We derive a product rule satisfied by restricted Schur polynomials. We focus mostly on the case that the restricted Schur polynomial is built using two matrices, although our analysis easily extends to more than two matrices. This product rule allows us to compute exact multi-point correlation functions of restricted Schur polynomials, in the free field theory limit. As an example of the use of our formulas, we compute two point functions of certain single trace operators built using two matrices and three point functions of certain restricted Schur polynomials, exactly, in the free field theory limit. Our results suggest that gravitons become strongly coupled at sufficiently high energy, while the restricted Schur polynomials for totally antisymmetric representations remain weakly interacting at these energies. This is in perfect accord with the half-BPS (single matrix) results of hep-th/0512312. Finally, by studying the interaction of two restricted Schur polynomials we suggest a physical interpretation for the labels of the restricted Schur polynomial: the composite operator χ R,(rn,rm) (Z, X) is constructed from the half BPS "partons" χ rn (Z) and χ rm (X).

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Operators in N = 4 super Yang-Mills theory with an R-charge of O(N 2 ) are dual to backgrounds which are asymtotically AdS 5 ×S 5 . In this article we develop efficient techniques that allow the computation of correlation functions in these backgrounds. We find that (i) contractions between fields in the string words and fields in the operator creating the background are the field theory accounting of the new geometry, (ii) correlation functions of probes in these backgrounds are given by the free field theory contractions but with rescaled propagators and (iii) in these backgrounds there are no open string excitations with their special end point interactions; we have only closed string excitations.

Classifying transients based on multi-band lightcurves is a challenging but crucial problem in the era of GAIA and LSST since the sheer volume of transients will make spectroscopic classification unfeasible. We present a nonparametric classifier that predicts the transient's class given training data. It implements two novel components: the use of the BAGIDIS wavelet methodology -a characterization of functional data using hierarchical wavelet coefficients -as well as the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The classifier is simple to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant. Hence, BAGIDIS does not need the light curves to be aligned to extract features. Further, BAGIDIS is nonparametric so it can be used effectively in blind searches for new objects. We demonstrate the effectiveness of our classifier against the Supernova Photometric Classification Challenge to correctly classify supernova lightcurves as Type Ia or non-Ia. We train our classifier on the spectroscopically-confirmed subsample (which isn't representative) and show that it works well for supernova with observed lightcurve timespans greater than 100 days (roughly 55% of the dataset). For such data, we obtain a Ia efficiency of 80.5% and a purity of 82.4%, yielding a highly competitive challenge score of 0.49. This indicates that our "model-blind" approach may be particularly suitable for the general classification of astronomical transients in the era of large synoptic sky surveys.