11,414 research outputs found
Distribution of Gaussian Process Arc Lengths
We present the first treatment of the arc length of the Gaussian Process (GP)
with more than a single output dimension. GPs are commonly used for tasks such
as trajectory modelling, where path length is a crucial quantity of interest.
Previously, only paths in one dimension have been considered, with no
theoretical consideration of higher dimensional problems. We fill the gap in
the existing literature by deriving the moments of the arc length for a
stationary GP with multiple output dimensions. A new method is used to derive
the mean of a one-dimensional GP over a finite interval, by considering the
distribution of the arc length integrand. This technique is used to derive an
approximate distribution over the arc length of a vector valued GP in
by moment matching the distribution. Numerical simulations
confirm our theoretical derivations.Comment: 10 pages, 4 figures, Accepted to The 20th International Conference on
Artificial Intelligence and Statistics (AISTATS
The habitability of stagnant-lid Earths around dwarf stars
The habitability of a planet depends on various factors, such as delivery of
water during the formation, the co-evolution of the interior and the
atmosphere, as well as the stellar irradiation which changes in time. Since an
unknown number of rocky exoplanets may operate in a one-plate convective
regime, i.e., without plate tectonics, we aim at understanding under which
conditions planets in such a stagnant-lid regime may support habitable surface
conditions. Understanding the interaction of the planetary interior and
outgassing of volatiles with the atmosphere in combination with the evolution
of the host star is crucial to determine the potential habitability. M-dwarf
stars in particular possess a high-luminosity pre-main sequence phase which
endangers the habitability of planets around them via water loss. We therefore
explore the potential of secondary outgassing from the planetary interior to
rebuild a water reservoir allowing for habitability at a later stage. We
compute the boundaries of the habitable zone around M, K, G, and F-dwarf stars
using a 1D cloud-free radiative-convective climate model accounting for the
outgassing history of CO2 and H2O from an interior evolution and outgassing
model for different interior compositions and stellar luminosity evolutions.
The outer edge of the habitable zone strongly depends on the amount of CO2
outgassed from the interior, while the inner edge is mainly determined via the
stellar irradiation, as soon as a sufficiently large water reservoir has been
outgassed. A build-up of a secondary water reservoir for planets around M-dwarf
stars is possible even after severe water loss during the high luminosity
pre-main sequence phase as long as some water has been retained within the
mantle. Earth-like stagnant-lid planets allow for habitable surface conditions
within a continuous habitable zone that is dependent on interior composition.Comment: 15 pages, accepted by A&A, abstract shortene
Mean age gradient and asymmetry in the star formation history of the Small Magellanic Cloud
We derive the star formation history in four regions of the Small Magellanic
Cloud (SMC) using the deepest VI color-magnitude diagrams (CMDs) ever obtained
for this galaxy. The images were obtained with the Advanced Camera for Surveys
onboard the Hubble Space Telescope and are located at projected distances of
0.5-2 degrees from the SMC center, probing the main body and the wing of the
galaxy. We derived the star-formation histories (SFH) of the four fields using
two independent procedures to fit synthetic CMDs to the data. We compare the
SFHs derived here with our earlier results for the SMC bar to create a deep
pencil-beam survey of the global history of the central SMC. We find in all the
six fields observed with HST a slow star formation pace from 13 to 5-7 Gyr ago,
followed by a ~ 2-3 times higher activity. This is remarkable because dynamical
models do not predict a strong influence of either the LMC or the Milky Way
(MW) at that time. The level of the intermediate-age SFR enhancement
systematically increases towards the center, resulting in a gradient in the
mean age of the population, with the bar fields being systematically younger
than the outer ones. Star formation over the most recent 500 Myr is strongly
concentrated in the bar, the only exception being the area of the SMC wing. The
strong current activity of the latter is likely driven by interaction with the
LMC. At a given age, there is no significant difference in metallicity between
the inner and outer fields, implying that metals are well mixed throughout the
SMC. The age-metallicity relations we infer from our best fitting models are
monotonically increasing with time, with no evidence of dips. This may argue
against the major merger scenario proposed by Tsujimoto and Bekki 2009,
although a minor merger cannot be ruled out.Comment: 30 pages, 16 figures, accepted for publication in Ap
Recommended from our members
Ectopic expression of the HLXB9 gene is associated with an altered nuclear position in t(7;12) leukaemias
This article is available open access through the publisher’s website at the link below. Copyright @ 2009 Macmillan Publishers Ltd.No abstract available (Letter to the editor).The Leukaemia Research Fun
Collective modes and ballistic expansion of a Fermi gas in the BCS-BEC crossover
We evaluate the frequencies of collective modes and the anisotropic expansion
rate of a harmonically trapped Fermi superfluid at varying coupling strengths
across a Feshbach resonance driving a BCS-BEC crossover. The equations of
motion for the superfluid are obtained from a microscopic mean-field expression
for the compressibility and are solved within a scaling ansatz. Our results
confirm non-monotonic behavior in the crossover region and are in quantitative
agreement with current measurements of the transverse breathing mode by Kinast
{\it et al.} [Phys. Rev. Lett. {\bf 92}, 150402 (2004)] and of the axial
breathing mode by Bartenstein {\it et al.} [Phys. Rev. Lett. {\bf 92}, 203201
(2004)].Comment: 4 pages and 4 figures; proof version with more extensive discussions
on the comparison between theoretical results and experimental findings; to
appear in Phys. Rev. Lett. (Nov. 2004
The monkey's perspective
The sequencing of the genome of a female rhesus macaque (Macaca mulatta) of Indian origin will provide us with biomedical and evolutionary insights into both humans and Old World monkeys
Bulk and surface energetics of lithium hydride crystal: benchmarks from quantum Monte Carlo and quantum chemistry
We show how accurate benchmark values of the surface formation energy of
crystalline lithium hydride can be computed by the complementary techniques of
quantum Monte Carlo (QMC) and wavefunction-based molecular quantum chemistry.
To demonstrate the high accuracy of the QMC techniques, we present a detailed
study of the energetics of the bulk LiH crystal, using both pseudopotential and
all-electron approaches. We show that the equilibrium lattice parameter agrees
with experiment to within 0.03 %, which is around the experimental uncertainty,
and the cohesive energy agrees to within around 10 meV per formula unit. QMC in
periodic slab geometry is used to compute the formation energy of the LiH (001)
surface, and we show that the value can be accurately converged with respect to
slab thickness and other technical parameters. The quantum chemistry
calculations build on the recently developed hierarchical scheme for computing
the correlation energy of a crystal to high precision. We show that the
hierarchical scheme allows the accurate calculation of the surface formation
energy, and we present results that are well converged with respect to basis
set and with respect to the level of correlation treatment. The QMC and
hierarchical results for the surface formation energy agree to within about 1
%.Comment: 16 pages, 4 figure
Breathing in Low Mass Galaxies: A Study of Episodic Star Formation
We simulate the collapse of isolated dwarf galaxies using SPH + N-Body
simulations including a physically motivated description of the effects of
supernova feedback. As the gas collapses and stars form, the supernova feedback
disrupts enough gas to temporarily quench star formation. The gas flows outward
into a hot halo, where it cools until star formation can continue once more and
the cycle repeats. The star formation histories of isolated Local Group dwarf
galaxies exhibit similar episodic bursts of star formation. We examine the mass
dependence of the stellar velocity dispersions and find that they are no less
than half the velocity of the halos measured at the virial radius.Comment: 5 pages, 3 figures, accepted ApJ. Full resolution figures and movies
available at http://hpcc.astro.washington.edu/feedbac
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