Search results for "basis"

Incoherent dispersive shocks in the spectral evolution of random waves

2013

We predict theoretically and numerically the existence of incoherent dispersive shock waves. They manifest themselves as an unstable singular behavior of the spectrum of incoherent waves that evolve in a noninstantaneous nonlinear environment. This phenomenon of "spectral wave breaking" develops in the weakly nonlinear regime of the random wave. We elaborate a general theoretical formulation of these incoherent objects on the basis of a weakly nonlinear statistical approach: a family of singular integro-differential kinetic equations is derived, which provides a detailed deterministic description of the incoherent dispersive shock wave phenomenon.

Spectrum cartography using adaptive radial basis functions: Experimental validation

2017

In this paper, we experimentally validate the functionality of a developed algorithm for spectrum cartography using adaptive Gaussian radial basis functions (RBF). The RBF are strategically centered around representative centroid locations in a machine learning context. We assume no prior knowledge about neither the power spectral densities (PSD) of the transmitters nor their locations. Instead, the received signal power at each location is estimated as a linear combination of different RBFs. The weights of the RBFs, their Gaussian decaying parameters and locations are jointly optimized using expectation maximization with a least squares loss function and a quadratic regularizer. The perfor…

MS-CASPT2 analysis of the UV thermochromism of octamethyltrisilane

2006

We interpret the reversal of the direction of the thermochromic shift of the first absorption band of peralkylated oligosilanes as the silicon chain is extended, based on multistate complete active space second-order perturbation theory (MS-CASPT2) calculations for octamethyltrisilane, Si3Me8. The observed shift is attributed to the effect of b1 distortions from ground state equilibrium geometry on vertical excited state energies and intensities. A generally contracted basis set of atomic natural orbitals (ANOs) at a ground state geometry optimized in the second-order Moller–Plesset perturbation theory (MP2) approximation with Dunning's correlation consistent triple-zeta basis set (cc-pVTZ)…

Nitrogen interstitial defects in silicon. A quantum mechanical investigation of the structural, electronic and vibrational properties

2019

The vibrational features of eight interstitial nitrogen related defects in silicon have been investigated at the first principles quantum mechanical level by using a periodic supercell approach, a hybrid functionals, an all electron Gaussian type basis set and the Crystal code. The list includes defects that will be indicated as Ni (one N atom forming a bridge between two Si atoms), Ni-Ns (one interstitial and one substitutional N atom linked to the same Si atom), Ni-Ni (two Ni defects linked to the same couple of silicon atoms) and Ni-Sii-Ni (two Ni defects linked to the same interstitial silicon atom). Four 〈0 0 1〉 split interstitial (dumbbell) defects have also been considered, in which …

Implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 with optimally reduced auxiliary basis dependence.

2008

An implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 using a single Slater-type geminal has been obtained with the aid of automated term generation and evaluation techniques. In contrast to a previously reported computer code [T. Shiozaki et al., J. Chem. Phys. 129, 071101 (2008)], our implementation features a reduced dependence on the auxiliary basis set due to the use of a reformulated evaluation of the so-called Z-intermediate rather than straight forward insertion of an auxiliary basis expansion, which allows an unambiguous comparison to more approximate CCSD-F12 models. First benchmark results for total correlation energies and reactio…

2018

Electrocardiographic imaging (ECGI) strongly relies on a priori assumptions and additional information to overcome ill-posedness. The major challenge of obtaining good reconstructions consists in finding ways to add information that effectively restricts the solution space without violating properties of the sought solution. In this work, we attempt to address this problem by constructing a spatio-temporal basis of body surface potentials (BSP) from simulations of many focal excitations. Measured BSPs are projected onto this basis and reconstructions are expressed as linear combinations of corresponding transmembrane voltage (TMV) basis vectors. The novel method was applied to simulations o…

More wavelet-like orthonormal bases for the lowest Landau level: Some considerations

1994

In a previous work, Antoine and I (1994) have discussed a general procedure which 'projects' arbitrary orthonormal bases of L2(R) into orthonormal bases of the lowest Landau level. In this paper, we apply this procedure to a certain number of examples, with particular attention to the spline bases. We also discuss Haar, Littlewood-Paley and Journe bases.

Separatrix reconstruction to identify tipping points in an eco-epidemiological model

2018

Many ecological systems exhibit tipping points such that they suddenly shift from one state to another. These shifts can be devastating from an ecological point of view, and additionally have severe implications for the socio-economic system. They can be caused by overcritical perturbations of the state variables such as external shocks, disease emergence, or species removal. It is therefore important to be able to quantify the tipping points. Here we present a study of the tipping points by considering the basins of attraction of the stable equilibrium points. We address the question of finding the tipping points that lie on the separatrix surface, which partitions the space of system traj…

Block Based Deconvolution Algorithm Using Spline Wavelet Packets

2010

This paper presents robust algorithms to deconvolve discrete noised signals and images. The idea behind the algorithms is to solve the convolution equation separately in different frequency bands. This is achieved by using spline wavelet packets. The solutions are derived as linear combinations of the wavelet packets that minimize some parameterized quadratic functionals. Parameters choice, which is performed automatically, determines the trade-off between the solution regularity and the initial data approximation. This technique, which id called Spline Harmonic Analysis, provides a unified computational scheme for the design of orthonormal spline wavelet packets, fast implementation of the…

Is the p-Value a Suitable Basis for the Construction of Measures of Evidence? Comment on “The Role of p-Values in Judging the Strength of Evidence an…

2020

Dr. Gibson has to be congratulated for having enriched the wealth of articles written in response to the ASA statement on p-values of 2016 by a valuable and thoughtful contribution. We particularly...