7,331 research outputs found
Optimal Re-Embeddings of Border Basis Schemes
Border basis schemes are open subschemes of Hilbert schemes parametrizing
0-dimensional subschemes of of given length. They yield open
coverings and are easy to describe and to compute with. Our topic is to find
re-embeddings of border basis schemes into affine spaces of minimal dimension.
Given , an ideal ,
and a tuple of indeterminates, in previous papers the authors developed
techniques for computing -separating re-embeddings of , i.e., of
isomorphisms .
Here these general techniques are developed further and improved by
constructing a new algorithm for checking candidate tuples and by using the
Gr\"obner fan of the linear part of advantageously.
Then we apply this to the ideals defining border basis schemes
, where is an order ideal of terms, and
to their natural generating polynomials. The fact that these ideals are
homogeneous w.r.t. the arrow grading allows us to look for suitable tuples
more systematically. Using the equivalence of indeterminates modulo the square
of the maximal ideal, we compute the Gr\"obner fan of the linear part of the
ideal quickly and determine which indeterminates should be in when we are
looking for optimal re-embeddings. Specific applications include re-embeddings
of border basis schemes where and where
consists of all terms up to some degree.Comment: This preprint will not be published. It has been split into several
parts which will be extended and published separately. When the last part is
finished, this preprint will be withdraw
The X-CLASS - redMaPPer galaxy cluster comparison: I. Identification procedures
We performed a detailed and, for a large part interactive, analysis of the
matching output between the X-CLASS and redMaPPer cluster catalogues. The
overlap between the two catalogues has been accurately determined and possible
cluster positional errors were manually recovered. The final samples comprise
270 and 355 redMaPPer and X-CLASS clusters respectively. X-ray cluster matching
rates were analysed as a function of optical richness. In a second step, the
redMaPPer clusters were correlated with the entire X-ray catalogue, containing
point and uncharacterised sources (down to a few 10^{-15} erg s^{-1} cm^{-2} in
the [0.5-2] keV band). A stacking analysis was performed for the remaining
undetected optical clusters. Main results show that neither of the wavebands
misses any massive cluster (as coded by X-ray luminosity or optical richness).
After correcting for obvious pipeline short-comings (about 10% of the cases
both in optical and X-ray), ~50% of the redMaPPer (down to a richness of 20)
are found to coincide with an X-CLASS cluster; when considering X-ray sources
of any type, this fraction increases to ~ 80%; for the remaining objects, the
stacking analysis finds a weak signal within 0.5 Mpc around the cluster optical
centers. The fraction of clusters totally dominated by AGN-type emission
appears to be of the order of a few percent. Conversely ~ 40% of the X-CLASS
clusters are identified with a redMaPPer (down to a richness of 20) - part of
the non-matches being due to the fact that the X-CLASS sample extends further
out than redMaPPer (z<1 vs z<0.6); extending the correlation down to a richness
of 5, raises the matching rate to ~ 65%.Comment: 15 pages, 20 figures, 2 table
Explicit height estimates for CM curves of genus 2
In this paper we make explicit the constants of Habegger and Pazuki's work
from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding
to genus 2 curves with CM by them and potentially good reduction outside a
predefined set of primes. We also simplify some of the arguments
Animal lameness detection with radar sensing
Lameness is a significant problem for performance horses and farmed animals, with severe impact on animal welfare and treatment costs. Lameness is commonly diagnosed through subjective scoring methods performed by trained veterinary clinicians, but automatic methods using suitable sensors would improve efficiency and reliability. In this paper, we propose the use of radar micro-Doppler signatures for contactless and automatic identification of lameness, and present preliminary results for dairy cows, sheep, and horses. These proof-of-concept results are promising, with classification accuracy above 85% for dairy cows, around 92% for horses, and close to 99% for sheep
3D density reconstruction of a screeching supersonic jet by synchronized multi-camera Background Oriented Schlieren
International audienceThis work describes the application of 3D Background Oriented Schlieren (3DBOS) to the experimental analysis of the mean and instantaneous 3D structures of supersonic under-expanded screeching jets. These jets feature various dynamical states as the jet nozzle pressure ratio (NPR) is varied. Hence, six flow conditions were considered using acoustic measurements and 3D density reconstructions. Relying on the latter and on Proper Orthogonal Decomposition (POD) to isolate the main flow features, clear visualizations of the instantaneous 3D state and the reconstructed average dynamics of modes A1 and C, that are respectively axisymmetric and helical, were obtained
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