The Experts below are selected from a list of 17115 Experts worldwide ranked by ideXlab platform
Andreas Gruneis - One of the best experts on this subject based on the ideXlab platform.
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from plane waves to local Gaussians for the simulation of correlated periodic systems
Journal of Chemical Physics, 2016Co-Authors: George H Booth, Theodoros Tsatsoulis, Garnet Kinlic Chan, Andreas GruneisAbstract:We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Moller–Plesset perturbation theory.
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from plane waves to local Gaussians for the simulation of correlated periodic systems
arXiv: Strongly Correlated Electrons, 2016Co-Authors: George H Booth, Theodoros Tsatsoulis, Garnet Kinlic Chan, Andreas GruneisAbstract:We present a simple, robust and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cut-off radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artefacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid and water adsorption on a LiH surface, at the level of second-order M\{o}ller--Plesset perturbation theory.
Ofer Zeitouni - One of the best experts on this subject based on the ideXlab platform.
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on the limitation of spectral methods from the gaussian hidden clique problem to rank one perturbations of gaussian tensors
IEEE Transactions on Information Theory, 2017Co-Authors: Andrea Montanari, Daniel Reichman, Ofer ZeitouniAbstract:We consider the following detection problem: given a realization of a symmetric matrix X of dimension $n$ , distinguish between the hypothesis that all upper triangular variables are independent and identically distributed (i.i.d). Gaussians variables with mean 0 and variance 1 and the hypothesis, where X is the sum of such matrix and an independent rank-one perturbation. This setup applies to the situation, where under the alternative, there is a planted principal submatrix B of size $L$ for which all upper triangular variables are i.i.d. Gaussians with mean 1 and variance 1, whereas all other upper triangular elements of X not in B are i.i.d. Gaussians variables with mean 0 and variance 1. We refer to this as the “Gaussian hidden clique problem.” When $L=(1+\epsilon )\sqrt {n}$ ( $\epsilon >0$ ), it is possible to solve this detection problem with probability $1-o_{n}(1)$ by computing the spectrum of X and considering the largest eigenvalue of X. We prove that this condition is tight in the following sense: when $L no algorithm that examines only the eigenvalues of X can detect the existence of a hidden Gaussian clique, with error probability vanishing as $n\to \infty $ . We prove this result as an immediate consequence of a more general result on rank-one perturbations of $k$ -dimensional Gaussian tensors. In this context, we establish a lower bound on the critical signal-to-noise ratio below which a rank-one signal cannot be detected.
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on the limitation of spectral methods from the gaussian hidden clique problem to rank one perturbations of gaussian tensors
Neural Information Processing Systems, 2015Co-Authors: Andrea Montanari, Daniel Reichman, Ofer ZeitouniAbstract:We consider the following detection problem: given a realization of a symmetric matrix X of dimension n, distinguish between the hypothesis that all upper triangular variables are i.i.d. Gaussians variables with mean 0 and variance 1 and the hypothesis that there is a planted principal submatrix B of dimension L for which all upper triangular variables are i.i.d. Gaussians with mean 1 and variance 1 , whereas all other upper triangular elements of X not in B are i.i.d. Gaussians variables with mean 0 and variance 1. We refer to this as the 'Gaussian hidden clique problem'. When L = (1 + ∊) √n (∊ > 0), it is possible to solve this detection problem with probability 1 - on(1) by computing the spectrum of X and considering the largest eigenvalue of X. We prove that when L < (1 - ∊) √n no algorithm that examines only the eigenvalues of X can detect the existence of a hidden Gaussian clique, with error probability vanishing as n → ∞. The result above is an immediate consequence of a more general result on rank-one perturbations of k-dimensional Gaussian tensors. In this context we establish a lower bound on the critical signal-to-noise ratio below which a rank-one signal cannot be detected.
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on the limitation of spectral methods from the gaussian hidden clique problem to rank one perturbations of gaussian tensors
arXiv: Statistics Theory, 2014Co-Authors: Andrea Montanari, Daniel Reichman, Ofer ZeitouniAbstract:We consider the following detection problem: given a realization of a symmetric matrix ${\mathbf{X}}$ of dimension $n$, distinguish between the hypothesis that all upper triangular variables are i.i.d. Gaussians variables with mean 0 and variance $1$ and the hypothesis where ${\mathbf{X}}$ is the sum of such matrix and an independent rank-one perturbation. This setup applies to the situation where under the alternative, there is a planted principal submatrix ${\mathbf{B}}$ of size $L$ for which all upper triangular variables are i.i.d. Gaussians with mean $1$ and variance $1$, whereas all other upper triangular elements of ${\mathbf{X}}$ not in ${\mathbf{B}}$ are i.i.d. Gaussians variables with mean 0 and variance $1$. We refer to this as the `Gaussian hidden clique problem.' When $L=(1+\epsilon)\sqrt{n}$ ($\epsilon>0$), it is possible to solve this detection problem with probability $1-o_n(1)$ by computing the spectrum of ${\mathbf{X}}$ and considering the largest eigenvalue of ${\mathbf{X}}$. We prove that this condition is tight in the following sense: when $L<(1-\epsilon)\sqrt{n}$ no algorithm that examines only the eigenvalues of ${\mathbf{X}}$ can detect the existence of a hidden Gaussian clique, with error probability vanishing as $n\to\infty$. We prove this result as an immediate consequence of a more general result on rank-one perturbations of $k$-dimensional Gaussian tensors. In this context we establish a lower bound on the critical signal-to-noise ratio below which a rank-one signal cannot be detected.
Jurg Hutter - One of the best experts on this subject based on the ideXlab platform.
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fast evaluation of solid harmonic gaussian integrals for local resolution of the identity methods and range separated hybrid functionals
arXiv: Chemical Physics, 2017Co-Authors: Dorothea Golze, Jan Wilhelm, Niels Benedikter, Marcella Iannuzzi, Jurg HutterAbstract:An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb and Gaussian-type operators, that occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both, integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets.
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fast evaluation of solid harmonic gaussian integrals for local resolution of the identity methods and range separated hybrid functionals
Journal of Chemical Physics, 2017Co-Authors: Dorothea Golze, Jan Wilhelm, Niels Benedikter, Marcella Iannuzzi, Jurg HutterAbstract:An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb, and Gaussian-type operators, which occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both integrals and their derivatives. In particular, our method is ...
Xilin Chen - One of the best experts on this subject based on the ideXlab platform.
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discriminant analysis on riemannian manifold of gaussian distributions for face recognition with image sets
IEEE Transactions on Image Processing, 2018Co-Authors: Wen Wang, Ruiping Wang, Zhiwu Huang, Shiguang Shan, Xilin ChenAbstract:To address the problem of face recognition with image sets, we aim to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as the Gaussian mixture model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. Since in the light of information geometry, the Gaussians lie on a specific Riemannian manifold, this paper presents a method named discriminant analysis on Riemannian manifold of Gaussian distributions (DARG). We investigate several distance metrics between Gaussians and accordingly two discriminative learning frameworks are presented to meet the geometric and statistical characteristics of the specific manifold. The first framework derives a series of provably positive definite probabilistic kernels to embed the manifold to a high-dimensional Hilbert space, where conventional discriminant analysis methods developed in Euclidean space can be applied, and a weighted Kernel discriminant analysis is devised which learns discriminative representation of the Gaussian components in GMMs with their prior probabilities as sample weights. Alternatively, the other framework extends the classical graph embedding method to the manifold by utilizing the distance metrics between Gaussians to construct the adjacency graph, and hence the original manifold is embedded to a lower-dimensional and discriminative target manifold with the geometric structure preserved and the interclass separability maximized. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB, and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art.
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discriminant analysis on riemannian manifold of gaussian distributions for face recognition with image sets
Computer Vision and Pattern Recognition, 2015Co-Authors: Wen Wang, Ruiping Wang, Zhiwu Huang, Shiguang Shan, Xilin ChenAbstract:This paper presents a method named Discriminant Analysis on Riemannian manifold of Gaussian distributions (DARG) to solve the problem of face recognition with image sets. Our goal is to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as Gaussian Mixture Model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. In the light of information geometry, the Gaussians lie on a specific Riemannian manifold. To encode such Riemannian geometry properly, we investigate several distances between Gaussians and further derive a series of provably positive definite probabilistic kernels. Through these kernels, a weighted Kernel Discriminant Analysis is finally devised which treats the Gaussians in GMMs as samples and their prior probabilities as sample weights. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art.
L. H. Wasserman - One of the best experts on this subject based on the ideXlab platform.
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Unbiased Inclination Distributions for Objects in the Kuiper Belt
The Astronomical Journal, 2010Co-Authors: Amanda A. S. Gulbis, Susan D. Benecchi, J. L. Elliot, Elisabeth R. Adams, Marc W. Buie, David E. Trilling, L. H. WassermanAbstract:Using data from the Deep Ecliptic Survey (DES), we investigate the inclination distributions of objects in the Kuiper Belt. We present a derivation for observational bias removal and use this procedure to generate unbiased inclination distributions for Kuiper Belt objects (KBOs) of different DES dynamical classes, with respect to the Kuiper Belt Plane. Consistent with previous results, we find that the inclination distribution for all DES KBOs is well fit by the sum of two Gaussians, or a Gaussian plus a generalized Lorentzian, multiplied by sin i. Approximately 80% of KBOs are in the high-inclination grouping. We find that Classical object inclinations are well fit by sin i multiplied by the sum of two Gaussians, with roughly even distribution between Gaussians of widths 2.0 -0.5/+0.6 degrees and 8.1 -2.1/+2.6 degrees. Objects in different resonances exhibit different inclination distributions. The inclinations of Scattered objects are best matched by sin i multiplied by a single Gaussian that is centered at 19.1 -3.6/+3.9 degrees with a width of 6.9 -2.7/+4.1 degrees. Centaur inclinations peak just below 20 degrees, with one exceptionally high-inclination object near 80 degrees. The currently observed inclination distribution of the Centaurs is not dissimilar to that of the Scattered Extended KBOs and Jupiter-family comets, but is significantly different from the Classical and Resonant KBOs. While the sample sizes of some dynamical classes are still small, these results should begin to serve as a critical diagnostic for models of Solar System evolution.
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unbiased inclination distributions for objects in the kuiper belt
DPS, 2009Co-Authors: Amanda A. S. Gulbis, Susan D. Benecchi, J. L. Elliot, Elisabeth R. Adams, Marc W. Buie, David E. Trilling, L. H. WassermanAbstract:Using data from the Deep Ecliptic Survey (DES), we investigate the inclination distributions of objects in the Kuiper Belt. We present a derivation for observational bias removal and use this procedure to generate unbiased inclination distributions for Kuiper Belt objects (KBOs) of different DES dynamical classes, with respect to the Kuiper Belt plane. Consistent with previous results, we find that the inclination distribution for all DES KBOs is well fit by the sum of two Gaussians, or a Gaussian plus a generalized Lorentzian, multiplied by sin i. Approximately 80% of KBOs are in the high-inclination grouping. We find that Classical object inclinations are well fit by sin i multiplied by the sum of two Gaussians, with roughly even distribution between Gaussians of widths 2.0+0.6 –0.5° and 8.1+2.6 –2.1°. Objects in different resonances exhibit different inclination distributions. The inclinations of Scattered objects are best matched by sin i multiplied by a single Gaussian that is centered at 19.1+3.9 –3.6° with a width of 6.9+4.1 –2.7°. Centaur inclinations peak just below 20°, with one exceptionally high-inclination object near 80°. The currently observed inclination distribution of the Centaurs is not dissimilar to that of the Scattered Extended KBOs and Jupiter-family comets, but is significantly different from the Classical and Resonant KBOs. While the sample sizes of some dynamical classes are still small, these results should begin to serve as a critical diagnostic for models of solar system evolution.
