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In the modern world of gigantic datasets, which scientists and practioners of all fields of learning are confronted with, the availability of robust, scalable and easy-to-use methods for pattern recognition and data mining are of paramount importance, so as to be able to cope with the avalanche of data in a meaningful way. This concise and pedagogical research monograph introduces the reader to two specific aspects - clustering techniques and dimensionality reduction - in the context of complex network analysis. The first chapter provides a short introduction into relevant graph theoretical notation; chapter 2 then reviews and compares a number of cluster definitions from different fields of science. In the subsequent chapters, a first-principles approach to graph clustering in complex networks is developed using methods from statistical physics and the reader will learn, that even today, this field significantly contributes to the understanding and resolution of the related statistical inference issues. Finally, an application chapter examines real-world networks from the economic realm to show how the network clustering process can be used to deal with large, sparse datasets where conventional analyses fail.

Economic schools --- Operational research. Game theory --- Statistical physics --- Computer science --- informatica --- statistiek --- economisch denken --- speltheorie --- fysica

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Collective behavior in systems with many components, blow-ups with emergence of microstructures are proofs of the double, continuum and atomistic, nature of macroscopic systems, an issue which has always intrigued scientists and philosophers. Modern technologies have made the question more actual and concrete with recent, remarkable progresses also from a mathematical point of view. The book focuses on the links connecting statistical and continuum mechanics and, starting from elementary introductions to both theories, it leads to actual research themes. Mathematical techniques and methods from probability, calculus of variations and PDE are discussed at length.

Ergodic theory. Information theory --- Mathematical physics --- wiskunde --- fysica --- informatietheorie

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Algebra --- Differential geometry. Global analysis --- Mathematical physics --- Elementary particles --- Physics --- algebra --- elementaire deeltjes --- differentiaal geometrie --- kwantumleer --- wiskunde --- fysica

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Geometry --- Mathematical analysis --- Mathematical physics --- Physics --- analyse (wiskunde) --- wiskunde --- fysica --- geometrie

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Astrophysics --- Measuring methods in physics --- Nuclear physics --- Chemical technology --- meetmethoden --- quarks --- astrofysica --- deeltjesfysica --- kernenergie