215 research outputs found
Introducing Mexican needlets for CMB analysis: Issues for practical applications and comparison with standard needlets
Over the last few years, needlets have a emerged as a useful tool for the
analysis of Cosmic Microwave Background (CMB) data. Our aim in this paper is
first to introduce in the CMB literature a different form of needlets, known as
Mexican needlets, first discussed in the mathematical literature by Geller and
Mayeli (2009a,b). We then proceed with an extensive study of the properties of
both standard and Mexican needlets; these properties depend on some parameters
which can be tuned in order to optimize the performance for a given
application. Our second aim in this paper is then to give practical advice on
how to adjust these parameters in order to achieve the best properties for a
given problem in CMB data analysis. In particular we investigate localization
properties in real and harmonic spaces and propose a recipe on how to quantify
the influence of galactic and point source masks on the needlet coefficients.
We also show that for certain parameter values, the Mexican needlets provide a
close approximation to the Spherical Mexican Hat Wavelets (whence their name),
with some advantages concerning their numerical implementation and the
derivation of their statistical properties.Comment: 40 pages, 11 figures, published version, main modification: added
section on more realistic galactic and point source mask
The resource decisions and documents of undergraduate engineering students in mathematics courses
This thesis concerns a multiple case study, carried out at three Norwegian universities. The goal was to find similarities and differences between how engineering students from different university contexts used resources to learn mathematics, and how they made decisions regarding their use of resources. My project had an inductive focus, networking thematic analysis (Braun & Clarke, 2006) with the theoretical framework of the documentational approach to didactics (Gueudet & Trouche, 2009). After my analysis, I also compared my results and conclusions to those of authors who have conducted research projects with a similar focus (i.e. Anastasikis, 2018; Gueudet & Pepin, 2016; Kanwal, 2018; Pepin & Kock, 2019). I generally found that my results were consistent with their reflections, but I had also identified trends that went beyond the ideas within the field.
Given the wide focus of the project, the result are numerous, and vary greatly in generality and theoretic value. There are two overarching results that I consider particularly significant to the field of research:
I identify an overall structure to students’ decision regarding resources. Students almost exclusively consider resources that are emphasized within the course at hand; that they are familiar with from previous educational experiences or that they are familiar with from non-mathematical activities (for instance YouTube and Google). They primarily make their decisions based on what seems suitable for the task at hand, with preference as a secondary concern. Examinations have a significant impact on what they consider suitable. Their preference for resources are based on quality criteria such as simplicity and that they are able to use the resources efficiently.
I introduce the notion of didactical resource purposes. Students use resources for the four purposes of introduction, practice, evaluation and explanation. That is, they use resources to learn the theory and foundations of a topic; to gain experience working mathematically within the confines of the topic; to evaluate their answers, their learning process or their understanding of the topic and to actively search for information when they realize that there is a fact that they do not recall or an aspect of the topic that they do not understand well enough to accomplish their goals.publishedVersio
Directional Variations of the Non-Gaussianity Parameter f_NL
We investigate local variations of the primordial non-Gaussianity parameter
f_NL in the WMAP data, looking for possible influence of foreground
contamination in the full-sky estimate of f_NL. We first improve the needlet
bispectrum estimate in (Rudjord et al. 2009) on the full-sky to f_NL= 73 +/- 31
using the KQ75 mask on the co-added V+W channel. We find no particular values
of f_NL estimates close to the galactic plane and conclude that foregrounds are
unlikely to affect the estimate of f_NL in the V and W bands even for the
smaller KQ85 mask. In the Q band however, we find unexpectedly high values of
f_NL in local estimates close to the galactic mask, as well as significant
discrepancies between Q band estimates and V/W band estimates. We therefore
conclude that the Q band is too contaminated to be used for non-Gaussianity
studies even with the larger KQ75 mask. We further noted that the local f_NL
estimates on the V+W channel are positive on all equatorial bands from the
north to the south pole. The probability for this to happen in a universe with
f_NL = 0 is less than one percent.Comment: 6 pages, 2 figures, included section on non-Gaussian maps, references
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On the linear term correction for needlets/wavelets non-Gaussianity estimators
We derive the linear correction term for needlet and wavelet estimators of
the bispectrum and the non-linearity parameter fNL on cosmic microwave
background radiation data. We show that on masked WMAP-like data with
anisotropic noise, the error bars improve by 10-20% and almost reach the
optimal error bars obtained with the KSW estimator (Komatsu et al 2005). In the
limit of full-sky and isotropic noise, this term vanishes. We apply needlet and
wavelet estimators to the WMAP 7-year data and obtain our best estimate
fNL=37.5 \pm 21.8.Comment: 10 pages, submitted to Ap
Data Quality of Surgery for Carotid Artery Stenosis. Are the National Vascular Registries Reliable?
AbstractObjectivesTo study completeness of reporting carotid endarterectomies, including peri-operative stroke and mortality rate, in a national vascular registry, NorKar, and a national administrative registry, The Norwegian Patient Register (NPR).DesignComparative registry-based national study.MaterialsMember hospitals of NorKar, including 89% of carotid endarterectomies in Norway, were compared with relevant data in NPR for the years 2000–2002.MethodsWe compared procedure-codes, diagnosis-codes, in-hospital death and the occurrence of peri-operative stroke after treatment for carotid artery stenosis in the two registries to evaluate completeness.ResultsCompared with the NPR numbers, 16% of carotid endarterectomies were missing in the reports from member hospitals of NorKar. Further, during this three-year period, there was an under-reporting of seven strokes and two deaths. The discrepancy was most pronounced in 2001.ConclusionsThere is an under-reporting of patients operated on for carotid artery stenosis in NorKar according to NPR numbers as well as an under-reporting of early deaths and strokes. There is a need for better quality data in the NorKar Registry. Registry quality would be likely to improve if patient identifiable data were available in both registries
Needatool: A Needlet Analysis Tool for Cosmological Data Processing
We introduce NeedATool (Needlet Analysis Tool), a software for data analysis
based on needlets, a wavelet rendition which is powerful for the analysis of
fields defined on a sphere. Needlets have been applied successfully to the
treatment of astrophysical and cosmological observations, and in particular to
the analysis of cosmic microwave background (CMB) data. Usually, such analyses
are performed in real space as well as in its dual domain, the harmonic one.
Both spaces have advantages and disadvantages: for example, in pixel space it
is easier to deal with partial sky coverage and experimental noise; in harmonic
domain, beam treatment and comparison with theoretical predictions are more
effective. During the last decade, however, wavelets have emerged as a useful
tool for CMB data analysis, since they allow to combine most of the advantages
of the two spaces, one of the main reasons being their sharp localisation. In
this paper, we outline the analytical properties of needlets and discuss the
main features of the numerical code, which should be a valuable addition to the
CMB analyst's toolbox.Comment: software available at:
http://www.fisica.uniroma2.it/~pietrobon/dp_files/dp_NeedATool_download.htm
Non-Gaussianities in the local curvature of the 5-year WMAP data
Using the 5 year WMAP data, we re-investigate claims of non-Gaussianities and
asymmetries detected in local curvature statistics of the 1 year WMAP data. In
Hansen et al 2004, it was found that the northern ecliptic hemisphere was
non-Gaussian at the ~1% level testing the densities of hill-, lake and saddle
points based on the second derivatives of the CMB temperature map. The 5 year
WMAP data has a much lower noise level and better control of systematics. Using
these, we find that the anomalies are still present at a consistent level. Also
the direction of maximum non-Gaussianity remains. Due to limited availability
of computer resources, Hansen et al. 2004 were unable to calculate the full
covariance matrix for the chi^2 test used. Here we apply the full covariance
matrix instead of the diagonal approximation and find that the
non-Gaussianities disappear and there is no preferred non-Gaussian direction.
We compare with simulations of weak lensing to see if this may cause the
observed non-Gaussianity when using diagonal covariance matrix. We conclude
that weak lensing does not produce non-Gaussianity in the local curvature
statistics at the scales investigated in this paper. The cause of the
non-Gaussian detection in the case of a diagonal matrix remains unclear.Comment: 7 pages, 6 figures, included test on weak lensing simulation
Primordial Non-Gaussianity and the NRAO VLA Sky Survey
The NRAO VLA Sky Survey (NVSS) is the only dataset that allows an accurate
determination of the auto-correlation function (ACF) on angular scales of
several degrees for Active Galactic Nuclei (AGNs) at typical redshifts . Surprisingly, the ACF is found to be positive on such large scales
while, in the framework of the standard hierarchical clustering scenario with
Gaussian primordial perturbations it should be negative for a
redshift-independent effective halo mass of order of that found for
optically-selected quasars. We show that a small primordial non-Gaussianity can
add sufficient power on very large scales to account for the observed NVSS ACF.
The best-fit value of the parameter , quantifying the amplitude of
primordial non-Gaussianity of local type is (
error bar) and ( confidence level),
corresponding to a detection of non-Gaussianity significant at the confidence level. The minimal halo mass of NVSS sources is found to
be () strikingly
close to that found for optically selected quasars. We discuss caveats and
possible physical and systematic effects that can impact on the results.Comment: 6 pages, 5 figure
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