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

Fluid mechanical model of the acoustic impedance of small orifices

A fluid mechanical model of the acoustic behavior of small orifices is presented which predicts orifice resistance and reactance as a function of incident sound pressure level, frequency, and orifice geometry. Agreement between predicted and measured values is excellent. The model shows the following: (1) The acoustic flow in immediate neighborhood of the orifice can be modeled as a locally spherical flow. Within this near field, the flow is, to a first approximation, unsteady and incompressible. (2) At very low sound pressure levels, the orifice viscous resistance is directly related to the effect of boundary-layer displacement along the walls containing the orifice, and the orifice reactance is directly related to the inertia of the oscillating flow in the neighborhood of the orifice. (3) For large values of the incident acoustic pressure, the impedance is dominated by nonlinear jet-like effects. (4) For low values of the pressure, the resistance and reactance are roughly equal

Efficient state-space inference of periodic latent force models

Latent force models (LFM) are principled approaches to incorporating solutions to differen-tial equations within non-parametric inference methods. Unfortunately, the developmentand application of LFMs can be inhibited by their computational cost, especially whenclosed-form solutions for the LFM are unavailable, as is the case in many real world prob-lems where these latent forces exhibit periodic behaviour. Given this, we develop a newsparse representation of LFMs which considerably improves their computational efficiency,as well as broadening their applicability, in a principled way, to domains with periodic ornear periodic latent forces. Our approach uses a linear basis model to approximate onegenerative model for each periodic force. We assume that the latent forces are generatedfrom Gaussian process priors and develop a linear basis model which fully expresses thesepriors. We apply our approach to model the thermal dynamics of domestic buildings andshow that it is effective at predicting day-ahead temperatures within the homes. We alsoapply our approach within queueing theory in which quasi-periodic arrival rates are mod-elled as latent forces. In both cases, we demonstrate that our approach can be implemented efficiently using state-space methods which encode the linear dynamic systems via LFMs.Further, we show that state estimates obtained using periodic latent force models can re-duce the root mean squared error to 17% of that from non-periodic models and 27% of thenearest rival approach which is the resonator model (S ̈arkk ̈a et al., 2012; Hartikainen et al.,2012.

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

Gauge fixing and equivariant cohomology

The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully analysed, and demonstrates that different choices of gauge-fixing fermion can lead to different quantum theories.Comment: 18 pages LaTe

Shock tube instrumentation techniques for study of hypervelocity entry problems

Shock tube instrumentation methods for convective heat transfer study and radiative properties of high temperature gas at conditions simulating hypervelocity entr

Deactivation of TEM-1 beta-Lactamase investigated by isothermal batch and non-isothermal continuous enzyme membrane reactor methods

The thermal deactivation of TEM-1 β-lactamase was examined using two experimental techniques: a series of isothermal batch assays and a single, continuous, non-isothermal assay in an enzyme membrane reactor (EMR). The isothermal batch-mode technique was coupled with the three-state Equilibrium Model of enzyme deactivation, while the results of the EMR experiment were fitted to a four-state molten globule model . The two methods both led to the conclusions that the thermal deactivation of TEM-1 β -lactamase does not follow the Lumry-Eyring model and that the Teq of the enzyme (the point at which active and inactive states are present in equal amounts due to thermodynamic equilibrium) is at least 10 °C from the Tm (melting temperature), contrary to the idea that the true temperature optimum of a biocatalyst is necessarily close to the melting temperature

Telehealth for expanding the reach of early autism training to parents.

Although there is consensus that parents should be involved in interventions designed for young children with autism spectrum disorder (ASD), parent participation alone does not ensure consistent, generalized gains in children's development. Barriers such as costly intervention, time-intensive sessions, and family life may prevent parents from using the intervention at home. Telehealth integrates communication technologies to provide health-related services at a distance. A 12 one-hour per week parent intervention program was tested using telehealth delivery with nine families with ASD. The goal was to examine its feasibility and acceptance for promoting child learning throughout families' daily play and caretaking interactions at home. Parents became skilled at using teachable moments to promote children's spontaneous language and imitation skills and were pleased with the support and ease of telehealth learning. Preliminary results suggest the potential of technology for helping parents understand and use early intervention practices more often in their daily interactions with children

Breaking the habit: measuring and predicting departures from routine in individual human mobility

Researchers studying daily life mobility patterns have recently shown that humans are typically highly predictable in their movements. However, no existing work has examined the boundaries of this predictability, where human behaviour transitions temporarily from routine patterns to highly unpredictable states. To address this shortcoming, we tackle two interrelated challenges. First, we develop a novel information-theoretic metric, called instantaneous entropy, to analyse an individual’s mobility patterns and identify temporary departures from routine. Second, to predict such departures in the future, we propose the first Bayesian framework that explicitly models breaks from routine, showing that it outperforms current state-of-the-art predictor