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Mathematics --- Computer. Automation --- computers --- informatica --- externe fixatie (geneeskunde

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Outside the professional circles of topography and applied mathematics, the life and work of André-Louis Cholesky (1875–1918) are still relatively unknown to the scientific community. This new book appreciably widens the exposure of his remarkable personal achievements in topography and mathematics to a much larger international audience.   Cholesky is also interesting to historians because he is a perfect representative of the "scientists engineers" that, since the early 19th century, had issued from the French scientific high schools. Because they had received a high level of mathematical education, they were able to innovate in their practice of engineering. In the case of Cholesky, this resulted in original contributions in artillery, topography, numerical analysis and graphical calculation. In addition, the book places his education and works within the history of several European countries through the 17th to 19th centuries.   The book begins with Cholesky's biography, followed by his family’s history and an introduction to topography. It continues with a historical analysis of an unpublished paper (translated into English) in which Cholesky explained his method for linear systems. Cholesky's other works are then described, such as his participation in teaching at a superior "school by correspondence" founded by Léon Eyrolles. His important unpublished book in French on graphical calculation, which is reproduced in its entirety, is analyzed in detail and compared to similar contemporary publications. The biography of Ernest Benoit, who wrote the first paper on Cholesky's method, is provided. Various documents, highlighting the life and the personality of Cholesky, round out his story and end the book.

Mathematics --- Computer. Automation --- toegepaste wiskunde --- informatica --- externe fixatie (geneeskunde --- wiskunde

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Using an elegant mixture of geometry, graph theory and linear analysis, this monograph completely solves a problem lying at the interface of Isogeometric Analysis (IgA) and Finite Element Methods (FEM). The recent explosion of IgA, strongly tying Computer Aided Geometry Design to Analysis, does not easily apply to the rich variety of complex shapes that engineers have to design and analyse. Therefore new developments have studied the extension of IgA to unstructured unions of meshes, similar to those one can find in FEM. The following problem arises: given an unstructured planar quadrilateral mesh, construct a C1-surface, by piecewise Bézier or B-Spline patches defined over this mesh. This problem is solved for C1-surfaces defined over plane bilinear Bézier patches, the corresponding results for B-Splines then being simple consequences. The method can be extended to higher-order quadrilaterals and even to three dimensions, and the most recent developments in this direction are also mentioned here.

Geometry --- Mathematics --- Computer. Automation --- informatica --- externe fixatie (geneeskunde --- wiskunde --- geometrie

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This volume discusses the theoretical foundations of a new inter- and intra-disciplinary meta-research discipline, which can be succinctly called cognitive metamathematics, with the ultimate goal of achieving a global instance of concrete Artificial Mathematical Intelligence (AMI). In other words, AMI looks for the construction of an (ideal) global artificial agent being able to (co-)solve interactively formal problems with a conceptual mathematical description in a human-style way. It first gives formal guidelines from the philosophical, logical, meta-mathematical, cognitive, and computational points of view supporting the formal existence of such a global AMI framework, examining how much of current mathematics can be completely generated by an interactive computer program and how close we are to constructing a machine that would be able to simulate the way a modern working mathematician handles solvable mathematical conjectures from a conceptual point of view. The thesis that it is possible to meta-model the intellectual job of a working mathematician is heuristically supported by the computational theory of mind, which posits that the mind is in fact a computational system, and by the meta-fact that genuine mathematical proofs are, in principle, algorithmically verifiable, at least theoretically. The introduction to this volume provides then the grounding multifaceted principles of cognitive metamathematics, and, at the same time gives an overview of some of the most outstanding results in this direction, keeping in mind that the main focus is human-style proofs, and not simply formal verification. The first part of the book presents the new cognitive foundations of mathematics’ program dealing with the construction of formal refinements of seminal (meta-)mathematical notions and facts. The second develops positions and formalizations of a global taxonomy of classic and new cognitive abilities, and computational tools allowing for calculation of formal conceptual blends are described. In particular, a new cognitive characterization of the Church-Turing Thesis is presented. In the last part, classic and new results concerning the co-generation of a vast amount of old and new mathematical concepts and the key parts of several standard proofs in Hilbert-style deductive systems are shown as well, filling explicitly a well-known gap in the mechanization of mathematics concerning artificial conceptual generation.

Mathematics --- Computer. Automation --- neuronale netwerken --- computers --- informatica --- externe fixatie (geneeskunde

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This book brings together two important trends: graph algorithms and high-performance computing. Efficient and scalable execution of graph processing applications in data or network analysis requires innovations at multiple levels: algorithms, associated data structures, their implementation and tuning to a particular hardware. Further, programming languages and the associated compilers play a crucial role when it comes to automating efficient code generation for various architectures. This book discusses the essentials of all these aspects. The book is divided into three parts: programming, languages, and their compilation. The first part examines the manual parallelization of graph algorithms, revealing various parallelization patterns encountered, especially when dealing with graphs. The second part uses these patterns to provide language constructs that allow a graph algorithm to be specified. Programmers can work with these language constructs without worrying about their implementation, which is the focus of the third part. Implementation is handled by a compiler, which can specialize code generation for a backend device. The book also includes suggestive results on different platforms, which illustrate and justify the theory and practice covered. Together, the three parts provide the essential ingredients for creating a high-performance graph application. The book ends with a section on future directions, which offers several pointers to promising topics for future research. This book is intended for new researchers as well as graduate and advanced undergraduate students. Most of the chapters can be read independently by those familiar with the basics of parallel programming and graph algorithms. However, to make the material more accessible, the book includes a brief background on elementary graph algorithms, parallel computing and GPUs. Moreover it presents a case study using Falcon, a domain-specific language for graph algorithms, to illustrate the concepts.

Mathematics --- Computer. Automation --- informatica --- externe fixatie (geneeskunde --- software engineering