Duality and Lorentzian Kac-Moody Algebras

A review is given of ideas in electromagnetic duality and connections to integrable field theories with soliton solutions. This leads on to a summary of recent work on Lorentzian algebras.Comment: 8 pages, Invited talk at Workshop on Integrable Theories, Solitons and Duality. To appear in JHEP proceeding

Two Simple Resistant Regression Estimators

Two simple resistant regression estimators with OP(n−1/2) convergence rate are presented. Ellipsoidal trimming can be used to trim the cases corresponding to predictor variables x with large Mahalanobis distances, and the forward response plot of the residuals versus the fitted values can be used to detect outliers. The first estimator uses ten forward response plots corresponding to ten different trimming proportions, and the final estimator corresponds to the “best” forward response plot. The second estimator is similar to the elemental resampling algorithm, but sets of O(n) cases are used instead of randomly selected elemental sets. These two estimators should be regarded as new tools for outlier detection rather than as replacements for existing methods. Outliers should always be examined to see if they follow a pattern, are recording errors, or if they could be explained adequately by an alternative model. Using scatterplot matrices of fitted values and residuals from several resistant estimators is a very useful method for comparing the different estimators and for checking the assumptions of the regression model

Exact electromagnetic duality

This talk, given at several conferences and meetings, explains the background leading to the formulation of the exact electromagnetic duality conjecture believed to be valid in N=4 supersymmetric SU(2) gauge theory

Spin and abelian electromagnetic duality on four-manifolds

We investigate the electromagnetic duality properties of an abelian gauge theory on a compact oriented four-manifold by analysing the behaviour of a generalised partition function under modular transformations of the dimensionless coupling constants. The true partition function is invariant under the full modular group but the generalised partition function exhibits more complicated behaviour depending on topological properties of the four-manifold concerned. It is already known that there may be "modular weights" which are linear combinations of the Euler number and Hirzebruch signature of the four-manifold. But sometimes the partition function transforms only under a subgroup of the modular group (the Hecke subgroup). In this case it is impossible to define real spinor wave functions on the four-manifold. But complex spinors are possible provided the background magnetic fluxes are appropriately fractional rather that integral. This gives rise to a second partition function which enables the full modular group to be realised by permuting the two partition functions, together with a third. Thus the full modular group is realised in all cases. The demonstration makes use of various constructions concerning integral lattices and theta functions that seem to be of intrinsic interest.Comment: 29 pages, Plain Te

Possibilities of performance : new ways of teaching dramatic literature

This essay is aimed at students and teachers of dramatic literature and encourages a teaching method which seelcs to elicit responses based on performance. The two teaching activities described are practica1 drama workshops complemented by the viewing of film andlor television versions of the same play on video. The banquet scene from Macbeth (Act 3, Scene 4) is analysed from the point of view of what students can learn from the two complementary methods. There is also a similar, though much briefer, treatment of an extract from Strindberg's Miss Julie to indicate how such an approach can be used when teaching any form of dramatic literature. The condusion drawn is that such teaching methods encourage an active learning experience. A performance demands a close study of the text, while the text in turn should be treated as a blueprint for performance

Large Scale Baryon Isocurvature Inhomogeneities

Big bang nucleosynthesis constraints on baryon isocurvature perturbations are determined. A simple model ignoring the effects of the scale of the perturbations is first reviewed. This model is then extended to test the claim that large amplitude perturbations will collapse, forming compact objects and preventing their baryons from contributing to the observed baryon density. It is found that baryon isocurvature perturbations are constrained to provide only a slight increase in the density of baryons in the universe over the standard homogeneous model. In particular it is found that models which rely on power laws and the random phase approximation for the power spectrum are incompatible with big bang nucleosynthesis unless an {\em ad hoc}, small scale cutoff is included.Comment: 11pages + 8figures, LaTeX (2.09), postscript figures available via anonymous ftp from oddjob.uchicago.edu:/ftp/ibbn/fig?.ps where ?=1-8 or via email from [email protected], Fermilab-Pub-94/???-A and UMN-TH-1307/9

Primordial Nucleosynthesis and the Abundances of Beryllium and Boron

The ability to now make measurements of Be and B as well as put constraints on \lisix\ abundances in metal-poor stars has led to a detailed reexamination of Big Bang Nucleosynthesis in the A\groughly6 regime. The nuclear reaction network has been significantly expanded with many new rates added. It is demonstrated that although a number of $A>7$ reaction rates are poorly determined, even with extreme values chosen, the standard homogeneous model is unable to produce significant yields (Be/H and B/H $<10^{-17}$ when $A\le7$ abundances fit) above $A=7$ and the \liseven/\lisix\ ratio always exceeds 500. We also preliminarily explore inhomogeneous models, such as those inspired by a first order quark-hadron phase transition, where regions with high neutron/proton ratios can allow some leakage up to $A>7$. However models that fit the $A\le7$ abundances still seem to have difficulty in obtaining significant $A>7$ yields.Comment: Plain TeX, 28 pages, 8 figures (not included, but available from authors). UMN-TH-1020/9

Robust Regression with High Coverage

An important parameter for several high breakdown regression algorithm estimators is the number of cases given weight one, called the coverage of the estimator. Increasing the coverage is believed to result in a more stable estimator, but the price paid for this stability is greatly decreased resistance to outliers. A simple modification of the algorithm can greatly increase the coverage and hence its statistical performance while maintaining high outlier resistance