Overlap Matrix Research Articles

Effective-mode analysis of the dynamics of weakly bound molecular systems by an example of hydrogen-bonded water clusters

A method for the analysis of internal dynamics of nonlinear weakly bound polymolecular systems based on the effective-mode approach is proposed. The method enables one to estimate the number of the governing collective degrees of freedom of the system of interest at a preset accuracy under particular conditions and analyze the character of the modes depending on the activation energy of the system and the duration of its dynamic propagation, which provides qualitative and quantitative information about the coupling of diverse motions and the respective energy redistribution. The method is applied to the analysis of the dynamics of small water clusters stabilized by hydrogen bonds, which are unique spectacular examples of the systems with a pronounced coupling between the intramolecular and substantially delocalized intermolecular oscillations. The dynamic trajectories were generated in the adiabatic approximation at the Born-Oppenheimer level with the use of the quantum chemical description of selected clusters at the $\mathrm{MP}2/6\ensuremath{-}311++G(d,p)$ level. The initial conditions corresponded to different variants of the excitation of low-frequency normal modes, and the dynamic runs were carried out at a time step of 0.5 fs and the whole duration of 50 to 100 ps. Different prevailing characters of the cluster dynamics were identified depending on the molecular size, the total activation energy, and the mean potential-energy-increment to kinetic-energy-increment ratio, from an efficient accumulation of the excess kinetic energy on the effective modes of the cluster to the dissociation of the cluster into constituting fragments. The signs of the corresponding processes in the overlap matrices of the effective-mode vectors, kinetic-energy distribution over the modes, and the correlation between the number of the modes and the mean kinetic energy of the cluster are distinguished.

Downward quantum learning from element 118: Automated generation of Fermi-Löwdin orbitals for all atoms.

A new algorithm based on a rigorous theorem and quantum data computationally mined from element 118 guarantees automated construction of initial Fermi-Löwdin-Orbital (FLO) starting points for all elements in the Periodic Table. It defines a means for constructing a small library of scalable FLOs for universal use in molecular and solid-state calculations. The method can be systematically improved for greater efficiency and for applications to excited states such as x-ray excitations and optically silent excitations. FLOs were introduced to recast the Perdew-Zunger self-interaction correction (PZSIC) into an explicit unitarily invariant form. The FLOs are generated from a set of N quasi-classical electron positions, referred to as Fermi-Orbital descriptors (FODs), and a set of N-orthonormal single-electron orbitals. FOD positions, when optimized, minimize the PZSIC total energy. However, creating sets of starting FODs that lead to a positive definite Fermi orbital overlap matrix has proven to be challenging for systems composed of open-shell atoms and ions. The proof herein guarantees the existence of a FLOSIC solution and further guarantees that if a solution for N electrons is found, it can be used to generate a minimum of N - 1 and a maximum of 2N - 2 initial starting points for systems composed of a smaller number of electrons. Applications to heavy and super-heavy atoms are presented. All starting solutions reported here were obtained from a solution for element 118, Oganesson.

CCNB2 as a potential biomarker of bladder cancer via the high throughput technology.

Bladder cancer and oral squamous cell carcinoma (OSCC) seriously affect people's health. However, the relationship between bladder cancer and OSCC remains unclear. Got GSE138206, GSE146483, GSE184616, and bladder cancer datasets GSE65635, GSE100926 from Gene Expression Omnibus database. Weighted gene co-expression network analysis was used to identify the significant module. Functional enrichment analysis was performed via the Gene Ontology analysis and Kyoto Encyclopedia of Genes and Genomes. Furthermore, the Gene Set Enrichment Analysis was also used to complete the enrichment analysis. Comparative Toxicogenomics Database found most relevant diseases to core genes. TargetScan is used to forecast analysis of microRNA and target genes. In Gene Ontology analysis, differentially expressed genes were mostly concentrated in cell differentiation, extrallular region, structural molecule activity, and actin binding. In Kyoto Encyclopedia of Genes and Genomes analysis, the differentially expressed genes were mainly enriched in PI3K-Akt signaling pathway, pathway in cancer, and extracellular matrix-receptor interaction. Seven hub genes (cyclin B2 [CCNB2], TK1, CDC20, PCNA, CKS1B, CDCA5, MCM4) were obtained. Hub genes (CCNB2, CDC20) are highly expressed in OSCC and bladder cancer samples. CCNB2 was one common oncogene of bladder cancer and OSCC.

Filtering time-dependent covariance matrices using time-independent eigenvalues

We propose a data-driven, model-free, way to reduce the noise of covariance matrices of time-varying systems. If the true covariance matrix is time-invariant, non-linear shrinkage of the eigenvalues is known to yield the optimal estimator for large matrices. Such a method outputs eigenvalues that are highly dependent on the inputs, as common sense suggests. When the covariance matrix is time-dependent, we show that it is generally better to use the set of eigenvalues that encode the average influence of the future on present eigenvalues resulting in a set of time-independent average eigenvalues. This situation is widespread in nature, one example being financial markets, where non-linear shrinkage remains the gold-standard filtering method. Our approach outperforms non-linear shrinkage both for the Frobenius norm distance, which is the typical loss function used for covariance filtering and for financial portfolio variance minimization, which makes our method generically relevant to many problems of multivariate inference. Further analysis of financial data suggests that the expected overlap between past eigenvectors and future ones is systematically overestimated by methods designed for constant covariances matrices. Our method takes a simple empirical average of the eigenvector overlap matrix, which is enough to outperform non-linear shrinkage.

Generalized nonorthogonal matrix elements. II: Extension to arbitrary excitations

Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication [H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021)], I introduced a generalized extension to the nonorthogonal Wick's theorem that allows matrix elements to be derived between excited configurations from a pair of reference determinants with a singular nonorthogonal orbital overlap matrix. However, that work only provided explicit expressions for one- and two-body matrix elements between singly- or doubly-excited configurations. Here, this framework is extended to compute generalized nonorthogonal matrix elements between higher-order excitations. Pre-computing and storing intermediate values allows one- and two-body matrix elements to be evaluated with an O(1) scaling relative to the system size, and the LIBGNME computational library is introduced to achieve this in practice. These advances make the evaluation of all nonorthogonal matrix elements almost as easy as their orthogonal counterparts, facilitating a new phase of development in nonorthogonal electronic structure theory.

Pivot invariance of multiconfiguration perturbation theory via frame vectors.

Multiconfiguration perturbation theory (MCPT) is a general framework for correcting the reference function of arbitrary structures. The variants of MCPT introduced so far differ in the specification of their zero-order Hamiltonian, i.e., the partitioning. A common characteristic of MCPT variants is that no numerical procedure is invoked when handling the overlap of the reference function and determinants spanning the configuration space. This comes at the price of pinpointing a principal term in the determinant expansion of the reference, rendering the PT results dependent on this choice. It is here shown that the pivot dependence of MCPT can be eliminated by using an overcomplete set of projected determinants in the space orthogonal and complementary to the reference. The projected determinants form a so-called frame, a generalization of the notion of basis, allowing for redundancy of the set. The simple structure of the frame overlap matrix facilitates overlap treatment in closed form, a feature shared by previous MCPT variants. In particular, the Moore-Penrose inverse of singular matrices appearing in frame-based MCPT can be constructed without the need for any pivoting algorithm or numerical zero threshold. Pilot numerical studies are performed for the singlet-triplet gap of biradicaloid systems, relying on geminal-based, incomplete model space reference function. Comparison with previous MCPT variants as well as illustration of pivot invariance is provided.

Obtaining Electronic Properties of Molecules through Combining Density Functional Tight Binding with Machine Learning.

We have introduced a machine learning workflow that allows for optimizing electronic properties in the density functional tight binding method (DFTB). The workflow allows for the optimization of electronic properties by generating two-center integrals, either by training basis function parameters directly or by training a spline model for the diatomic integrals, which are then used to build the Hamiltonian and the overlap matrices. Using our workflow, we have managed to obtain improved electronic properties, such as charge distributions, dipole moments, and approximated polarizabilities. While both machine learning approaches enabled us to improve on the electronic properties of the molecules as compared with existing DFTB parametrizations, only by training on the basis function parameters we were able to obtain consistent Hamiltonians and overlap matrices in the physically reasonable ranges or to improve on multiple electronic properties simultaneously.

Multiqubit state learning with entangling quantum generative adversarial networks

The increasing success of classical generative adversarial networks (GANs) has inspired several quantum versions of GANs. Fully quantum mechanical applications of such quantum GANs have been limited to one- and two-qubit systems. In this paper, we investigate the entangling quantum GAN (EQ-GAN) for multiqubit learning. We show that the EQ-GAN can learn a circuit more efficiently compared with a SWAP test. We also consider the EQ-GAN for learning eigenstates that are variational quantum eigensolver (VQE)-approximated, and find that it generates excellent overlap matrix elements when learning VQE states of small molecules. However, this does not directly translate into a good estimate of the energy due to a lack of phase estimation. Finally, we consider random state learning with the EQ-GAN for up to six qubits, using different two-qubit gates, and show that it is capable of learning completely random quantum states, something which could be useful in quantum state loading.

Real-space entanglement spectra of parton states in fractional quantum Hall systems

Real-space entanglement spectra (RSES) capture characteristic features of the topological order encoded in the fractional quantum Hall (FQH) states. In this work, we numerically compute, using Monte Carlo methods, the RSES and the counting of edge excitations of non-Abelian FQH states constructed using the parton theory. Efficient numerical computation of RSES of parton states is possible, thanks to their product-of-Slater-determinant structure, allowing us to compute the spectra in systems of up to 80 particles. Specifically, we compute the RSES of the parton states $\phi_2^2$, $\phi_2^3$, and $\phi_3^2$, where $\phi_n$ is the wave function of $n$ filled Landau levels, in the ground state as well as in the presence of bulk quasihole states. We then explicitly demonstrate a one-to-one correspondence of RSES of the parton states with representations of the Kac-Moody algebras satisfied by their edge currents. We also show that for the lowest Landau level projected version of these parton states, the spectra match with that obtained from the edge current algebra. We also perform a computation of spectra of the overlap matrices corresponding to the edge excitations of the parton states with a constrained number of particles in the different parton Landau levels. Counting in these matches the individual branches present in RSES, providing insight about how different branches are formed.

Generalized quantum assisted simulator

We provide a noisy intermediate-scale quantum framework for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithm does not require any classical–quantum feedback loop, bypass the barren plateau problem and does not necessitate any complicated measurements such as the Hadamard test. We introduce the notion of the hybrid density matrix, which allows us to disentangle the different steps of our algorithm and delegate classically demanding tasks to the quantum computer. Our algorithm proceeds in three disjoint steps. First, we select the ansatz, followed by measuring overlap matrices on a quantum computer. The final step involves classical post-processing data from the second step. Our algorithm has potential applications in solving the Navier–Stokes equation, plasma hydrodynamics, quantum Boltzmann training, quantum signal processing and linear systems. Our entire framework is compatible with current experiments and can be implemented immediately.

Calculations of shake-up satellites intensities in photoelectron spectra by generalized configuration interaction method

Satellites i.e. two-hole-one-particle states appear due to many-electron correlations in photoelectron spectra in addition to main lines corresponding to one-hole states. The correct assignment of these states is important for understanding the photoionization processes and for materials analysis by photoelectron spectroscopy. In the present work two different existing methods, which use overlap or Coulomb interaction matrix elements are considered and a new method is proposed. In this technique many-electron effects of satellites origin and interactions between satellite states are accounted for simultaneously by solving secular matrix. The method is applied to satellite states 2p −23p(4p), 2p −23s, 2p −23d of Ne photoionization for which contradiction between two interpretations existed. The results of calculations unambiguously support one the interpretations.

The cosine-sine decomposition with different-orbitals-for-different-spins determinants

The spin decomposition of a spin-contaminated different-orbitals-for-different-spins (DODS) wave function is formulated in terms of the Krylov space of the operator. The number of determinants that contribute to the various projected spin eigenfunctions depends on the sparsity of the orbital overlap matrix X between the α and β spatial orbitals. The cosine-sine decomposition (CSD) procedure may be applied to this overlap matrix, and the resulting redundant orbital transformations may be applied to the α and β spatial orbitals. This produces a sparse X′ matrix in the transformed basis in which each row or column has either one or two nonzero elements. This sparse X′ matrix simplifies the spin-decomposition procedure in three ways: 1) it reduces the number of contributing determinants within the Krylov basis functions and within the projected spin functions, 2) it reduces the effective orbital dimension through elimination of the frozen core and frozen virtual orbitals, and 3) it simplifies the spin-decomposition procedure in both the original and transformed bases by limiting the Krylov space dimension. These simplifications all reduce the computational effort for the spin-decomposition process. This procedure is implemented within a string-based DODS determinant formulation and applied to spin projection of unrestricted Hartree–Fock determinants.

Rotational tunneling in molecular crystals revisited: Realization of pocket states

Pocket states have been widely used for analyzing tunneling spectra of XH3- and XH4-groups (X = C, N) in molecular and ionic crystals. The present approach consists in realizations of these pocket states based on exact solutions of the Mathieu equation, both for potentials of 2-fold and 3-fold symmetry. With Gaussians decorated by trigonometric functions quantitative values for the overlap matrix elements h, the overlap g and effective transition matrix elements heff are obtained. For potentials not too small, heff agrees very well with the exact solution hM from the Mathieu equation. Potential dependent results provide a better view on both, advantages and limitations of the pocket state formalism. For 2-fold symmetry, pocket states can be fitted to both ground state functions. A combination of the two solutions leads to an increased agreement between heff and hM. For 3-fold symmetry a more direct access to experimental data is reached, particularly for small tetrahedral molecules like CH4. The overlap g which can be deduced from observed tunnel splittings, is predicted within the pocket state formalism. Experimental data for solid CH4 II are well reproduced.

Bioinformatics role of the WGCNA analysis and co-expression network identifies of prognostic marker in lung cancer

Lung cancer is the most talked about cancer in the world. It is also one of the cancers that currently has a high mortality rate. The aim of our research is to find more effective therapeutic targets and prognostic markers for human lung cancer. First, we download gene expression data from the GEO database. We performed weighted co-expression network analysis on the selected genes, we then constructed scale-free networks and topological overlap matrices, and performed correlation modular analysis with the cancer group. We screened the 200 genes with the highest correlation in the cyan module for functional enrichment analysis and protein interaction network construction, found that most of them focused on cell division, tumor necrosis factor-mediated signaling pathways, cellular redox homeostasis, reactive oxygen species biosynthesis, and other processes, and were related to the cell cycle, apoptosis, HIF-1 signaling pathway, p53 signaling pathway, NF-κB signaling pathway, and several cancer disease pathways are involved. Finally, we used the GEPIA website data to perform survival analysis on some of the genes with GS > 0.6 in the cyan module. CBX3, AHCY, MRPL12, TPGB, TUBG1, KIF11, LRRC59, MRPL17, TMEM106B, ZWINT, TRIP13, and HMMR was identified as an important prognostic factor for lung cancer patients. In summary, we identified 12 mRNAs associated with lung cancer prognosis. Our study contributes to a deeper understanding of the molecular mechanisms of lung cancer and provides new insights into drug use and prognosis.

Efficacy and safety of Daoyin and massage for lumbar disc herniation: A protocol for overview of systematic reviews.

Background:Lumbar disc herniation (LDH) is a common disease, which can cause low back pain, sciatica, and even disability. The treatment of LDH is a global challenge. Conservative therapy with non-drugs is considered to be the first choice for patients with LDH. In recent years, an increasing number of systematic reviews and meta analyses on Daoyin and massage interventions in lumbar disc herniation have been implemented. However, the evidence quality and methodological quality of these systematic reviews/meta analyses are unknown and need to be systematically evaluated. This overview aims to systematically summarize and critically appraise the current evidence on Daoyin and massage for LDH.Methods:Eight electronic data will be retrieved, including China National Knowledge Infrastructure (CNKI), Wanfang database (WF), China Biomedical database (CBM), Chinese Scientific Journals Database (VIP), PubMed, Cochrane Library, Web of Science (WOS), and EMBASE from their inception to March 1, 2022. The reporting quality, methodological quality, risk of bias, quality of evidence will be assessed by using The Preferred Reporting Items for Systematic Reviews and Meta-analyses 2020 (PRISMA 2020), the Assessment of Multiple Systematic Reviews 2 (AMSTAR-2), the Risk of Bias in Systematic Review (ROBIS), and the Grading of Recommendations Assessment, Development, and Evaluation (GRADE). Two independent researchers conducted literature screening, data extraction, and quality evaluation process. In addition, we will establish an overlap matrix and calculate the corrected covered area to evaluate the impact of overlapping areas on conclusions.Results:The results will be published in a peer-reviewed journal.Conclusion:This overview will provide comprehensive evidence of Daoyin and massage for treating lumbar disc herniation.Systematic review registration:INPLASY202210019.

Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions.

Atomic fingerprints are commonly used for the characterization of local environments of atoms in machine learning and other contexts. In this work, we study the behavior of two widely used fingerprints, namely, the smooth overlap of atomic positions (SOAP) and the atom-centered symmetry functions (ACSFs), under finite changes of atomic positions and demonstrate the existence of manifolds of quasi-constant fingerprints. These manifolds are found numerically by following eigenvectors of the sensitivity matrix with quasi-zero eigenvalues. The existence of such manifolds in ACSF and SOAP causes a failure to machine learn four-body interactions, such as torsional energies that are part of standard force fields. No such manifolds can be found for the overlap matrix (OM) fingerprint due to its intrinsic many-body character.

CeRNA Network and Functional Enrichment Analysis of Preeclampsia by Weighted Gene Coexpression Network Analysis.

Background Preeclampsia (PE) is a multisystemic syndrome which has short- and long-term risk to mothers and children and has pluralistic etiology. Objective This study is aimed at constructing a competitive endogenous RNA (ceRNA) network for pathways most related to PE using a data mining strategy based on weighted gene coexpression network analysis (WGCNA). Methods We focused on pathways involving hypoxia, angiogenesis, and epithelial mesenchymal transition according to the gene set variation analysis (GSVA) scores. The gene sets of these three pathways were enriched by gene set enrichment analysis (GSEA). WGCNA was used to study the underlying molecular mechanisms of the three pathways in the pathogenesis of PE by analyzing the relationship among pathways and genes. The soft threshold power (β) and topological overlap matrix allowed us to obtain 15 modules, among which the red module was chosen for the downstream analysis. We chose 10 hub genes that satisfied ∣log2Fold Change | >2 and had a higher degree of connectivity within the module. These candidate genes were subsequently confirmed to have higher gene significance and module membership in the red module. Coexpression networks were established for the hub genes to unfold the connection between the genes in the red module and PE. Finally, ceRNA networks were constructed to further clarify the underlying molecular mechanism involved in the occurrence of PE. 56 circRNAs, 17 lncRNAs, and 20 miRNAs participated in the regulation of the hub genes. Coagulation factor II thrombin receptor (F2R) and lumican (LUM) were considered the most relevant genes, and ceRNA networks of them were constructed. Conclusion The microarray data mining process based on bioinformatics methods constructed lncRNA and miRNA networks for ten hub genes that were closely related to PE and focused on ceRNAs of F2R and LUM finally. The results of our study may provide insight into the mechanisms underlying PE occurrence.

Complex band structure with non-orthogonal basis set: analytical properties and implementation in the SIESTA code

The complex band structure (CBS), although not directly observable, determines many properties of a material where the periodicity is broken, such at surfaces, interfaces and defects. Furthermore, its knowledge helps in the interpretation of electronic transport calculations and in the study of topological materials. Here we extend the transfer matrix method, often used to compute the complex bands, to electronic structures constructed using an atomic non-orthogonal basis set. We demonstrate that when the overlap matrix is not the identity, the non-orthogonal case, spurious features appear in the analytic continuation of the band structure to the complex plane. The properties of these are studied both numerically and analytically and discussed in the context of existing literature. Finally, a numerical implementation to extract the CBS from periodic calculations carried out with the density functional theory code siesta is presented. This is constructed as a simple post-processing tool, and it is therefore amenable to high-throughput studies of insulators and semiconductors.

Optimizing weighted gene co-expression network analysis with a multi-threaded calculation of the topological overlap matrix.

Biomolecular networks are often assumed to be scale-free hierarchical networks. The weighted gene co-expression network analysis (WGCNA) treats gene co-expression networks as undirected scale-free hierarchical weighted networks. The WGCNA R software package uses an Adjacency Matrix to store a network, next calculates the topological overlap matrix (TOM), and then identifies the modules (sub-networks), where each module is assumed to be associated with a certain biological function. The most time-consuming step of WGCNA is to calculate TOM from the Adjacency Matrix in a single thread. In this paper, the single-threaded algorithm of the TOM has been changed into a multi-threaded algorithm (the parameters are the default values of WGCNA). In the multi-threaded algorithm, Rcpp was used to make R call a C++ function, and then C++ used OpenMP to start multiple threads to calculate TOM from the Adjacency Matrix. On shared-memory MultiProcessor systems, the calculation time decreases as the number of CPU cores increases. The algorithm of this paper can promote the application of WGCNA on large data sets, and help other research fields to identify sub-networks in undirected scale-free hierarchical weighted networks. The source codes and usage are available at https://github.com/do-somethings-haha/multi-threaded_calculate_unsigned_TOM_from_unsigned_or_signed_Adjacency_Matrix_of_WGCNA.

Scalable ab initio fragmentation methods based on a truncated expansion of the non-orthogonal molecular orbital model.

An alternative formulation of the non-orthogonal molecular orbital model of electronic structure theory is developed based on the expansion of the inverse molecular orbital overlap matrix. From this model, a hierarchy of ab initio fragment-based quantum chemistry methods, referred to as the nth-order expanded non-orthogonal molecular orbital methods, are developed using a minimal number of approximations, each of which is frequently employed in intermolecular interaction theory. These novel methods are compared to existing fragment-based quantum chemistry methods, and the implications of those significant differences, where they exist, between the methods developed herein and those already existing methods are examined in detail. Computational complexities and theoretical scaling are also analyzed and discussed. Future extensions for the hierarchy of methods, to account for additional intrafragment and interfragment interactions, are outlined.