Local Correlation Methods Research Articles

Multiple-level Logarithmic Wavelets for Mammographic Contrast Enhancement: A Statistical Analysis for Wavelet Selection

Low doses radiation in mammography results in low contrast images. In this paper we propose a method to enhance the contrast in mammography; it combines the modification of the coefficients of the Logarithmic Discrete Wavelet Transform using the Local Correlation method and Symmetric Logarithmic Image Processing model. Experimental results shown the better performance for the anomalies known as calcifications and masses. This paper also presents a methodology to select a combination of decomposition levels to be processed for good contrast improvement according to the values of measures based on region of interest. This procedure relies on Principal Components Analysis of the data. The experiments show that the chosen combination of levels can improve the contrast in mammograms, and that the regions of interest definition is an important factor to explain the poor contrast improvement of some anomalies.

Explicitly correlated orbital optimized contracted pair correlation methods: Foundations and applications

Pair correlation methods are able to achieve highly accurate solutions for chemical problems. Unfortunately, their applicability is generally restricted to medium-sized molecules due to storage requirements and computational costs. These restrictions can be partly overcome by local correlation methods. These methods use physical and mathematical criteria to decide which interactions are of such a long range that they do not have to be computed and saved. In our new ansatz, we define an alternative way towards local correlation. The range of interactions is strictly bound to the decay of integrals over Gaussian type geminals in the atomic orbital basis. The number of variables is reduced by orders of magnitude applying an efficient contraction scheme, leading to a naturally local representation of correlation effects. This scheme is extended by orbital optimization to describe multi-reference problems and explicit correlation to improve the basis set convergence.

Comparison and combination of "direct" and fragment based local correlation methods: Cluster in molecules and domain based local pair natural orbital perturbation and coupled cluster theories.

Local correlation theories have been developed in two main flavors: (1) "direct" local correlation methods apply local approximation to the canonical equations and (2) fragment based methods reconstruct the correlation energy from a series of smaller calculations on subsystems. The present work serves two purposes. First, we investigate the relative efficiencies of the two approaches using the domain-based local pair natural orbital (DLPNO) approach as the "direct" method and the cluster in molecule (CIM) approach as the fragment based approach. Both approaches are applied in conjunction with second-order many-body perturbation theory (MP2) as well as coupled-cluster theory with single-, double- and perturbative triple excitations [CCSD(T)]. Second, we have investigated the possible merits of combining the two approaches by performing CIM calculations with DLPNO methods serving as the method of choice for performing the subsystem calculations. Our cluster-in-molecule approach is closely related to but slightly deviates from approaches in the literature since we have avoided real space cutoffs. Moreover, the neglected distant pair correlations in the previous CIM approach are considered approximately. Six very large molecules (503-2380 atoms) were studied. At both MP2 and CCSD(T) levels of theory, the CIM and DLPNO methods show similar efficiency. However, DLPNO methods are more accurate for 3-dimensional systems. While we have found only little incentive for the combination of CIM with DLPNO-MP2, the situation is different for CIM-DLPNO-CCSD(T). This combination is attractive because (1) the better parallelization opportunities offered by CIM; (2) the methodology is less memory intensive than the genuine DLPNO-CCSD(T) method and, hence, allows for large calculations on more modest hardware; and (3) the methodology is applicable and efficient in the frequently met cases, where the largest subsystem calculation is too large for the canonical CCSD(T) method.

Nature of the guest-host interactions for dibromine in the T, P, and H clathrate cages.

The guest-host intermolecular potentials for the ground states of Br2 in the tetrakaidecahedral (T), pentakaidecahedral (P), and hexakaidecahedral clathrate (H) cages have been calculated using ab initio local correlation methods. Applying the local correlation energy partitioning analysis together with first-order symmetry adapted perturbation theory, we obtain a detailed understanding of the nature of the interactions. In particular, the debated question concerning the possible presence of halogen bonding (XB) is carefully analyzed. In the case of the T cage, given its smaller size, the Br-O distance is too short leading to a larger exchange-repulsion for XB orientations which therefore do not represent minima. For the other two cages, the Br-O distance is too large leading to little orbital overlap effects and thus weaker donor-acceptor interactions; however, these orientations coincide with the global minima.

Compressed representation of dispersion interactions and long-range electronic correlations.

The description of electron correlation in quantum chemistry often relies on multi-index quantities. Here, we examine a compressed representation of the long-range part of electron correlation that is associated with dispersion interactions. For this purpose, we perform coupled-cluster singles and doubles (CCSD) computations on localized orbitals, and then extract the portion of CCSD amplitudes corresponding to dispersion energies. Using singular value decomposition, we uncover that a very compressed representation of the amplitudes is possible in terms of occupied-virtual geminal pairs located on each monomer. These geminals provide an accurate description of dispersion energies at medium and long distances. The corresponding virtual orbitals are examined by further singular value decompositions of the geminals. We connect each component of the virtual space to the multipole expansion of dispersion energies. Our results are robust with respect to basis set change and hold for systems as large as the benzene-methane dimer. This compressed representation of dispersion energies paves the way to practical and accurate approximations for dispersion, for example, in local correlation methods.

Local Descriptors of Dynamic and Nondynamic Correlation.

Quantitatively accurate electronic structure calculations rely on the proper description of electron correlation. A judicious choice of the approximate quantum chemistry method depends upon the importance of dynamic and nondynamic correlation, which is usually assesed by scalar measures. Existing measures of electron correlation do not consider separately the regions of the Cartesian space where dynamic or nondynamic correlation are most important. We introduce real-space descriptors of dynamic and nondynamic electron correlation that admit orbital decomposition. Integration of the local descriptors yields global numbers that can be used to quantify dynamic and nondynamic correlation. Illustrative examples over different chemical systems with varying electron correlation regimes are used to demonstrate the capabilities of the local descriptors. Since the expressions only require orbitals and occupation numbers, they can be readily applied in the context of local correlation methods, hybrid methods, density matrix functional theory, and fractional-occupancy density functional theory.

Accuracy of Explicitly Correlated Local PNO-CCSD(T).

In recent years PNO-based local correlation methods have gained popularity since they allow Coupled Cluster (CC) calculations with reduced computational costs, yet only a few systematic studies concerning their accuracy are available, in particular for the explicitly correlated versions. In this work we take a deeper look at the explicitly correlated local PNO-CCSD(F12*)(T0) and PNO-CCSD(F12*)(T) methods. The first variant uses the so-called semicanonical triples correction (T0) which neglects off-diagonal elements in the occupied block of the Fock matrix. In PNO-CCSD(F12*)(T) this approximation is avoided by means of Laplace transformation techniques and convergence to the canonical results in the limit of no PNO truncation is restored. We assess the accuracy of both methods using well established benchmark sets for reaction energies and weak molecular interactions and take a look at a system with strong cooperative many-body effects. For reaction energies a close agreement with canonical methods is observed, and chemical accuracy can be reached. Also for weak intermolecular interactions the accuracy is easily controlled, and the methods even allow for improving existing benchmark data.

A Critical Comparison of Some Metrological Parameters Characterizing Local Digital Image Correlation and Grid Method

The main metrological performance of two full-field measurement techniques, namely local digital image correlation (DIC) and grid method (GM), are compared in this paper. The fundamentals of these techniques are first briefly recalled. The formal link which exists between them is then given (the details of the calculation are in Appendix 1). Under mild assumptions, it is shown that GM theoretically gives the same result as DIC, since the formula providing the displacement with GM is the solution of the minimization of the cost function used in DIC in the particular case of a regular marking. In practice however, the way the solution is found being totally different from one technique to another, they feature different metrological performance. Some of the metrological characteristics of DIC and GM are studied in this paper. Since neither guideline nor precise standard is available to perform a fair comparison between them, a methodology must first be defined. It is proposed here to rely on three metrological parameters, namely the displacement resolution, the bias and the spatial resolution, to assess the metrological performance of each technique. These three parameters are thoroughly defined in the paper. Some of these quantities depend on external parameters such as the pattern of the surface of interest, so the same set of grid images is processed with both techniques. Only the contribution of the camera sensor noise to the displacement resolution is considered in this study. The displacement resolution, the bias and the spatial resolution are not independent but linked. These links are therefore studied in depth for DIC and GM and compared. In particular, it is shown that the product between the displacement resolution and the spatial resolution can be considered as a metric to perform this comparison. The extension to speckled patterns of the lessons drawn from grids is finally addressed in the last part of the paper. As a general conclusion, it can be said that for the value of the bias fixed in this study, the additional cost due to grid depositing offers GM to feature a better compromise than subset-based local DIC between displacement resolution and spatial resolution.

Nature of the valence excited states of bromine in the T and P clathrate cages.

The guest-host intermolecular potentials for the valence excited states of Br2 in the tetrakaidecahedral(T) and pentakaidecahedral(P) clathrate cages have been calculated using ab initio local correlation methods. We find that the excited states are more strongly bound than the corresponding ground states even in the small T cage where bromine has a tight fit. The angular dependence of the interaction energies is quite anisotropic; this reflects in the corresponding electronic shifts where regions of maxima for blue-shifts in the T cage indicate the presence of halogen bonding. We predict a large temperature dependence of the electronic shifts and compare absolute values with recent experimental studies. This stringent test indicates the reliability of local correlation treatments to describe weak intermolecular forces in ground and excited states.

Local correlation and orbit determination for DOR signals in Chang’E-3

The X-band Delta-Differential One-way Range is first formally used in Chang’E-3 spacecraft, and will be continually used for other Chinese future deep space navigation. We have carried out researches on each DOR tone using local correlation method which is quite different from the conventional VLBI correlator. The CE-3 signal interferometry processing is completed with this method. High precision Delta-DOR group delay and radio source correction are obtained for orbit determination. The phase noise of local correlation is significantly smaller than that of the VLBI conventional correlator. The ephemeris from local correlation is about 20 m different from the precise ephemeris of CE-3 project, and the corresponding equivalent residual delay is about 0.4 ns. Experiment result shows that local correlation is more suitable for weak signal processing, and it can be used for the future Chinese lunar and other deep space exploration projects.

Differentially correlated genes in co-expression networks control phenotype transitions

Background: Co-expression networks are a tool widely used for analysis of “Big Data” in biology that can range from transcriptomes to proteomes, metabolomes and more recently even microbiomes. Several methods were proposed to answer biological questions interrogating these networks. Differential co-expression analysis is a recent approach that measures how gene interactions change when a biological system transitions from one state to another. Although the importance of differentially co-expressed genes to identify dysregulated pathways has been noted, their role in gene regulation is not well studied. Herein we investigated differentially co-expressed genes in a relatively simple mono-causal process (B lymphocyte deficiency) and in a complex multi-causal system (cervical cancer). Methods: Co-expression networks of B cell deficiency (Control and BcKO) were reconstructed using Pearson correlation coefficient for two mus musculus datasets: B10.A strain (12 normal, 12 BcKO) and BALB/c strain (10 normal, 10 BcKO). Co-expression networks of cervical cancer (normal and cancer) were reconstructed using local partial correlation method for five datasets (total of 64 normal, 148 cancer). Differentially correlated pairs were identified along with the location of their genes in BcKO and in cancer networks. Minimum Shortest Path and Bi-partite Betweenness Centrality where statistically evaluated for differentially co-expressed genes in corresponding networks. Results: We show that in B cell deficiency the differentially co-expressed genes are highly enriched with immunoglobulin genes (causal genes). In cancer we found that differentially co-expressed genes act as “bottlenecks” rather than causal drivers with most flows that come from the key driver genes to the peripheral genes passing through differentially co-expressed genes. Using in vitro knockdown experiments for two out of 14 differentially co-expressed genes found in cervical cancer (FGFR2 and CACYBP), we showed that they play regulatory roles in cancer cell growth. Conclusion: Identifying differentially co-expressed genes in co-expression networks is an important tool in detecting regulatory genes involved in alterations of phenotype.

Communication: Multipole approximations of distant pair energies in local correlation methods with pair natural orbitals.

The accuracy of multipole approximations for distant pair energies in local second-order Møller-Plesset perturbation theory (LMP2) as introduced by Hetzer et al. [Chem. Phys. Lett. 290, 143 (1998)] is investigated for three chemical reactions involving molecules with up to 92 atoms. Various iterative and non-iterative approaches are compared, using different energy thresholds for distant pair selection. It is demonstrated that the simple non-iterative dipole-dipole approximation, which has been used in several recent pair natural orbitals (PNO)-LMP2 and PNO-LCCSD (local coupled-cluster with singles and doubles) methods, may underestimate the distant pair energies by up to 50% and can lead to significant errors in relative energies, unless very tight thresholds are used. The accuracy can be much improved by including higher multipole orders and by optimizing the distant pair amplitudes iteratively along with all other amplitudes. A new approach is presented in which very small special PNO domains for distant pairs are used in the iterative approach. This reduces the number of distant pair amplitudes by 3 orders of magnitude and keeps the additional computational effort for the iterative optimization of distant pair amplitudes minimal.

Differentially correlated genes in co-expression networks control phenotype transitions.

Co-expression networks are a tool widely used for analysis of "Big Data" in biology that can range from transcriptomes to proteomes, metabolomes and more recently even microbiomes. Several methods were proposed to answer biological questions interrogating these networks. Differential co-expression analysis is a recent approach that measures how gene interactions change when a biological system transitions from one state to another. Although the importance of differentially co-expressed genes to identify dysregulated pathways has been noted, their role in gene regulation is not well studied. Herein we investigated differentially co-expressed genes in a relatively simple mono-causal process (B lymphocyte deficiency) and in a complex multi-causal system (cervical cancer). Co-expression networks of B cell deficiency (Control and BcKO) were reconstructed using Pearson correlation coefficient for two mus musculus datasets: B10.A strain (12 normal, 12 BcKO) and BALB/c strain (10 normal, 10 BcKO). Co-expression networks of cervical cancer (normal and cancer) were reconstructed using local partial correlation method for five datasets (total of 64 normal, 148 cancer). Differentially correlated pairs were identified along with the location of their genes in BcKO and in cancer networks. Minimum Shortest Path and Bi-partite Betweenness Centrality where statistically evaluated for differentially co-expressed genes in corresponding networks. Results: We show that in B cell deficiency the differentially co-expressed genes are highly enriched with immunoglobulin genes (causal genes). In cancer we found that differentially co-expressed genes act as "bottlenecks" rather than causal drivers with most flows that come from the key driver genes to the peripheral genes passing through differentially co-expressed genes. Using in vitro knockdown experiments for two out of 14 differentially co-expressed genes found in cervical cancer (FGFR2 and CACYBP), we showed that they play regulatory roles in cancer cell growth. Identifying differentially co-expressed genes in co-expression networks is an important tool in detecting regulatory genes involved in alterations of phenotype.

Near-Edge X-ray Absorption Fine Structure within Multilevel Coupled Cluster Theory.

Core excited states are challenging to calculate, mainly because they are embedded in a manifold of high-energy valence-excited states. However, their locality makes their determination ideal for local correlation methods. In this paper, we demonstrate the performance of multilevel coupled cluster theory in computing core spectra both within the core-valence separated and the asymmetric Lanczos implementations of coupled cluster linear response theory. We also propose a visualization tool to analyze the excitations using the difference between the ground-state and excited-state electron densities.

SparseMaps--A systematic infrastructure for reduced-scaling electronic structure methods. III. Linear-scaling multireference domain-based pair natural orbital N-electron valence perturbation theory.

Multi-reference (MR) electronic structure methods, such as MR configuration interaction or MR perturbation theory, can provide reliable energies and properties for many molecular phenomena like bond breaking, excited states, transition states or magnetic properties of transition metal complexes and clusters. However, owing to their inherent complexity, most MR methods are still too computationally expensive for large systems. Therefore the development of more computationally attractive MR approaches is necessary to enable routine application for large-scale chemical systems. Among the state-of-the-art MR methods, second-order N-electron valence state perturbation theory (NEVPT2) is an efficient, size-consistent, and intruder-state-free method. However, there are still two important bottlenecks in practical applications of NEVPT2 to large systems: (a) the high computational cost of NEVPT2 for large molecules, even with moderate active spaces and (b) the prohibitive cost for treating large active spaces. In this work, we address problem (a) by developing a linear scaling "partially contracted" NEVPT2 method. This development uses the idea of domain-based local pair natural orbitals (DLPNOs) to form a highly efficient algorithm. As shown previously in the framework of single-reference methods, the DLPNO concept leads to an enormous reduction in computational effort while at the same time providing high accuracy (approaching 99.9% of the correlation energy), robustness, and black-box character. In the DLPNO approach, the virtual space is spanned by pair natural orbitals that are expanded in terms of projected atomic orbitals in large orbital domains, while the inactive space is spanned by localized orbitals. The active orbitals are left untouched. Our implementation features a highly efficient "electron pair prescreening" that skips the negligible inactive pairs. The surviving pairs are treated using the partially contracted NEVPT2 formalism. A detailed comparison between the partial and strong contraction schemes is made, with conclusions that discourage the strong contraction scheme as a basis for local correlation methods due to its non-invariance with respect to rotations in the inactive and external subspaces. A minimal set of conservatively chosen truncation thresholds controls the accuracy of the method. With the default thresholds, about 99.9% of the canonical partially contracted NEVPT2 correlation energy is recovered while the crossover of the computational cost with the already very efficient canonical method occurs reasonably early; in linear chain type compounds at a chain length of around 80 atoms. Calculations are reported for systems with more than 300 atoms and 5400 basis functions.

Sparse maps--A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory.

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

Performance of local correlation methods for halogen bonding: The case of Br2-(H2O)n,n = 4,5 clusters and Br2@5(12)6(2) clathrate cage.

The performance of local correlation methods is examined for the interactions present in clusters of bromine with water where the combined effect of hydrogen bonding (HB), halogen bonding (XB), and hydrogen-halogen (HX) interactions lead to many interesting properties. Local methods reproduce all the subtleties involved such as many-body effects and dispersion contributions provided that specific methodological steps are followed. Additionally, they predict optimized geometries that are nearly free of basis set superposition error that lead to improved estimates of spectroscopic properties. Taking advantage of the local correlation energy partitioning scheme, we compare the different interaction environments present in small clusters and those inside the 5(12)6(2) clathrate cage. This analysis allows a clear identification of the reasons supporting the use of local methods for large systems where non-covalent interactions play a key role.

A study of binary local histogram correlation for automatic detection of optical printed Chinese character recognition errors

In optical printed Chinese character recognition (OPCCR), some recognition errors would often occur, especially in recognition of similar characters. The recognition errors are commonly checked and corrected manually, because automatic detection of the errors is difficult. Hence, in this paper, we propose a binary local histogram correlation (BLHC) method for automatic detection of OPCCR errors. In the method, the recognized characters are converted into OPCCR images. The images of optical printed Chinese character (OPCC) and OPCCR are filtered using differential low pass filter (DLPF) and segmented into binary images using adaptive threshold segmentation. The binary images are divided into blocks and the histograms of the blocks are selected as the features of local structures. The correlations of the local histograms between OPCC and OPCCR are utilized to determine whether OPCCR errors occur. In image block division, three division methods are studied to see the affects on error detection risk (EDR) and error detection rate. To validate the BLHC method, some experiments have been done. Experiment results showed that BLHC method using 1/2 offset second division has the advantages of simple programming, fast computation and high error detection rate.

Linear-Scaling Coupled Cluster with Perturbative Triple Excitations: The Divide-Expand-Consolidate CCSD(T) Model.

We propose a reformulation of the traditional (T) triples correction to the coupled cluster singles and doubles (CCSD) energy in terms of local Hartree-Fock (HF) orbitals such that its structural form aligns with our recently developed linear-scaling divide-expand-consolidate (DEC) coupled cluster family of local correlation methods. In a DEC-CCSD(T) calculation, a basis of local occupied and virtual HF orbitals is used to partition the correlated calculation on the full system into a number of independent atomic fragment and pair fragment calculations, each performed within a truncated set of the complete orbital space. In return, this leads to a massively parallel algorithm for the evaluation of the DEC-CCSD(T) correlation energy, which formally scales linearly with the size of the full system and has a tunable precision with respect to a conventional CCSD(T) calculation via a single energy-based input threshold. The theoretical developments are supported by proof of concept DEC-CCSD(T) calculations on a series of medium-sized molecular systems.

Linear-scaling implementation of the direct random-phase approximation.

We report the linear-scaling implementation of the direct random-phase approximation (dRPA) for closed-shell molecular systems. As a bonus, linear-scaling algorithms are also presented for the second-order screened exchange extension of dRPA as well as for the second-order Møller-Plesset (MP2) method and its spin-scaled variants. Our approach is based on an incremental scheme which is an extension of our previous local correlation method [Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The approach extensively uses local natural orbitals to reduce the size of the molecular orbital basis of local correlation domains. In addition, we also demonstrate that using natural auxiliary functions [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], the size of the auxiliary basis of the domains and thus that of the three-center Coulomb integral lists can be reduced by an order of magnitude, which results in significant savings in computation time. The new approach is validated by extensive test calculations for energies and energy differences. Our benchmark calculations also demonstrate that the new method enables dRPA calculations for molecules with more than 1000 atoms and 10,000 basis functions on a single processor.