A Framework for Quantifying the Degeneracies of Exoplanet Interior Compositions

Several transiting super-Earths are expected to be discovered in the coming few years. While tools to model the interior structure of transiting planets exist, inferences about the composition are fraught with ambiguities. We present a framework to quantify how much we can robustly infer about super-Earth and Neptune-size exoplanet interiors from radius and mass measurements. We introduce quaternary diagrams to illustrate the range of possible interior compositions for planets with four layers (iron core, silicate mantles, water layers, and H/He envelopes). We apply our model to CoRoT-7b, GJ 436b, and HAT-P-11b. Interpretation of planets with H/He envelopes is limited by the model uncertainty in the interior temperature, while for CoRoT-7b observational uncertainties dominate. We further find that our planet interior model sharpens the observational constraints on CoRoT-7b's mass and radius, assuming the planet does not contain significant amounts of water or gas. We show that the strength of the limits that can be placed on a super-Earth's composition depends on the planet's density; for similar observational uncertainties, high-density super-Mercuries allow the tightest composition constraints. Finally, we describe how techniques from Bayesian statistics can be used to take into account in a formal way the combined contributions of both theoretical and observational uncertainties to ambiguities in a planet's interior composition. On the whole, with only a mass and radius measurement an exact interior composition cannot be inferred for an exoplanet because the problem is highly underconstrained. Detailed quantitative ranges of plausible compositions, however, can be found.Comment: 20 pages, 10 figures, published in Ap

Multivariable Repetitive-predictive Controllers using Frequency Decomposition

Repetitive control is a methodology for the tracking of a periodic reference signal. This paper develops a new approach to repetitive control systems design using receding horizon control with frequency decomposition of the reference signal. Moreover, design and implementation issues for this form of repetitive predictive control are investigated from the perspectives of controller complexity and the effects of measurement noise. The analysis is supported by a simulation study on a multi-input multi-output robot arm where the model has been constructed from measured frequency response data, and experimental results from application to an industrial AC motor

INS3D: An incompressible Navier-Stokes code in generalized three-dimensional coordinates

The operation of the INS3D code, which computes steady-state solutions to the incompressible Navier-Stokes equations, is described. The flow solver utilizes a pseudocompressibility approach combined with an approximate factorization scheme. This manual describes key operating features to orient new users. This includes the organization of the code, description of the input parameters, description of each subroutine, and sample problems. Details for more extended operations, including possible code modifications, are given in the appendix

Old and New Fields on Super Riemann Surfaces

The ``new fields" or ``superconformal functions" on $N=1$ super Riemann surfaces introduced recently by Rogers and Langer are shown to coincide with the Abelian differentials (plus constants), viewed as a subset of the functions on the associated $N=2$ super Riemann surface. We confirm that, as originally defined, they do not form a super vector space.Comment: 9 pages, LaTex. Published version: minor changes for clarity, two new reference

Pyrotechnic shock at the orbiter/external tank forward attachment

During the initial certification test of the forward structural attachment of the space shuttle orbiter to the external tank, pyrotechnic shock from actuation of the separation device resulted in structural failure of the thermal protection tiles surrounding the attachment. Because of the high shock associated with the separation bolt, the development of alternative low shock separation designs was initiated. Two concepts that incorporate a 5.08 centimeter frangible nut as the release device were developed and tested

Do less-advantaged students avoid prestigious universities? An applicant-centred approach to understanding UCAS decision-making

Less-advantaged students are under-represented at prestigious universities, but can we infer that they actively avoid them? This research measured university applicants’ knowledge of 115 UK universities. Using card-sort tasks within an interview format, 56 Year 13 students from different types of 16–19 education described how they chose five courses for their application form. Significant cross-cohort trends in knowledge and understanding demonstrated the influence of different educational environments, but within-cohort variation showed that applicant characteristics could over-ride environmental factors. The only cohort where every student understood relative status was an independent school providing individual, career-focused guidance. Limited resources in state-sector schools and colleges necessitated ‘opt-in’ models of guidance, meaning that only highly motivated students were well-informed. When students knew that universities are ranked by national league tables, this informed their decision-making strategy, but reliance on word-of-mouth rather than fact-based information resulted in some students over-estimating status and graduate outcomes. A new conceptual framework blending developmental and cognitive psychology explained persistent class-based progression trends whilst demonstrating how personal agency or educational interventions enabled some less-advantaged students to enter prestigious universities. There was no evidence that prestigious universities were actively avoided, but some students had insufficient knowledge or understanding to make status-based distinctions

The effects of donepezil in Alzheimer's disease - Results from a multinational trial

Donepezil has been shown to be well tolerated and to improve cognition and global function in patients with mild to moderately severe Alzheimer's disease (AD). The current trial was undertaken to investigate further the efficacy and safety of donepezil, in a multinational setting, in patients with mild to moderately severe AD. This 30-week, placebo-controlled, parallel-group study consisted of a 24-week, double-blind treatment phase followed by a 6-week, single-blind, placebo washout. Eight hundred and eighteen patients with mild to moderately severe AD were randomly allocated to treatment with single, daily doses of 5 or 10 mg donepezil, or placebo. The two primary efficacy measures were: a cognitive performance test, the Alzheimer's Disease Assessment Scale-cognitive subscale (ADAS-cog) and a global evaluation, the Clinician's Interview-Based Impression of Change with caregiver input (CIBIC plus). Secondary outcome measures included the Sum of the Boxes of the Clinical Dementia Rating Scale (CDR-SB), a modified Interview for Deterioration in Daily living activities in Dementia (IDDD) and a patient-rated quality of life assessment. Statistically significant improvements in cognitive and global function were observed, as evaluated by ADAS-cog and CIBIC plus, respectively, in both the 5 and 10 mg/day donepezil groups, compared with placebo. Treatment-associated changes were also observed in functional skills, as shown by improved scores on the CDR-SB and the complex-tasks component of the IDDD. A dose-response effect was evident, with the 10 mg/day donepezil group demonstrating greater benefits in all outcome measures than the 5 mg/day group. Donepezil was well tolerated by this patient population and did not produce any clinically significant laboratory test abnormalities. The results of this study confirm that donepezil is effective and well tolerated in treating the symptoms of mild to moderately severe AD

Revised Annotations, Sex-Biased Expression, and Lineage-Specific Genes in the Drosophila melanogaster group

Here, we provide revised gene models for D. ananassae, D. yakuba, and D. simulans, which include UTRs and empirically verified intron-exon boundaries, as well as ortholog groups identified using a fuzzy reciprocal-best-hit blast comparison. Using these revised annotations, we perform differential expression testing using the cufflinks suite to provide a broad overview of differential expression between reproductive tissues and the carcass. We identify thousands of genes that are differentially expressed across tissues in D. yakuba and D. simulans, with roughly 60% agreement in expression patterns of orthologs in D. yakuba and D. simulans. We identify several cases of putative polycistronic transcripts, pointing to a combination of transcriptional read-through in the genome as well as putative gene fusion and fission events across taxa. We furthermore identify hundreds of lineage specific genes in each species with no blast hits among transcripts of any other Drosophila species, which are candidates for neofunctionalized proteins and a potential source of genetic novelty.Comment: Revised manuscript, also available online preprint at G3: Genes, Genomes, Genetics. Gene models, ortholog calls, and tissue specific expression results are available at http://github.com/ThorntonLab/GFF or the UCSC browser on the Thornton Lab public track hub at http://genome.ucsc.ed

A Feynman-Kac Formula for Anticommuting Brownian Motion

Motivated by application to quantum physics, anticommuting analogues of Wiener measure and Brownian motion are constructed. The corresponding Ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established. This machinery is used to provide a Feynman-Kac formula for a class of Hamiltonians. Several specific examples are considered.Comment: 21 page