Climate Variability Indices—A Guided Tour

Complexity - A Guided Tour

What enables individually simple insects like ants to act with such precision and purpose as a group? How do trillions of neurons produce something as extraordinarily complex as consciousness? In this remarkably clear...

A guided tour through TYPELAB

This report gives a survey of TYPELAB, a specification and verification environment that integrates interactive proof development and automated proof search. TYPELAB is based on a constructive type theory, the Calculus of Constructions, which can be understood as a combination of a typed λ-calculus and an expressive higher-order logic. Distinctive features of the type system are dependent funct...

A Random Forest Guided Tour

The random forest algorithm, proposed by L. Breiman in 2001, has been extremely successful as a general-purpose classification and regression method. The approach, which combines several randomized decision trees and aggregates their predictions by averaging, has shown excellent performance in settings where the number of variables is much larger than the number of observations. Moreover, it is...

Dimension Reduction: A Guided Tour

We give a tutorial overview of several geometric methods for dimension reduction. We divide the methods into projective methods and methods that model the manifold on which the data lies. For projective methods, we review projection pursuit, principal component analysis (PCA), kernel PCA, probabilistic PCA, canonical correlation analysis, oriented PCA, and several techniques for sufficient dime...

A Guided Tour of Mathematical Physics