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 $\mathbb{R}^n$ 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

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