Inference of inhomogeneous clouds in an exoplaent atmosphere

We present new visible and infrared observations of the hot Jupiter Kepler-7b to determine its atmospheric properties. Our analysis allows us to (1) refine Kepler-7b's relatively large geometric albedo of Ag = 0.35 ± 0.02, (2) place upper limits on Kepler-7b thermal emission that remains undetected in both Spitzer bandpasses and (3) report a westward shift in the Kepler optical phase curve. We argue that Kepler-7b's visible flux cannot be due to thermal emission or Rayleigh scattering from H2 molecules. We therefore conclude that high altitude, optically reflective clouds located west from the substellar point are present in its atmosphere. We find that a silicate-based cloud composition is a possible candidate. Kepler-7b exhibits several properties that may make it particularly amenable to cloud formation in its upper atmosphere. These include a hot deep atmosphere that avoids a cloud cold trap, very low surface gravity to suppress cloud sedimentation, and a planetary equilibrium temperature in a range that allows for silicate clouds to potentially form in the visible atmosphere probed by Kepler. Our analysis does not only present evidence of optically thick clouds on Kepler-7b but also yields the first map of clouds in an exoplanet atmosphere.

Full and hat inductive definitions are equivalent in NBG

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA 0, those in second order set theory extending NBG (as well as those in n + 3-th order number theory extending the so-called Bernays−Gödel expansion of full n + 2-order number theory etc.) are. In this article, we establish the equivalence between Δ10\bf-LFP and Δ10\bf-FP, which assert the existence of a least and of a (not necessarily least) fixed point, respectively, for positive elementary operators (or between Δn+20\bf-LFP and Δn+20\bf-FP). Our proof also shows the equivalence between ID 1 and ^ID1, both of which are defined in the standard way but with the starting theory PA replaced by ZFC (or full n + 2-th order number theory with global well-ordering).

Forcing for hat inductive definitions in arithmetic

By forcing, we give a direct interpretation of inline image into Avigad's inline image. To the best of the author's knowledge, this is one of the simplest applications of forcing to “real problems”.

Mining the Ecosystem to Improve Type Inference For Dynamically Typed Languages

Dynamically typed languages lack information about the types of variables in the source code. Developers care about this information as it supports program comprehension. Ba- sic type inference techniques are helpful, but may yield many false positives or negatives. We propose to mine information from the software ecosys- tem on how frequently given types are inferred unambigu- ously to improve the quality of type inference for a single system. This paper presents an approach to augment existing type inference techniques by supplementing the informa- tion available in the source code of a project with data from other projects written in the same language. For all available projects, we track how often messages are sent to instance variables throughout the source code. Predictions for the type of a variable are made based on the messages sent to it. The evaluation of a proof-of-concept prototype shows that this approach works well for types that are sufficiently popular, like those from the standard librarie, and tends to create false positives for unpopular or domain specific types. The false positives are, in most cases, fairly easily identifiable. Also, the evaluation data shows a substantial increase in the number of correctly inferred types when compared to the non-augmented type inference.

Inference of evolutionary forces acting on human biological pathways

Because natural selection is likely to act on multiple genes underlying a given phenotypic trait, we study here the potential effect of ongoing and past selection on the genetic diversity of human biological pathways. We first show that genes included in gene sets are generally under stronger selective constraints than other genes and that their evolutionary response is correlated. We then introduce a new procedure to detect selection at the pathway level based on a decomposition of the classical McDonald–Kreitman test extended to multiple genes. This new test, called 2DNS, detects outlier gene sets and takes into account past demographic effects and evolutionary constraints specific to gene sets. Selective forces acting on gene sets can be easily identified by a mere visual inspection of the position of the gene sets relative to their two-dimensional null distribution. We thus find several outlier gene sets that show signals of positive, balancing, or purifying selection but also others showing an ancient relaxation of selective constraints. The principle of the 2DNS test can also be applied to other genomic contrasts. For instance, the comparison of patterns of polymorphisms private to African and non-African populations reveals that most pathways show a higher proportion of nonsynonymous mutations in non-Africans than in Africans, potentially due to different demographic histories and selective pressures.

A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions

In this article we study subsystems SIDᵥ of the theory ID₁ in which fixed point induction is restricted to properly stratified formulas.

An intercontinental comparison of chironomid palaeotemperature inference models: Europe vs North America

Chironomid-temperature inference models based on North American, European and combined surface sediment training sets were compared to assess the overall reliability of their predictions. Between 67 and 76 of the major chironomid taxa in each data set showed a unimodal response to July temperature, whereas between 5 and 22 of the common taxa showed a sigmoidal response. July temperature optima were highly correlated among the training sets, but the correlations for other taxon parameters such as tolerances and weighted averaging partial least squares (WA-PLS) and partial least squares (PLS) regression coefficients were much weaker. PLS, weighted averaging, WA-PLS, and the Modern Analogue Technique, all provided useful and reliable temperature inferences. Although jack-knifed error statistics suggested that two-component WA-PLS models had the highest predictive power, intercontinental tests suggested that other inference models performed better. The various models were able to provide good July temperature inferences, even where neither good nor close modern analogues for the fossil chironomid assemblages existed. When the models were applied to fossil Lateglacial assemblages from North America and Europe, the inferred rates and magnitude of July temperature changes varied among models. All models, however, revealed similar patterns of Lateglacial temperature change. Depending on the model used, the inferred Younger Dryas July temperature decrease ranged between 2.5 and 6°C.

GMM Based Inference with Standard Stratified Samples when the Aggregate Shares are Known

We show how to do efficient moment based inference using the generalized method of moments (GMM) when data is collected by standard stratified sampling and the maintained assumption is that the aggregate shares are known.

Polytomies and bayesian phylogenetic inference

Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short edge lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.

Moment Based Inference with Stratified Data

Many datasets used by economists and other social scientists are collected by stratified sampling. The sampling scheme used to collect the data induces a probability distribution on the observed sample that differs from the target or underlying distribution for which inference is to be made. If this effect is not taken into account, subsequent statistical inference can be seriously biased. This paper shows how to do efficient semiparametric inference in moment restriction models when data from the target population is collected by three widely used sampling schemes: variable probability sampling, multinomial sampling, and standard stratified sampling.

Polytomies and bayesian phylogenetic inference

Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short edge lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.