Diagonal Values Research Articles

Adaptive Detection for Double STBCs Based on QR Decomposition

This study proposes an efficient detection algorithm for double space-time block codes (DSTBCs) to improve the algorithm of Kim et al. The proposed algorithm applies QR decomposition to the channel matrix of the DSTBC to obtain an upper triangular matrix. The diagonal entries of the upper triangular matrix contain two different values. The proposed algorithm adaptively determines the number of candidates for the DSTBC according to the ratio of these two diagonal values. When their ratio is large, the number of the candidates decreases. Finally, the detection result is searched among the candidates based on a maximum-likelihood criterion. Numerical results demonstrate that the computational complexity for the search process can be reduced by 70% with little performance loss at a bit error rate (BER)of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> .

Anisotropic Inhomogeneous Metamaterials Using Nonuniform Transmission-Line Grids Aligned With the Principal Axes

We present a method for realizing electromagnetically inhomogeneous and anisotropic metamaterials using nonuniform transmission-line grids. The desired material parameter tensors are decomposed into their constituent eigenvectors and eigenvalues. Transmission lines are then aligned with the eigenvectors of the permeability tensor and loaded with reactive circuit elements to attain the desired eigenvalues (diagonal permeability and permittivity values). The method is shown for two separate 2-D transformation optical devices: a collimator and a field rotator. The collimator is simulated as a continuous inhomogeneous medium as well as a subwavelength-structured transmission-line grid, and the results closely agree.

The EEG during Solution of Mathematical Logical Tasks

A model creating a dominant focus in the CNS arising on solution of specially constructed mathematical logical tasks was developed. The dominant state was accompanied by increases in coherence in the delta range. The low-frequency ranges (dealt, theta, alpha) showed increases in combinations of potentials in the frontal cortex. In the high-frequency ranges (beta1, beta2, gamma), coherence decreased in the frontal areas of the cortex, while increases were seen in the central, parietal, temporal, and occipital areas, with a predominance in the left hemisphere. Significant changes in the numbers of connections (increases) were seen in diagonal coherence values. Analysis of EEG spectral power showed that solution of tasks was associated with generalized increases in values in the delta range across the cortex. Theta activity increased in the frontal cortex and gamma activity increased in the occipital areas. Spectral power in the alpha range mainly decreased.

The effect of isoflurane anesthesia on the electroencephalogram assessed by harmonic wavelet bicoherence-based indices

Bicoherence quantifies the degree of quadratic phase coupling among different frequency components within a signal. Previous studies, using Fourier-based methods of bicoherence calculation (FBIC), have demonstrated that electroencephalographic bicoherence can be related to the end-tidal concentration of inhaled anesthetic drugs. However, FBIC methods require excessively long sections of the encephalogram. This problem might be overcome by the use of wavelet-based methods. In this study, we compare FBIC and a recently developed wavelet bicoherence (WBIC) method as a tool to quantify the effect of isoflurane on the electroencephalogram. We analyzed a set of previously published electroencephalographic data, obtained from 29 patients who underwent elective abdominal surgery under isoflurane general anesthesia combined with epidural anesthesia. Nine potential indices of the electroencephalographic anesthetic effect were obtained from the WBIC and FBIC techniques. The relationship between each index and end-tidal concentrations of isoflurane was evaluated using correlation coefficients (r), the inter-individual variations (CV) of index values, the coefficient of determination (R2) of the PKPD models and the prediction probability (PK). The WBIC-based indices tracked anesthetic effects better than the traditional FBIC-based ones. The DiagBic_En index (derived from the Shannon entropy of the diagonal bicoherence values) performed best [r = 0.79 (0.66–0.92), CV = 0.08 (0.05–0.12), R2 = 0.80 (0.75–0.85), PK = 0.79 (0.75–0.83)]. Short data segments of ∼10–30 s were sufficient to reliably calculate the indices of WBIC. The wavelet-based bicoherence has advantages over the traditional Fourier-based bicoherence in analyzing volatile anesthetic effects on the electroencephalogram.

New thiocyanato and azido adducts of the redox-active Fe(η5-C5Me5)(η2-dppe) center: Synthesis and study of the Fe(II) and Fe(III) complexes

The new thiocyanato- (5) and azido- (6) complexes were synthesized and studied under their Fe(II) and Fe(III) redox states. For the first time among the various [Fe(η5-C5Me5)(η2-dppe)]-based cationic radicals studied so far, the magnitude and spatial orientation of the g-tensor diagonal values were experimentally determined for 5[PF6]. These data are in good agreement with those issued from a DFT modelization. The changes experienced by the electronic structure of the Fe(II) complexes subsequent to oxidation are reminiscent of these previously observed for the known arylalkynyl analogues, albeit some differences can be pointed out. Thus, the differences observed in the 1H NMR spectra of 5[PF6] and 6[PF6] are attributed to a slower electronic spin relaxation and to the differently oriented magnetic anisotropy. The sizeable spin density evidenced by DFT on the terminal atom of the ligands of the Fe(III) complexes renders these new paramagnetic metallo-ligands quite appealing for accessing larger polynuclear molecular assemblies with magnetically interacting centers.

Theoretical investigation of electrical and mechanical properties of ZnO crystal

In this paper, various physical properties of ZnO piezoelectric crystal have been calculated by the methods of density functional theory and density functional perturbation theory. These tensors may be defined as second derivatives of an appropriately defined energy functional with respect to the atomic displacement, electric field or strain perturbations. We have calculated the electronic and mechanical properties of ZnO crystal such as band gap, elastic, compliance and piezoelectric tensors, and also bulk modulus of hexagonal phase. These calculations have been performed under boundary condition of constant electric field and zero temperature. The results show that hexagonal ZnO has a direct band gap of 0.82 eV, its elastic tensor for the frozen-ion is smaller than the relaxed-ion and the diagonal values of frozen-ion compliance tensor S are larger than relaxed-ion ones. The calculated properties are in good agreement with the reported experimental results. Keywords: Band structure, elastic tensor, piezoelectric tensor, bulk module.

An analytical effective tensor and its approximation properties for upscaling flows through generalized composites

The direct numerical simulation of flows through composites is difficult due to the fine-scale heterogeneity in the media and also due to the complexity of the dynamic systems. Thus, flow based on upscaling of the effective diffusion has become an important step in practical simulations of flow through composites. In this paper, an analytical form for computing the effective diffusion tensor is proposed when the variable coefficient is locally isotropic, K( x) = k( x) I, where k(x) is a scalar function, not necessarily periodic, and may be defined as a step function. Currently, similar results are obtained by numerical means and require a special (re)design of a numerical code and may be computationally demanding. The proposed analytical upscaled tensor approximates the one obtained from the periodic cell-problem in the context of classical homogenization theory. The diagonal values are computed by an averaging procedure of the well known Cardwell and Parsons bounds. The off-diagonals are derived from the rotation of an angle related to the center of mass of the unit cell or representative elementary volume (REV). When comparing the proposed form with various known analytical and numerical results, it shows to be accurate within less than 3% on average. The comparisons include realistic reservoirs description and analytical results, such as the concentric spheres of Hashin–Shtrikman and the two and four-phase checkerboard geometries. Moreover, convergence results corroborate theoretical ones from classical homogenization literature. Convergence is obtained by performing successive refinement from an initial coarse description of a given heterogeneous medium, which include the SPE10 comparative solution project.

Study of the Kramers rare earth ions ground multiplet with a large orbital contribution by multifrequency EPR spectroscopy: in scintillator

Abstract A multifrequency Electron Paramagnetic Resonance (EPR) investigation of Ce 3 + impurities in PbWO 4 single-crystals at the conventional microwave frequency (CMF) (X-band: 9.43 GHz) and at the high frequencies/fields (HF) 95, 190 and 285 GHz was carried out. The resulting spectra are well described at all frequencies by an axial spin-Hamiltonian corresponding to an effective spin one-half system in a tetragonal site symmetry. The diagonal values of the effective g matrix of the lowest doublet of the ground multiplet, g ‖ and g ⊥ , are frequency dependent at high fields. For the magnetic field perpendicular to the tetragonal axis, the g ⊥ -parameter exhibits also a small azimuthal angular dependence, which is frequency dependent, corresponding to the tetragonal S 4 symmetry. These HF effects are associated with the mixing by the large Zeeman interaction of some of the upper-lying doublets of the ground multiplet into the lowest-lying doublet states. The CMF and multifrequency HF-EPR analysis gives a good description of the magnetic properties and allows an estimation of the crystal field splitting of the ground multiplet of Ce 3 + ions with tetragonal symmetry S 4 in the PbWO 4 scintillator.

The best constant of Sobolev inequality corresponding to a bending problem of a beam on an interval

Green function of 2-point simple-type self-adjoint boundary value problem for 4-th order linear ordinary differential equation, which represents bending of a beam with the boundary condition as clamped, Dirichlet, Neumann and free. The construction of Green function needs the symmetric orthogonalization method in some cases. Green function is the reproducing kernel for suitable set of Hilbert space and inner product. As an application, the best constants of the corresponding Sobolev inequalities are expressed as the maximum of the diagonal values of Green function.

Computing continuous core/periphery structures for social relations data with MINRES/SVD

When diagonal values are missing or excluded, MINRES is a natural continuous model for the core/periphery structure of a symmetric social network matrix. Symmetric models, however, are not so useful when dealing with asymmetric data. Singular value decomposition (SVD) is a natural choice to model asymmetry, but this method also requires the presence of diagonal values. In this paper we offer an alternative, more general, approach to continuous core/periphery structures, the minimum residual singular value decomposition (MINRES/SVD), where each node in the network receives two indices, an “in-coreness” and an “out-coreness.” The algorithm for computing these coreness vectors is a least squares computation similar to, but distinct from the SVD, again because of the missing diagonal values. And in contrast to the standard, symmetric MINRES algorithm, we can more accurately model asymmetric matrices. This allows us to distinguish, for example, countries in the world economy that are more in the exporting core than they are in the importing core. We propose two nested PRE (proportional reduction of error) measures of fit: (1) the PRE from the MINRES vector with respect to the data and (2) the PRE of the product of the two MINRES/SVD vectors. Applying the resulting method to citations between journals and to international trade in clothing, we illustrate insights gained from being able to model asymmetrical flow patterns. Finally, two permutation tests are introduced to test independently for the MINRES and MINRES/SVD results.

Castelnuovo–Mumford regularity of deficiency modules

Let d ∈ N and let M be a finitely generated graded module of dimension ⩽ d over a Noetherian homogeneous ring R with local Artinian base ring R 0 . Let beg ( M ) , gendeg ( M ) and reg ( M ) respectively denote the beginning, the generating degree and the Castelnuovo–Mumford regularity of M. If i ∈ N 0 and n ∈ Z , let d M i ( n ) denote the R 0 -length of the n-th graded component of the i-th R + -transform module D R + i ( M ) of M and let K i ( M ) denote the i-th deficiency module of M. Our main result says, that reg ( K i ( M ) ) is bounded in terms of beg ( M ) and the “diagonal values” d M j ( − j ) with j = 0 , … , d − 1 . As an application of this we get a number of further bounding results for reg ( K i ( M ) ) .

Effective soft-decision demosaicking using directional filtering and embedded artifact refinement

Demosaicking is an interpolation process that transforms a color filter array (CFA) image into a full-color image in a single-sensor imaging pipeline. In all demosaicking techniques, the interpolation of the green components plays a central role in dictating the visual quality of reconstructed images because green light is of maximum sensitivity in the human visual system. Guided by this point, we propose a new soft-decision demosaicking algorithm using directional filtering and embedded artifact refinement. The novelty of this approach is twofold. First, we lift the constraint of the Bayer CFA that results in the absence of diagonal neighboring green color values for directionally recovering diagonal edges. The developed directional interpolation method is fairly robust in dealing with the four edge features, namely, vertical, horizontal, 45-deg diagonal, and 135-deg diagonal. In addition, the proposed embedded refinement scheme provides an efficient way for soft-decision-based algorithms to achieve improved results with fewer computations. We have compared this new approach to six state-of-the-art methods, and it can outstandingly preserve more edge details and handle fine textures well, without requiring a high computational cost.

Comparing all-author and first-author co-citation analyses of information science

Although it is generally understood that different citation counting methods can produce quite different author rankings, and although “optimal” author co-citation counting methods have been identified theoretically, studies that compare author co-citation counting methods in author co-citation analysis (ACA) studies are still rare. The present study applies strict all-author-based ACA to the Information Science (IS) field, in that all authors of all cited references in a classic IS dataset are counted, and in that even the diagonal values of the co-citation matrix are computed in their theoretically optimal form. Using Scopus instead of SSCI as the data source, we find that results from a theoretically optimal all-author ACA appear to be excellent in practice, too, although in a field like IS where co-authorship levels are relatively low, its advantages over classic first-author ACA appear considerably smaller than in the more highly collaborative ones targeted before. Nevertheless, we do find some differences between the two approaches, in that first-author ACA appears to favor theorists who presumably tend to work alone, while all-author ACA appears to paint a somewhat more recent picture of the field, and to pick out some collaborative author clusters.

Linearized force constants method for lattice dynamics in mixed semiconductors

A simple and accurate method of calculating phonon spectra in mixed semiconductors alloys, on the basis of preliminarily (from first principles) relaxed atomic structure, is proposed and tested for (Zn,Be)Se and (Ga,In)As solid solutions. The method uses an observation that the interatomic force constants, calculated ab initio for a number of microscopic configurations in the systems cited, show a clear linear variation of the main (diagonal) values of the interatomic force constants with the corresponding bond length. We formulate simple rules about how to recover the individual 3×3 subblocks of the force constants matrix in their local (bonds-related) coordinate systems and how to transform them into a global (crystal cell-related) coordinate system. Test calculations done for 64-atom supercells representing different concentrations of (Zn,Be)Se and (Ga,In)As show that the phonon frequencies and compositions of eigenvectors are faithfully reproduced in a linearized force constants calculation, as compared to true ab initio calculations.

All‐author vs. first‐author co‐citation analysis of the Information Science field using Scopus

AbstractAlthough many studies on the various ways of allocating credit among co‐authors have brought into general recognition that different citation counting methods can result in quite different author rankings, studies on different author co‐citation counting methods are still largely missing. This paper examines whether different co‐citation counting methods produce different results in author co‐citation analysis studies of the intellectual structure of research fields, and if so, in what ways they differ. Our results indicate that, with respect to the major specialties and how they relate to each other, the intellectual structures of the Information Science field identified through author co‐citation analyses based on different co‐citation counting methods are largely equivalent, but when it comes to detailed structure, results differ in a number of ways. In particular, classic first‐author co‐citation analysis appears to better represent the theoretical and methodological aspects of the field whereas all‐author co‐citation analysis favors more recent empirical studies, and picks out some tightly collaborative research groups or projects. We experiment with using meaningful diagonal values in a co‐citation matrix rather than using statistically generated values, and observe favorable results. We also employ a new visualization technique for reporting the results of a classic author co‐citation analysis, using a bipartite graph that represents all the information in the factor matrix of specialties and author loadings as author and factor vertices connected by edges with loadings as similarity‐measure line values, laid out algorithmically in two dimensions.

The cholesky factorization in interior point methods

The paper concerns the Cholesky factorization of symmetric positive definite matrices arising in interior point methods. Our investigation is based on a property of the Cholesky factorization which interprets “small” diagonal values during factorization as degeneracy in the scaled optimization problem. A practical, scaling independent technique, based on the above property, is developed for the modified Cholesky factorization of interior point methods. This technique increases the robustness of Cholesky factorizations performed during interior point iterations when the optimization problem is degenerate. Our investigations show also the limitations of interior point methods with the recent implementation technology and floating point arithmetic standard. We present numerical results on degenerate linear programming problems of NETLIB.

Dealing with large diagonals in kernel matrices

In kernel methods, all the information about the training data is contained in the Gram matrix. If this matrix has large diagonal values, which arises for many types of kernels, then kernel methods do not perform well: We propose and test several methods for dealing with this problem by reducing the dynamic range of the matrix while preserving the positive definiteness of the Hessian of the quadratic programming problem that one has to solve when training a Support Vector Machine, which is a common kernel approach for pattern recognition.

On the computation of the absolute hardness of thin solid films

A study has been conducted in order to evaluate the descriptive capability of a modified form of the models advanced by Jönsson and Hogmark, Burnett and Rickerby, Chicot and Lesage and Korsunsky et al., regarding the composite hardness measurements carried out on different substrate–film systems. The modification that has been introduced involves the incorporation of the indentation size effect on both the substrate and film hardness through the power relationship, for the description of the change in hardness with the indentation diagonal, earlier proposed by Meyer. The modified models were first evaluated employing the data already published by Chicot et al., for Ti and TiC films formed on the surface of a chromium steel of a high carbon content. Subsequently, they were tested employing the data obtained experimentally with three under stoichiometric TiN x coatings, deposited by PVD magnetron sputtering on 316L stainless steel. It has been determined that the composite hardness measured on such systems can be satisfactorily described by means of any of the four models analyzed. However, it has also been found that the model proposed by Korsunsky and co-workers not only gives rise to the minimum quadratic difference between most of the measured and predicted values of the composite hardness, but also provides useful information regarding the film toughness. An optimization procedure is outlined which can be used in order to compute unambiguously and simultaneously all the constants involved in any of the four modified models, taking into consideration all the experimental measurements. The models advanced by Burnett and Rickerby, Chicot and Lesage and Korsunsky et al. have been found to predict a smooth increase in hardness as the indentation diagonal decreases, outside the range of experimental measurements. On the contrary, it has been shown that the model advanced by Jönsson and Hogmark breaks down when tested outside the range of experimental values of hardness, particularly at low indentation diagonal values.

Local earthquake tomography between rays and waves: fat ray tomography

The limitations of ray-based forward solutions in seismic tomography are theoretically well known. To correctly represent the physical forward problem in seismic tomography, application of full three-dimensional (3-D) wave theory would be required. Up to now this is not possible for the size of a typical local earthquake study. With the concept of fat rays resembling the waves Fresnel volume, a more complete, physically consistent and accurate solution to the forward problem is available. In this paper, we present an approach to include fat rays in local earthquake tomography, called Fatomo. The comparative study with synthetic data and inversion results with Fatomo and a ray-based approach to local earthquake tomography, SIMULPS, reveals new insights into the role of resolution and model parameterization in local earthquake tomography. Intuitively expected effects of fat rays on resolution estimates, such as higher node sampling values and lower resolution diagonal element values for wider fat rays can be seen in the results. For ideal model parameterization, differences between fat ray and ray tomography are small. Our results document, however, that the influence of model parameterization is less critical for fat ray tomography than for ray tomography.

COVARIANT TECHNIQUES FOR COMPUTATION OF THE HEAT KERNEL

The heat kernel associated with an elliptic second-order partial differential operator of Laplace type acting on smooth sections of a vector bundle over a Riemannian manifold, is studied. A general manifestly covariant method for computation of the coefficients of the heat kernel asymptotic expansion is developed. The technique enables one to compute explicitly the diagonal values of the heat kernel coefficients, so called Hadamard–Minakshisundaram–De Witt–Seeley coefficients, as well as their derivatives. The elaborated technique is applicable for a manifold of arbitrary dimension and for a generic Riemannian metric of arbitrary signature. It is very algorithmic, and well suited to automated computation. The fourth heat kernel coefficient is computed explicitly for the first time. The general structure of the heat kernel coefficients is investigated in detail. On the one hand, the leading derivative terms in all heat kernel coefficients are computed. On the other hand, the generating functions in closed covariant form for the covariantly constant terms and some low-derivative terms in the heat kernel coefficients are constructed by means of purely algebraic methods. This gives, in particular, the whole sequence of heat kernel coefficients for an arbitrary locally symmetric space.