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This is the first textbook on attribute exploration, its theory, its algorithms for applications, and some of its many possible generalizations. Attribute exploration is useful for acquiring structured knowledge through an interactive process, by asking queries to an expert. Generalizations that handle incomplete, faulty, or imprecise data are discussed, but the focus lies on knowledge extraction from a reliable information source. The method is based on Formal Concept Analysis, a mathematical theory of concepts and concept hierarchies, and uses its expressive diagrams. The presentation is self-contained. It provides an introduction to Formal Concept Analysis with emphasis on its ability to derive algebraic structures from qualitative data, which can be represented in meaningful and precise graphics.
Computer science. --- Data mining. --- Algebra. --- Ordered algebraic structures. --- Computer Science. --- Data Mining and Knowledge Discovery. --- Order, Lattices, Ordered Algebraic Structures. --- Comprehension (Theory of knowledge) --- Lattice theory. --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Knowledge, Theory of --- Logic --- Philosophy --- Mathematics --- Mathematical analysis --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra
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This thesis presents a qualitative advance in our understanding of quantum effects in layered magnetic materials. The nearest neighbor Heisenberg ferromagnetic ranks among the oldest and most fundamental models of quantum many body effects. It has long been established that in one dimension quantum fluctuations lead to a quantum disordered ground state with fractional excitations called spinons." In two dimensions, the ground state of the Heisenberg model displays static order and to first approximation the dynamics can be described as semi-classical spin waves. Through theoretical advances the author demonstrates that at high energy around particular points in reciprocal space these semi-classical spin-waves deconfine into fractional excitations akin to the one-dimensional spinons. He thereby provides the first explanation of a long-standing experimental observation. In the second half of his thesis Bastien Dalla Piazza develops a unified description of the magnetic excitation spectra of a range of cuprate parent compounds to the high temperature superconductors.
Electricity & Magnetism --- Physics --- Physical Sciences & Mathematics --- Antiferromagnetism. --- Lattice theory. --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Ferromagnetism --- Magnetism. --- Quantum theory. --- Optical materials. --- Magnetism, Magnetic Materials. --- Quantum Information Technology, Spintronics. --- Quantum Physics. --- Optical and Electronic Materials. --- Magnetic materials. --- Quantum computers. --- Spintronics. --- Quantum physics. --- Electronic materials. --- Electronic materials --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Magnetoelectronics --- Spin electronics --- Microelectronics --- Nanotechnology --- Computers --- Materials --- Mathematical physics --- Electricity --- Magnetics --- Optics --- Fluxtronics --- Spinelectronics
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