Product and other fine structure in polynomial resolutions of mapping spaces

Let Map_T(K,X) denote the mapping space of continuous based functions between two based spaces K and X. If K is a fixed finite complex, Greg Arone has recently given an explicit model for the Goodwillie tower of the functor sending a space X to the suspension spectrum \Sigma^\infty Map_T(K,X). Applying a generalized homology theory h_* to this tower yields a spectral sequence, and this will converge strongly to h_*(Map_T(K,X)) under suitable conditions, e.g. if h_* is connective and X is at least dim K connected. Even when the convergence is more problematic, it appears the spectral sequence can still shed considerable light on h_*(Map_T(K,X)). Similar comments hold when a cohomology theory is applied. In this paper we study how various important natural constructions on mapping spaces induce extra structure on the towers. This leads to useful interesting additional structure in the associated spectral sequences. For example, the diagonal on Map_T(K,X) induces a `diagonal' on the associated tower. After applying any cohomology theory with products h^*, the resulting spectral sequence is then a spectral sequence of differential graded algebras. The product on the E_\infty -term corresponds to the cup product in h^*(Map_T(K,X)) in the usual way, and the product on the E_1-term is described in terms of group theoretic transfers. We use explicit equivariant S-duality maps to show that, when K is the sphere S^n, our constructions at the fiber level have descriptions in terms of the Boardman-Vogt little n-cubes spaces. We are then able to identify, in a computationally useful way, the Goodwillie tower of the functor from spectra to spectra sending a spectrum X to \Sigma ^\infty \Omega ^\infty X.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-28.abs.htm

Micellization in the presence of polyelectrolyte

We present a simple model to study micellization of amphiphiles condensed on a rodlike polyion. Although the mean field theory leads to a first order micellization transition for sufficiently strong hydrophobic interactions, the simulations show that no such thermodynamic phase transition exists. Instead, the correlations between the condensed amphiphiles can result in a structure formation very similar to micelles.Comment: 8 pages, 7 figure

Combining Semantic Wikis and Controlled Natural Language

We demonstrate AceWiki that is a semantic wiki using the controlled natural language Attempto Controlled English (ACE). The goal is to enable easy creation and modification of ontologies through the web. Texts in ACE can automatically be translated into first-order logic and other languages, for example OWL. Previous evaluation showed that ordinary people are able to use AceWiki without being instructed

How to Evaluate Controlled Natural Languages

This paper presents a general framework how controlled natural languages can be evaluated and compared on the basis of user experiments. The subjects are asked to classify given statements (in the language to be tested) as either true or false with respect to a certain situation that is shown in a graphical notation called "ontographs". A first experiment has been conducted that applies this framework to the language Attempto Controlled English (ACE)

Futility Analysis in the Cross-Validation of Machine Learning Models

Many machine learning models have important structural tuning parameters that cannot be directly estimated from the data. The common tactic for setting these parameters is to use resampling methods, such as cross--validation or the bootstrap, to evaluate a candidate set of values and choose the best based on some pre--defined criterion. Unfortunately, this process can be time consuming. However, the model tuning process can be streamlined by adaptively resampling candidate values so that settings that are clearly sub-optimal can be discarded. The notion of futility analysis is introduced in this context. An example is shown that illustrates how adaptive resampling can be used to reduce training time. Simulation studies are used to understand how the potential speed--up is affected by parallel processing techniques.Comment: 22 pages, 5 figure

Codeco: A Grammar Notation for Controlled Natural Language in Predictive Editors

Existing grammar frameworks do not work out particularly well for controlled natural languages (CNL), especially if they are to be used in predictive editors. I introduce in this paper a new grammar notation, called Codeco, which is designed specifically for CNLs and predictive editors. Two different parsers have been implemented and a large subset of Attempto Controlled English (ACE) has been represented in Codeco. The results show that Codeco is practical, adequate and efficient