Gaussian Sets Research Articles

Coupled-cluster based basis sets for valence correlation calculations. New primitives, frozen atomic natural orbitals, and basis sets from double to hextuple zeta for atoms H, He, and B-Ne.

A series of new basis sets generated from coupled-cluster theory are presented. Sets of primitive Gaussians for angular momentum shells containing occupied orbitals are optimized and extended until the Hartree-Fock energy improvement per electron falls below 10 μH. This same energy threshold is applied to the energy from the coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) approximation and taken as a guide to the generation of sets of polarization functions, constructed at the level of second-order many-body perturbation theory, once it is shown that practically indistinguishable results are obtained if the more costly CCSD(T) approach is used. A variant of the usual atomic natural orbitals (ANOs) grounded on the frozen natural orbital idea is explored, leading to the frozen ANO (FANO) contraction scheme, whose truncation pattern and convergence capabilities are thoroughly tested. Due to its superior description of the single determinant solution, the FANOs are proposed as the recommended contraction approach. FANO basis sets of sizes ranging from double to hextuple zeta are provided for atoms H through Ne and examined in atomic and molecular calculations.

MODELING PINUS ELLIOTTII GROWTH WITH MULTITEMPORAL LANDSAT DATA: A STUDY CASE IN SOUTHERN BRAZIL

Abstract Remote sensing data are a key proxy to forest monitoring and management at local, regional and global scales. Considering the hypothesis that NDVI and EVI can be used at least during one decade to monitor Pinus elliottii in Southern Brazil, the objective of this study was to identify saturation time after planting of these vegetation indices in a Pinus elliottii plantation and the most suitable index by adjusting theoretical functions to each one of them. Based on Landsat Surface Reflectance Higher-Level Data Products, 32 scenes were selected between 1984 to 2015. A set of theoretical polynomial, gaussian and logistic mathematical functions were applied to fit the experimental data on vegetation indices. The determination coefficient (R²) and RMSE at 95% probability were also used. Finally, EVI efficiency was tested by changing the L parameter. The logistic model was the one that best explained the data resulting from NDVI and EVI over time. NDVI was more effective than EVI for this forest monitoring, identifying the forest growth pattern until its 18 years of age. EVI may have been saturated after 14 years and the L factor may be set to near to zero to achieve a higher coefficient of determination.

SPECTRAL CHARACTERISTICS OF CONFORMATION ISOMERS OF MESO-OCTAMETHYL-CALIX(4)PYRROLE BASED ON QUANTUM-CHEMICAL CALCULATIONS

The structure optimization and calculation of electronic absorption spectra of meso-octa-methylcalix(4)pyrrole conformers was performed by density- functional theory using hybrid B3LYP functional in cc-pVTZ basis set of Gaussian 09 package. Analysis of experimental UV-Vis spectra of solutions of calix(4)pyrrole was carried out in various solvents. The conclusion on the existence of a dynamic equilibrium between conformers in solutions of meso-octamethylcalix(4)pyrrole was made.

Microwave synthesis of some N-phenylhydrazine-1-carbothioamide Schiff bases

We have synthesized and characterized a series of carbothioamide derivatived molecules, obtained by reaction of aromatic aldehyde (Anisaldehyde, 9-anthraldehyde, cinnamaldehyde, indole-3-carboxaldehyde, 1-naphthaldehyde and o-vanillin) with an equimolar amount of 4-phenylthiosemicarbazide with microwave irradiation. The synthesized compounds have been characterized by FT-IR, 1H NMR and 13C NMR spectroscopy. Quantum calculations of the physical properties, based on density functional theory method at B3LYP/6-31+G(d,p) level of theory, were performed, by means of the Gaussian 09W set of programs. The theoretical 1H NMR chemical shift results of the studied compounds have been calculated at B3LYP method and standard 6-31+G(d,p) basis set using the standard Gauge-Independent Atomic Orbital approach. The calculated values are also compared with the experimental data available for these molecules. A good linear relationship between the experimental and calculated data has been obtained.

Direct inversion of the iterative subspace (DIIS) convergence accelerator for crystalline solids employing Gaussian basis sets

When dealing with crystalline solids, convergence of iterative procedures such as self-consistent field (SCF) or coupled–perturbed equations is often more difficult than in the case of molecular systems, specially when a local basis set of atom-centered Gaussians is adopted. Reasons are usually to be found in the close packing of atoms and peculiar chemical characters, such as metallic bond. In this work, a periodic implementation of the direct inversion of the iterative subspace (DIIS) method for crystalline solids is presented for SCF and electric field response up to second order. The error vectors are computed in reciprocal space and implemented for the energy, polarizability and up to second hyperpolarizability. The performance of different DIIS flavors is benchmarked on a representative set of 42 systems including metallic, ionic, molecular and covalent crystals, bulk crystals, surfaces and nanotubes, adopting all-electron basis sets as well as pseudopotentials. Interestingly, it is seen that the error vectors evaluated in the central (gamma) point of the Brillouin zone are sufficient in all cases for an optimal DIIS performance.

On Quantitative Noise Stability and Influences for Discrete and Continuous Models

Keller and Kindler recently established a quantitative version of the famous Benjamini–Kalai–Schramm theorem on the noise sensitivity of Boolean functions. Their result was extended to the continuous Gaussian setting by Keller, Mossel and Sen by means of a Central Limit Theorem argument. In this work we present a unified approach to these results, in both discrete and continuous settings. The proof relies on semigroup decompositions together with a suitable cut-off argument, allowing for the efficient use of the classical hypercontractivity tool behind these results. It extends to further models of interest such as families of log-concave measures and Cayley and Schreier graphs. In particular we obtain a quantitative version of the Benjamini–Kalai–Schramm theorem for the slices of the Boolean cube.

Kernel partial correlation: a novel approach to capturing conditional independence in graphical models for noisy data

ABSTRACTGraphical models capture the conditional independence structure among random variables via existence of edges among vertices. One way of inferring a graph is to identify zero partial correlation coefficients, which is an effective way of finding conditional independence under a multivariate Gaussian setting. For more general settings, we propose kernel partial correlation which extends partial correlation with a combination of two kernel methods. First, a nonparametric function estimation is employed to remove effects from other variables, and then the dependence between remaining random components is assessed through a nonparametric association measure. The proposed approach is not only flexible but also robust under high levels of noise owing to the robustness of the nonparametric approaches.

Learning directed acyclic graph models based on sparsest permutations

We consider the problem of learning a Bayesian network or directed acyclic graph model from observational data. A number of constraint‐based, score‐based and hybrid algorithms have been developed for this purpose. Statistical consistency guarantees of these algorithms rely on the faithfulness assumption, which has been shown to be restrictive especially for graphs with cycles in the skeleton. We here propose the sparsest permutation (SP) algorithm, showing that learning Bayesian networks is possible under strictly weaker assumptions than faithfulness. This comes at a computational price, thereby indicating a statistical‐computational trade‐off for causal inference algorithms. In the Gaussian noiseless setting, we prove that the SP algorithm boils down to finding the permutation of the variables with the sparsest Cholesky decomposition of the inverse covariance matrix, which is equivalent toℓ0‐penalized maximum likelihood estimation. We end with a simulation study showing that in line with the proven stronger consistency guarantees, and the SP algorithm compares favourably to standard causal inference algorithms in terms of accuracy for a given sample size. Copyright © 2018 John Wiley & Sons, Ltd.

An Empirical Evaluation of the Parameters of Trilateral Filter for Noise Removal Implementation on Gaussian and Impulsive Noise

Since 1998, the Bilateral filter (BF) is worldwide accepted for its performance in practical point of view under Gaussian noise however the Bilateral filter has a poor performance for impulsive noise. Based on the combining of the Rank-Ordered Absolute Differences (ROAD) detection technique and the Bilateral filter for automatically reducing or persecuting of impulsive and Gaussian noise, this Trilateral filter (TF) has been proposed by Roman Garnett et al. since 2005 but the Trilateral filter efficiency is rest absolutely on spatial, radiometric, ROAD and joint impulsivity variance. Hence, this paper computationally determines the optimized values of the spatial, radiometric, ROAD and joint impulsivity variance of the Trilateral filter (TF) for maximum performance. In the experiment, nine noisy standard images (Girl-Tiffany, Pepper, Baboon, House, Resolution, Lena, Airplain, Mobile and Pentagon) under both five power-level Gaussian noise setting and five density impulsive noise setting, are used for estimating optimized parameters of Trilateral filter and for demonstrating the its overall performance, which is compared with classical noise removal techniques such as median filter, linear smoothing filter and Bilateral filter (BF). From the noise removal results of empirically experiments with the highest PSNR criterion, the trilateral filter with the optimized parameters has the superior performance because the ROAD variance and joint impulsivity variance can be statistically analyzed and estimated for each experimental case.

Continuous-variable steering and incompatibility via state-channel duality

The term Einstein-Podolsky-Rosen steering refers to a quantum correlation intermediate between entanglement and Bell nonlocality, which has been connected to another fundamental quantum property: measurement incompatibility. In the finite-dimensional case, efficient computational methods to quantify steerability have been developed. In the infinite-dimensional case, however, less theoretical tools are available. Here, we approach the problem of steerability in the continuous variable case via a notion of state-channel correspondence, which generalizes the well-known Choi-Jamio\l{}kowski correspondence. Via our approach we are able to generalize the connection between steering and incompatibility to the continuous variable case and to connect the steerability of a state with the incompatibility breaking property of a quantum channel, e.g., noisy NOON states and amplitude damping channels. Moreover, we apply our methods to the Gaussian steering setting, proving, among other things, that canonical quadratures are sufficient for steering Gaussian states.

Variational inference for probabilistic Poisson PCA

Many application domains such as ecology or genomics have to deal with multivariate non Gaussian observations. A typical example is the joint observation of the respective abundances of a set of species in a series of sites, aiming to understand the co-variations between these species. The Gaussian setting provides a canonical way to model such dependencies, but does not apply in general. We consider here the multivariate exponential family framework for which we introduce a generic model with multivariate Gaussian latent variables. We show that approximate maximum likelihood inference can be achieved via a variational algorithm for which gradient descent easily applies. We show that this setting enables us to account for covariates and offsets. We then focus on the case of the Poisson-lognormal model in the context of community ecology.

Replication-Based Outer Bounds: On the Optimality of “Half the Cake” for Rank-Deficient MIMO Interference Networks

In order to gain new insights into multiple-input–multiple-output (MIMO) interference networks, the optimality of $\sum _{k=1}^{K} M_{k}/2$ (half the cake per user) degrees of freedom is explored for a $K$ -user MIMO interference channel where the cross-channels have arbitrary rank constraints, and the $k$ th transmitter and receiver are equipped with $M_{k}$ antennas each. The result consolidates and significantly generalizes results from prior studies by Krishnamurthy et al., of rank-deficient interference channels where all users have $M$ antennas; and by Tang et al., of full rank interference channels where the $k$ th user pair has $M_{k}$ antennas. The broader outcome of this paper is a novel class of replication-based outer bounds for arbitrary rank-constrained MIMO interference networks where replicas of existing users are added as auxiliary users and the network connectivity is chosen to ensure that any achievable scheme for the original network also works in the new network. The replicated network creates a new perspective of the problem, so that even simple arguments such as user cooperation become quite powerful when applied in the replicated network, giving rise to stronger outer bounds, than when applied directly in the original network. Remarkably, the replication-based bounds are broadly applicable not only to MIMO interference channels with arbitrary rank-constraints, but much more broadly, even beyond Gaussian settings.

Links between causal effects and causal association for surrogacy evaluation in a gaussian setting

Two paradigms for the evaluation of surrogate markers in randomized clinical trials have been proposed: the causal effects paradigm and the causal association paradigm. Each of these paradigms rely on assumptions that must be made to proceed with estimation and to validate a candidate surrogate marker (S) for the true outcome of interest (T). We consider the setting in which S and T are Gaussian and are generated from structural models that include an unobserved confounder. Under the assumed structural models, we relate the quantities used to evaluate surrogacy within both the causal effects and causal association frameworks. We review some of the common assumptions made to aid in estimating these quantities and show that assumptions made within one framework can imply strong assumptions within the alternative framework. We demonstrate that there is a similarity, but not exact correspondence between the quantities used to evaluate surrogacy within each framework, and show that the conditions for identifiability of the surrogacy parameters are different from the conditions, which lead to a correspondence of these quantities.

Spatial Expectile Predictions for Elliptical Random Fields

In this work, we consider an elliptical random field. We propose some spatial expectile predictions at one site given observations of the field at some other locations. To this aim, we first give exact expressions for conditional expectiles, and discuss problems that occur for computing these values. A first affine expectile regression predictor is detailed, an explicit iterative algorithm is obtained, and its distribution is given. Direct simple expressions are derived for some particular elliptical random fields. The performance of this expectile regression is shown to be very poor for extremal expectile levels, so that a second predictor is proposed. We prove that this new extremal prediction is asymptotically equivalent to the true conditional expectile. We also provide some numerical illustrations, and conclude that Expectile Regression may perform poorly when one leaves the Gaussian random field setting.

Dispersion and density of states of phonons and electrons in an α-B12 crystal determined from first principles

Using the DFT method, we study the phonon properties of an α-B12 rhombohedral crystal in the basis set of plane waves and its electronic structure in the localized basis set of Gaussians. It follows from the phonon dispersion that the crystal possesses a dynamical stability. The effective Born charges, the oscillator strengths, the transverse–longitudinal splitting, and the dielectric functions of dipole modes are calculated. We show that charge transfer from polar to equatorial atoms takes place in a В12 icosahedron, while В–В bonds have predominantly a covalent character. In the density of states of acoustic modes, we reveal a structure that can manifest itself in the spectra of disordered boron compounds. From the dispersion of electronic bands, the occurrence of an indirect energy gap follows. The overlap of partial densities implies the hybridization of s and p electronic states in boron atoms.

Relations Between Information and Estimation in Discrete-Time Lévy Channels

Fundamental relations between information and estimation have been established in the literature for the discrete-time Gaussian and Poisson channels. In this work, we demonstrate that such relations hold for a much larger class of observation models. We introduce the natural family of discrete-time L\'evy channels where the distribution of the output conditioned on the input is infinitely divisible. For L\'evy channels, we establish new representations relating the mutual information between the channel input and output to an optimal expected estimation loss, thereby unifying and considerably extending results from the Gaussian and Poisson settings. We demonstrate the richness of our results by working out two examples of L\'evy channels, namely the gamma channel and the negative binomial channel, with corresponding relations between information and estimation. Extensions to the setting of mismatched estimation are also presented.

Achieving algorithmic resilience for temporal integration through spectral deferred corrections

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of Gaussian or spectral collocation nodes over a time interval and uses an iterative application of lower-order time discretizations applied to a correction equation to improve the solution at these nodes. Each deferred correction sweep increases the formal order of accuracy of the method up to the limit inherent in the accuracy defined by the collocation points. In this paper, we demonstrate that SDC is well suited to recovering from soft (transient) hardware faults in the data. A strategy where extra correction iterations are used to recover from soft errors and provide algorithmic resilience is proposed. Specifically, in this approach the iteration is continued until the residual (a measure of the error in the approximation) is small relative to the residual on the first correction iteration and changes slowly between successive iterations. We demonstrate the effectiveness of this strategy for both canonical test problems and a comprehen- sive situation involving a mature scientific application code that solves the reacting Navier-Stokes equations for combustion research.

Algebraic Identifiability of Gaussian Mixtures

We prove that all moment varieties of univariate Gaussian mixtures have the expected dimension. Our approach rests on intersection theory and Terracini's classification of defective surfaces. The analogous identifiability result is shown to be false for mixtures of Gaussians in dimension three and higher. Their moments up to third order define projective varieties that are defective. Our geometric study suggests an extension of the Alexander-Hirschowitz Theorem for Veronese varieties to the Gaussian setting.

Quantile predictions for elliptical random fields

In this article, we consider elliptical random fields. We propose some quantile predictions at one site, given observations at some other locations. To this end, we first give exact expressions for conditional quantiles, and discuss problems that occur when computing these values. A first affine regression quantile predictor is presented in detail, an explicit formula is obtained, and its distribution is given. Direct simple expressions are derived for some particular elliptical random fields. As the performance of this regression quantile turns out to be very poor for extremal quantile levels, a second predictor is proposed. We prove that this new extremal predictor is asymptotically equivalent to the true conditional quantile. Through numerical illustrations, we show that quantile regression may perform poorly outside the usual Gaussian random field setting. This justifies the use of the proposed extremal quantile predictions.

Faint Object Detection in Multi-Epoch Observations via Catalog Data Fusion

Abstract Astronomy in the time-domain era faces several new challenges. One of them is the efficient use of observations obtained at multiple epochs. The work presented here addresses faint object detection and describes an incremental strategy for separating real objects from artifacts in ongoing surveys. The idea is to produce low-threshold single-epoch catalogs and to accumulate information across epochs. This is in contrast to more conventional strategies based on co-added or stacked images. We adopt a Bayesian approach, addressing object detection by calculating the marginal likelihoods for hypotheses asserting that there is no object or one object in a small image patch containing at most one cataloged source at each epoch. The object-present hypothesis interprets the sources in a patch at different epochs as arising from a genuine object; the no-object hypothesis interprets candidate sources as spurious, arising from noise peaks. We study the detection probability for constant-flux objects in a Gaussian noise setting, comparing results based on single and stacked exposures to results based on a series of single-epoch catalog summaries. Our procedure amounts to generalized cross-matching: it is the product of a factor accounting for the matching of the estimated fluxes of the candidate sources and a factor accounting for the matching of their estimated directions. We find that probabilistic fusion of multi-epoch catalogs can detect sources with similar sensitivity and selectivity compared to stacking. The probabilistic cross-matching framework underlying our approach plays an important role in maintaining detection sensitivity and points toward generalizations that could accommodate variability and complex object structure.