Diagonal Correction Research Articles

The multichannel i-propyl + O2 reaction system: A model of secondary alkyl radical oxidation.

The i-propyl + O2 reaction mechanism has been investigated by definitive quantum chemical methods to establish this system as a benchmark for the combustion of secondary alkyl radicals. Focal point analyses extrapolating to the abinitio limit were performed based on explicit computations with electron correlation treatments through coupled cluster single, double, triple, and quadruple excitations and basis sets up to cc-pV5Z. The rigorous coupled cluster single, double, and triple excitations/cc-pVTZ level of theory was used to fully optimize all reaction species and transition states, thus, removing some substantial flaws in reference geometries existing in the literature. The vital i-propylperoxy radical (MIN1) and its concerted elimination transition state (TS1) were found 34.8 and 4.4kcal mol-1 below the reactants, respectively. Two β-hydrogen transfer transition states (TS2, TS2') lie above the reactants by (1.4, 2.5) kcal mol-1 and display large Born-Oppenheimer diagonal corrections indicative of nearby surface crossings. An α-hydrogen transfer transition state (TS5) is discovered 5.7kcal mol-1 above the reactants that bifurcates into equivalent α-peroxy radical hanging wells (MIN3) prior to a highly exothermic dissociation into acetone + OH. The reverse TS5 → MIN1 intrinsic reaction path also displays fascinating features, including another bifurcation and a conical intersection of potential energy surfaces. An exhaustive conformational search of two hydroperoxypropyl (QOOH) intermediates (MIN2 and MIN3) of the i-propyl + O2 system located nine rotamers within 0.9kcal mol-1 of the corresponding lowest-energy minima.

A Rehabilitation of Pixel-Based Spectral Reconstruction from RGB Images.

Recently, many deep neural networks (DNN) have been proposed to solve the spectral reconstruction (SR) problem: recovering spectra from RGB measurements. Most DNNs seek to learn the relationship between an RGB viewed in a given spatial context and its corresponding spectra. Significantly, it is argued that the same RGB can map to different spectra depending on the context with respect to which it is seen and, more generally, that accounting for spatial context leads to improved SR. However, as it stands, DNN performance is only slightly better than the much simpler pixel-based methods where spatial context is not used. In this paper, we present a new pixel-based algorithm called A++ (an extension of the A+ sparse coding algorithm). In A+, RGBs are clustered, and within each cluster, a designated linear SR map is trained to recover spectra. In A++, we cluster the spectra instead in an attempt to ensure neighboring spectra (i.e., spectra in the same cluster) are recovered by the same SR map. A polynomial regression framework is developed to estimate the spectral neighborhoods given only the RGB values in testing, which in turn determines which mapping should be used to map each testing RGB to its reconstructed spectrum. Compared to the leading DNNs, not only does A++ deliver the best results, it is parameterized by orders of magnitude fewer parameters and has a significantly faster implementation. Moreover, in contradistinction to some DNN methods, A++ uses pixel-based processing, which is robust to image manipulations that alter the spatial context (e.g., blurring and rotations). Our demonstration on the scene relighting application also shows that, while SR methods, in general, provide more accurate relighting results compared to the traditional diagonal matrix correction, A++ provides superior color accuracy and robustness compared to the top DNN methods.

Introducing MPEC: Massively parallel electron correlation.

We have developed a new program for carrying out improved internally contracted Multi-reference Configuration Interaction Singles and Doubles (i2cMRCISD) calculations. It is designed from the ground up to be used on distributed memory parallel computers. Tests show good scaling properties with the number of cores per node and the number nodes. This program features Gaussian basis sets with ℓ > 6; scalar special relativity via the spin-free method; convergence to C∞v, D∞v, or spherical electronic states; special code to determine Rydberg orbitals; both uncontracted and contracted MRCISD wavefunctions; one and two electron properties, including full spin-orbit matrix elements with the Breit interaction; analytic calculation of Born-Oppenheimer diagonal correction for multi-configuration Hartree-Fock wavefunctions; and analytic calculation of second order Born-Oppenheimer corrections for Hartree-Fock wavefunctions. The program can be obtained from software.nasa.gov.

Vibronic interactions in trilobite and butterfly Rydberg molecules

Ultralong-range Rydberg molecules provide an exciting testbed for molecular physics at exaggerated scales. In the so-called trilobite and butterfly Rydberg molecules, the Born-Oppenheimer approximation can fail due to strong nonadiabatic couplings arising from the combination of radial oscillations and rapid energy variations in the adiabatic potential energy curves. We utilize an accurate coupled-channel treatment of the vibronic system to observe the breakdown of Born-Oppenheimer physics, such as nonadiabatic trapping and decay of molecular states found near pronounced avoided crossings in the adiabatic potential curves. Even for vibrational states localized far away from avoided crossings, a single-channel model is quantitatively sufficient only after including the diagonal nonadiabatic corrections to the Born-Oppenheimer potentials. Our results indicate the importance of including nonadiabatic physics in the description of ultralong-range Rydberg molecules and in the interpretation of measured vibronic spectra.

Morphometric features of dental arches in the period of mixed dentition

Based on the results of a biometric study of plaster models of the jaws obtained in 38 children in the period of early mixed dentition (8–9 years old) with a neutral location of the first permanent molars and optimal incisal overlap corresponding to the optimal functional occlusion of this age category, the limits of variability of the dental arcade index were calculated arcs with macro-, micro- and normodental type of the dental system. The total value of the width of the crowns of 12 teeth in children in the period of early mixed dentition from 92 mm to 97 mm in the upper jaw and from 85 mm to 90 mm in the lower jaw is an indicator of the normodontic type of the dental system, while the length of the dental arch is less than 92 mm in the upper jaw and 85 mm on the lower jaw indicates that such arches belong to microdont ones, and more than 97 mm on the upper jaw and 90 mm on the lower jaw – to macrodont ones. In the early period of mixed dentition, the value of the arcade index, as the ratio of the width of the dental arch to its length, in the range from 0.57 c.u. up to 0.64 c.u. is an indicator of the mesoarcade type of dental arches, and an increase (more than 0.64 a.u.) or a decrease (less than 0.57 a.u.) of this value indicates that the dental arches belong to the brachiarcade or dolichoarcade types, respectively. When constructing a dental diagnostic triangle in children with anomalies in the shape of the dental arches in the early removable dentition, it is advisable to take into account that the value of the incisor-molar diagonals is established not by determining linear parameters, but by calculating the ratio of the length of the dental arch to the value of the diagonal correction factor (upper jaw – 1 .05; lower jaw – 1.07).

Efimov physics implications at p -wave fermionic unitarity

Efimov physics at $p$-wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long-range interaction potential energy, but without producing a true Efimov effect. This analysis treats the total orbital angular momenta and parities, ${J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+},{1}^{+},{1}^{\ensuremath{-}}$, and ${2}^{\ensuremath{-}}$, for either three spin-polarized fermions ($\ensuremath{\uparrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$) or two spin-up and one spin-down fermion ($\ensuremath{\downarrow}\ensuremath{\uparrow}\ensuremath{\uparrow}$). Our results for the long-range interaction in some of those cases agree with previous work by Werner and Castin and by Blume et al., namely, in cases where the $s$-wave scattering length goes to infinity. The present results extend those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and we consider additional unitarity scenarios where the $p$-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.

Scaling High-Quality Pairwise Link-Based Similarity Retrieval on Billion-Edge Graphs

SimRank is an attractive link-based similarity measure used in fertile fields of Web search and sociometry. However, the existing deterministic method by Kusumoto et al. [ 24 ] for retrieving SimRank does not always produce high-quality similarity results, as it fails to accurately obtain diagonal correction matrix D . Moreover, SimRank has a “connectivity trait” problem: increasing the number of paths between a pair of nodes would decrease its similarity score. The best-known remedy, SimRank++ [ 1 ], cannot completely fix this problem, since its score would still be zero if there are no common in-neighbors between two nodes. In this article, we study fast high-quality link-based similarity search on billion-scale graphs. (1) We first devise a “varied- D ” method to accurately compute SimRank in linear memory. We also aggregate duplicate computations, which reduces the time of [ 24 ] from quadratic to linear in the number of iterations. (2) We propose a novel “cosine-based” SimRank model to circumvent the “connectivity trait” problem. (3) To substantially speed up the partial-pairs “cosine-based” SimRank search on large graphs, we devise an efficient dimensionality reduction algorithm, PSR # , with guaranteed accuracy. (4) We give mathematical insights to the semantic difference between SimRank and its variant, and correct an argument in [ 24 ] that “if D is replaced by a scaled identity matrix (1-Ɣ)I, their top-K rankings will not be affected much”. (5) We propose a novel method that can accurately convert from Li et al. SimRank ~{S} to Jeh and Widom’s SimRank S . (6) We propose GSR # , a generalisation of our “cosine-based” SimRank model, to quantify pairwise similarities across two distinct graphs, unlike SimRank that would assess nodes across two graphs as completely dissimilar. Extensive experiments on various datasets demonstrate the superiority of our proposed approaches in terms of high search quality, computational efficiency, accuracy, and scalability on billion-edge graphs.

Transport Corrections and Sensitivities in the Discrete-Ordinates Method

Methods for approximately accounting for the terms neglected in a finite (L’th-order) Legendre expansion of the scattering source in the transport equation are called transport corrections. This paper derives adjoint-based sensitivities of a neutron or gamma-ray transport response for problems that use diagonal, Bell-Hansen-Sandmeier (BHS), or n’th-Cesàro-mean-of-order-2 (Cesàro) transport corrections in the discrete-ordinates method. For diagonal and BHS transport corrections, there is a sensitivity to the L + 1ʹth scattering cross-section moment, and the sensitivity to nuclide and material densities requires this contribution. For the Cesàro transport correction, the sensitivities to the scattering cross section for the l’th moment are multiplied by a simple function of l and the scattering expansion order L. Numerical results for a keff problem and a fixed-source problem verify the derivation and implementation of the sensitivity equations into the SENSMG multigroup sensitivity code. The Cesàro transport correction yields inaccurate responses for both problems.

Disk

Measuring similarities among different nodes is important in graph analysis. SimRank is one of the most popular similarity measures. Given a graph G ( V , E ) and a source node u , a single-source Sim-Rank query returns the similarities between u and each node v ∈ V. This type of query is often used in link prediction, personalized recommendation and spam detection. While dealing with a large graph is beyond the ability of a single machine due to its limited memory and computational power, it is necessary to process single-source SimRank queries in a distributed environment, where the graph is partitioned and distributed across multiple machines. However, most current solutions are based on shared-memory model, where the whole graph is loaded into a shared memory and all processors can access the graph randomly. It is difficult to deploy such algorithms on shared-nothing model. In this paper, we present DISK, a distributed framework for processing single-source SimRank queries. DISK follows the linearized formulation of SimRank, and consists of offline and online phases. In the offline phase, a tree-based method is used to estimate the diagonal correction matrix of SimRank accurately, and in the online phase, single-source similarities are computed iteratively. Under this framework, we propose different optimization techniques to boost the indexing and queries. DISK guarantees both accuracy and parallel scalability, which distinguishes itself from existing solutions. Its accuracy, efficiency, parallel scalability and scalability are also verified by extensive experimental studies. The experiments show that DISK scales up to graphs of billions of nodes and edges, and answers online queries within seconds, while ensuring the accuracy bounds.

Regularized Born-Oppenheimer molecular dynamics

While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of Mead-Truhlar minimal coupling, this paper presents a new closure of the nuclear Born-Oppenheimer equation, thereby leading to a molecular dynamics scheme capturing geometric phase effects. Specifically, a semiclassical closure of the nuclear Ehrenfest dynamics is obtained through a convenient prescription for the nuclear Bohmian trajectories. The conical intersections are suitably regularized in the resulting nuclear particle motion and the associated Lorentz force involves a smoothened Berry curvature identifying a loop-dependent geometric phase. In turn, this geometric phase rapidly reaches the usual topological index as the loop expands away from the original singularity. This feature reproduces the phenomenology appearing in recent exact nonadiabatic studies, as shown explicitly in the Jahn-Teller problem for linear vibronic coupling. Likewise, a newly proposed regularization of the diagonal correction term is also shown to reproduce quite faithfully the energy surface presented in recent nonadiabatic studies.

Analysis of QED and non-adiabaticity effects on the rovibrational spectrum of H3 + using geometry-dependent effective nuclear masses.

The influence of QED effects (including one- and two-electron Lamb-shift, Araki-Sucher term, one-loop self-energy, and finite nuclear size correction) together with non-adiabatic effects on the rovibrational bound states of H3 + has been investigated. Non-adiabaticity is modeled by using geometry-dependent effective nuclear masses together with only one single potential energy surface. In conclusion, for rovibrational states below 20 000 cm-1, QED and relativistic effects do nearly compensate, and a potential energy surface based on Born-Oppenheimer energies and diagonal adiabatic corrections has nearly the same quality as the one including relativity with QED; the deviations between the two approaches for individual rovibrational states are mostly below 0.02 cm-1. The inclusion of non-adiabatic effects is important, and it reduces deviations from experiments mostly below 0.1 cm-1.

Hydrogen energy-level shifts induced by the atom motion: Crossover from the Lamb shifts to the motion-induced shifts

When the hydrogen atom moves, the proton current generates a magnetic field which interacts with the hydrogen electron. A simple analysis shows that for the hydrogen velocity [Formula: see text] the dominant interaction between the hydrogen momentum and the electron is of order of [Formula: see text], where [Formula: see text] is the fine structure constant, v is the atom velocity, c is the speed of light and m is the electron mass. Using the Bethe–Salpeter equation, the two velocity-dependent operators of this order are derived. As is well known, the degeneracy of the energy levels with the same principal quantum number, n, and the same quantum number of the total angular momentum, j, but the different orbital angular momenta [Formula: see text] is removed by the radiative corrections (the Lamb shift) that are proportional to [Formula: see text]. It is shown that the velocity-dependent perturbation interactions remove this degeneracy as well. There is, however, an important difference between the Lamb shifts and the energy-level shifts induced by the atom motion. The Lamb shift is the diagonal correction to the energy separately for each of the degenerate states. The velocity-dependent perturbation interactions result in the off-diagonal energy corrections between the mutually degenerate states. The joint effect of these two perturbations, which are essentially different in their origin, is analyzed. Given their order of magnitude, the crossover from the Lamb shifts to the motion-induced shifts should occur at the atom velocity [Formula: see text], where [Formula: see text] is a numerical factor dependent on n and j. An experiment using the orbital motion of the Earth is proposed to test the developed theory.

High Accuracy ab Initio Calculations of Rotational-Vibrational Levels of the HCN/HNC System.

Highly accurate ab initio calculations of vibrational and rotational-vibrational energy levels of the HCN/HNC (hydrogen cyanide/hydrogen isocyanide) isomerising system are presented for several isotopologues. All-electron multireference configuration interaction (MRCI) electronic structure calculations were performed using basis sets up to aug-cc-pCV6Z on a grid of 1541 geometries. The ab initio energies were used to produce an analytical potential energy surface (PES) describing the two minima simultaneously. An adiabatic Born-Oppenheimer diagonal correction (BODC) correction surface as well as a relativistic correction surface were also calculated. These surfaces were used to compute vibrational and rotational-vibrational energy levels up to 25 000 cm-1 which reproduce the extensive set of experimentally known HCN/HNC levels with a root-mean-square deviation σ = 1.5 cm-1. We studied the effect of nonadiabatic effects by introducing opportune radial and angular corrections to the nuclear kinetic energy operator. Empirical determination of two nonadiabatic parameters results in observed energies up to 7000 cm-1 for four HCN isotopologues (HCN, DCN, H13CN, and HC15N) being reproduced with σ = 0.37 cm-1. The height of the isomerization barrier, the isomerization energy and the dissociation energy were computed using a number of models; our best results are 16 809.4, 5312.8, and 43 729 cm-1, respectively.

Generation of correlated pseudorandom varibales

When Monte Carlo method is used to study many problems, it is sometimes necessary to sample correlated pseudorandom variables. Previous studies have shown that the Cholesky decomposition method can be used to generate correlated pseudorandom variables when the covariance matrix satisfies the positive eigenvalue condition. However, some covariance matrices do not satisfy the condition. In this study, the theoretical formula for generating correlated pseudorandom variables is deduced, and it is found that Cholesky decomposition is not the only way to generate multidimensional correlated pseudorandom variables. The other matrix decomposition methods can be used to generate multidimensional relevant random variables if the positive eigenvalue condition is satisfied. At the same time, we give the formula for generating the multidimensional random variable by using the covariance matrix, the relative covariance matrix and the correlation coefficient matrix to facilitate the later use. In order to verify the above theory, a simple test example with 33 relative covariance matrix is used, and it is found that the correlation coefficient results obtained by Jacobi method are consistent with those from the Cholesky method. The correlation coefficients are more close to the real values with increasing the sampling number. After that, the antineutrino energy spectra of Daya Bay are generated by using Jacobi matrix decomposition and Cholesky matrix decomposition method, and their relative errors of each energy bin are in good agreement, and the differences are less than 5.0% in almost all the energy bins. The above two tests demonstrate that the theoretical formula for generating correlated pseudorandom variables is corrected. Generating correlated pseudorandom variables is used in nuclear energy to analyze the uncertainty of nuclear data library in reactor simulation, and many codes have been developed, such as one-, two-and three-dimensional TSUNAMI, SCALE-SS, XSUSA, and SUACL. However, when the method of generating correlated pseudorandom variables is used to decompose the 238U radiation cross section covariance matrix, it is found that the negative eigenvalue appears and previous study method cannot be used. In order to deal with the 238U radiation cross section covariance matrix and other similar matrices, the zero correction is proposed. When the zero correction is used in Cholesky diagonal correction and Jacobi eigenvalue zero correction, it is found that Jacobi negative eigenvalue zero correction error is smaller than that with Cholesky diagonal correction. In future, the theory about zero correction will be studied and it will focus on ascertaining which correction method is better for the negative eigenvalue matrix.

Newton-like Method with Diagonal Correction for Distributed Optimization

We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are attractive due to their inexpensive iterations, but have a drawback of slow convergence rates. This motivates the incorporation of second order information in the distributed methods, but this task is challenging: although the Hessians which arise in the algorithm design respect the sparsity of the network, their inverses are dense, hence rendering distributed implementations difficult. We overcome this challenge and propose a class of distributed Newton-like methods, which we refer to as distributed quasi-newton (DQN). The DQN family approximates the Hessian inverse by (1) splitting the Hessian into its diagonal and off-diagonal parts, (2) inverting the diagonal part, and (3) approximating the inverse of the off-diagonal part through a weighted linear function. The approxim...

On the Bethe–Wigner–Shapiro limit of the rate coefficient for the capture of a rotating quadrupolar polarisable diatom by an ion

ABSTRACTThe low-energy (Bethe–Wigner–Shapiro) behaviour of the rate coefficient for capture of a polarisable quadrupolar rotationally excited diatom by an ion is calculated. The multichannel character of capture shows itself in the dependence of the effective attractive potential on the intrinsic angular momentum of the diatom and in a nonadiabatic diagonal correction to the potential. The predicted energy dependence of the rate coefficients is compared with previous numerically accurate results for the capture of H2 molecules by H2+ ions.

First fullyab initiopotential energy surface of methane with a spectroscopic accuracy

Full 9-dimensional ab initio potential energy surfaces for the methane molecule are constructed using extended electronic structure coupled-cluster calculations with various series of basis sets following increasing X cardinal numbers: cc-pVXZ (X = 3, 4, 5, 6), aug-cc-ACVXZ (X = 3, 4, 5), and cc-pCVXZ-F12 (X = 3, 4). High-order dynamic electron correlations including triple and quadrupole excitations as well as relativistic and diagonal Born-Oppenheimer breakdown corrections were accounted for. Analytical potential functions are parametrized as non-polynomial expansions in internal coordinates in irreducible tensor representation. Vibrational energy levels are reported using global variational nuclear motion calculations with exact kinetic energy operator and a full account of the tetrahedral symmetry of CH4. Our best ab initio surface including above-mentioned contributions provides the rms (obs.-calc.) errors of less than 0.11 cm−1 for vibrational band centers below 4700 cm−1, and ∼0.3 cm−1 for all 229 assigned experimentally determined vibrational levels up to the Icosad range <7900 cm−1 without empirically adjusted parameters. These results improve the accuracy of ab initio methane vibrational predictions by more than an order of magnitude with respect to previous works. This is an unprecedented accuracy of first-principles calculations of a five-atomic molecule for such a large data set. New ab initio potential results in significantly better band center predictions even in comparison with best available empirically corrected potential energy surfaces. The issues related to the basis set extrapolation and an additivity of various corrections at this level of accuracy are discussed.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Return Linkages and Volatility Spillover Effect Between Stock Markets and Currency Markets

This article undertakes the analysis of volatility and volatility spillover between stock market and currency market in India. Daily closing levels of the benchmark indices are taken for the period 1 April 2003–31 December 2013. The data are analysed through unit root tests, Autoregressive Conditionally Heteroskedastic (ARCH) family models, Johansen’s cointergation test, vector error correction model and diagonal Vector Error Correction Heteroskedastic (VECH) model. The results indicate a bidirectional volatility spillover between the Indian stock market and a currency market. The findings of the study also suggest that both the markets move in tandem with each other and there is a long-run relationship between these two markets.

Iterative universal state selective correction for the Brillouin-Wigner multireference coupled-cluster theory.

As a further development of the previously introduced a posteriori Universal State-Selective (USS) corrections [K. Kowalski, J. Chem. Phys. 134, 194107 (2011); J. Brabec et al., ibid. 136, 124102 (2012)], we suggest an iterative form of the USS correction by means of correcting effective Hamiltonian matrix elements. We also formulate USS corrections via the left Bloch equations. The convergence of the USS corrections with excitation level towards the full configuration interaction (FCI) limit is also investigated. Various forms of the USS and simplified diagonal USS corrections at the singles and doubles and perturbative triple levels are numerically assessed on several model systems and on the ozone and tetramethyleneethane molecules. It is shown that the iterative USS correction can successfully replace the previously developed a posteriori Brillouin-Wigner coupled cluster size-extensivity correction, while it is not sensitive to intruder states and performs well also in other cases when the a posteriori one fails, like, e.g., for the asymmetric vibration mode of ozone.