Robust stabilization of chained systems via hybrid control

Published versio

XLIII. Extract from a memoir entitled "Considerations on colours, and several of their singular appearances." Read in the mathematical and physical class of the French National Institute, Ventose 13, an 13

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A latitude-dependent wind model for Mira's cometary head

We present a 3D numerical simulation of the recently discovered cometary structure produced as Mira travels through the galactic ISM. In our simulation, we consider that Mira ejects a steady, latitude-dependent wind, which interacts with a homogeneous, streaming environment. The axisymmetry of the problem is broken by the lack of alignment between the direction of the relative motion of the environment and the polar axis of the latitude-dependent wind. With this model, we are able to produce a cometary head with a ``double bow shock'' which agrees well with the structure of the head of Mira's comet. We therefore conclude that a time-dependence in the ejected wind is not required for reproducing the observed double bow shock.Comment: 4 pages, 4 figures, accepted for publication in ApJ

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

Time series prediction via aggregation : an oracle bound including numerical cost

We address the problem of forecasting a time series meeting the Causal Bernoulli Shift model, using a parametric set of predictors. The aggregation technique provides a predictor with well established and quite satisfying theoretical properties expressed by an oracle inequality for the prediction risk. The numerical computation of the aggregated predictor usually relies on a Markov chain Monte Carlo method whose convergence should be evaluated. In particular, it is crucial to bound the number of simulations needed to achieve a numerical precision of the same order as the prediction risk. In this direction we present a fairly general result which can be seen as an oracle inequality including the numerical cost of the predictor computation. The numerical cost appears by letting the oracle inequality depend on the number of simulations required in the Monte Carlo approximation. Some numerical experiments are then carried out to support our findings

Understanding the local structure of Eu3+- and Y3+-stabilized zirconia: insights from luminescence and X-ray absorption spectroscopic investigations

This study combines bulk structural and spectroscopic investigations of Eu$^{3+}$- or Y$^{3+}$/Eu$^{3+}$ co-doped tetragonal and cubic zirconia polymorphs to gain an indepth understanding of the solid solution formation process. Our bulk structural characterizations show that the dopant is homogenously distributed in the ZrO$_{2}$ host structure resulting in an increase of the bulk symmetry with increasing dopant substitution (from 8 to 26 mol%). The local site symmetry around the Eu$^{3+}$ dopant, however, determined with luminescence spectroscopy (TRLFS), remains low in all samples. Results obtained with X-ray pair distribution function and X-ray absorption spectroscopy show that the average coordination environment in the stabilized zirconia structures remains practically unchanged. Despite this very constant average dopant environment, siteselective TRLFS data show the presence of three nonequivalent Eu$^{3+}$ environments in the ZrO$_{2}$ solid structures. These Eu$^{3+}$ environments are assumed to arise from Eu$^{3+}$ incorporation at superficial sites, which increase in abundance as the size of the crystallites decrease, and incorporation on two bulk sites differing in the location of the oxygen vacancies with respect to the dopant cation

Detecting modules in dense weighted networks with the Potts method

We address the problem of multiresolution module detection in dense weighted networks, where the modular structure is encoded in the weights rather than topology. We discuss a weighted version of the q-state Potts method, which was originally introduced by Reichardt and Bornholdt. This weighted method can be directly applied to dense networks. We discuss the dependence of the resolution of the method on its tuning parameter and network properties, using sparse and dense weighted networks with built-in modules as example cases. Finally, we apply the method to data on stock price correlations, and show that the resulting modules correspond well to known structural properties of this correlation network.Comment: 14 pages, 6 figures. v2: 1 figure added, 1 reference added, minor changes. v3: 3 references added, minor change