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Deep Learning
The core of this book are deep learning methods and neural networks. This chapter considers deep feed-forward neural (FN) networks. We introduce the...
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Rényi 100, Quantitative and qualitative (in)dependence
We discuss recent developments in the following important areas of Alfréd Rényi’s research interest: axiomatization of quantitative dependence...
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Anamorphosis Reformed: From Optical Illusions to Immersive Perspectives
We discuss a definition of conical anamorphosis that sets it at the foundation of both classical and curvilinear perspectives. In this view,...
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Anamorphosis Reformed: From Optical Illusions to Immersive Perspectives
We discuss a definition of conical anamorphosis that sets it at the foundation of both classical and curvilinear perspectives. In this view,...
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Adjoint Sensitivities and RBF Mesh Morphing
Optimizations based on adjoint sensitivity data are presented in this Chapter. RBF are adopted to set up an advanced filtering tool suitable for...
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Freiburg 1921–1953
In October 1921, some months after his 50th birthday, Zermelo moved to Freiburg im Breisgau in southwestern Germany, where he subsequently lived for...
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The Method of Characteristics: A Geometric Approach to Sufficient Conditions for a Local Minimum
So far, our focus has been on necessary conditions for optimality. The conditions of the Pontryagin maximum principle, Theorem 2.2.1, collectively...
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Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints
We consider the generalized Nash equilibrium problem (GNEP), in which each player’s strategy set may depend on the rivals’ strategies through shared...
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Mathematical modeling, cases
This chapter focuses on the modeling of optimization problems where objective and constraint functions are typically nonlinear. Several examples of...
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Convergence and Concentration of Metrics and Measures
When we speak of measures μ on a metric space X, we always assume that X is a Polish space, i.e., complete with a countable base, and that “measure”...
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Partial Geometric Regularity of Some Optimal Connected Transportation Networks
We consider a continuous optimization model of a one-dimensional connected transportation network under the assumption that the cost of...
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Comparing Mean Response When There Are Three or More Treatments
From the investigator’s point of view, the primary function of this chapter is to provide methods that extend the comparison of treatment or group...
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Adaptive and Robust Control Design
As mentioned in Chapter 1, to cope with uncertain systems, special control techniques must be applied. Among these techniques are adaptive, robust...
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Other mathematical components
In addition to Chapter 2, ‘Derivation of Navier-Stokes solvers’, we will explain other important mathematical components and tools which are...
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Introduction to Barndorff-Nielsen (1983) On a Formula for the Distribution of the Maximum Likelihood Estimator
This searching and far-reaching paper has helped shape the area of inference for parametric models during the past decade. By turns historical and...