20 research outputs found
Averaging of density kernel estimators
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method relies on minimizing an easily tractable approximation of the integrated square error of the combination. It provides, at a small computational cost, a final solution that improves on the initial estimators in most cases. The average estimator is proved to be asymptotically as efficient as the best possible combination (the oracle), with an error term that decreases faster than the minimax rate obtained with separated learning and validation samples. The performances are tested numerically, with results that compare favorably to other existing procedures in terms of mean integrated square errors
SOI-based micro-mechanical terahertz detector operating at room-temperature
We present a micro-mechanical terahertz (THz) detector fabricated on a
silicon on insulator (SOI) substrate and operating at room-temperature. The
device is based on a U-shaped cantilever of micrometric size, on top of which
two aluminum half-wave dipole antennas are deposited. This produces an
absorption extending over the THz frequency range. Due to the
different thermal expansion coefficients of silicon and aluminum, the absorbed
radiation induces a deformation of the cantilever, which is read out optically
using a m laser diode. By illuminating the detector with an amplitude
modulated, 2.5 THz quantum cascade laser, we obtain, at room-temperature and
atmospheric pressure, a responsivity of pm/W for the
fundamental mechanical bending mode of the cantilever. This yields an
noise-equivalent-power of 20 nW/Hz at 2.5THz. Finally, the low
mechanical quality factor of the mode grants a broad frequency response of
approximately 150kHz bandwidth, with a response time of s
Cell shape analysis of random tessellations based on Minkowski tensors
To which degree are shape indices of individual cells of a tessellation
characteristic for the stochastic process that generates them? Within the
context of stochastic geometry and the physics of disordered materials, this
corresponds to the question of relationships between different stochastic
models. In the context of image analysis of synthetic and biological materials,
this question is central to the problem of inferring information about
formation processes from spatial measurements of resulting random structures.
We address this question by a theory-based simulation study of shape indices
derived from Minkowski tensors for a variety of tessellation models. We focus
on the relationship between two indices: an isoperimetric ratio of the
empirical averages of cell volume and area and the cell elongation quantified
by eigenvalue ratios of interfacial Minkowski tensors. Simulation data for
these quantities, as well as for distributions thereof and for correlations of
cell shape and volume, are presented for Voronoi mosaics of the Poisson point
process, determinantal and permanental point processes, and Gibbs hard-core and
random sequential absorption processes as well as for Laguerre tessellations of
polydisperse spheres and STIT- and Poisson hyperplane tessellations. These data
are complemented by mechanically stable crystalline sphere and disordered
ellipsoid packings and area-minimising foam models. We find that shape indices
of individual cells are not sufficient to unambiguously identify the generating
process even amongst this limited set of processes. However, we identify
significant differences of the shape indices between many of these tessellation
models. Given a realization of a tessellation, these shape indices can narrow
the choice of possible generating processes, providing a powerful tool which
can be further strengthened by density-resolved volume-shape correlations.Comment: Chapter of the forthcoming book "Tensor Valuations and their
Applications in Stochastic Geometry and Imaging" in Lecture Notes in
Mathematics edited by Markus Kiderlen and Eva B. Vedel Jense
Practical simulation and estimation for Gibbs Delaunay-Voronoi tessellations with geometric hardcore interaction
General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed as extensions of Ord's process, are considered. The interaction may occur on each cell of the tessellation and between neighbour cells. The tessellation may also be subjected to a geometric hardcore interaction, forcing the cells not to be too large, too small, or too flat. This setting, natural for applications, introduces some theoretical difficulties since the interaction is not necessarily hereditary. Mathematical results available for studying these models are reviewed and further outcomes are provided. They concern the existence, the simulation and the estimation of such tessellations. Based on these results, tools to handle these objects in practice are presented: how to simulate them, estimate their parameters and validate the fitted model. Some examples of simulated tessellations are studied in detail.Gibbs point process Random tessellations Stochastic geometry Pseudo-likelihood estimator Spatial statistics