Decomposition Of Pairs Research Articles

Thick-restarted joint Lanczos bidiagonalization for the GSVD

The computation of the partial generalized singular value decomposition (GSVD) of large-scale matrix pairs can be approached by means of iterative methods based on expanding subspaces, particularly Krylov subspaces. We consider the joint Lanczos bidiagonalization method, and analyze the feasibility of adapting the thick restart technique that is being used successfully in the context of other linear algebra problems. Numerical experiments illustrate the effectiveness of the proposed method. We also compare the new method with an alternative solution via equivalent eigenvalue problems, considering accuracy as well as computational performance. The analysis is done using a parallel implementation in the SLEPc library.

Multiclass imbalanced learning with one-versus-one decomposition and spectral clustering

In many real-world applications, an algorithm needs to learn multiclass classification models from data with imbalanced class distributions. Multiclass imbalanced learning is currently receiving increased attention from researchers. In contrast to traditional imbalanced learning on binary datasets, multiclass imbalanced learning faces great challenges from the variety of changes in the class distributions as well as the inadequate performance of multiclass classification algorithms. In this paper, we propose a novel data preprocessing-based method to solve this problem. The proposed method combines a one-versus-one (OVO) decomposition of class pairs and a spectral clustering technique. This method first decomposes a multiclass dataset into several binary-class datasets. Then, it uses spectral clustering to divide the minority classes of binary-class subsets into subspaces and oversamples them according to the characteristics of the data. Sampling based on spectral clustering takes into account the distribution of the data and effectively avoids oversampling outliers. After the data approximately reaches the equilibrium point, multiclass classifiers can be trained from these rebalanced data. We compared the proposed method with five state-of-the-art multiclass imbalanced learning methods on seven multiclass datasets, using multiclass area under the ROC curve (MAUC), the precision of minor classes (Pmin) and the average precision of all classes (Pavg) as the performance metrics. The experimental results show that our proposed method has the best overall performance.

Compositional inhomogeneities in type-I and type-II superlattices for GaAsSbN-based solar cells: Effect of thermal annealing

GaAsSbN alloys is recognized as an effective candidate to incorporate in multijunction solar cell applications due to its advantages of being grown lattice-matched to GaAs and its capability to achieve bandgap around 1.0 eV. Recently, the use of superlattice (SL) structures that permit type–II (GaAsSb/GaAsN) and type-I (GaAsSbN/GaAs) alignments showed a strongly heightened luminescence and a significant EQE compared to their thicker quaternary bulk counterparts. In this work, the correlation between the compositional distribution and its optical properties in both SL structures before and after RTA treatment is analyzed. Firstly, while N is confined following the nominal design, Sb presents a strong segregation to the upper layers achieving similar compositional profiles along the growth direction even after the RTA. However, the SL type-II approach presents a higher interface quality and a much lower trend to cluster formation than SL type-I. Secondly, RTA gives place to an improvement of the interface roughness, together to a decrease of the area associated to clusters in both structures. The blueshift and the improvement of the PL intensity induced by annealing in both samples is more correlated to the decomposition of nitrogen pairs to isolated substitutional nitrogen than to the dissolution of Sb inhomogeneities. A different distribution of new substitutional N atoms around Sb clusters could explain the differences in the PL improvement of both SLs during the annealing. SL type-II approach is the best design to minimize cluster formation and to obtain more abrupt interfaces and mainly describe the optical enhancement compared to SL type-I structures.

Study of ion transmission in an electrolyte of graphene quantum dots under ultraviolet light

Graphene quantum dots (GQDs) can be used in electrolytes to improve ion transmission and conductivity, but this practice needs further investigation to improve its efficiency. This work focuses on the study of ion transmission in GQD electrolytes under ultraviolet light. A hydrothermal method was used to synthesise GQDs by using three-dimensional graphenes (3DGs) as a carbon precursor. Microstructural characterization showed that the GQDs were distributed at a distance of 10–20 nm, and that the surface of each GQD consisted solely of functional hydroxy groups. In addition, the GQDs exhibited excitation-dependent photoluminescent behaviour under excitation wavelengths, with maximum excitation and emission wavelengths at 360 nm and 452 nm, respectively. The electron transfer of GQDs was studied using electrochemical impedance spectroscopy (EIS) under ultraviolet irradiation (the GQDs were used as an electrolyte). Our results reveal that GQDs have good absorbance under ultraviolet light, and facilitate the decomposition of electron-hole pairs and improve electron transfer rates in solution. These results are attributed to the fact that the surfaces of GQDs only contain hydroxy functional groups. The number of H+ ions increases when GQDs are ionized under acidic conditions, resulting in the acceleration of ion transmission. Our findings have important implications for subjects such as water purification, electrolyte additives, and the simulation of ion transmission.

Compatible pairs of commuting isometries

The paper is devoted to pairs of commuting isometries. A unique decomposition of such pairs into a compatible and a completely non-compatible part is constructed. The compatible part is fully described.

Partitioning of on-demand electron pairs.

The on-demand generation and separation of entangled photon pairs are key components of quantum information processing in quantum optics. In an electronic analogue, the decomposition of electron pairs represents an essential building block for using the quantum state of ballistic electrons in electron quantum optics. The scattering of electrons has been used to probe the particle statistics of stochastic sources in Hanbury Brown and Twiss experiments and the recent advent of on-demand sources further offers the possibility to achieve indistinguishability between multiple sources in Hong-Ou-Mandel experiments. Cooper pairs impinging stochastically at a mesoscopic beamsplitter have been successfully partitioned, as verified by measuring the coincidence of arrival. Here, we demonstrate the splitting of electron pairs generated on demand. Coincidence correlation measurements allow the reconstruction of the full counting statistics, revealing regimes of statistically independent, distinguishable or correlated partitioning, and have been envisioned as a source of information on the quantum state of the electron pair. The high pair-splitting fidelity opens a path to future on-demand generation of spin-entangled electron pairs from a suitably prepared two-electron quantum-dot ground state.

Paraunitary generation/correlation of QAM complementary sequence pairs

A unique decomposition of arbitrary pairs of complementary sequences (including standard binary, polyphase and QAM sequences as well as non-standard sequences and kernels) based on paraunitary matrices is presented. This decomposition allows us to describe the internal structure of any sequence pair of length L using basic paraunitary matrices defined by an ordered set of L complex coefficients named the omega vector. When the omega vector is sparse, the canonic form is compact and leads to an efficient implementation of a generator/correlator. We show that sequences generated by the standard algorithm have the sparsest known omega vector (log2 L non-zero elements out of L) and, thus, the most efficient generator/correlator. The equivalence of paraunitary matrices and Z transforms of complementary sequences allows us to apply the rich results from the theory of perfect reconstruction filter-banks to the field of sequence design. We introduce a new generator/correlator algorithm for sequences in standard and non-standard QAM constellations that is based on this equivalence. Both rectangular and hexagonal constellations are considered and the cardinality of the generated set of unique complementary sequences is either determined or estimated for a number of important cases. We show, in the case of the standard 16-QAM constellation, that the paraunitary algorithm generates the same number of sequences as the published algorithms based on generalized Boolean functions. In the case of 64-QAM, the proposed algorithm generates more sequences than known algorithms. We introduce an algorithm for generating 256-QAM sequences and derive a tight upper bound on the number of generated sequences.

On the decomposition of families of quasinormal operators

The canonical injective decomposition of a jointly quasinormal family of operators is given. Relations between the decomposition of a quasinormal operator T and the decompo- sition of a partial isometry in the polar decomposition of T are described. The decomposition of pairs of commuting quasinormal partial isometries and its applications to pairs of com- muting quasinormal operators is shown. Examples are given.

Skeleton-based segmentation and decomposition of raster pairs of shapes

The problem of discrete shape and its skeleton decomposition is considered in this work--so-called skeleton-based shape segmentation problem. An approach to construct the isomorphic skeleton-based decompositions for pairs of shapes is proposed. Based on these isomorphic decompositions of skeletons, isomorphic shapes decompositions with meaningful parts reflecting shape structure could be constructed. The last feature provides an opportunity to apply the proposed method to shape comparison and shape morphing problems. Experiments confirm the correctness of methods proposed.

Effect of thermal annealing on the blueshift of energy gap and nitrogen rearrangement in GaAsSbN

We report on the blueshift of energy gap and the nitrogen rearrangement resulting from the thermal treatment of GaAsSbN samples. The composition ranges of N and Sb are from 2% to 3% and from 7% to 11%, respectively. By comparing the photoluminescence peak energy and absorption energy gap, we found that the thermal annealing leads to compositional homogenization. When the annealing temperature is higher than 750 °C, the local vibration mode (LVM) absorbance of isolated substitutional nitrogen NAs starts to increase with the temperature. This finding supports the argument that nitrogen pairs thermally dissociate to isolated nitrogen. In additions, the increase of LVM absorbance accompanies the blueshift of energy gap, suggesting that the blueshift is the consequence of the nitrogen rearrangement. The decomposition of nitrogen pairs has also been observed by photoreflectance spectroscopy (PR). Multiple peaks were resolved from the PR spectra of as-grown GaAsSbN. They are relevant to transitions from regions with different nitrogen pairings and isolated nitrogen. As the annealing temperature increases, the peaks gradually merge to that of isolated nitrogen, indicating the decomposition of nitrogen pairings.

Perturbation bounds for the periodic Schur decomposition

This paper is devoted to the perturbation analysis for periodic regular matrix pairs. We present perturbation bounds for the periodic Schur decomposition of periodic regular matrix pairs with distinct eigenvalues, which extend the main result of Sun (SIAM J. Matrix Anal. Appl. 16:1328–1340, 1995). The results are illustrated by a numerical example.

Behavior of inclusions with different value and orientation of topological dipoles in ferroelectric smectic films

Cholesteric droplets in ferroelectric free-standing films with tunable anchoring on the droplet boundary are investigated. A droplet and satellite topological defect(s) form a topological dipole. We obtained droplets with different angles α between two radial lines from the droplet center to −1/2 topological defects. Droplets with parallel dipoles form linear chains in which the interparticle distances decrease with increasing the defect angle α. For the first time, the dependence of the interparticle distance on the angle between topological defects was measured. We can adjust the magnitude and orientation of topological dipoles formed by the droplets. For the first time, the droplets with antiparallel topological dipoles were prepared in a smectic film. Interaction of the droplets with parallel and antiparallel dipoles differs drastically. Formation of antiparallel dipoles leads to a decomposition of the droplet pairs and chains of droplets. Our observations may be used to change the magnitude, anisotropy of the interparticle interaction, and structures of inclusions in liquid crystal media.

Fixed rank solutions of the matrix equation with statistical applications

By applying the canonical correlation decomposition of matrix pairs, the general fixed rank least square solutions of matrix equation Xβ=Y are derived. As statistical applications, an algorithm for computing the least square estimator of the multivariate reduced rank regression model Y=Xβ+ϵ, r(β)=t is given.

Angular momentum decomposition of Richardson's pairs

The angular momentum decomposition of pairs obtained using Richardson's exact solution of the pairing Hamiltonian for the deformed $^{174}\mathrm{Yb}$ nucleus are displayed. The probabilities for low angular momenta of the collective pairs are strikingly different from the ones obtained in the BCS ground state.

Thermolysis of polyethylene hydroperoxides in the melt, Part 12: Mechanisms and kinetics of thermolysis

The thermolysis of polyethylene hydroperoxides is attributed to the reaction of two hydroperoxide groups. This bimolecular reaction appears as a first-order reaction with the mean values of the hydroperoxide concentrations that can be used for the experimental verification of the kinetics. In low molecular mass liquids and solutions these findings would be irreconcilable. However, in polymer melts, this contradiction is more apparent than real. It is a consequence of the heterogeneous kinetics valid in polymer melts. The bimolecular reaction involves the decomposition of pairs of hydroperoxide groups that are relatively close in the elementary oxidation volumes. By diffusion these hydroperoxide groups can come close enough for reaction. From the chemical point of view the decomposition is a bimolecular reaction. However, from the kinetic point of view it is a first-order reaction of the hydroperoxide pairs. The dependency of the first-order rate on the initial hydroperoxide concentration is explained by the heterogeneous kinetics. The activation energy of the overall process can be related to the sum of the activation energies pertaining to the chemical reaction and to the diffusion process.

Density functional theory-symmetry adapted perturbation treatment energy decomposition of nucleic acid base pairs taken from DNA crystal geometry

First- and second-order perturbation energies for H-bonded and stacked structures of nucleic acid base pairs in DNA crystal geometries were determined using the density functional theory symmetry adapted perturbation treatment method. Considerably larger stabilization of the former pairs is due to electrostatic and induction energies. Total E(1) energies for both pairs are, however, similar and the same is true for dispersion energy.

Decomposition and Group Theoretic Characterization of Pairs of Inverse Relations of the Riordan Type

A new solution to Riordan’s problem of combinatorial identities classification is presented. An algebgraic characterization of pairs of inverse relations of the Riordan type is given. The use of the integral representation approach for generating new types of combinatorial identities is demonstrated.

On f-Vectors and Relative Homology

We find strong necessary conditions on the f-vectors, Betti sequences, and relative Betti sequence of a pair of simplicial complexes. We also present an example showing that these conditions are not sufficient. If only the difference between two Betti sequences is specified, and not the individual Betti sequences, then the characterization is complete, and the characterization of all pairs of simplicial complexes matches the characterization of pairs of near-cones. Our necessary conditions rely upon a combinatorial decomposition of pairs of simplicial complexes that reflects the homology and relative homology of the complexes.

On solutions of matrix equation AXB + CYD = F

In this paper, the matrix equation with two unknown matrices X, Y of form AXB + CYD = F is discussed. By applying the canonical correlation decomposition (CCD) of matrix pairs, we obtain expressions of the least-squares solutions of the matrix equation, and sufficient and necessary conditions for the existence and uniqueness of the solutions. We also derive a general form of the solutions. We also study the least-squares Hermitian (skew-Hermitian) solutions of equation AXA H + CYC H = F.

Modifying the generalized singular value decomposition with application with application in direction-of-arrival finding

We consider updating and downdating problems for the generalized singular value decomposition (GSVD) of matrix pairs when new rows are added to one of the matrices or old rows are deleted. Two classes of algorithms are developed, one based on the CS decomposition formulation of the GSVD and the other based on the generalized eigenvalue decomposition formulation. In both cases we show that the updating and downdating problems can be reduced to a rank-one SVD updating problem. We also provide perturbation analysis for the cases when the added or deleted rows are subject to errors. Numerical experiments on direction-of-arrival (DOA) finding with colored noises are carried out to demonstrate the tracking ability of the algorithms.