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About 6,531 papers for “atomic decomposition”

Atomic decomposition of molecular properties

Ignat Harczuk · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2016

In this thesis, new methodology of computing properties aimed for multipleapplications is developed. We use quantum mechanics to compute propertiesof molecules, and having these properties as a basis, we set up equations basedon a classical reasoning. These approximations are shown to be quite good inmany cases, and makes it possible to calculate linear and non-linear propertiesof large systems.The calculated molecular properties are decomposed into atomic propertiesusing the LoProp algorithm, which is a method only dependent on the overlapmatrix. This enables the expression of the molecular properties in the two-site atomic basis, giving atomic, and bond-centric force-fields in terms of themolecular multi-pole moments and polarizabilities. Since the original LoProptransformation was formulated for static fields, theory is developed which makesit possible to extract the frequency-dependent atomic properties as well. Fromthe second-order perturbation of the electron density with respect to an externalfield, LoProp is formulated to encompass the first order hyperpolarizability.The original Applequist formulation is extended into a quadratic formula-tion, which produces the second-order shift in the induced dipole moments of thepoint-dipoles from the hyperpolarizability. This enables the calculation of a to-tal hyperpolarizability in systems consisting of interacting atoms and molecules.The first polarizability α and the first hyperpolarizability β obtained via theLoProp transformation are used to calculate this response with respect to anexternal field using the quadratic Applequist equations.In the last part, the implemented analytical response LoProp procedureand the quadratic Applequist formalism is applied to various model systems.The polarizable force-field that is obtained from the decomposition of the staticmolecular polarizability α is tested by studying the one-photon absorption spec-trum of the green fluorescent protein. From the frequency dispersion of thepolarizability α(ω), the effect of field perturbations is evaluated in classicaland QM/MM applications. Using the dynamical polarizabilities, the Rayleigh-scattering of aerosol clusters consisting of water and cis–pinonic acid moleculesis studied. The LoProp hyperpolarizability in combination with the quadraticApplequist equations is used to test the validity of the model on sample wa-ter clusters of varying sizes. Using the modified point-dipole model developedby Thole, the hyper-Rayleigh scattering intensity of a model collagen triple-helix is calculated. The atomic dispersion coefficients are calculated from thedecomposition of the real molecular polarizability at imaginary frequencies. Fi-nally, using LoProp and a capping procedure we demonstrate how the QM/MMmethodology can be used to compute x-ray photoelectron spectra of a polymer.

Cited by 0Open access

Atomic decomposition in regulated domains

Hanninen, Teemu · Università del Salento · 2005

We obtain atomic decomposition formulas for weighted Bergman spaces , , where belongs to the class of regulated domains. We are able to construct atomic decomposition directly on a give regulated domain by using its geometric properties.

Cited by 0Open access

Transfer operators and atomic decomposition

Alexander Arbieto, Daniel Smania · arXiv (Cornell University) · 2019

We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, the dynamics and the underlying phase space have very low regularity. In particular it is often possible to obtain exponential decay of correlations, the Central Limit Theorem and almost sure invariance principle for fairly general observables, including unbounded ones.

Cited by 5Open access

Atomic Decomposition by Basis Pursuit

Scott Shaobing Chen, David L. Donoho, Michael A. Saunders · SIAM Journal on Scientific Computing · 1998

The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries --- stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for decomposition have been proposed, including the method of frames (MOF), Matching pursuit (MP), and, for special dictionaries, the best orthogonal basis (BOB). Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution. BP has interesting relations to ideas in areas as diverse as ill-posed problems, in abstract harmonic analysis, total variation denoising, and multiscale edge denoising. BP in highly overcomplete dictionaries leads to large-scale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked successfully only because of recent advances in linear programming by interior-point methods. We obtain reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.

Cited by 6,899

Atomic Decomposition for ISAR Imaging

Omar A. Yeste-Ojeda, Jesús Grajal · 2006

We explore the capabilities of atomic decomposition (AD) for ISAR imaging. On the contrary to our previous work with AD where our research was focused on radar signal detection and maximization of sensitivity, the main concern in ISAR imaging based on AD is to obtain focused images, target feature extraction and low computational burden.

Cited by 3

Atomic decomposition in regulated domains

Teemu Hänninen · Università del Salento · 2013

We obtain atomic decomposition formulas for weighted Bergman spaces , , where belongs to the class of regulated domains. We are able to construct atomic decomposition directly on a give regulated domain by using its geometric properties.

Cited by 1Open access

Polar Alignment and Atomic Decomposition

Zhenan Fan, Halyun Jeong, Yifan Sun et al. · arXiv (Cornell University) · 2019

Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple and geometric form of convex duality. This duality correspondence yields a general notion of alignment that leads to an intuitive and complete description of how atoms participate in the final decomposition of the solution. The resulting geometric perspective leads to variations of existing algorithms effective for large-scale problems. We illustrate these ideas with many examples, including applications in matrix completion and morphological component analysis for the separation of mixtures of signals.

Cited by 3Open access

Atomic Decomposition of Financial Data.

Greenblatt, Seth A · RePEc: Research Papers in Economics

When looking at a time series, it is often instructive to consider the data as observations sampled from a noisy version of some underlying data generating process. This data generating process may be considered to be a function from a function space. We can specify very simple functions, known as atoms, which may be taken in linear combinations to represent any function within a particular function space. The atoms are described as members of a family of functions indexed by parameters. Quite commonly used for functions underlying time series data are the parameters location and frequency. This type of atom is known as a time-frequency atom. After we have specified the family of atoms that we wish to use to represent our underlying data generating process, the difficult problem of choosing the most effective, parsimonious representation from this family remains to be solved. Several techniques, such as Matching Pursuit and Basis Pursuit, have been suggested to solve this problem. In the current study, we investigate the use of several families of atoms, both individually and in combination, to decompose exchange rate data in search of structure that has been overlooked in more traditional approaches. Citation Copyright 1998 by Kluwer Academic Publishers.

Cited by 1

Atomic Decomposition by Basis Pursuit

Scott Shaobing Chen, David L. Donoho, Michael A. Saunders · SIAM Review · 2001

The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries---stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for decomposition have been proposed, including the method of frames (MOF), matching pursuit (MP), and, for special dictionaries, the best orthogonal basis (BOB). Basis pursuit (BP) is a principle for decomposing a signal into an "optimal"' superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution. BP has interesting relations to ideas in areas as diverse as ill-posed problems, abstract harmonic analysis, total variation denoising, and multiscale edge denoising. BP in highly overcomplete dictionaries leads to large-scale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked successfully only because of recent advances in linear and quadratic programming by interior-point methods. We obtain reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.

Cited by 5,079

Atomic Decomposition via Polar Alignment

Zhenan Fan, Halyun Jeong, Yifan Sun et al. · Foundations and Trends® in Optimization · 2020

Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple and geometric form of convex duality. This duality correspondence yields a general notion of alignment that leads to an intuitive and complete description of how atoms participate in the final decomposition of the solution. The resulting geometric perspective leads to variations of existing algorithms effective for large-scale problems. We illustrate these ideas with many examples, including applications in matrix completion and morphological component analysis for the separation of mixtures of signals.

Cited by 8

Atomic decomposition based voltage flicker detection

Linchuan Li · 2013

A new detection method of voltage flicker was proposed in this paper.Voltage flicker dictionary was designed by analyzing voltage flicker characteristics based on the atomic decomposition.Firstly,the fundamental frequency component was extracted,then the Matching Pursuits(MP) algorithm was used to extract voltage flicker from the residual signals.In each iteration step,the voltage flicker parameters were obtained and used to distinguish whether the voltage flicker was correct or not.The iteration stopped until the extracted signal was a fake one.Three different voltage flickers were simulated.Simulation results showed that the voltage flicker parameters are accuracy,and the method is with small computational complexity.The voltage flicker parameters supply a strong basis to regulate the voltage flicker.

Cited by 0