Bench Plot and Mixed Effects Models: First steps toward a comprehensive benchmark analysis toolbox

Benchmark experiments produce data in a very specific format. The observations are drawn from the performance distributions of the candidate algorithms on resampled data sets. In this paper we introduce new visualisation techniques and show how formal test procedures can be used to evaluate the results. This is the first step towards a comprehensive toolbox of exploratory and inferential analysis methods for benchmark experiments

Spider-Man, the Child and the Trickster -- Archetypal Analysis in R

Archetypal analysis has the aim to represent observations in a multivariate data set as convex combinations of extremal points. This approach was introduced by Cutler and Breiman (1994); they defined the concrete problem, laid out the theoretical foundations and presented an algorithm written in Fortran, which is available on request. In this paper we present the R package archetypes which is available on the Comprehensive R Archive Network. The package provides an implementation of the archetypal analysis algorithm within R and different exploratory tools to analyze the algorithm during its execution and its final result. The application of the package is demonstrated on two examples

Exploratory Analysis of Benchmark Experiments -- An Interactive Approach

The analysis of benchmark experiments consists in a large part of exploratory methods, especially visualizations. In Eugster et al. [2008] we presented a comprehensive toolbox including the bench plot. This plot visualizes the behavior of the algorithms on the individual drawn learning and test samples according to specific performance measures. In this paper we show an interactive version of the bench plot can easily uncover details and relations unseen with the static version

Local twistors and the conformal field equations

This note establishes the connection between Friedrich's conformal field equations and the conformally invariant formalism of local twistors.Comment: LaTeX2e Minor corrections of misprints et

Weighted and Robust Archetypal Analysis

Archetypal analysis represents observations in a multivariate data set as convex combinations of a few extremal points lying on the boundary of the convex hull. Data points which vary from the majority have great influence on the solution; in fact one outlier can break down the archetype solution. This paper adapts the original algorithm to be a robust M-estimator and presents an iteratively reweighted least squares fitting algorithm. As required first step, the weighted archetypal problem is formulated and solved. The algorithm is demonstrated using both an artificial and a real world example

On the Ricci tensor in type II B string theory

Let $\nabla$ be a metric connection with totally skew-symmetric torsion \T on a Riemannian manifold. Given a spinor field $\Psi$ and a dilaton function $\Phi$, the basic equations in type II B string theory are \bdm \nabla \Psi = 0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi = b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations between the length ||\T||^2 of the torsion form, the scalar curvature of $\nabla$, the dilaton function $\Phi$ and the parameters $a,b,\mu$. The main results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the connection. In particular, if the supersymmetry $\Psi$ is non-trivial and if the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d \T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is divergence-free. We show that the latter condition is satisfied in many examples constructed out of special geometries. A special case is $a = b$. Then the divergence of the energy-momentum tensor vanishes if and only if one condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T = 0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq 0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2

General Relativistic Scalar Field Models in the Large

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.Comment: 22 pages, latex, AGG 1

From Spider-Man to Hero - Archetypal Analysis in R

Archetypal analysis has the aim to represent observations in a multivariate data set as convex combinations of extremal points. This approach was introduced by Cutler and Breiman (1994); they defined the concrete problem, laid out the theoretical foundations and presented an algorithm written in Fortran. In this paper we present the R package archetypes which is available on the Comprehensive R Archive Network. The package provides an implementation of the archetypal analysis algorithm within R and different exploratory tools to analyze the algorithm during its execution and its final result. The application of the package is demonstrated on two examples.