Reproducing pairs of measurable functions and partial inner product spaces

We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. More precisely, we examine the case where the defining measurable functions take their values in a partial inner product space (PIP spaces). Several examples, both discrete and continuous, are presented.Comment: 20 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1505.0418

Partial inner product spaces, metric operators and generalized hermiticity

Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is, the simplest case of a partial inner product space (PIP space). Next, we introduce several generalizations of the notion of similarity between operators and explore to what extend they preserve spectral properties. Then we apply some of the previous results to operators on a particular PIP space, namely, a scale of Hilbert spaces generated by a metric operator. Finally, we reformulate the notion of pseudo-hermitian operators in the preceding formalism.Comment: 23 pages, 4 figures (in LaTeX

Energy-based Self-attentive Learning of Abstractive Communities for Spoken Language Understanding

Abstractive community detection is an important spoken language understanding task, whose goal is to group utterances in a conversation according to whether they can be jointly summarized by a common abstractive sentence. This paper provides a novel approach to this task. We first introduce a neural contextual utterance encoder featuring three types of self-attention mechanisms. We then train it using the siamese and triplet energy-based meta-architectures. Experiments on the AMI corpus show that our system outperforms multiple energy-based and non-energy based baselines from the state-of-the-art. Code and data are publicly available.Comment: Update baseline

Compositional abstraction and safety synthesis using overlapping symbolic models

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems

A global model for the combustion of gas mixtures released from forest fuels

International audienc

Wavelets on the Two-Sphere and Other Conic Sections

We survey the construction of the continuous wavelet transform (CWT) on the twosphere. Then we discuss the discretization of the spherical CWT, obtaining various types of discrete frames. Finally, we give some indications on the construction of a CWT on other conic section

Classification of General Sequences by Frame-Related Operators

This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We investigate these operators for arbitrary sequences, which in general lead to possibly unbounded operators. We characterize various classes of sequences in terms of these operators and vice-versa. Finally, we classify these sequences by operators applied on orthonormal bases

Sol–gel processing and characterization of (RE-Y)-zirconia powders for thermal barrier coatings

The effect of doping on the structural, morphological and thermal properties of ZrO2–XO1.5 (X=Y, La, Sm, Er) solid solutions for thermal barrier (TBC) applications was investigated. Oxide powders of various compositions from 9.7 to 40 mol% XO1.5 (X=Y, La, Sm, Er) were synthesised by the sol–gel route. The structural analysis of the powders was performed using X-ray diffraction analysis coupled with Rietveld refinements and the measurement of their specific surface area with the BET method. For each rare earth dopant, the morphology of the powders varies from monoliths to agglomerates of thinner particles when the doping amount increases. In order to determine the specific heat, the thermal diffusivity at room temperature and the thermal expansion coefficient of some selected compositions, DSC, laser thermal diffusivity and hightemperature dilatometry measurements were performed on samples densified by Spark Plasma Sintering. Working thermal characterisation indicated that zirconia doped with 30 mol% SmO1.5 and ErO1.5 have better insulation properties and a lower thermal expansion coefficient than our reference YSZ ceramic. These various compositions are very promising for the elaboration of multilayer TBCs by the sol–gel process