these generators, the given model is converted into an ordinary differential equation. An adaptive approach, the generalized exp(-S(χ)) expansion technique has been utilized to uncover closed-form solitary wave solutions. The findings reveal a range of soliton types, including exponential, rational, hyperbolic, and trigonometric functions, represented as bright, singular, rational, periodic, and new solitary waves. These results are illustrated numerically and accompanied by insightful physical interpretations, enriching the comprehension of the complex dynamics modeled by these equations. Our approach’s novelty lies in applying a new methodology to this problem, yielding a variety of novel optical soliton solutions. Additionally, we employ bifurcation and chaos techniques for a qualitative analysis of the model, extracting a planar system from the original equation and mapping all possible phase portraits. A thorough sensitivity analysis of the governing equation is also presented. These results highlight the effectiveness of our methodology in tackling nonlinear problems in both mathematics and engineering, surpassing previous research efforts.
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Al Alwan, Basem, Muhammad Abu Bakar, Waqas Ali Faridi, Antoniu-Claudiu Turcu, Ali Akgül, and Mohammed Sallah. "The Propagating Exact Solitary Waves Formation of Generalized Calogero–Bogoyavlenskii–Schiff Equation with Robust Computational Approaches." Fractal and Fractional 7, no. 2 (2023): 191. http://dx.doi.org/10.3390/fractalfract7020191.
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The generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) is examined and analyzed in this paper. It has several applications in plasma physics and soliton theory, where it forecasts the soliton wave propagation profiles. In order to obtain the analytically exact solitons, the model under consideration is a nonlinear partial differential equation that is turned into an ordinary differential equation by using the next traveling wave transformation. The new extended direct algebraic technique and the modified auxiliary equation method are applied to the generalized Calogero–Bogoyavlenskii–Schiff equation to get new solitary wave profiles. As a result, novel and generalized analytical wave solutions are acquired in which singular solutions, mixed singular solutions, mixed complex solitary shock solutions, mixed shock singular solutions, mixed periodic solutions, mixed trigonometric solutions, mixed hyperbolic solutions, and periodic solutions are included with numerous soliton families. The propagation of the acquired soliton solution is graphically presented in contour, two- and three-dimensional visualization by selecting appropriate parametric values. It is graphically demonstrated how wave number impacts the obtained traveling wave structures.
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Teixeira, Guilherme S. ,., and Marco D. De Campos. "Influence of Wind Angle Incidence and Architectural Elements on the External Pressure Coefficient of Hyperbolic Paraboloid Roofs." DESIGN, CONSTRUCTION, MAINTENANCE 2 (June 30, 2022): 208–16. http://dx.doi.org/10.37394/232022.2022.2.27.
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In the study of wind loads in buildings, the aerodynamics of roofs with parabolic shapes, which cause complex pressure distributions due to their sensitivity to wind, are often omitted and neglected by several codes and norms. In this way, computer simulations are a viable and reliable alternative. Here, wind action was considered in an innovative project composed of parabolic and circumferential generatrices: the Church of Saint Francis of Assisi. Designed by Brazilian architect Oscar Niemeyer in Belo Horizonte, Brazil, two paraboloid vaults and three circular arches of reinforced concrete composed its structure. This work generated great international recognition for the architect after 1943, as the design of the roofs did not require walls. For geometry modeling, Autodesk AutoCAD software was adopted, and the models were considered in a control volume. The simulations were performed using Ansys Workbench software and the RNG K-Epsilon turbulence model. The wind speed at different heights was calculated using the Power-law approximation. A basic wind speed of 30 m/s was adopted, and the mesh used was composed of tetrahedrons. To validate the methodology, different models with hyperbolic-paraboloid roofs from the literature were considered. In addition, the visualization of the flow around the geometry from the streamlines, the wind profile, and the analysis of the isobaric lines of the external pressure coefficients for different directions of incidence and architectural elements that make up the building were presented.
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Adamadziev, Kurban Radjabovich, and Abduragim Suleymanovich Akhmedov. "ANALYSIS OF TRENDS IN THE DYNAMICS OF THREE KEY SOCIAL INDICATORS OF THE ECONOMY OF THE RUSSIAN FEDERATION (ACCORDING TO DATA FOR 2005-2022)." Scientific Review: Theory and Practice 14, no. 7 (2024): 1379–92. http://dx.doi.org/10.35679/2226-0226-2024-14-7-1379-1392.
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The work is devoted to the development of methods and computer tools for the analysis of key socio-economic indicators of the Russian Federation, per capita monetary income, expenses and wages of employees of the organization, based on statistical data for 18 years (for 2005-2022). To analyze the relationships and trends of key indicators, both classical statistical methods were used (visualization using various graphs and calculation coefficients), as well as methods of econometric modeling. The developed tools and computer model are based on the identification of relationships and dependencies between time series of key socio-economic indicators using methods of linear, hyperbolic, power, exponential and parabolic correlation and regression. The methodology also includes the calculation and analysis of coefficients characterizing the ratio of wages to income; expenses to income and expenses to wages, as well as visualization and analysis of changes in these relations for 2005-2022. Quantitative analysis in economics involves the development and comparison of a large number of options that differ in the initial data, the form of communication and other parameters. In this case, it becomes necessary to repeatedly perform the same computational operations. The computer model developed by the authors, based on MS Excel, allows you to automate the execution of the same type of calculations for various indicators and their ratios. The proposed toolkit has been developed and tested on the example of three key social indicators of the economy of the Russian Federation for 2005-2022). For all three key social indicators under consideration, it was possible to construct statistically significant models of various types, quantitatively characterizing their relationship, which can be assessed as positive and quite close.
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Buynevich, Ilya. "Neoichnology of vertebrate traces along the western barrier coast of Ukraine: preservation potential and subsurface visualization." GEO&BIO 2023, no. 24 (2023): 99–105. http://dx.doi.org/10.53452/gb2407.
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A diverse quite of vertebrate traces covers beach, aeolian, and bay-side (deflation flats) surfaces along the NW Black Sea coast of Ukraine. These include avian, ungulate, and canid footprints, as well as mammal burrows (length >5 cm; depth ~2 cm). The preservation of biogenic structures is enhanced by rapid burial (low-energy sedimentation or event deposition), algal mat formation, and salt encrustation. Continuous high-frequency (800 MHz) ground-penetrating radar (GPR) imaging aided in visualizing subsurface sections of an active burrow complex within a beach-dune ridge. Images near an active fox burrow captured distinct subsurface anomalies (point-source hyperbolic diffractions) in the upper aeolian section above the water table. Unfilled tunnel sections are easily distinguished from buried roots and other targets based on signal velocity and polarity reversals relative to air-to-sediment response at the ground surface. The diffraction geometry (angle) is related to signal velocity, providing valuable information about relative saturation of the overlying substrate. Decimeter-scale deformation of shallow reflections may be attributed to tracking surfaces, with similar examples found immediately below modern surfaces affected by anthropogenic trampling. It is likely that muddy lagoonal tracking surfaces may be preserved under layers of sand (overwash or aeolian deposition) and, following saltwater expulsion, may be recognized in geophysical images as clear deformed paleo-surfaces. Heavy-mineral concentrations (e.g. magnetite-rich sand) are common for beach and dune horizons that have undergone reworking and such anomalies often accentuate physical and biogenic deformation structures. Due to moderate-to-high fraction of ferri- and paramagnetic minerals, these anomalies are also well-expressed in GPR images due to its electromagnetic signal response. A conceptual framework of trace preservation potential (taphonomy) and geophysical recognition (GPR) suitability is proposed for this coastal region, with implications to paleo-environmental reconstruction.
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Demchyshyn, A. A., and O. S. Kaleniuk. "Computer-aided modeling and visualization of sound waves propagation in a Tapered Quarter Wavelength Tube." System technologies 1, no. 156 (2025): 3–11. https://doi.org/10.34185/1562-9945-1-156-2025-01.
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The paper presents the algorithmic basis for computer-aided modeling of sound wave propagation in an acoustic system with an acoustic design in the form of a straight and folded tapered quarter wavelength tube (TQWT). The aim of the modeling is to compare the systems by fidelity of the signal reproduced and localize acoustic excitation zone inside the acoustic system, where installation of a layer of absorbing material is effective for control of wave propagation. The computer-aided modeling of acoustic wave propagation utilizes an algorithm based on a hyperbolic differential equation with attenuation component. A web application has been developed in JS programming language for CPU and GLSL ES language for parallel computing on GPU, which works according to the presented algorithm to simulate the wave propagation process. The program visualizes wave propagation in real-time based on the initial parameters of the environ-ment, such as: the geometric configuration of acoustic enclosure (constructed using line segments), the coordinates of the location and geometric configuration of the wave source, angular velocity of the generator and the wave amplitude, the Courant number, the attenuation coefficient, the size of the simulation grid. The software made it possible to calculate the constructive and destructive interference maps of the wave generated by the speaker’s front side with the wave emerging from the acous-tic system’s port of straight and folded tapered pipe. With a grid size of 512 x 288, the algo-rithm achieved a processing speed of over than 75 time-steps per second using a processor with parallel computing Intel UHD 630. The maps showed that the zones of acoustic excitation were located inside the acoustic enclosure opposite to the wave source. It is shown that the acoustic enclosure in the form of a folded TQWT effectively suppresses high and medium frequencies by attenuating the wave with the configuration of the walls behind the broadband source. The con-figuration prevents unpredictable amplification or attenuation of the specified frequencies and, as a result, increases the fidelity of signal reproduction.
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David, M. Jimreeves, Manikandan Mathur, R. N. Govardhan, and J. H. Arakeri. "The kinematic genesis of vortex formation due to finite rotation of a plate in still fluid." Journal of Fluid Mechanics 839 (February 2, 2018): 489–524. http://dx.doi.org/10.1017/jfm.2017.908.
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We present a combined experimental and numerical study of an idealized model of the propulsive stroke of the turning manoeuvre in fish. Specifically, we use the framework of Lagrangian coherent structures (LCSs) to describe the kinematics of the flow that results from a thin plate performing a large angle rotation about its tip in still fluid. Temporally and spatially well-resolved velocity fields are obtained using a two-dimensional, incompressible finite-volume solver, and are validated by comparisons with experimentally measured velocity fields and alternate numerical simulations. We then implement the recently proposed variational theory of LCSs to extract the hyperbolic and elliptic LCSs in the numerically generated velocity fields. Detailed LCS analysis is performed for a plate motion profile described by $\dot{\unicode[STIX]{x1D703}}(t)=\unicode[STIX]{x1D6FA}_{max}\sin ^{2}(\unicode[STIX]{x1D714}t)$ during $0\leqslant t\leqslant t_{o}$ and zero otherwise. The stopping time $t_{o}$ is given by $t_{o}=\unicode[STIX]{x03C0}/\unicode[STIX]{x1D714}=10~\text{s}$, the value of $\unicode[STIX]{x1D6FA}_{max}$ chosen to give a stopping angle of $\unicode[STIX]{x1D703}_{max}=90^{\circ }$, resulting in a Reynolds number $Re=c^{2}\unicode[STIX]{x1D6FA}_{max}/\unicode[STIX]{x1D708}=785.4$, where $c$ is the plate chord length and $\unicode[STIX]{x1D708}=10^{-6}~\text{m}^{2}~\text{s}^{-1}$ the kinematic viscosity of water. The flow comprises a starting and a stopping vortex, resulting in a pair of oppositely signed vortices of unequal strengths that move away from the plate in a direction closely aligned with the final plate orientation at $t/t_{o}\approx 2$. The hyperbolic LCSs are shown to encompass the fluid material that is advected away from the plate for $t>t_{o}$, henceforth referred to as the advected bulk. The starting and stopping vortices, identified using elliptic LCSs and hence more objective than Eulerian vortex detection methods, constitute only around two thirds of the advected bulk area. The advected bulk is traced back to $t=0$ to identify five distinct lobes of fluid that eventually form the advected bulk, and hence map the long-term fate of various regions in the fluid at $t=0$. The five different lobes of fluid are then shown to be delineated by repelling LCS boundaries at $t=0$. The linear momentum of the advected bulk region is shown to account for approximately half of the total impulse experienced by the plate in the direction of its final orientation, thus establishing its dynamical significance. We provide direct experimental evidence for the kinematic relevance of hyperbolic and elliptic LCSs using novel dye visualization experiments, and also show that attracting hyperbolic LCSs provide objective characterization of the spiral structures often observed in vortical flows. We conclude by showing that qualitatively similar LCSs persist for several other plate motion profiles and stopping angles as well.
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Iqbal, Muhammad, Muhammad Bilal Riaz, Muhammad Aziz Ur Rehman, Tomas Martinovic, and Jan Martinovic. "Demonstration of Sensitive Analysis and Optical Soliton Patterns in a (4+1) Dimensional Boiti-Leon-Manna Pempinelli Equation: Dynamic Insights into Bifurcation, Chaotic Behavior." Chaos Theory and Applications 7, no. 1 (2024): 1–9. https://doi.org/10.51537/chaos.1518307.
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This study aims to find exact solutions for a mathematical problem known as the (4+1)-dimensional Boiti Leon Manna Pempinelli (BLMP) equation. In order to convert the governing equation into an ordinary differential equation, we make use of an appropriate wave transformation. This transformation enables the investigation of mathematical solutions, exaggerated outcomes, and normal solutions. Furthermore, in order to accurately determine the solution to this wave, we make use of the modified Khater method. We apply the given approach to find rational, the trigonometric, and hyperbolic solutions. The selected solutions provide graphic representations that accurately depict the physical behavior of the model. Using their visualization, we are able to demonstrate how their behavior changes over time in a four-dimensional space. The use of a visual representation, which involves selecting suitable values for arbitrary components, improves the understanding of the dynamical system. Furthermore, we conduct a sensitivity analysis of the dynamical system to determine the stability of the solution. The dynamical system engages in a discussion about the existence of chaotic dynamics within the Boiti Leon Manna Pempinelli equation. It is possible to depict these chaotic phenomena using two-dimensional and three-dimensional phase portraits.
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Zhang, Guojian, Zhiyang Wang, Wengang Sang, et al. "Research on Dynamic Deformation Laws of Super High-Rise Buildings and Visualization Based on GB-RAR and LiDAR Technology." Remote Sensing 15, no. 14 (2023): 3651. http://dx.doi.org/10.3390/rs15143651.
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It is well-known that structures composed of super high-rise buildings accumulate damages gradually due to ultra-long loads, material aging, and component defects. Thus, the bearing capacity of the structures can be significantly decreased. In addition, these effects may cause inestimable life and property losses upon strong winds, earthquakes, and other heavy loads. Hence, it is necessary to develop real-time health monitoring methods for super high-rise buildings to deeply understand the running state during operation, timely discover potential safety potentials, and to provide reference data for reinforcement design. Along these lines, in this work, the built super high-rise buildings (Yunding Building) and super high-rise buildings (the Main Tower of the Shandong International Financial Center), under construction, were selected as the research objects. The overall dynamic deformation laws of super high-rise buildings were monitored by using ground-based real aperture radar (GB-RAR) technology for its advantages in non-contact measurement, remote monitoring, and real-time display of observation results. Denoising of the observation data was also carried out based on wavelet analysis. The visualization of the space state of the Yunding Building was realized based on handheld LiDAR technology. From the acquired results, it was demonstrated that the measuring accuracy of GB-RAR could reach the submillimeter level, while the noises under a natural state of wavelet analysis were eliminated well. The maximum deformation values of the Yunding Building and the Main Tower of Shandong International Financial Center under their natural state were 9.63 mm and 16.46 mm, respectively. Under sudden wind loads, the maximum deformation of the Yunding Building could be as high as 895.79 mm. The overall motion state switched between an S-shaped pattern, hyperbolic-type, and oblique line, presented the characteristics of nonlinear elastic deformation.
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Bliyeva, Dana, Dossan Baigereyev, and Kholmatzhon Imomnazarov. "Computer Simulation of the Seismic Wave Propagation in Poroelastic Medium." Symmetry 14, no. 8 (2022): 1516. http://dx.doi.org/10.3390/sym14081516.
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This article presents an algorithm for the numerical solution of an initial-boundary value problem for a symmetric t-hyperbolic system of partial differential equations. This problem is based on continual filtration model, which describes the propagation of seismic waves in a poroelastic medium saturated with a fluid characterized by such physical parameters as the propagation velocities of longitudinal P- (fast and slow) and transverse S-waves, the density of the medium materials, and porosity. The system of linearized equations of saturated porous media is formulated in terms of physical variables of the velocity–stress tensor of the porous matrix and the velocity–pressure of the saturating fluid in the absence of energy dissipation. The solution is implemented numerically using an explicit finite difference upwind scheme built on a staggered grid to avoid the appearance of oscillations in the solution functions. The program code implementing parallel computing is developed in the high-performance Julia programming language. The possibility of using the approach is demonstrated by the example of solving the problem of propagation of seismic waves from a source located in the formation. Computational experiments based on real data from oil reservoirs have been implemented, and dynamic visualization of solutions consistent with the first waves arrival times has been obtained.
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Wylie, Korey P., and Jason R. Tregellas. "Rootlets Hierarchical Principal Component Analysis for Revealing Nested Dependencies in Hierarchical Data." Mathematics 13, no. 1 (2024): 72. https://doi.org/10.3390/math13010072.
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Hierarchical clustering analysis (HCA) is a widely used unsupervised learning method. Limitations of HCA, however, include imposing an artificial hierarchy onto non-hierarchical data and fixed two-way mergers at every level. To address this, the current work describes a novel rootlets hierarchical principal component analysis (hPCA). This method extends typical hPCA using multivariate statistics to construct adaptive multiway mergers and Riemannian geometry to visualize nested dependencies. The rootlets hPCA algorithm and its projection onto the Poincaré disk are presented as examples of this extended framework. The algorithm constructs high-dimensional mergers using a single parameter, interpreted as a p-value. It decomposes a similarity matrix from GL(m, ℝ) using a sequence of rotations from SO(k), k << m. Analysis shows that the rootlets algorithm limits the number of distinct eigenvalues for any merger. Nested clusters of arbitrary size but equal correlations are constructed and merged using their leading principal components. The visualization method then maps elements of SO(k) onto a low-dimensional hyperbolic manifold, the Poincaré disk. Rootlets hPCA was validated using simulated datasets with known hierarchical structure, and a neuroimaging dataset with an unknown hierarchy. Experiments demonstrate that rootlets hPCA accurately reconstructs known hierarchies and, unlike HCA, does not impose a hierarchy on data.
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Jhangeer, Adil, Ali R. Ansari, Ariana Abdul Rahimzai, Beenish, and Abdul Qadeer Khan. "Exploring chaos and sensitivity in the Ivancevic option pricing model through perturbation analysis." PLOS ONE 19, no. 11 (2024): e0312805. http://dx.doi.org/10.1371/journal.pone.0312805.
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This study explores the Ivancevic Option Pricing Model, a nonlinear wave-based alternative to the Black-Scholes model, using adaptive nonlinear Schrödingerr equations to describe the option-pricing wave function influenced by stock price and time. Our focus is on a comprehensive analysis of this equation from multiple perspectives, including the study of soliton dynamics, chaotic patterns, wave structures, Poincaré maps, bifurcation diagrams, multistability, Lyapunov exponents, and an in-depth evaluation of the model’s sensitivity. To begin, a wave transformation is applied to convert the partial differential equation into an ordinary differential equation, from which soliton solutions are derived using the ( G ′ G ) method. We explore various forms of the option price function at different time points, including singular-kink, periodic, hyperbolic, trigonometric, exponential, and complex solutions. Furthermore, we simulate 3D surface plots and 2D graphs for the real, imaginary, and modulus components of some of the obtained solutions, assigning specific parameter values to enhance visualization. These graphical representations offer valuable insights into the dynamics and patterns of the solutions, providing a clearer understanding of the model’s behavior and potential applications. Additionally, we analyze the system’s dynamic behavior when a perturbing force is introduced, identifying chaotic patterns using the Lyapunov exponent, Sensitivity, multistability analysis, RK4 method, wave structures, bifurcation diagrams, and Poincaré maps.
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Muthu, Bala Anand, and Claudia Cherubini. "Underwater Digital Twin Sensor Network-Based Maritime Communication and Monitoring Using Exponential Hyperbolic Crisp Adaptive Network-Based Fuzzy Inference System." Water 17, no. 9 (2025): 1324. https://doi.org/10.3390/w17091324.
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The underwater conditions of the coastal ecosystem require careful monitoring to anticipate potential environmental hazards. Moreover, the unique characteristics of the marine underwater environment have presented numerous challenges for the advancement of underwater sensor networks. Current studies have not extensively integrated Digital Twins with underwater sensor networks aimed at monitoring the marine ecosystem. Consequently, this study proposes a decision-making framework based on Underwater Digital Twins (UDTs) utilizing the Exponential Hyperbolic Crisp Adaptive Network-based Fuzzy Inference System (EHC-ANFIS). The process begins with the initialization and registration of an Underwater Autonomous Vehicle (UAV). Subsequently, data are collected from the sensor network and relayed to the UDT model. The optimal path is determined using Adaptive Pheromone Ant Colony Optimization (AP-ACO) to ensure efficient data transmission. Following this, data compression is achieved through the Sliding–Huffman Coding (SHC) algorithm. The Twisted Koblitz Curve Cryptography (TKCC) method is employed to enhance data security. Additionally, an Anomaly Detection System (ADS) is trained, which involves collecting and pre-processing sensor network data. A Radial Chart is then utilized for effective visualization. Anomalies are detected using the CosLU-Variational Shake-Long Short-Term Memory (CosLU-VS-LSTM) approach. For standard data, decision-making based on the UDT model is conducted using EHC-ANFIS, with a fuzzification duration of 21,045 milliseconds. Finally, alerts are dispatched to the Maritime Alert Command Centre (MACC). This approach enhances maritime communication and monitoring along coastal areas, with specific reference to the Coromandel Coast, thereby contributing to the protection of the coastal ecosystem.
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Titkov, Sergey O., Igor M. Garanzha, Anton V. Tanasoglo, and Milena M. Pisareva. "Features of wind effect on the structure of a steel hyperbolic cooling tower." Earthquake Engineering. Construction Safety, no. 4 (August 25, 2024): 35–56. http://dx.doi.org/10.37153/2618-9283-2024-4-35-56.
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Introduction. Paper considers methods for analyzing the impact of wind flow on chimney-type frame-and-sheath 12-sided steel cooling tower (SCT) with irrigation area of 1600 m2. The main goal of conducting numerical and experimental studies of wind flow around the SCT is to verify the experimental data obtained in wind tunnel, as well as to select turbulence model that most accurately describes the phenomena obtained during experimental studies. The development of chimney-type frame-and-sheath steel cooling towers faces number of unsolved problems, which significantly complicates the design process. The main obstacle is lack of clearly substantiated values of loads and impacts on such structures in current regulatory documents. Wind action, being inconstant in strength and direction, has a significant impact on the bearing capacity of cooling tower, taking into account its shape. These studies will not only clarify the calculated values of wind pressure, but also develop more effective methods for calculating loads on cooling towers. Materials and methods. The work is based on use of such approaches of construction aerodynamics as tensometric weight studies, method of drainage of models, methods of wind flow visualization "velocimetry", or shadow method, method of silk threads, allowing to fully evaluate the behavior of the structure in wind flow. Using AutoCAD CFD software was performed numerical analysis with subsequent comparison of data obtained results with experimental studies. During experimental part of study were used models made by means of 3D printing for blowing in construction wind tunnel, taking into account the frame of steel casing of cooling tower to determine the actual diagrams of wind pressure distribution on tower frame-casing cooling tower with hyperbolic shape, taking into account the seasonality of operation, as well as stages of construction, to identify the most unfavorable design situations of the wind influence. Results. The values of the total wind pressure coefficients Cx, Cy, CMz have been determined, confirming the high comparability of the experimental data within the range from 95 % to 100 % with national standards. The values and nature of the distribution of local aerodynamic coefficients Cp differ from those proposed in regulatory documents in terms of peak values at an active pressure of 30 % to 50 %, the length of the region and zones with negative pressures that occur when a vortex comes off. The independence of the aerodynamic coefficient Cp from the Reynolds number Re within the range from 2,71 × 105 to 3,29 × 105. Theory Reynolds Averaged Navier-Stokes SST k-ω DES analysis has been substantiated, most accurately describing the nature of wind flow around design models. Conclusions. The data of experimental studies allowed to establish the values of the coefficients of total wind pressure, similarity criteria, as well as the values and nature of the distribution of local aerodynamic coefficients on the design of the cooling tower. Based on the results of numerical and experimental studies is proposed refined method for standardizing the wind effect on frame-and-sheath 12-sided steel cooling tower with irrigation area of 1600 m2 taking into account the seasonality of operation and construction stages.