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Recent years have seen a growing trend to derive models of macroscopic phenomena encountered in the fields of engineering, physics, chemistry, ecology, self-organisation theory and econophysics from various variational or extremum principles. Through the link between the integral extremum of a functional and the local extremum of a function (explicit, for example, in the Pontryagin's maximum principle variational and extremum principles are mutually related. Thus it makes sense to consider them within a common context. The main goal of the present book is to collect various mathematica

Calculus of variations. --- Extremal problems (Mathematics) --- Mathematical physics. --- Physical mathematics --- Physics --- Graph theory --- Problems, Extremal (Mathematics) --- Calculus of variations --- Geometric function theory --- Maxima and minima --- Isoperimetrical problems --- Variations, Calculus of --- Mathematics --- Extremal problems --- Extremal problems (Mathematics).

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This book provides professionals with a large selection of algorithms, kernels and solutions ready for implementation and suitable for standard pattern discovery problems in fields such as bioinformatics, text analysis and image analysis. It also serves as an introduction for students and researchers to the growing field of kernel-based pattern analysis, demonstrating with examples how to handcraft an algorithm or a kernel for a new specific application, and covering all the necessary conceptual and mathematical tools to do so.

Artificial intelligence. Robotics. Simulation. Graphics --- Mathematical statistics --- 681.3*I5 --- 681.3*I5 Pattern recognition (Computing methodologies) --- Pattern recognition (Computing methodologies) --- Algorithms --- Kernel functions --- Machine learning --- Pattern perception --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Learning, Machine --- Artificial intelligence --- Machine theory --- Functions, Kernel --- Functions of complex variables --- Geometric function theory --- Algorism --- Algebra --- Arithmetic --- Data processing --- Foundations --- Machine Learning. --- Algorithms. --- Data processing. --- Kernel functions. --- Machine learning. --- Data analysis --- Network analysis --- Grading --- Computer software --- Apprentissage automatique --- Algorithmes --- Noyaux (Mathématiques) --- Perception de structure --- Informatique --- Pattern perception - Data processing. --- Algorithme