Nonlinear Poisson autoregression

We study statistical properties of a class of non-linear models for regression analysis of count time series. Under mild conditions, it is shown that a perturbed version of the model is geometrically ergodic and possesses moments of any order. This result turns out to be instrumental on deriving large sample properties of the maximum likelihood estimators of the regression parameters. The theory is illustrated with examples.     

On the hyperreflexivity of power partial isometries

Necessary and sufficient conditions for hyperreflexivity of completely non-unitary power partial isometries are given.     

Intra-cavity generation of superpositions of Laguerre–Gaussian beams

In this paper we demonstrate experimentally the intra-cavity generation of a coherent superposition of Laguerre–Gaussian modes of zero radial order but opposite azimuthal order. The superposition is created with a simple intra-cavity stop that creates equal losses for the two azimuthal modes, and we show that by adjustment of the stop we can produce modes up to azimuthal order 8. The fact that we have a coherent superposition rather than an incoherent superposition is verified by intensity measurements, propagation measurements and a decomposition of the field by an inner product executed on a phase-only spatial light modulator. Such fields have relevance in quantum information and optical trapping.     

Uncertainty quantification in a chemical system using error estimate-based mesh adaption

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.