1,166 research outputs found
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 for a population size , 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
Aubry sets vs Mather sets in two degrees of freedom
We study autonomous Tonelli Lagrangians on closed surfaces. We aim to clarify
the relationship between the Aubry set and the Mather set, when the latter
consists of periodic orbits which are not fixed points. Our main result says
that in that case the Aubry set and the Mather set almost always coincide.Comment: Revised and expanded version. New proof of Lemma 2.3 (formerly Lemma
14
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 } and the {\em weak polynomial entropy }. Both are
infinite when the topological entropy is positive and they satisfy
. 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 of a stationary
process . We suppose that the process is either or
-mixing. We provide a model selection procedure based on a generalization
of Mallows' 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
Level set based eXtended finite element modelling of the response of fibrous networks under hygroscopic swelling
Materials like paper, consisting of a network of natural fibres, exposed to
variations in moisture, undergo changes in geometrical and mechanical
properties. This behaviour is particularly important for understanding the
hygro-mechanical response of sheets of paper in applications like digital
printing. A two-dimensional microstructural model of a fibrous network is
therefore developed to upscale the hygro-expansion of individual fibres,
through their interaction, to the resulting overall expansion of the network.
The fibres are modelled with rectangular shapes and are assumed to be perfectly
bonded where they overlap. For realistic networks the number of bonds is large
and the network is geometrically so complex that discretizing it by
conventional, geometry-conforming, finite elements is cumbersome. The
combination of a level-set and XFEM formalism enables the use of regular,
structured grids in order to model the complex microstructural geometry. In
this approach, the fibres are described implicitly by a level-set function. In
order to represent the fibre boundaries in the fibrous network, an XFEM
discretization is used together with a Heaviside enrichment function. Numerical
results demonstrate that the proposed approach successfully captures the
hygro-expansive properties of the network with fewer degrees of freedom
compared to classical FEM, preserving desired accuracy.Comment: 27 pages, 22 figures, 4 tables, J. Appl. Mech. June 19, 202
Combined assimilation of IASI and MLS observations to constrain tropospheric and stratospheric ozone in a global chemical transport model
Accurate and temporally resolved fields of free-troposphere ozone are of
major importance to quantify the intercontinental transport of pollution and
the ozone radiative forcing. We consider a global chemical transport model
(MOdèle de Chimie Atmosphérique à Grande Échelle, MOCAGE) in
combination with a linear ozone chemistry scheme to examine the impact of
assimilating observations from the Microwave Limb Sounder (MLS) and the
Infrared Atmospheric Sounding Interferometer (IASI). The assimilation of the
two instruments is performed by means of a variational algorithm (4D-VAR) and
allows to constrain stratospheric and tropospheric ozone simultaneously. The
analysis is first computed for the months of August and November 2008 and
validated against ozonesonde measurements to verify the presence of
observations and model biases. Furthermore, a longer analysis of 6 months
(July–December 2008) showed that the combined assimilation of MLS and IASI is
able to globally reduce the uncertainty (root mean square error, RMSE) of the
modeled ozone columns from 30 to 15% in the
upper troposphere/lower stratosphere (UTLS, 70–225 hPa). The assimilation of
IASI tropospheric ozone observations (1000–225 hPa columns, TOC – tropospheric O<sub>3</sub> column)
decreases the RMSE of the model from 40 to 20% in the tropics
(30° S–30° N), whereas it is not effective at higher latitudes.
Results are confirmed by a comparison with additional ozone data sets like the
Measurements of OZone and wAter vapour by aIrbus in-service airCraft (MOZAIC)
data, the Ozone Monitoring Instrument (OMI) total ozone columns and several
high-altitude surface measurements. Finally, the analysis is found to be
insensitive to the assimilation parameters. We conclude that the combination
of a simplified ozone chemistry scheme with frequent satellite observations
is a valuable tool for the long-term analysis of stratospheric and
free-tropospheric ozone
Sparsity and Incoherence in Compressive Sampling
We consider the problem of reconstructing a sparse signal from a
limited number of linear measurements. Given randomly selected samples of
, where is an orthonormal matrix, we show that minimization
recovers exactly when the number of measurements exceeds where is the number of
nonzero components in , and is the largest entry in properly
normalized: . The smaller ,
the fewer samples needed.
The result holds for ``most'' sparse signals supported on a fixed (but
arbitrary) set . Given , if the sign of for each nonzero entry on
and the observed values of are drawn at random, the signal is
recovered with overwhelming probability. Moreover, there is a sense in which
this is nearly optimal since any method succeeding with the same probability
would require just about this many samples
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