Understanding exoplanet formation, structure and evolution in 2010

In this short review, we summarize our present understanding (and non-understanding) of exoplanet formation, structure and evolution, in the light of the most recent discoveries. Recent observations of transiting massive brown dwarfs seem to remarkably confirm the predicted theoretical mass-radius relationship in this domain. This mass-radius relationship provides, in some cases, a powerful diagnostic to distinguish planets from brown dwarfs of same mass, as for instance for Hat-P-20b. If confirmed, this latter observation shows that planet formation takes place up to at least 8 Jupiter masses. Conversely, observations of brown dwarfs down to a few Jupiter masses in young, low-extinction clusters strongly suggest an overlapping mass domain between (massive) planets and (low-mass) brown dwarfs, i.e. no mass edge between these two distinct (in terms of formation mechanism) populations. At last, the large fraction of heavy material inferred for many of the transiting planets confirms the core-accretion scenario as been the dominant one for planet formation.Comment: Invited review, IAU Symposium No. 276, The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolutio

Possible climates on terrestrial exoplanets

What kind of environment may exist on terrestrial planets around other stars? In spite of the lack of direct observations, it may not be premature to speculate on exoplanetary climates, for instance to optimize future telescopic observations, or to assess the probability of habitable worlds. To first order, climate primarily depends on 1) The atmospheric composition and the volatile inventory; 2) The incident stellar flux; 3) The tidal evolution of the planetary spin, which can notably lock a planet with a permanent night side. The atmospheric composition and mass depends on complex processes which are difficult to model: origins of volatile, atmospheric escape, geochemistry, photochemistry. We discuss physical constraints which can help us to speculate on the possible type of atmosphere, depending on the planet size, its final distance for its star and the star type. Assuming that the atmosphere is known, the possible climates can be explored using Global Climate Models analogous to the ones developed to simulate the Earth as well as the other telluric atmospheres in the solar system. Our experience with Mars, Titan and Venus suggests that realistic climate simulators can be developed by combining components like a "dynamical core", a radiative transfer solver, a parametrisation of subgrid-scale turbulence and convection, a thermal ground model, and a volatile phase change code. On this basis, we can aspire to build reliable climate predictors for exoplanets. However, whatever the accuracy of the models, predicting the actual climate regime on a specific planet will remain challenging because climate systems are affected by strong positive destabilizing feedbacks (such as runaway glaciations and runaway greenhouse effect). They can drive planets with very similar forcing and volatile inventory to completely different states.Comment: In press, Proceedings of the Royal Society A 31 pages, 6 figure

A nonparametric model-based estimator for the cumulative distribution function of a right censored variable in a finite population

In survey analysis, the estimation of the cumulative distribution function (cdf) is of great interest: it allows for instance to derive quantiles estimators or other non linear parameters derived from the cdf. We consider the case where the response variable is a right censored duration variable. In this framework, the classical estimator of the cdf is the Kaplan-Meier estimator. As an alternative, we propose a nonparametric model-based estimator of the cdf in a finite population. The new estimator uses auxiliary information brought by a continuous covariate and is based on nonparametric median regression adapted to the censored case. The bias and variance of the prediction error of the estimator are estimated by a bootstrap procedure adapted to censoring. The new estimator is compared by model-based simulations to the Kaplan-Meier estimator computed with the sampled individuals: a significant gain in precision is brought by the new method whatever the size of the sample and the censoring rate. Welfare duration data are used to illustrate the new methodology.Comment: 18 pages, 5 figure

Maxwell demon in Granular gas: a new kind of bifurcation? The hypercritical bifurcation

This paper starts with the investigation of the behaviour of a set of two subsystems which are able to exchange some internal quantity according to a given flux function. It is found that this sytem exhibit a bifurcation when the flux passes through a maximum and that its kind (super-critical/sub-critical) depends on the dissymmetry of the flux function near the maximum. It is also found a new kind of bifurcation when the flux function is symmetric: we call it hypercritical bifurcation because it generates much stronger fluctuations than the super-critical one. The effect of a white noise is then investigated. We show that an experimental set-up, leading to the Maxwell demon in granular gas, displays all these kinds of bifurcation, just by changing the parameters of excitation. It means that this system is much less simple as it was thought.Comment: 19 pages, 10 figure

Cluster-Aided Mobility Predictions

Predicting the future location of users in wireless net- works has numerous applications, and can help service providers to improve the quality of service perceived by their clients. The location predictors proposed so far estimate the next location of a specific user by inspecting the past individual trajectories of this user. As a consequence, when the training data collected for a given user is limited, the resulting prediction is inaccurate. In this paper, we develop cluster-aided predictors that exploit past trajectories collected from all users to predict the next location of a given user. These predictors rely on clustering techniques and extract from the training data similarities among the mobility patterns of the various users to improve the prediction accuracy. Specifically, we present CAMP (Cluster-Aided Mobility Predictor), a cluster-aided predictor whose design is based on recent non-parametric bayesian statistical tools. CAMP is robust and adaptive in the sense that it exploits similarities in users' mobility only if such similarities are really present in the training data. We analytically prove the consistency of the predictions provided by CAMP, and investigate its performance using two large-scale datasets. CAMP significantly outperforms existing predictors, and in particular those that only exploit individual past trajectories

Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity

We report an order-N approach to compute the Kubo Hall conductivity for disorderd two-dimensional systems reaching tens of millions of orbitals, and realistic values of the applied external magnetic fields (as low as a few Tesla). A time-evolution scheme is employed to evaluate the Hall conductivity $\sigma_{xy}$ using a wavepacket propagation method and a continued fraction expansion for the computation of diagonal and off-diagonal matrix elements of the Green functions. The validity of the method is demonstrated by comparison of results with brute-force diagonalization of the Kubo formula, using (disordered) graphene as system of study. This approach to mesoscopic system sizes is opening an unprecedented perspective for so-called reverse engineering in which the available experimental transport data are used to get a deeper understanding of the microscopic structure of the samples. Besides, this will not only allow addressing subtle issues in terms of resistance standardization of large scale materials (such as wafer scale polycrystalline graphene), but will also enable the discovery of new quantum transport phenomena in complex two-dimensional materials, out of reach with classical methods.Comment: submitted PRB pape

Stable variable selection for right censored data: comparison of methods

The instability in the selection of models is a major concern with data sets containing a large number of covariates. This paper deals with variable selection methodology in the case of high-dimensional problems where the response variable can be right censored. We focuse on new stable variable selection methods based on bootstrap for two methodologies: the Cox proportional hazard model and survival trees. As far as the Cox model is concerned, we investigate the bootstrapping applied to two variable selection techniques: the stepwise algorithm based on the AIC criterion and the L1-penalization of Lasso. Regarding survival trees, we review two methodologies: the bootstrap node-level stabilization and random survival forests. We apply these different approaches to two real data sets. We compare the methods on the prediction error rate based on the Harrell concordance index and the relevance of the interpretation of the corresponding selected models. The aim is to find a compromise between a good prediction performance and ease to interpretation for clinicians. Results suggest that in the case of a small number of individuals, a bootstrapping adapted to L1-penalization in the Cox model or a bootstrap node-level stabilization in survival trees give a good alternative to the random survival forest methodology, known to give the smallest prediction error rate but difficult to interprete by non-statisticians. In a clinical perspective, the complementarity between the methods based on the Cox model and those based on survival trees would permit to built reliable models easy to interprete by the clinician.Comment: nombre de pages : 29 nombre de tableaux : 2 nombre de figures :