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2015
Chapter 11 considered spectral expansions of square-integrable random variables, random vectors and random fields of the form $$\displaystyle{U =\sum _{k\in \mathbb{N}_{0}}u_{k}\varPsi _{k},}$$ where \(U \in L^{2}(\varTheta,\mu;\mathcal{U})\), \(\mathcal{U}\) is a Hilbert space in which the corresponding deterministic variables/vectors/fields ...
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Chapter 11 considered spectral expansions of square-integrable random variables, random vectors and random fields of the form $$\displaystyle{U =\sum _{k\in \mathbb{N}_{0}}u_{k}\varPsi _{k},}$$ where \(U \in L^{2}(\varTheta,\mu;\mathcal{U})\), \(\mathcal{U}\) is a Hilbert space in which the corresponding deterministic variables/vectors/fields ...
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2003
The objective of conformational search is to find all preferred conformations of a molecule. Those conformations are associated with local minima of the potential energy surface. Deeper local minima may correspond to observable, partially stable states of the molecule.
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The objective of conformational search is to find all preferred conformations of a molecule. Those conformations are associated with local minima of the potential energy surface. Deeper local minima may correspond to observable, partially stable states of the molecule.
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1999
Sophisticated search techniques form the backbone of modern machine learning and data analysis. Computer systems that are able to extract information from huge data sets (data mining), to recognize patterns, to do classification, or to suggest diagnoses, in short, systems that are adaptive and — to some extent — able to learn, fundamentally rely on ...
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Sophisticated search techniques form the backbone of modern machine learning and data analysis. Computer systems that are able to extract information from huge data sets (data mining), to recognize patterns, to do classification, or to suggest diagnoses, in short, systems that are adaptive and — to some extent — able to learn, fundamentally rely on ...
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Stochastic Optimization Methods
2013This chapter introduces some methods aimed at solving difficult optimization problems arising in many engineering fields. By difficult optimization problems, we mean those that are not convex. Recall that for the class of non-convex problems, there is no algorithm capable of guaranteeing, in a reasonable amount of time (by reasonable time, we mean ...
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