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Register a new userDetailed Models of super-Earths: How well can we infer bulk properties?
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The field of extrasolar planets has rapidly expanded to include the detection of planets with masses smaller than that of Uranus. Many of these are expected to have little or no hydrogen and helium gas and we might find Earth analogs among them. In this paper we describe our detailed interior models for a rich variety of such massive terrestrial and ocean planets in the 1-to-10 earth-mass range (super-Earths). The grid presented here allows the characterization of the bulk composition of super-Earths detected in transit and with a measured mass. We show that, on average, planet radius measurements to better than 5%, combined with mass measurements to better than 10% would permit us to distinguish between an icy or rocky composition. This is due to the fact that there is a maximum radius a rocky terrestrial planet may achieve for a given mass. Any value of the radius above this maximum terrestrial radius implies that the planet contains a large (> 10%) amount of water (ocean planet).
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The problem of estimating the effect of missing higher orders in perturbation theory is analyzed with emphasis in the application to Higgs production in gluon-gluon fusion. Well-known mathematical methods for an approximated completion of the perturbative series are applied with the goal to not truncate the series, but complete it in a well-defined way, so as to increase the accuracy - if not the precision - of theoretical predictions. The uncertainty arising from the use of the completion procedure is discussed and a recipe for constructing a corresponding probability distribution function is proposed.
In this paper, we consider the problem of learning models with a latent factor structure. The focus is to find what is possible and what is impossible if the usual strong factor condition is not imposed. We study the minimax rate and adaptivity issues in two problems: pure factor models and panel regression with interactive fixed effects. For pure factor models, if the number of factors is known, we develop adaptive estimation and inference procedures that attain the minimax rate. However, when the number of factors is not specified a priori, we show that there is a tradeoff between validity and efficiency: any confidence interval that has uniform validity for arbitrary factor strength has to be conservative; in particular its width is bounded away from zero even when the factors are strong. Conversely, any data-driven confidence interval that does not require as an input the exact number of factors (including weak ones) and has shrinking width under strong factors does not have uniform coverage and the worst-case coverage probability is at most 1/2. For panel regressions with interactive fixed effects, the tradeoff is much better. We find that the minimax rate for learning the regression coefficient does not depend on the factor strength and propose a simple estimator that achieves this rate. However, when weak factors are allowed, uncertainty in the number of factors can cause a great loss of efficiency although the rate is not affected. In most cases, we find that the strong factor condition (and/or exact knowledge of number of factors) improves efficiency, but this condition needs to be imposed by faith and cannot be verified in data for inference purposes.
Recent work has presented intriguing results examining the knowledge contained in language models (LM) by having the LM fill in the blanks of prompts such as Obama is a _ by profession. These prompts are usually manually created, and quite possibly sub-optimal; another prompt such as Obama worked as a _ may result in more accurately predicting the correct profession. Because of this, given an inappropriate prompt, we might fail to retrieve facts that the LM does know, and thus any given prompt only provides a lower bound estimate of the knowledge contained in an LM. In this paper, we attempt to more accurately estimate the knowledge contained in LMs by automatically discovering better prompts to use in this querying process. Specifically, we propose mining-based and paraphrasing-based methods to automatically generate high-quality and diverse prompts, as well as ensemble methods to combine answers from different prompts. Extensive experiments on the LAMA benchmark for extracting relational knowledge from LMs demonstrate that our methods can improve accuracy from 31.1% to 39.6%, providing a tighter lower bound on what LMs know. We have released the code and the resulting LM Prompt And Query Archive (LPAQA) at https://github.com/jzbjyb/LPAQA.
Using the perturbative QCD amplitudes for $Bto pipi$ and $Bto Kpi$, we have performed an extensive study of the parameter space where the theoretical predictions for the branching ratios are consistent with recent experimental data. From this allowed range of parameter space, we predict the mixing induced CP asymmetry for $B to pi^+pi^-$ with about 11% uncertainty and the other CP asymmetries for $Bto pipi$, $Kpi$ with 40% ~ 47% uncertainty. These errors are expected to be reduced as we restrict the parameter space by studying other decay modes and by further improvements in the experimental data.
The estimated stellar masses of galaxies are widely used to characterize how the galaxy population evolves over cosmic time. If stellar masses can be estimated in a robust manner, free from any bias, global diagnostics such as the stellar mass function can be used to constrain the physics of galaxy formation. We explore how galaxy stellar masses, estimated by fitting broad-band spectral energy distributions (SEDs) with stellar population models, can be biased as a result of commonly adopted assumptions for the star-formation and chemical enrichment histories, recycled fractions and dust attenuation curves of galaxies. We apply the observational technique of broad-band SED fitting to model galaxy SEDs calculated by the theoretical galaxy formation model GALFORM, isolating the effect of each of these assumptions. We find that, averaged over the entire galaxy population, the common assumption of exponentially declining star-formation histories does not adversely affect stellar mass estimation. We show that fixing the metallicity in SED fitting or using sparsely sampled metallicity grids can introduce mass dependent systematics into stellar mass estimates. We find that the common assumption of a star-dust geometry corresponding to a uniform foreground dust screen can cause the stellar masses of dusty model galaxies to be significantly underestimated. Finally, we show that stellar mass functions recovered by applying SED fitting to model galaxies at high redshift can differ significantly in both shape and normalization from the intrinsic mass functions predicted by a given model. Given these differences, our methodology of using stellar masses estimated from model galaxy SEDs offers a new, self-consistent way to compare model predictions with observations.
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