Search results for "Functional analysis"
showing 10 items of 1059 documents
The central limit theorem for linear eigenvalue statistics of the sum of independent random matrices of rank one
2014
International audience
Design rules for nonlinear spectral compression in optical fibers
2016
International audience; We present comprehensive design rules to optimize the process of spectral compression arising from nonlinear pulse propagation in an optical fiber. Extensive numerical simulations are used to predict the performance characteristics of the process as well as to identify the optimal operational conditions within the space of system parameters. It is shown that the group-velocity dispersion of the fiber is not detrimental and, in fact, helps achieve optimum compression. We also demonstrate that near-transform-limited rectangular and parabolic pulses can be generated in the region of optimum compression.
Quantizations from reproducing kernel spaces
2012
Abstract The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of L 2 ( C , d 2 z / π ) based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family depending on a nonnegative parameter s . We examine some interesting issues, mainly related to CS quantization, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules. The question of mathematical and physical equivalences between the s -dependent quantizations is also considered.
Showing the Invisible: The Economic Cycle of Stone Tools
2023
This contribution takes place in a broader theme, that of “the invisible economy of recyclable materials”. It aims to illustrate the phenomena of recovery of materials from lithic tools and their consequences. The classification of tools by material, although classic, is not relevant from a technical point of view. The material of a tool, in particular its mechanical properties, is to be taken into consideration in its technical analysis, but it cannot constitute a determining criterion in a classification system. Function should come first, as most functional categories use multiple materials. The most striking example, if one can say so, is that of the striking supports, where one finds, …
Optimal recovery of a radiating source with multiple frequencies along one line
2020
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.
Learning-based multiresolution transforms with application to image compression
2013
In Harten's framework, multiresolution transforms are defined by predicting finer resolution levels of information from coarser ones using an operator, called prediction operator, and defining details (or wavelet coefficients) that are the difference between the exact and predicted values. In this paper we use tools of statistical learning in order to design a more accurate prediction operator in this framework based on a training sample, resulting in multiresolution decompositions with enhanced sparsity. In the case of images, we incorporate edge detection techniques in the design of the prediction operator in order to avoid Gibbs phenomenon. Numerical tests are presented showing that the …
Simplified model of mean double step (MDS) in human body movement
2012
In this paper we present a simplified and useful model of the human body movement based on the full gait cycle description, called the Mean Double Step (MDS). It enables the parameterization and simplification of the human movement. Furthermore it allows a description of the gait cycle by providing standardized estimators to transform the gait cycle into a periodical movement process. Moreover the method of simplifying the MDS model and its compression are demonstrated. The simplification is achieved by reducing the number of bars of the spectrum and I or by reducing the number of samples describing the MDS both in terms of reducing their computational burden and their resources for the dat…
An Efficient Method for the Visualization of Spectral Images Based on a Perception-Oriented Spectrum Segmentation
2010
We propose a new method for the visualization of spectral images. It involves a perception-based spectrum segmentation using an adaptable thresholding of the stretched CIE standard observer colormatching functions. This allows for an underlying removal of irrelevant channels, and, consequently, an alleviation of the computational burden of further processings. Principal Components Analysis is then used in each of the three segments to extract the Red, Green and Blue primaries for final visualization. A comparison framework using two different datasets shows the efficiency of the proposed method.
A coupled cluster calculation of the spectrum of urea
2001
Several coupled cluster methods have been used to compute the vertical excitation energies and oscillator strengths of the lowest singlet states of urea. Except for one excitation, the results are in good agreement with experiment, but previously non-detected transitions have been found.
The Interaction of State Transitions and Chlororespiration in the Xanthophycean Alga Pleurochloris Meiringensis
1990
Wavelength dependent State I-State II-transitions have been shown to exist in chlorophytes and red algae. Little is known about the regulation of energy distribution between the photosystems of chlorophyll c-containing plants. Previously it was shown that in the xanthophycean alga Pleurochloris meiringensis two states of energy distribution could be established [l]: In state “D” light is preferentially transferred to PS II, whereas in state “L” PS I is favoured. These state regulations strictly depend on the intensity and not on the wavelength of prei1lumination. In this paper we give new evidence that chlororespiration is involved in the mechanism of state “L”-state “D”-transitions.