Residual noise covariance for Planck low-resolution data analysis

Aims: Develop and validate tools to estimate residual noise covariance in Planck frequency maps. Quantify signal error effects and compare different techniques to produce low-resolution maps. Methods: We derive analytical estimates of covariance of the residual noise contained in low-resolution maps produced using a number of map-making approaches. We test these analytical predictions using Monte Carlo simulations and their impact on angular power spectrum estimation. We use simulations to quantify the level of signal errors incurred in different resolution downgrading schemes considered in this work. Results: We find an excellent agreement between the optimal residual noise covariance matrices and Monte Carlo noise maps. For destriping map-makers, the extent of agreement is dictated by the knee frequency of the correlated noise component and the chosen baseline offset length. The significance of signal striping is shown to be insignificant when properly dealt with. In map resolution downgrading, we find that a carefully selected window function is required to reduce aliasing to the sub-percent level at multipoles, ell > 2Nside, where Nside is the HEALPix resolution parameter. We show that sufficient characterization of the residual noise is unavoidable if one is to draw reliable contraints on large scale anisotropy. Conclusions: We have described how to compute the low-resolution maps, with a controlled sky signal level, and a reliable estimate of covariance of the residual noise. We have also presented a method to smooth the residual noise covariance matrices to describe the noise correlations in smoothed, bandwidth limited maps.

Arvoja näkyvissä : Kaunokirjallisuuden etiikka Ludwig Wittgensteinin filosofian valossa

The goal of this dissertation was to study whether it is possible and meaningful to apply Ludwig Wittgenstein s distinction between saying (Sagen) and showing (Zeigen) to ethically oriented literary criticism. The following questions were used as the primary guidelines: 1. Is it possible, in the context of literary criticism, to put in practice Wittgenstein s ethical conceptions, which are quite theoretical and metaphysical by nature? 2. If so, what practical literary devices do authors use if they want to demonstrate their ethical values within the frame of a fictional work? 3. Does philosophy offer useful ethical consepts that open us new and interesting readings in fiction? The philosophical background of Wittgenstein s distinction is clarified in chapter I. This clarification is based on his main works, Tractatus logico-philosophicus and Philosophishe Untersuchungen, the published correspondence between Wittgenstein and Paul Engelmann, and selected Wittgenstein research and papers. Analyzing ethics and it s expression in Georg Trakl s poetry further elucidates Wittgenstein s concept of showing. The concept that a literary work is an act of an author was used as a starting point. The presumption was that analyzing this act of an author will reveal how ethical values can be demonstrated in literature. Categorizing an author s act at different levels of literary expression provides the structure of this study. In chapters IV - XIII literary devices useful for demonstrating ethics are examined and explained using examples from the works of Joseph Conrad, Charles Dickens, Nikolay Leskov, Ludwig Uhland, Eino Leino, Pentti Haanpää and Maria Jotuni. The concepts and views of researchers and writers such as Mihail Bahtin, Peter Juhl, E. D. Hirsch, Peter Lamarque and Stein Haugom Olsen are used. The concepts outlined in previous chapters are then applied in three case studies: Aeschylus s Oresteia trilogy, J-L. Runeberg s poem Sven Dufva and Sofi Oksanen s novel Puhdistus (Purge). On the whole, Wittgenstein s idea that ethical values can be demonstrated (shown) by means of literature is revealed as a fruitful point of departure for a more exact ethical reading, offering a new perspective on literary works.