2,100 research outputs found
A Statistical Method for Estimating Luminosity Functions using Truncated Data
The observational limitations of astronomical surveys lead to significant
statistical inference challenges. One such challenge is the estimation of
luminosity functions given redshift and absolute magnitude measurements
from an irregularly truncated sample of objects. This is a bivariate density
estimation problem; we develop here a statistically rigorous method which (1)
does not assume a strict parametric form for the bivariate density; (2) does
not assume independence between redshift and absolute magnitude (and hence
allows evolution of the luminosity function with redshift); (3) does not
require dividing the data into arbitrary bins; and (4) naturally incorporates a
varying selection function. We accomplish this by decomposing the bivariate
density into nonparametric and parametric portions. There is a simple way of
estimating the integrated mean squared error of the estimator; smoothing
parameters are selected to minimize this quantity. Results are presented from
the analysis of a sample of quasars.Comment: 30 pages, 9 figures, Accepted for publication in Ap
Area and Length Minimizing Flows for Shape Segmentation
©1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.Presented at the 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 17-19, 1997, San Juan, Puerto Rico.DOI: 10.1109/CVPR.1997.609390Several active contour models have been proposed to unify the curve evolution framework with classical energy minimization techniques for segmentation, such as snakes. The essential idea is to evolve a curve (in 20) or a surface (in 30) under constraints from image forces so that it clings to features of interest in an intensity image. Recently the evolution equation has. been derived from first principles as the gradient flow that minimizes a modified length functional, tailored io features such as edges. However, because the flow may be slow to converge in practice, a constant (hyperbolic) term is added to keep the curve/surface moving in the desired direction. In this paper, we provide a justification for this term based on the gradient flow derived from a weighted area functional, with image dependent weighting factor. When combined with the earlier modified length gradient flow we obtain a pde which offers a number of advantages, as illustrated by several examples of shape segmentation on medical images. In many cases the weighted area flow may be used on its own, with significant computational savings
Resonant Orbits and the High Velocity Peaks Towards the Bulge
We extract the resonant orbits from an N-body bar that is a good
representation of the Milky Way, using the method recently introduced by Molloy
et al. (2015). By decomposing the bar into its constituent orbit families, we
show that they are intimately connected to the boxy-peanut shape of the
density. We highlight the imprint due solely to resonant orbits on the
kinematic landscape towards the Galactic centre. The resonant orbits are shown
to have distinct kinematic features and may be used to explain the cold
velocity peak seen in the APOGEE commissioning data (Nidever at al., 2012). We
show that high velocity peaks are a natural consequence of the motions of stars
in the 2:1 orbit family and that stars on other higher order resonances can
contribute to the peaks. The locations of the peaks vary with bar angle and,
with the tacit assumption that the observed peaks are due to the 2:1 family, we
find that the locations of the high velocity peaks correspond to bar angles in
the range 10 < theta_bar < 25 (deg). However, some important questions about
the nature of the peaks remain, such as their apparent absence in other surveys
of the Bulge and the deviations from symmetry between equivalent fields in the
north and south. We show that the absence of a peak in surveys at higher
latitudes is likely due to the combination of a less prominent peak and a lower
number density of bar supporting orbits at these latitudes.Comment: 7 Figures, 1 Table, Now includes figures & discussion of higher order
resonances, Minor revisions to text throughout, Conclusions unchange
Tau functions as Widom constants
We define a tau function for a generic Riemann-Hilbert problem posed on a
union of non-intersecting smooth closed curves with jump matrices analytic in
their neighborhood. The tau function depends on parameters of the jumps and is
expressed as the Fredholm determinant of an integral operator with block
integrable kernel constructed in terms of elementary parametrices. Its
logarithmic derivatives with respect to parameters are given by contour
integrals involving these parametrices and the solution of the Riemann-Hilbert
problem. In the case of one circle, the tau function coincides with Widom's
determinant arising in the asymptotics of block Toeplitz matrices. Our
construction gives the Jimbo-Miwa-Ueno tau function for Riemann-Hilbert
problems of isomonodromic origin (Painlev\'e VI, V, III, Garnier system, etc)
and the Sato-Segal-Wilson tau function for integrable hierarchies such as
Gelfand-Dickey and Drinfeld-Sokolov.Comment: 26 pages, 6 figure
Rotationally-Driven Fragmentation for the Formation of the Binary Protostellar System L1551 IRS 5
Either bulk rotation or local turbulence is widely invoked to drive
fragmentation in collapsing cores so as to produce multiple star systems. Even
when the two mechanisms predict different manners in which the stellar spins
and orbits are aligned, subsequent internal or external interactions can drive
multiple systems towards or away from alignment thus masking their formation
process. Here, we demonstrate that the geometrical and dynamical relationship
between the binary system and its surrounding bulk envelope provide the crucial
distinction between fragmentation models. We find that the circumstellar disks
of the binary protostellar system L1551 IRS 5 are closely parallel not just
with each other but also with their surrounding flattened envelope.
Measurements of the relative proper motion of the binary components spanning
nearly 30 yr indicate an orbital motion in the same sense as the envelope
rotation. Eliminating orbital solutions whereby the circumstellar disks would
be tidally truncated to sizes smaller than are observed, the remaining
solutions favor a circular or low-eccentricity orbit tilted by up to
25 from the circumstellar disks. Turbulence-driven fragmentation
can generate local angular momentum to produce a coplanar binary system, but
which bears no particular relationship with its surrounding envelope. Instead,
the observed properties conform with predictions for rotationally-driven
fragmentation. If the fragments were produced at different heights or on
opposite sides of the midplane in the flattened central region of a rotating
core, the resulting protostars would then exhibit circumstellar disks parallel
with the surrounding envelope but tilted from the orbital plane as is observed.Comment: Accepted for publication in Ap
Resonant Clumping and Substructure in Galactic Discs
We describe a method to extract resonant orbits from N-body simulations
exploiting the fact that they close in a frame rotating with a constant pattern
speed. Our method is applied to the N-body simulation of the Milky Way by Shen
et al. (2010). This simulation hosts a massive bar, which drives strong
resonances and persistent angular momentum exchange. Resonant orbits are found
throughout the disc, both close to the bar itself and out to the very edges of
the disc. Using Fourier spectrograms, we demonstrate that the bar is driving
kinematic substructure even in the very outer parts of the disc. We identify
two major orbit families in the outskirts of the disc that make significant
contributions to the kinematic landscape, namely the m:l = 3:-2 and 1:-1
families resonating with the pattern speed of the bar. A mechanism is described
that produces bimodal distributions of Galactocentric radial velocities at
selected azimuths in the outer disc. It occurs as a result of the temporal
coherence of particles on the 3:-2 resonant orbits, which causes them to arrive
simultaneously at pericentre or apocentre. This resonant clumping, due to the
in-phase motion of the particles through their epicycle, leads to both inward
and outward moving groups which belong to the same orbital family and
consequently produce bimodal radial velocity distributions. This is a possible
explanation of the bimodal velocity distributions observed towards the Galactic
anti-Centre by Liu et al. (2012). Another consequence is that transient
overdensities appear and dissipate (in a symmetric fashion) on timescales equal
to the their epicyclic period resulting in a periodic pulsing of the disc's
surface density.Comment: 11 Figures, 1 Table. Accepted for publication in ApJ. Version 2
reflects minor changes to the text. Animation referenced in Figure 7 is
available at http://hubble.shao.ac.cn/~shen/resonantclumping/DensMovie.mp
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