Search results for " approximation"
showing 10 items of 575 documents
Approximation of functions over manifolds : A Moving Least-Squares approach
2021
We present an algorithm for approximating a function defined over a $d$-dimensional manifold utilizing only noisy function values at locations sampled from the manifold with noise. To produce the approximation we do not require any knowledge regarding the manifold other than its dimension $d$. We use the Manifold Moving Least-Squares approach of (Sober and Levin 2016) to reconstruct the atlas of charts and the approximation is built on-top of those charts. The resulting approximant is shown to be a function defined over a neighborhood of a manifold, approximating the originally sampled manifold. In other words, given a new point, located near the manifold, the approximation can be evaluated…
Low-Rate Reduced Complexity Image Compression using Directionlets
2006
The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) discontinuities, like edges and contours, that are anisotropic and characterized by geometrical regularity along different directions. In our previous work, we proposed a construction of critically sampled perfect reconstruction anisotropic transform with directional vanishing moments (DVM) imposed in the corresponding basis functions, called directionlets. Here, we show that the computational complexity of our transform is comparable to the co…
The integral‐direct coupled cluster singles and doubles model
1996
An efficient and highly vectorized implementation of the coupled cluster singles and doubles (CCSD) model using a direct atomic integral technique is presented. The minimal number of n6processes has been implemented for the most time consuming terms and point group symmetry is used to further reduce operation counts and memory requirements. The significantly increased application range of the CCSD method is illustrated with sample calculations on several systems with more than 500 basis functions. Furthermore, we present the basic trends of an open ended algorithm and discuss the use of integral prescreening. © 1996 American Institute of Physics.
Group Nonnegative Matrix Factorization with Sparse Regularization in Multi-set Data
2021
Constrained joint analysis of data from multiple sources has received widespread attention for that it allows us to explore potential connections and extract meaningful hidden components. In this paper, we formulate a flexible joint source separation model termed as group nonnegative matrix factorization with sparse regularization (GNMF-SR), which aims to jointly analyze the partially coupled multi-set data. In the GNMF-SR model, common and individual patterns of particular underlying factors can be extracted simultaneously with imposing nonnegative constraint and sparse penalty. Alternating optimization and alternating direction method of multipliers (ADMM) are combined to solve the GNMF-S…
Classification of Melanoma Lesions Using Sparse Coded Features and Random Forests
2016
International audience; Malignant melanoma is the most dangerous type of skin cancer, yet it is the most treatable kind of cancer, conditioned by its early diagnosis which is a challenging task for clinicians and dermatologists. In this regard, CAD systems based on machine learning and image processing techniques are developed to differentiate melanoma lesions from benign and dysplastic nevi using dermoscopic images. Generally, these frameworks are composed of sequential processes: pre-processing, segmentation, and classification. This architecture faces mainly two challenges: (i) each process is complex with the need to tune a set of parameters, and is specific to a given dataset; (ii) the…
Free-standing 2D metals from binary metal alloys
2020
Recent experiment demonstrated the formation of free-standing Au monolayers by exposing Au-Ag alloy to electron beam irradiation. Inspired by this discovery, we used semi-empirical effective medium theory simulations to investigate monolayer formation in 30 different binary metal alloys composed of late d-series metals Ni, Cu, Pd, Ag, Pt, and Au. In qualitative agreement with the experiment, we find that the beam energy required to dealloy Ag atoms from Au-Ag alloy is smaller than the energy required to break the dealloyed Au monolayer. Our simulations suggest that similar method could also be used to form Au monolayers from Au-Cu alloy and Pt monolayers from Pt-Cu, Pt-Ni, and Pt-Pd alloys.
Quantum Mechanical Modelling of Pure and Defective KNbO3 Perovskites
2000
Ab initio electronic structure calculations using the density-functional theory (DFT) are performed for KNbO3 with and without defects. Ferroelectric distortive transitions involve very small changes in energies and are therefore sensitive to DFT-approximations. This is discussed by comparing results obtained with the local density approximation (LDA) to those where generalized gradient approximations (GGA) are used. The results of ab initio calculations for F-type centers and bound hole polarons are compared to those obtained by a semiempirical method of the Intermediate Neglect of the Differential Overlap (INDO), based on the HartreeFock formalism. Supercells with 40 and 320 atoms were us…
Electrical transport with temperature-induced spin disorder in NiMnSb
2019
Abstract We investigate theoretically the combined effect of phonons and magnons caused by finite temperatures on the electrical resistivity of nonstoichiometric half-Heusler NiMnSb alloy. The coherent potential approximation within the alloy analogy model is employed for an efficient treatment of chemical impurities, atomic displacements, and magnetic disorder. Spin fluctuations of local Mn moments are described by two models: (i) uncompensated disordered local moment approach and (ii) tilting of the moments. The calculated resistivity agrees with experimental data, the agreement is good up to 600 K. We show that a strong magnetic disorder leads to a violation of the Matthiessen’s rule for…
First-Principles Simulation of Substitutional Defects in Perovskites
2000
The results of supercell calculations of electronic structure and related properties of substitutional impurities in perovskite oxides KNbO3 and KTaO3 are discussed. For Fe impurities in KNbO3, the results obtained in the local density approximation (LDA) and in the LDA+U approach (that allows an ad hoc treatment of nonlocality in exchange-correlation) are compared, and different impurity charge configurations are discussed. The study of off-centre Li defects in incipient ferroelectric KTaO3 have been done by the appropriately parametrized Intermediate Neglect of Differential Overlap (INDO) method. The interaction energies of two off-centre impurities in different relative configurations ar…
Iron-based Heusler compounds Fe2YZ: Comparison with theoretical predictions of the crystal structure and magnetic properties
2013
The present work reports on the new soft ferromagnetic Heusler phases Fe${}_{2}$NiGe, Fe${}_{2}$CuGa, and Fe${}_{2}$CuAl, which in previous theoretical studies have been predicted to exist in a tetragonal Heusler structure. Together with the known phases Fe${}_{2}$CoGe and Fe${}_{2}$NiGa these materials have been synthesized and characterized by powder x-ray diffraction, ${}^{57}$Fe M\"ossbauer spectroscopy, superconducting quantum interference device, and energy-dispersive x-ray measurements. In particular M\"ossbauer spectroscopy was used to monitor the degree of local atomic order/disorder and to estimate magnetic moments at the Fe sites from the hyperfine fields. It is shown that in con…