An Approximation to the Likelihood Function for Band-Power Estimates of CMB Anisotropies

Band-power estimates of cosmic microwave background fluctuations are now routinely used to place constraints on cosmological parameters. For this to be done in a rigorous fashion, the full likelihood function of band-power estimates must be employed. Even for Gaussian theories, this likelihood function is not itself Gaussian, for the simple reason that band-powers measure the {\em variance} of the random sky fluctuations. In the context of Gaussian sky fluctuations, we use an ideal situation to motivate a general form for the full likelihood function from a given experiment. This form contains only two free parameters, which can be determined if the 68% and 95% confidence intervals of the true likelihood function are known. The ansatz works remarkably well when compared to the complete likelihood function for a number of experiments. For application of this kind of approach, we suggest that in the future both 68% and 95% (and perhaps also the 99.7%) confidence intervals be given when reporting experimental results.Comment: Published versio

An SZ/X-ray galaxy cluster model and the X-ray follow-up of the Planck clusters

Sunyaev-Zel'dovich (SZ) cluster surveys will become an important cosmological tool over next few years, and it will be essential to relate these new surveys to cluster surveys in other wavebands. We present an empirical model of cluster SZ and X-ray observables constructed to address this question and to motivate, dimension and guide X-ray follow-up of SZ surveys. As an example application of the model, we discuss potential XMM-Newton follow-up of Planck clusters.Comment: 4 pages, 5 figures. To appear in the proceedings of the XXXXIIIrd Rencontres de Morion

Complexity of pattern classes and Lipschitz property

Rademacher and Gaussian complexities are successfully used in learning theory for measuring the capacity of the class of functions to be learned. One of the most important properties for these complexities is their Lipschitz property: a composition of a class of functions with a fixed Lipschitz function may increase its complexity by at most twice the Lipschitz constant. The proof of this property is non-trivial (in contrast to the other properties) and it is believed that the proof in the Gaussian case is conceptually more difficult then the one for the Rademacher case. In this paper we give a detailed prove of the Lipschitz property for the Rademacher case and generalize the same idea to an arbitrary complexity (including the Gaussian). We also discuss a related topic about the Rademacher complexity of a class consisting of all the Lipschitz functions with a given Lipschitz constant. We show that the complexity is surprisingly low in the one-dimensional case. The question for higher dimensions remains open

A New Local Temperature Distribution Function for X-ray Clusters: Cosmological Applications

(abridged) We present a new determination of the local temperature function of X-ray clusters. We use a new sample comprising fifty clusters for which temperature information is now available, making it the largest complete sample of its kind. It is therefore expected to significantly improve the estimation of the temperature distribution function of moderately hot clusters. We find that the resulting temperature function is higher than previous estimations, but agrees well with the temperature distribution function inferred from the BCS and RASS luminosity function. We have used this sample to constrain the amplitude of the matter fluctuations on cluster's scale of $8\sqrt[3]{\Omega_0}^{-1}h^{-1}$Mpc, assuming a mass-temperature relation based on recent numerical simulations. We find $\sigma_8 = 0.6\pm 0.02$ for an $\Omega_0 = 1$ model. Our sample provides an ideal reference at $z \sim 0$ to use in the application of the cosmological test based on the evolution of X-ray cluster abundance (Oukbir & Blanchard 1992, 1997). Using Henry's sample, we find that the abundance of clusters at $z = 0.33$ is significantly smaller, by a factor larger than 2, which shows that the EMSS sample provides strong evidence for evolution of the cluster abundance. A likelihood analysis leads to a rather high value of the mean density parameter of the universe: $\Omega =0.92 \pm 0.22$ (open case) and $\Omega =0.86 \pm 0.25$ (flat case), which is consistent with a previous, independent estimation based on the full EMSS sample by Sadat et al.(1998). Some systematic uncertainties which could alter this result are briefly discussed.Comment: 31 pages, 12 figures, mathches the version published in Astronomy and Astrophysic

MACiE: a database of enzyme reaction mechanisms.

SUMMARY: MACiE (mechanism, annotation and classification in enzymes) is a publicly available web-based database, held in CMLReact (an XML application), that aims to help our understanding of the evolution of enzyme catalytic mechanisms and also to create a classification system which reflects the actual chemical mechanism (catalytic steps) of an enzyme reaction, not only the overall reaction. AVAILABILITY: http://www-mitchell.ch.cam.ac.uk/macie/.EPSRC (G.L.H. and J.B.O.M.), the BBSRC (G.J.B. and J.M.T.—CASE studentship in association with Roche Products Ltd; N.M.O.B. and J.B.O.M.—grant BB/C51320X/1), the Chilean Government’s Ministerio de Planificacio´n y Cooperacio´n and Cambridge Overseas Trust (D.E.A.) for funding and Unilever for supporting the Centre for Molecular Science Informatics.application note restricted to 2 printed pages web site: http://www-mitchell.ch.cam.ac.uk/macie