Multifractal properties of power-law time sequences; application to ricepiles

We study the properties of time sequences extracted from a self-organized critical system, within the framework of the mathematical multifractal analysis. To this end, we propose a fixed-mass algorithm, well suited to deal with highly inhomogeneous one dimensional multifractal measures. We find that the fixed mass (dual) spectrum of generalized dimensions depends on both the system size L and the length N of the sequence considered, being however stable when these two parameters are kept fixed. A finite-size scaling relation is proposed, allowing us to define a renormalized spectrum, independent of size effects.We interpret our results as an evidence of extremely long-range correlations induced in the sequence by the criticality of the systemComment: 12 pages, RevTex, includes 9 PS figures, Phys. Rev. E (in press

CMB component separation by parameter estimation

We propose a solution to the CMB component separation problem based on standard parameter estimation techniques. We assume a parametric spectral model for each signal component, and fit the corresponding parameters pixel by pixel in a two-stage process. First we fit for the full parameter set (e.g., component amplitudes and spectral indices) in low-resolution and high signal-to-noise ratio maps using MCMC, obtaining both best-fit values for each parameter, and the associated uncertainty. The goodness-of-fit is evaluated by a chi^2 statistic. Then we fix all non-linear parameters at their low-resolution best-fit values, and solve analytically for high-resolution component amplitude maps. This likelihood approach has many advantages: The fitted model may be chosen freely, and the method is therefore completely general; all assumptions are transparent; no restrictions on spatial variations of foreground properties are imposed; the results may be rigorously monitored by goodness-of-fit tests; and, most importantly, we obtain reliable error estimates on all estimated quantities. We apply the method to simulated Planck and six-year WMAP data based on realistic models, and show that separation at the muK level is indeed possible in these cases. We also outline how the foreground uncertainties may be rigorously propagated through to the CMB power spectrum and cosmological parameters using a Gibbs sampling technique.Comment: 20 pages, 10 figures, submitted to ApJ. For a high-resolution version, see http://www.astro.uio.no/~hke/docs/eriksen_et_al_fgfit.p

Bayesian Power Spectrum Analysis of the First-Year WMAP data

We present the first results from a Bayesian analysis of the WMAP first year data using a Gibbs sampling technique. Using two independent, parallel supercomputer codes we analyze the WMAP Q, V and W bands. The analysis results in a full probabilistic description of the information the WMAP data set contains about the power spectrum and the all-sky map of the cosmic microwave background anisotropies. We present the complete probability distributions for each C_l including any non-Gaussianities of the power spectrum likelihood. While we find good overall agreement with the previously published WMAP spectrum, our analysis uncovers discrepancies in the power spectrum estimates at low l multipoles. For example we claim the best-fit Lambda-CDM model is consistent with the C_2 inferred from our combined Q+V+W analysis with a 10% probability of an even larger theoretical C_2. Based on our exact analysis we can therefore attribute the "low quadrupole issue" to a statistical fluctuation.Comment: 5 pages. 4 figures. For additional information and data see http://www.astro.uiuc.edu/~iodwyer/research#wma

Fast and precise map-making for massively multi-detector CMB experiments

Future cosmic microwave background (CMB) polarisation experiments aim to measure an unprecedentedly small signal - the primordial gravity wave component of the polarisation field B-mode. To achieve this, they will analyse huge datasets, involving years worth of time-ordered data (TOD) from massively multi-detector focal planes. This creates the need for fast and precise methods to complement the M-L approach in analysis pipelines. In this paper, we investigate fast map-making methods as applied to long duration, massively multi-detector, ground-based experiments, in the context of the search for B-modes. We focus on two alternative map-making approaches: destriping and TOD filtering, comparing their performance on simulated multi-detector polarisation data. We have written an optimised, parallel destriping code, the DEStriping CARTographer DESCART, that is generalised for massive focal planes, including the potential effect of cross-correlated TOD 1/f noise. We also determine the scaling of computing time for destriping as applied to a simulated full-season data-set for a realistic experiment. We find that destriping can out-perform filtering in estimating both the large-scale E and B-mode angular power spectra. In particular, filtering can produce significant spurious B-mode power via EB mixing. Whilst this can be removed, it contributes to the variance of B-mode bandpower estimates at scales near the primordial B-mode peak. For the experimental configuration we simulate, this has an effect on the possible detection significance for primordial B-modes. Destriping is a viable alternative fast method to the full M-L approach that does not cause the problems associated with filtering, and is flexible enough to fit into both M-L and Monte-Carlo pseudo-Cl pipelines.Comment: 16 pages, 14 figures. MNRAS accepted. Typos corrected and computing time/memory requirement orders-of-magnitude numbers in section 4 replaced by precise number

Graph Based Reduction of Program Verification Conditions

Increasing the automaticity of proofs in deductive verification of C programs is a challenging task. When applied to industrial C programs known heuristics to generate simpler verification conditions are not efficient enough. This is mainly due to their size and a high number of irrelevant hypotheses. This work presents a strategy to reduce program verification conditions by selecting their relevant hypotheses. The relevance of a hypothesis is determined by the combination of a syntactic analysis and two graph traversals. The first graph is labeled by constants and the second one by the predicates in the axioms. The approach is applied on a benchmark arising in industrial program verification

Sampling rare fluctuations of height in the Oslo ricepile model

We have studied large deviations of the height of the pile from its mean value in the Oslo ricepile model. We sampled these very rare events with probabilities of order $10^{-100}$ by Monte Carlo simulations using importance sampling. These simulations check our qualitative arguement [Phys. Rev. E, {\bf 73}, 021303, 2006] that in steady state of the Oslo ricepile model, the probability of large negative height fluctuations $\Delta h=-\alpha L$ about the mean varies as $\exp(-\kappa {\alpha}^4 L^3)$ as $L \to \infty$ with $\alpha$ held fixed, and $\kappa > 0$.Comment: 7 pages, 8 figure