A method for comparing chess openings

A quantitative method is described for comparing chess openings. Test openings and baseline openings are run through chess engines under controlled conditions and compared to evaluate the effectiveness of the test openings. The results are intuitively appealing and in some cases they agree with expert opinion. The specific contribution of this work is the development of an objective measure that may be used for the evaluation and refutation of chess openings, a process that had been left to thought experiments and subjective conjectures and thereby to a large variety of opinion and a great deal of debate.Comment: Updated in March, 2014 to correct a data entry error in the Caro-Kann openin

Bounds for twisted symmetric square LL-functions

Let $f\in S_k(N,\psi)$ be a newform, and let $\chi$ be a primitive character of conductor $q^{\ell}$. Assume that $q$ is a prime and $\ell>1$. In this paper we describe a method to establish convexity breaking bounds of the form L(\tfrac{1}{2},\Sym f\otimes\chi)\ll_{f,\varepsilon} q^{3/4\ell-\delta_{\ell}+\varepsilon} for some $\delta_{\ell}>0$ and any $\varepsilon>0$. In particular, for $\ell=3$ we show that the bound holds with $\delta_{\ell}=1/4$.Comment: 19 pages, (Extensively revised version

The circle method and bounds for LL-functions - I

Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\chi$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\otimes \chi)$ we establish the hybrid subconvex bound $$L(1/2+it,f\otimes\chi)\ll (M(3+|t|))^{1/2-1/18+\varepsilon},$$ for $t\in \mathbb R$. The implied constant depends only on the form $f$ and $\varepsilon$.Comment: 8 page

On Cross-correlating Weak Lensing Surveys

The present generation of weak lensing surveys will be superseded by surveys run from space with much better sky coverage and high level of signal to noise ratio, such as SNAP. However, removal of any systematics or noise will remain a major cause of concern for any weak lensing survey. One of the best ways of spotting any undetected source of systematic noise is to compare surveys which probe the same part of the sky. In this paper we study various measures which are useful in cross correlating weak lensing surveys with diverse survey strategies. Using two different statistics - the shear components and the aperture mass - we construct a class of estimators which encode such cross-correlations. These techniques will also be useful in studies where the entire source population from a specific survey can be divided into various redshift bins to study cross correlations among them. We perform a detailed study of the angular size dependence and redshift dependence of these observables and of their sensitivity to the background cosmology. We find that one-point and two-point statistics provide complementary tools which allow one to constrain cosmological parameters and to obtain a simple estimate of the noise of the survey.Comment: 17 pages, 9 Figures, Submitted to MNRA

Principal Components of CMB non-Gaussianity

The skew-spectrum statistic introduced by Munshi & Heavens (2010) has recently been used in studies of non-Gaussianity from diverse cosmological data sets including the detection of primary and secondary non-Gaussianity of Cosmic Microwave Background (CMB) radiation. Extending previous work, focussed on independent estimation, here we deal with the question of joint estimation of multiple skew-spectra from the same or correlated data sets. We consider the optimum skew-spectra for various models of primordial non-Gaussianity as well as secondary bispectra that originate from the cross-correlation of secondaries and lensing of CMB: coupling of lensing with the Integrated Sachs-Wolfe (ISW) effect, coupling of lensing with thermal Sunyaev-Zeldovich (tSZ), as well as from unresolved point-sources (PS). For joint estimation of various types of non-Gaussianity, we use the PCA to construct the linear combinations of amplitudes of various models of non-Gaussianity, e.g. $f^{\rm loc}_{\rm NL},f^{\rm eq}_{\rm NL},f^{\rm ortho}_{\rm NL}$ that can be estimated from CMB maps. Bias induced in the estimation of primordial non-Gaussianity due to secondary non-Gaussianity is evaluated. The PCA approach allows one to infer approximate (but generally accurate) constraints using CMB data sets on any reasonably smooth model by use of a lookup table and performing a simple computation. This principle is validated by computing constraints on the DBI bispectrum using a PCA analysis of the standard templates.Comment: 17 pages, 5 figures, 4 tables. Matches published versio