Original Matrices Research Articles

Effects of piezoelectric-phase orientations on magnetoelectric coefficient in AlN–FeCoSiB multiferroic composites

In this study, orientation dependences of ps11′, ps12′, pe33′ and d31′ for piezoelectric phase were investigated along arbitrary directions using relative experimental data and original matrices for AlN with point group of 6mm. Then, effects of various orientations of piezoelectric phase on magnetoelectric coefficient of AlN–FeCoSiB laminated multiferroic composites were studied. It was found that ps11′ is a constant while ps12′, pe33′ and d31′ exhibit high dependence on crystal orientations with their MAX values existing along [001]-axis. The magnetoelectric coefficient αE33′ increases with decreased angle θ apart from c-axis of AlN in range of 90°–0°; the MAX αE33′ = 5405 mV/cm Oe exists in AlN ∥ [001]—FeCoSiB. Along specific preferred orientations of piezoelectric phase, twofold–fivefold of enhancement of αE33 can be obtained compared to randomly arranged composites. Volume fraction is found to be independent of orientations of component phases, and the volume fraction for magnetic phase f around 0.75 obtains the largest αE33. The results suggest an approach of enhancing magnetoelectric coefficient of composite multiferroic materials through crystal-orientation controls of single crystals or textured ceramics.

Evaluation of Enterprise Learning Performance in the Process of Cooperation Innovation Using Heronian Mean Operator

In order to clarify the achievement and efficiency of enterprise learning in the process of cooperative innovation, a comprehensive criteria framework for the evaluation of enterprise learning performance is constructed taking the learning process and learning results as the construction idea based on organizational learning theory. And this paper proposes a novel dynamic evaluation method considering the interaction between attributes of learning performance. In this study, the criterion framework for the evaluation of enterprise learning performance in the process of cooperative innovation includes learning process performance and learning outcomes performance. The original matrices are given by managers and experts using fuzzy set theory, and a dynamic time sequence weight vector is calculated based on information entropy and time degree. The weight of learning performance attributes under different time series is calculated based on entropy measure method. The interactive information of learning performance attributes is integrated through the weight of learning performance attributes and the three‐parameter weighted Heronian mean operator considering the interaction between attributes. And then, the dynamic and comprehensive evaluation result of learning performance in the process of cooperative innovation could be computed by integrating the learning performance information under different time series with time sequence weight vector. Finally, a real case is studied to verify the scientificity and validity of the criteria framework for the evaluation of enterprise learning performance and the method proposed in this study. This study not only helps cooperative enterprises get feedback in time and adjust cooperative relationships and learning styles but also enriches the theory of interorganizational management and provides a theoretical basis for the process of enterprise cooperative innovation.

Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition

We present a new Riemannian metric, termed Log-Cholesky metric, on the manifold of symmetric positive definite (SPD) matrices via Cholesky decomposition. We first construct a Lie group structure and a bi-invariant metric on Cholesky space, the collection of lower triangular matrices whose diagonal elements are all positive. Such group structure and metric are then pushed forward to the space of SPD matrices via the inverse of Cholesky decomposition that is a bijective map between Cholesky space and SPD matrix space. This new Riemannian metric and Lie group structure fully circumvent swelling effect, in the sense that the determinant of the Fréchet average of a set of SPD matrices under the presented metric, called Log-Cholesky average, is between the minimum and the maximum of the determinants of the original SPD matrices. Comparing to existing metrics such as the affine-invariant metric and Log-Euclidean metric, the presented metric is simpler, more computationally efficient, and numerically stabler. In particular, parallel transport along geodesics under Log-Cholesky metric is given in a closed and easy-to-compute form.

Tri-Direction 2D-Fisher Discriminant Analysis (T2D-FDA) for Feature Extraction

A new image feature extraction method for face recognition called Tri-direction 2D-Fisher Discriminant Analysis (T2D-FDA) is proposed to deal with the Small Sample Size (SSS) problem in conventional 1D-Fisher Discriminant Analysis (1D-FDA). Moreover, the essence of T2D-FDA is investigated, and the equivalence of the left-multiplying 2D-FDA of the original image matrices and the left-multiplying D2D-FDA of diagonal image matrices is verified if each column is viewed as a computational unit. Different from the 1D-LDA based approaches, the T2D-FDA is based on 2D image matrices rather than column vectors, so the image matrix does not need to be transformed into a long vector before feature extraction. The advantage arising in this way is that the SSS problem does not exist anymore because within-class scatter matrices constructed is full-rank in T2D-FDA. The proposed method is applied to face recognition where only few training images exist for each subject. Experiment results show T2D-FDA outperforms the current linear subspace methods in SSS problem on four public databases: ORL, Yale, AR and FERET face databases.

Restarted global FOM and GMRES algorithms for the Stein-like matrix equation [formula omitted

In this paper, we propose the restarted global full orthogonalization method (Gl-FOM) and global generalized minimum residual (Gl-GMRES) method to solve the Stein-like matrix equation X+M(X)=C with M(X)=AXB,M(X)=AX⊤B,M(X)=AX¯B or M(X)=AXHB, respectively, where X is an unknown matrix to be solved. First, by using a real inner product in complex matrix spaces, a generalized global Arnoldi process is given. Then we demonstrate how to employ the restarted Gl-FOM and Gl-GMRES algorithms for solving the Stein-like matrix equation. The proposed algorithms take advantage of the shifted structure of the matrix equation and are implemented by the original coefficient matrices. Finally, some numerical examples are given to illustrate the effectiveness with comparison to some existing methods.

Spread OFDM-IM With Precoding Matrix and Low-Complexity Detection Designs

We propose a new spread orthogonal frequency division multiplexing with index modulation (S-OFDM-IM), which employs precoding matrices such as Walsh-Hadamard (WH) and Zadoff-Chu (ZC) to spread both non-zero data symbols of active sub-carriers and their indices, and then compress them into all available sub-carriers. This aims to increase the transmit diversity, exploiting both multipath and index diversities. As for the performance analysis, we derive the bit error probability (BEP) to provide an insight into the diversity and coding gains, and especially impacts of selecting various spreading matrices on these gains. This interestingly reveals an opportunity of using rotated versions of original WH and ZC matrices to further improve the BEP performance. More specifically, rotated matrices can enable S-OFDM-IM to harvest the maximum diversity gain, which is the number of sub-carriers, while benchmark schemes have diversity gains limited by two. Moreover, we propose three low-complexity detectors, namely minimum mean square error log-likelihood ratio, index pattern MMSE (IP-MMSE), and enhanced IP-MMSE, which achieve different levels of complexity and reliability. Simulation results are presented to prove the superiority of S-OFDM-IM over the benchmarks.

Orientational dependences of optical properties in BaMgF4

In this research, crystal orientation dependences of optical properties have been investigated for magnesium barium fluoride (BaMgF4) in three-dimensional space by means of coordinate transformations. The maximum nonlinear optical coefficients dij' and refraction indices nij' along specific orientations have been determined based on experimental data of BaMgF4 and original matrices for mm2 point group. All the nonlinear optical coefficients dij' show high dependence on crystal orientations compared with refraction indices nij', the latter can be treated as a constant (1.45 ± 0.02), which is both related to experimental data and crystal symmetry elements. The max d15' = 15 × 10−14 m/V and the max d31' = max d32' = 27 × 10−14 m/V can be both obtained along the spontaneous polarization axis, i.e., the Z-axis. Meanwhile, the max d24' = 26.7 × 10−14 m/V and the max d33' = 36 × 10−14 m/V lie along directions at angles of θ = 58° and 50.2° apart from the Z-axis, respectively. The result suggests that by adopting specific directions, the optical properties of BaMgF4 crystal can be optimally used.

Implementing model reduction to the JuliaFEM platform

JuliaFEM is an open source finite element method solver written in the Julia language. This paper presents an implementation of two common model reduction methods: the Guyan reduction and the Craig-Bampton method. The goal was to implement these algorithms to the JuliaFEM platform and demonstrate that the code works correctly. This paper first describes the JuliaFEM concept briefly after which it presents the theory of model reduction, and finally, it demonstrates the implemented functions in an example model. This paper includes instructions for using the implemented algorithms, and reference the code itself in GitHub. The reduced stiness and mass matrices give the same results in both static and dynamic analyses as the original matrices, which proves that the code works correctly. The code runs smoothly on relatively large model of 12.6 million degrees of freedom. In future, damping could be included in the dynamic condensation now that it has been shown to work.

Secured steganographic scheme for highly compressed color image using weighted matrix through DCT

Due to the rapid growth of internet technology and the advent of various image processing tools, people started using digital media for hidden communication to protect valuable information which is important for multimedia commercials, health-care, medical and defense applications. On the other hand, image authentication and tamper detection are essential, especially when it is utilized for evidence of legal action. In this paper, a weighted matrix based steganographic scheme has been designed for highly compressed (Quality Factor (QF) 40) color image through discrete cosine transform (DCT) to maintain a good balance between payload and imperceptibility. Here, the AC components are collected from quantized DCT coefficient matrices of YCbCr channel. Then, a series of original matrices are formed to hide secret data. The collection of AC components is controlled by 128 bits shared secret key. A predetermined weighted matrix is employed to select the embedding position within a coefficient matrix of a cover image through the sum of the entry-wise multiplication operation. The proposed scheme provides good embedding capacity with the high visual quality compared to existing state-of-the-art methods. Finally, different steganographic analysis and attacks are carried out to observe its imperceptibility and robustness.

Fast Electromigration Stress Evolution Analysis for Interconnect Trees Using Krylov Subspace Method

Electromigration effects are a key failure mechanism for copper-based dual damascene interconnects wires in semiconductor technologies. However, accurately predicting the time-to-failure for a complicated interconnect tree in a VLSI interconnect layout requires detailed knowledge of the stress evolutions over time, and is subject to time-varying currents and temperature. This is a challenging problem as one needs to solve the stress-based partial differential equations (PDEs) in the time domain for confined copper damascene interconnect trees for both void nucleation and void growth phases. To mitigate this problem, we propose a novel Krylov subspace-based method for fast numerical solutions to the stress PDEs. The new approach, which we call FastEM , is based on the finite-difference method which is used to first discretize the PDEs into linear time-invariant ordinary differential equations (ODEs). After discretization, a modified Krylov subspace-based reduction technique is applied in the frequency domain to reduce the size of the original system matrices so that they can be efficiently simulated in the time domain. The FastEM can perform the simulation process for both void nucleation and void growth phases under piecewise constant linear current density inputs and time-varying stressing temperatures. Furthermore, we show that the steady-state response of stress diffusion equations can be obtained from the resulting ODE system in the frequency domain, which agrees with the recently proposed voltage-based EM analysis method for EM immortality checks. Numerical results show that the proposed method can lead to about 1–2 orders of magnitude speed-up over existing finite-difference time-domain-based methods on large interconnect trees for both void nucleation and growth phases with negligible errors. We further show that for most of the interconnect trees tested; we only need a small number of dominant poles for sufficient accuracy.

Mitigating the adverse impact of batch effects in sample pattern detection.

It is well known that batch effects exist in RNA-seq data and other profiling data. Although some methods do a good job adjusting for batch effects by modifying the data matrices, it is still difficult to remove the batch effects entirely. The remaining batch effect can cause artifacts in the detection of patterns in the data. In this study, we consider the batch effect issue in the pattern detection among the samples, such as clustering, dimension reduction and construction of networks between subjects. Instead of adjusting the original data matrices, we design an adaptive method to directly adjust the dissimilarity matrix between samples. In simulation studies, the method achieved better results recovering true underlying clusters, compared to the leading batch effect adjustment method ComBat. In real data analysis, the method effectively corrected distance matrices and improved the performance of clustering algorithms. The R package is available at: https://github.com/tengfei-emory/QuantNorm. Supplementary data are available at Bioinformatics online.

Fast Decomposition of Three-Component Spectra of Fluorescence Quenching by White and Grey Methods of Data Modeling

‘White’ and ‘grey’ methods of data modeling have been employed to resolve the heterogeneous fluorescence from a fluorophore mixture of 9-cyanoanthracene (CNA), 10-chloro-9-cyanoanthracene (ClCNA) and 9,10-dicyanoanthracene (DCNA) into component individual fluorescence spectra. The three-component spectra of fluorescence quenching in methanol were recorded for increasing amounts of lithium bromide used as a quencher. The associated intensity decay profiles of differentially quenched fluorescence of single components were modeled on the basis of a linear Stern-Volmer plot. These profiles are necessary to initiate the fitting procedure in both ‘white’ and ‘grey’ modeling of the original data matrices. ‘White’ methods of data modeling, called also ‘hard’ methods, are based on chemical/physical laws expressed in terms of some well-known or generally accepted mathematical equations. The parameters of these models are not known and they are estimated by least squares curve fitting. ‘Grey’ approaches to data modeling, also known as hard-soft modeling techniques, make use of both hard-model and soft-model parts. In practice, the difference between ‘white’ and ‘grey’ methods lies in the way in which the ‘crude’ fluorescence intensity decays of the mixture components are estimated. In the former case they are given in a functional form while in the latter as digitized curves which, in general, can only be obtained by using dedicated techniques of factor analysis. In the paper, the initial values of the Stern-Volmer constants of pure components were evaluated by both ‘point-by-point’ and ‘matrix’ versions of the method making use of the concept of wavelength dependent intensity fractions as well as by the rank annihilation factor analysis applied to the data matrices of the difference fluorescence spectra constructed in two ways: from the spectra recorded for a few excitation lines at the same concentration of a fluorescence quencher or classically from a series of the spectra measured for one selected excitation line but for increasing concentration of the quencher. The results of multiple curve resolution obtained by all types of the applied methods have been scrutinized and compared. In addition, the effect of inadequacy of sample preparation and increasing instrumental noise on the shape of the resolved spectral profiles has been studied on several datasets mimicking the measured data matrices.Graphical ᅟ

Regularization and index reduction for linear differential–algebraic systems

In this paper, a necessary and sufficient condition for the existence of a proportional semistate feedback is established such that the closed loop system is regular and of index at most two. The condition is characterized by a rank condition that involves only the original system coefficient matrices. Also, a new rank condition ensuring that a given linear time-invariant descriptor system is regular and of index at most some specific value is also derived. The developed theory is illustrated through physical and numerical examples.

The Cohesiveness of the Oscillating Belousov-Zhabotinsky Reaction

The Oscillating Belousov-Zhabotinsky (B-Z) Reaction is a chemical reaction initially studied by Russian military officer Belousov. Oscillating reactions are characterized by a change in ion concentration overtime, a perpetual back and forth flow between two contrasting solutions. Numerous mechanisms have been proposed to underlie the B-Z reaction. The model known as the Oregonator provides a simplified mechanism to reach the oscillating state. In order to interrogate the mechanisms that enable the B-Z reaction, we performed an experiment using the Oregonator. The data was collected from the reaction at four different temperatures, 10, 22, 37, and 50°C. A Markovian Analysis was used to interpret the 300 pieces of data that were collected. The change in conductivity was measured in between each sample and the calculations were imputed into a square matrix. When the matrix was squared in each trial, we found that there were two transition states between the original and steady matrices, representing the intermediate reactions between the oscillations. These findings were unique because the transition matrices have never been analyzed using change in conductivity and Markovian sequencing. From the steady matrix at each temperature, the probability of “hopping” between different changes in conductivity was determined in the long-term analysis of the oscillations. These values were also compared to determine temperature’s effect on the cohesiveness of the oscillating B-Z reaction. The findings of this study are important to consider when applying the reaction into polymer gels, which mimic the pulsing motions of organs in the circulatory system. Understanding the oscillations of the B-Z reaction can help researchers better understand the movements of the polymer gel overtime.

Global FOM and GMRES algorithms for a class of complex matrix equations

In this paper, a generalized global Arnoldi process is given to produce an F -orthonormal basis of complex matrix space. Then we propose the global full orthogonalization method (Gl-FOM) and global generalized minimum residual (Gl-GMRES) method for solving a class of complex matrix equations. The new methods can be implemented by the original coefficient matrices. By using Schur complement, we give the expressions of the approximate solutions and the corresponding residuals. Some convergence results of the proposed methods are also derived. Finally, numerical examples are given to illustrate the effectiveness with comparison to other existing methods.

Orientation dependence of magnetoelectric coefficient in 1-3–type BaTiO3/CoFe2O4

Orientation dependence of magnetoelectric coefficient αE33 in 1-3–type BaTiO3/CoFe2O4 composites was calculated in arbitrary directions by three-dimensional coordinate transformation method. The space distributions of pc11′, pc12′, e31′ for piezoelectric phase and mc11′, mc12′, q31′ for magnetic phase were obtained independently using relative experimental data and original matrices for 4mm BaTiO3 and m3m CoFe2O4. Elastic stiffness coefficients show little orientation differences, while e31′ and q31′ exhibit high dependence on crystal orientation, with the MAX absolute e31′ = 2.96 C/m2 and the MAX q31′ = 556 × 10−12 m/A are found at θ = 0° and θ = 0°, ϕ = 45°, respectively. For space distribution of αE33′, BaTiO3||[001]/CoFe2O4||[001] combination has the maximum value which applies to both 1-3 p/m (1.485 V/A) and 1-3 m/p composites (1.529 V/A). Volume fraction is quite independent of orientations of both piezoelectric and magnetic phases and the volume fraction for magnetic phase f around 0.5 obtains the largest αE33. The results suggest an approach to significantly enhancing magnetoelectric coefficient of composite multiferroic materials through crystal orientation controls of single crystals and textured ceramics.

Distributed Estimation of All the Eigenvalues and Eigenvectors of Matrices Associated With Strongly Connected Digraphs

This letter considers the problem of estimating all the eigenvalues and eigenvectors of an irreducible matrix, corresponding to a strongly connected digraph, in the absence of knowledge on the global network topology. To this end, we propose a unified distributed strategy performed by each node in the network and relies only on the local information. The key idea is to transform the nonlinear problem of computing both the eigenvalues and eigenvectors of an irreducible matrix into a linear one. Specifically, we first transform distributively the irreducible matrix into a nonsingular irreducible matrix. Each node in the network then estimates in a distributed fashion the inverse of the nonsingular matrix by solving a set of linear equations based on a consensus-type algorithm. The eigenvalues and the corresponding eigenvectors are finally computed by exploiting the relations between the eigenvalues and eigenvectors of both the inverse and the original irreducible matrices. A numerical example is provided to demonstrate the effectiveness of the proposed distributed strategy.

Fourth-order wave equation in Bhabha–Madhavarao spin-3 2 theory

Within the framework of the Bhabha–Madhavarao formalism, a consistent approach to the derivation of a system of the fourth-order wave equations for the description of a spin-[Formula: see text] particle is suggested. For this purpose an additional algebraic object, the so-called [Formula: see text]-commutator ([Formula: see text] is a primitive fourth root of unity) and a new set of matrices [Formula: see text], instead of the original matrices [Formula: see text] of the Bhabha–Madhavarao algebra, are introduced. It is shown that in terms of the [Formula: see text] matrices we have succeeded in reducing a procedure of the construction of fourth root of the fourth-order wave operator to a few simple algebraic transformations and to some operation of the passage to the limit [Formula: see text], where [Formula: see text] is some (complex) deformation parameter entering into the definition of the [Formula: see text]-matrices. In addition, a set of the matrices [Formula: see text] and [Formula: see text] possessing the properties of projectors is introduced. These operators project the matrices [Formula: see text] onto the spins 1/2- and 3/2-sectors in the theory under consideration. A corresponding generalization of the obtained results to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out. The application to the problem of construction of the path integral representation in para-superspace for the propagator of a massive spin-[Formula: see text] particle in a background gauge field within the Bhabha–Madhavarao approach is discussed.

EMQIT: a machine learning approach for energy based PWM matrix quality improvement

BackgroundTranscription factor binding affinities to DNA play a key role for the gene regulation. Learning the specificity of the mechanisms of binding TFs to DNA is important both to experimentalists and theoreticians. With the development of high-throughput methods such as, e.g., ChiP-seq the need to provide unbiased models of binding events has been made apparent. We present EMQIT a modification to the approach introduced by Alamanova et al. and later implemented as 3DTF server. We observed that tuning of Boltzmann factor weights, used for conversion of calculated energies to nucleotide probabilities, has a significant impact on the quality of the associated PWM matrix.ResultsConsequently, we proposed to use receiver operator characteristics curves and the 10-fold cross-validation to learn best weights using experimentally verified data from TRANSFAC database. We applied our method to data available for various TFs. We verified the efficiency of detecting TF binding sites by the 3DTF matrices improved with our technique using experimental data from the TRANSFAC database. The comparison showed a significant similarity and comparable performance between the improved and the experimental matrices (TRANSFAC). Improved 3DTF matrices achieved significantly higher AUC values than the original 3DTF matrices (at least by 0.1) and, at the same time, detected notably more experimentally verified TFBSs.ConclusionsThe resulting new improved PWM matrices for analyzed factors show similarity to TRANSFAC matrices. Matrices had comparable predictive capabilities. Moreover, improved PWMs achieve better results than matrices downloaded from 3DTF server. Presented approach is general and applicable to any energy-based matrices.EMQIT is available online at http://biosolvers.polsl.pl:3838/emqit.ReviewersThis article was reviewed by Oliviero Carugo, Marek Kimmel and István Simon.

Impacts of salvage logging on biodiversity: a meta-analysis.

Logging to "salvage" economic returns from forests affected by natural disturbances has become increasingly prevalent globally. Despite potential negative effects on biodiversity, salvage logging is often conducted, even in areas otherwise excluded from logging and reserved for nature conservation, inter alia because strategic priorities for post-disturbance management are widely lacking.A review of the existing literature revealed that most studies investigating the effects of salvage logging on biodiversity have been conducted less than 5 years following natural disturbances, and focused on non-saproxylic organisms.A meta-analysis across 24 species groups revealed that salvage logging significantly decreases numbers of species of eight taxonomic groups. Richness of dead wood dependent taxa (i.e. saproxylic organisms) decreased more strongly than richness of non-saproxylic taxa. In contrast, taxonomic groups typically associated with open habitats increased in the number of species after salvage logging.By analysing 134 original species abundance matrices, we demonstrate that salvage logging significantly alters community composition in 7 of 17 species groups, particularly affecting saproxylic assemblages.Synthesis and applications. Our results suggest that salvage logging is not consistent with the management objectives of protected areas. Substantial changes, such as the retention of dead wood in naturally disturbed forests, are needed to support biodiversity. Future research should investigate the amount and spatio-temporal distribution of retained dead wood needed to maintain all components of biodiversity.