Level-Based Analysis of the Population-Based Incremental Learning Algorithm

The Population-Based Incremental Learning (PBIL) algorithm uses a convex combination of the current model and the empirical model to construct the next model, which is then sampled to generate offspring. The Univariate Marginal Distribution Algorithm (UMDA) is a special case of the PBIL, where the current model is ignored. Dang and Lehre (GECCO 2015) showed that UMDA can optimise LeadingOnes efficiently. The question still remained open if the PBIL performs equally well. Here, by applying the level-based theorem in addition to Dvoretzky--Kiefer--Wolfowitz inequality, we show that the PBIL optimises function LeadingOnes in expected time $\mathcal{O}(n\lambda \log \lambda + n^2)$ for a population size $\lambda = \Omega(\log n)$, which matches the bound of the UMDA. Finally, we show that the result carries over to BinVal, giving the fist runtime result for the PBIL on the BinVal problem.Comment: To appea

Enabling Gaia observations of naked-eye stars

The ESA Gaia space astrometry mission will perform an all-sky survey of stellar objects complete in the nominal magnitude range G = [6.0 - 20.0]. The stars with G lower than 6.0, i.e. those visible to the unaided human eye, would thus not be observed by Gaia. We present an algorithm configuration for the Gaia on-board autonomous object observation system that makes it possible to observe very bright stars with G = [2.0-6.0). Its performance has been tested during the in-orbit commissioning phase achieving an observation completeness of ~94% at G = 3 - 5.7 and ~75% at G = 2 - 3. Furthermore, two targeted observation techniques for data acquisition of stars brighter than G = 2.0 were tested. The capabilities of these two techniques and the results of the in-flight tests are presented. Although the astrometric performance for stars with G lower than 6.0 has yet to be established, it is clear that several science cases will benefit from the results of the work presented here.Comment: 12 pages, 5 figures. To appear in the proceedings of the SPIE 9143, 2014 Astronomical Instrumentation and Telescopes conferenc

Polynomial growth of volume of balls for zero-entropy geodesic systems

The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{pol}$} and the {\em weak polynomial entropy $h_{pol}^*$}. Both are infinite when the topological entropy is positive and they satisfy $h_{pol}^*\leq h_{pol}$. We first prove that the growth rate of the volume of balls is bounded above by means of the strong polynomial entropy and we show that for the flat torus this inequality becomes an equality. We then study the explicit example of the torus of revolution for which we can give an exact asymptotic equivalent of the growth rate of volume of balls, which we relate to the weak polynomial entropy.Comment: 22 page

A linear CO chemistry parameterization in a chemistry-transport model: evaluation and application to data assimilation

This paper presents an evaluation of a new linear parameterization valid for the troposphere and the stratosphere, based on a first order approximation of the carbon monoxide (CO) continuity equation. This linear scheme (hereinafter noted LINCO) has been implemented in the 3-D Chemical Transport Model (CTM) MOCAGE (MOdèle de Chimie Atmospherique Grande Echelle). First, a one and a half years of LINCO simulation has been compared to output obtained from a detailed chemical scheme output. The mean differences between both schemes are about ±25 ppbv (part per billion by volume) or 15% in the troposphere and ±10 ppbv or 100% in the stratosphere. Second, LINCO has been compared to diverse observations from satellite instruments covering the troposphere (Measurements Of Pollution In The Troposphere: MOPITT) and the stratosphere (Microwave Limb Sounder: MLS) and also from aircraft (Measurements of ozone and water vapour by Airbus in-service aircraft: MOZAIC programme) mostly flying in the upper troposphere and lower stratosphere (UTLS). In the troposphere, the LINCO seasonal variations as well as the vertical and horizontal distributions are quite close to MOPITT CO observations. However, a bias of ~−40 ppbv is observed at 700 Pa between LINCO and MOPITT. In the stratosphere, MLS and LINCO present similar large-scale patterns, except over the poles where the CO concentration is underestimated by the model. In the UTLS, LINCO presents small biases less than 2% compared to independent MOZAIC profiles. Third, we assimilated MOPITT CO using a variational 3D-FGAT (First Guess at Appropriate Time) method in conjunction with MOCAGE for a long run of one and a half years. The data assimilation greatly improves the vertical CO distribution in the troposphere from 700 to 350 hPa compared to independent MOZAIC profiles. At 146 hPa, the assimilated CO distribution is also improved compared to MLS observations by reducing the bias up to a factor of 2 in the tropics. This study confirms that the linear scheme is able to simulate reasonably well the CO distribution in the troposphere and in the lower stratosphere. Therefore, the low computing cost of the linear scheme opens new perspectives to make free runs and CO data assimilation runs at high resolution and over periods of several years

Adaptive density estimation for stationary processes

We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We suppose that the process is either $\beta$ or $\tau$-mixing. We provide a model selection procedure based on a generalization of Mallows' $C_p$ and we prove oracle inequalities for the selected estimator under a few prior assumptions on the collection of models and on the mixing coefficients. We prove that our estimator is adaptive over a class of Besov spaces, namely, we prove that it achieves the same rates of convergence as in the i.i.d framework

Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss-Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performence of the proposed method for these problems is illustrated in numerical examples

Impact of diet in shaping gut microbiota revealed by a comparative study in children from Europe and Rural Africa

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