Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: E/B decomposition of finite pixelized CMB maps   Separation of the E and B components of a microwave background polarization
map or a weak lensing map is an essential step in extracting science from it,
but when the map covers only part of the sky and/or is pixelized, this
decomposition cannot be done perfectly. We present a method for decomposing an
arbitrary sky map into a sum of three orthogonal components that we term ``pure
E'', ``pure B'' and ``ambiguous''. This method is useful both for providing
intuition for experimental design and for analyzing data sets in practice. We
show how to find orthonormal bases for all three components in terms of
bilaplacian eigenfunctions. The number of ambiguous modes is proportional to
the length of the map boundary so fairly round maps are preferred. For
real-world data analysis, we present a simple matrix eigenvalue method for
calculating nearly pure E and B modes in pixelized maps. We find that the
dominant source of leakage between E and B is aliasing of small-scale power
caused by the pixelization. This problem can be eliminated by heavily
oversampling the map, but is exacerbated by the fact that the E power spectrum
is expected to be much larger than the B power spectrum and extremely blue. We
found that a factor of 2 to 3 more pixels are needed in a polarization map to
achieve the same level of contamination by aliased power than in a temperature
map.

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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol