Whitney tower concordance of classical links

This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney disk framing obstructions. It is shown that the filtrations are completely classified by Milnor invariants together with new higher-order Sato-Levine and higher-order Arf invariants, which are obstructions to framing a twisted Whitney tower in the 4-ball bounded by a link in the 3-sphere. Applications include computation of the grope filtration, and new geometric characterizations of Milnor's link invariants.Comment: Only change is the addition of this comment: This paper subsumes the entire preprint "Geometric Filtrations of Classical Link Concordance" (arXiv:1101.3477v2 [math.GT]) and the first six sections of the preprint "Universal Quadratic Forms and Untwisting Whitney Towers" (arXiv:1101.3480v2 [math.GT]

Investor-state arbitration and SA's bilateral investment treaty policy framework review

Mandela Institute Working paper.Contribution to the DTI's review of South Africa’s bilateral investment treaty (BIT) policy framework

Analysis of Longitudinal Data in Craniofacial Research: Some Strategies

Although it is generally acknowledged that longitudinal data provide the most information on growth and development and other time-dependent phenomena, such data are often analyzed by conventional (cross-sectional) statistical methods. This widespread practice ignores the distinctive characteristics (e.g., covariance structure) of longitudinal data and may yield misleading results. The purpose of this article is to present some strategies and make available computer programs for the appropriate analysis of longitudinal data. User-friendly PC programs for the estimation of average growth curves, computation of tracking indices, prediction of future values, diagnosis, classification, clustering, estimation of missing values, and testing hypotheses concerning individual and group differences are presented. Benefits of these methods over the usual techniques are illustrated with the example of maxillary growth in the rhesus monkey.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67976/2/10.1177_10454411940050030101.pd

Characterization of a Differential Radio-Frequency Single-Electron Transistor

We have fabricated and characterized a new type of electrometer that couples two parallel single-electron transistors (SETs) to a radio-frequency tank circuit for use as a differential RF-SET. We demonstrate operation of this device in summing, differential, and single-SET operation modes, and use it to measure a Coulomb staircase from a differential single Cooper-pair box. In differential mode, the device is sensitive to uncorrelated input signals while screening out correlated ones.Comment: 3 pages, 3 figures, submitted to Applied Physics Letter

Asymptotic defectiveness of manufacturing plants: an estimate based on process learning curves

The paper describes a method for a preliminary estimation of asymptotic defectiveness of a manufacturing plant based on the prediction of its learning curve estimated during a p-chart setting up. The proposed approach provides process managers with the possibility of estimating the asymptotic variability of the process and the period of revision of p-chart control limits. An application of the method is also provided