Localization in 1D non-parametric latent space models from pairwise affinities

We consider the problem of estimating latent positions in a one-dimensional torus from pairwise affinities. The observed affinity between a pair of items is modeled as a noisy observation of a function $f(x^*_{i},x^*_{j})$ of the latent positions $x^*_{i},x^*_{j}$ of the two items on the torus. The affinity function $f$ is unknown, and it is only assumed to fulfill some shape constraints ensuring that $f(x,y)$ is large when the distance between $x$ and $y$ is small, and vice-versa. This non-parametric modeling offers a good flexibility to fit data. We introduce an estimation procedure that provably localizes all the latent positions with a maximum error of the order of $\sqrt{\log(n)/n}$, with high-probability. This rate is proven to be minimax optimal. A computationally efficient variant of the procedure is also analyzed under some more restrictive assumptions. Our general results can be instantiated to the problem of statistical seriation, leading to new bounds for the maximum error in the ordering

Apport de la diffraction des rayons X in situ à l'étude de l'oxydation des aciers à haute température (Influence des différents modes d'introduction de l'yttrium sur l'oxydation d'un alliage FeCrAl modèle, Rôle du titane et du niobium sur la tenue à la corrosion d'aciers ferritiques, Effets de la nitruration sur l'oxydation du 304)

CLERMONT FD-BCIU Sci.et Tech. (630142101) / SudocSudocFranceF

Détermination des contraintes résiduelles par diffraction des rayons X in situ. Comparaison avec les analyses RAMAN

National audienc

Localization in 1D non-parametric latent space models from pairwise affinities

We consider the problem of estimating latent positions in a one-dimensional torus from pairwise affinities. The observed affinity between a pair of items is modeled as a noisy observation of a function f (x * i , x * j) of the latent positions x * i , x * j of the two items on the torus. The affinity function f is unknown, and it is only assumed to fulfill some shape constraints ensuring that f (x, y) is large when the distance between x and y is small, and vice-versa. This non-parametric modeling offers a good flexibility to fit data. We introduce an estimation procedure that provably localizes all the latent positions with a maximum error of the order of log(n)/n, with highprobability. This rate is proven to be minimax optimal. A computationally efficient variant of the procedure is also analyzed under some more restrictive assumptions. Our general results can be instantiated to the problem of statistical seriation, leading to new bounds for the maximum error in the ordering

Influence of atmosphere on high‐temperature oxidation of Fe‐Cr‐Si model alloy

International audienceThe aim of this work is to show the influence of the gaseous environment on the ferritic Fe-Cr-Si model alloy oxidation during 70 h, at 900 °C and 950 °C. Two different atmospheres have been used: air or nitrogen containing 5 Vol.% hydrogen (N 2-5%H 2). After air oxidation, a non-adherent chromia scale formed. In the N 2-5%H 2 gaseous environment, it clearly appears that silicon segregation near the internal scale-metal interface is favoured. In this low oxygen containing gas, adherent chromia and silica scales have been formed. Silica subscale associated to an adherent chromia scale obtained in low oxygen conditions are a good protection barrier against carburisation

Effect of Niobium as Alloying Element on Austenitic Stainless Steels Oxidation

International audienceThis work shows the influence of sodium carbonate coatings on the austenitic AISI 330 (Fe-35Ni-19Cr-1.3Si) oxidation during 48 h, at 900 °C. The N2-5vol.% H2 gaseous environment was used to simulate industrial heat treatment conditions. Silica scale formation is promoted by low oxygen containing gaseous environments and the high alloy silicon content. On this alloy an amorphous silica scale is formed after the blank material oxidation. It indicates that silicon is free to diffuse in the alloy and forms a silica scale at the internal interface. On Na2CO3 coated specimens, no silica scale is formed. Then, sodium combines with silicon to form amorphous glass particles. A comparison has been performed with results obtained on a AISI 330Cb niobium containing alloy in the same oxidizing conditions. It is then concluded that sodium carbonate coatings could only favours silica formation on niobium containing alloy due to a reaction between sodium and niobium

Influence of NaOH and CaCl2 deposit on high temperature oxidation of Fe-Cr-Si model alloy.

International audienc

Effet de la vapeur d’eau sur la détermination des contraintes par diffraction des rayons X in situ dans la zircone moniclinique

National audienc

Influence de la vapeur d'eau sur l'oxydation du Zircaloy-4 à 500°C. Détermination des contraintes de croissance par diffraction des rayons X in situ.

International audienc