1,364 research outputs found
Radio Weak Lensing Shear Measurement in the Visibility Domain - II. Source Extraction
This paper extends the method introduced in Rivi et al. (2016b) to measure
galaxy ellipticities in the visibility domain for radio weak lensing surveys.
In that paper we focused on the development and testing of the method for the
simple case of individual galaxies located at the phase centre, and proposed to
extend it to the realistic case of many sources in the field of view by
isolating visibilities of each source with a faceting technique. In this second
paper we present a detailed algorithm for source extraction in the visibility
domain and show its effectiveness as a function of the source number density by
running simulations of SKA1-MID observations in the band 950-1150 MHz and
comparing original and measured values of galaxies' ellipticities. Shear
measurements from a realistic population of 10^4 galaxies randomly located in a
field of view of 1 deg^2 (i.e. the source density expected for the current
radio weak lensing survey proposal with SKA1) are also performed. At SNR >= 10,
the multiplicative bias is only a factor 1.5 worse than what found when
analysing individual sources, and is still comparable to the bias values
reported for similar measurement methods at optical wavelengths. The additive
bias is unchanged from the case of individual sources, but is significantly
larger than typically found in optical surveys. This bias depends on the shape
of the uv coverage and we suggest that a uv-plane weighting scheme to produce a
more isotropic shape could reduce and control additive bias.Comment: 11 pages, 8 figures, MNRAS accepte
Witt differentials in the h-topology
Recent important and powerful frameworks for the study of differential forms
by Huber-Joerder and Huber-Kebekus-Kelly based on Voevodsky's h-topology have
greatly simplified and unified many approaches. This article builds towards the
goal of putting Illusie's de Rham-Witt complex in the same framework by
exploring the h-sheafification of the rational de Rham-Witt differentials.
Assuming resolution of singularities in positive characteristic one recovers a
complete cohomological h-descent for all terms of the complex. We also provide
unconditional h-descent for the global sections and draw the expected
conclusions. The approach is to realize that a certain right Kan extension
introduced by Huber-Kebekus-Kelly takes the sheaf of rational de Rham-Witt
forms to a qfh-sheaf. As such, we state and prove many results about
qfh-sheaves which are of independent interest
On Lower Bounds for -multiplicities
A recent continuous family of multiplicity functions on local rings was
introduced by Taylor interpolating between Hilbert-Samuel and Hilbert-Kunz
multiplicities. The obvious goal is to use this as a tool for deforming results
from one to the other. The values in this family which do not match these
classic variants however are not known yet to be well-behaved. This article
explores lower bounds for these intermediate multiplicities as well as gives
evidence for analogies of the Watanabe-Yoshida minimality conjectures for
unmixed singular rings.Comment: 10 page
The s-multiplicity function of 2x2-determinantal rings
This article generalizes joint work of the first author and I. Swanson to the
-multiplicity recently introduced by the second author. For a field and
a -matrix of variables, we utilize Gr\"obner bases
to give a closed form the length where ,
is a sufficiently large power of , and is the homogeneous
maximal ideal of . This shows this length is always eventually a {\it
polynomial} function of for all .Comment: 9 pages, Errors fixe
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