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Author: Kyoya Tsutsui
Publisher:
ISBN:
Category : Cluster analysis
Languages : en
Pages : 134
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Book Description
Author: Kyoya Tsutsui
Publisher:
ISBN:
Category : Cluster analysis
Languages : en
Pages : 134
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Book Description
Author: Armin Iske
Publisher: Springer Science & Business Media
ISBN: 3642187544
Category : Mathematics
Languages : en
Pages : 195
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Book Description
This application-oriented work concerns the design of efficient, robust and reliable algorithms for the numerical simulation of multiscale phenomena. To this end, various modern techniques from scattered data modelling, such as splines over triangulations and radial basis functions, are combined with customized adaptive strategies, which are developed individually in this work. The resulting multiresolution methods include thinning algorithms, multi levelapproximation schemes, and meshfree discretizations for transport equa tions. The utility of the proposed computational methods is supported by their wide range of applications, such as image compression, hierarchical sur face visualization, and multiscale flow simulation. Special emphasis is placed on comparisons between the various numerical algorithms developed in this work and comparable state-of-the-art methods. To this end, extensive numerical examples, mainly arising from real-world applications, are provided. This research monograph is arranged in six chapters: 1. Introduction; 2. Algorithms and Data Structures; 3. Radial Basis Functions; 4. Thinning Algorithms; 5. Multilevel Approximation Schemes; 6. Meshfree Methods for Transport Equations. Chapter 1 provides a preliminary discussion on basic concepts, tools and principles of multiresolution methods, scattered data modelling, multilevel methods and adaptive irregular sampling. Relevant algorithms and data structures, such as triangulation methods, heaps, and quadtrees, are then introduced in Chapter 2.
Author: S.P. Singh
Publisher: Springer Science & Business Media
ISBN: 9401585776
Category : Mathematics
Languages : en
Pages : 580
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Book Description
Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.
Author: Valeria V. Krzhizhanovskaya
Publisher: Springer Nature
ISBN: 3030504336
Category : Computers
Languages : en
Pages : 679
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Book Description
The seven-volume set LNCS 12137, 12138, 12139, 12140, 12141, 12142, and 12143 constitutes the proceedings of the 20th International Conference on Computational Science, ICCS 2020, held in Amsterdam, The Netherlands, in June 2020.* The total of 101 papers and 248 workshop papers presented in this book set were carefully reviewed and selected from 719 submissions (230 submissions to the main track and 489 submissions to the workshops). The papers were organized in topical sections named: Part I: ICCS Main Track Part II: ICCS Main Track Part III: Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Agent-Based Simulations, Adaptive Algorithms and Solvers; Applications of Computational Methods in Artificial Intelligence and Machine Learning; Biomedical and Bioinformatics Challenges for Computer Science Part IV: Classifier Learning from Difficult Data; Complex Social Systems through the Lens of Computational Science; Computational Health; Computational Methods for Emerging Problems in (Dis-)Information Analysis Part V: Computational Optimization, Modelling and Simulation; Computational Science in IoT and Smart Systems; Computer Graphics, Image Processing and Artificial Intelligence Part VI: Data Driven Computational Sciences; Machine Learning and Data Assimilation for Dynamical Systems; Meshfree Methods in Computational Sciences; Multiscale Modelling and Simulation; Quantum Computing Workshop Part VII: Simulations of Flow and Transport: Modeling, Algorithms and Computation; Smart Systems: Bringing Together Computer Vision, Sensor Networks and Machine Learning; Software Engineering for Computational Science; Solving Problems with Uncertainties; Teaching Computational Science; UNcErtainty QUantIficatiOn for ComputationAl modeLs *The conference was canceled due to the COVID-19 pandemic.
Author: Samsul Ariffin Abdul Karim
Publisher: Springer Nature
ISBN: 9811589879
Category : Technology & Engineering
Languages : en
Pages : 180
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Book Description
This book presents theoretical modeling and numerical simulations applied to drive several applications towards Industrial Revolution 4.0 (IR 4.0). The topics discussed range from theoretical parts to extensive simulations involving many efficient algorithms as well as various statistical techniques. This book is suitable for postgraduate students, researchers as well as other scientists who are working in mathematics, statistics and numerical modeling and simulation.
Author: G. Brunnett
Publisher: Springer Science & Business Media
ISBN: 370916270X
Category : Computers
Languages : en
Pages : 357
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Book Description
Geometric Modelling is concerned with the computer aided design, manipulation, storage and transmission of geometric shape. It provides fundamental techniques to different areas of application as CAD/CAM, computer graphics, scientific visualization, and virtual Reality. 20 papers presented by leading experts give a state-of-the-art survey of the following topics: surface design and fairing; multiresolution models; reverse engineering; solid modelling; constrained based modelling.
Author: Archana Sangole
Publisher: Universal-Publishers
ISBN: 1581123191
Category : Technology & Engineering
Languages : en
Pages : 157
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Book Description
Researchers and data analysts are increasingly relying on graphical tools to assist them in modeling their data, generating their hypotheses, and gaining deeper insights on their experimentally acquired data. Recent advances in technology have made available more improved and novel modeling and analysis media that facilitate intuitive, task-driven exploratory analysis and manipulation of the displayed graphical representations. In order to utilize these emerging technologies researchers must be able to transform experimentally acquired data vectors into a visual form or secondary representation that has a simple structure and, is easily transferable into the media. As well, it is essential that it can be modified or manipulated within the display environment. This thesis presents a data-driven modeling technique that utilizes the basic learning strategy of an unsupervised clustering algorithm, called the self-organizing feature map, to adaptively learn topological associations inherent in the data and preserve them within the topology imposed by its predefined spherical lattice, thereby transforming the data into a 3D tessellated form. The tessellated graphical forms originate from a sphere thereby simplifying the process of computing its transformation parameters on re-orientation within an interactive, task-driven, graphical display medium. A variety of data sets including six sets of scattered 3D coordinate data, chaotic attractor data, the more commonly used Fisher s Iris flower data, medical numeric data, geographic and environmental data are used to illustrate the data-driven modeling and visualization mechanism. The modeling algorithm is first applied to scattered 3D coordinate data to understand the influence of the spherical topology on data organization. Two cases are examined, one in which the integrity of the spherical lattice is maintained during learning and, the second, in which the inter-node connections in the spherical lattice are adaptively changed during learning. In the analysis, scattered coordinate data of freeform objects with topology equivalent to a sphere and those whose topology is not equivalent to a sphere are used. Experiments demonstrate that it is possible to get reasonably good results with the degree of resemblance, determined by an average of the total normalized error measure, ranging from 6.2x10-5 1.1x10-3. The experimental analysis using scattered coordinate data facilitates an understanding of the algorithm and provides evidence of the topology-preserving capability of the spherical self-organizing feature map. The algorithm is later implemented using abstract, seemingly random, numeric data. Unlike in the case of 3D coordinate data, wherein the SOFM lattice is in the same coordinate frame (domain) as the input vectors, the numeric data is abstract. The criterion for deforming the spherical lattice is determined using mathematical and statistical functions as measures-of information that are tailored to reflect some aspect of meaningful, tangible, inter-vector relationships or associations embedded in the spatial data that reveal some physical aspect of the data. These measures are largely application-dependent and need to be defined by the data analyst or an expert. Interpretation of the resulting 3D tessellated graphical representation or form (glyph) is more complex and task dependent as compared to that of scattered coordinate data. Very simple measures are used in this analysis in order to facilitate discussion of the underlying mechanism to transform abstract numeric data into 3D graphical forms or glyphs. Several data sets are used in the analysis to illustrate how novel characteristics hidden in the data, and not easily apparent in the string of numbers, can be reflected via 3D graphical forms. The proposed data-driven modeling approach provides a viable mechanism to generate 3D tessellated representations of data that can be easily transferred to a graphical modeling and ana
Author: Gerald Farin
Publisher: Springer Science & Business Media
ISBN: 3642557872
Category : Technology & Engineering
Languages : en
Pages : 363
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Book Description
The nature of the physical Universe has been increasingly better understood in recent years, and cosmological concepts have undergone a rapid evolution (see, e.g., [11], [2],or [5]). Although there are alternate theories, it is generally believed that the large-scale relationships and homogeneities that we see can only be explainedby having the universe expand suddenlyin a very early “in?ationary” period. Subsequent evolution of the Universe is described by the Hubble expansion, the observation that the galaxies are ?ying away from each other. We can attribute di?erent rates of this expansion to domination of di?erent cosmological processes, beginning with radiation, evolving to matter domination, and, relatively recently, to vacuum domination (the Cosmological Constant term)[4]. We assume throughout that we will be relying as much as possible on observational data, with simulations used only for limited purposes, e.g., the appearance of the Milky Wayfrom nearbyintergalactic viewpoints. The visualization of large-scale astronomical data sets using?xed, non-interactive animations has a long history. Several books and ?lms exist, ranging from “Cosmic View: The Universe in Forty Jumps” [3] by Kees Boeke to “Powers of 10” [6,13] by Charles and Ray Eames, and the recent Imax ?lm “Cosmic Voyage” [15]. We have added our own contribution [9], “Cosmic Clock,” which is an animation based entirely on the concepts and implementation described in this paper.
Author: G. Farin
Publisher: Elsevier
ISBN: 0444511040
Category : Computers
Languages : en
Pages : 849
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Book Description
This book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed, thus creating a one-of-a-kind collection of authoritative articles. There are chapters outlining basic theory in tutorial style, as well as application-oriented articles. Aspects which are covered include: Historical outline Curve and surface methods Scientific Visualization Implicit methods Reverse engineering. This book is meant to be a reference text for researchers in the field as well as an introduction to graduate students wishing to get some exposure to this subject.
Author: Larry L. Schumaker
Publisher: SIAM
ISBN: 1611973902
Category : Science
Languages : en
Pages : 420
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Book Description
This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.
