Number Of Nonzero Elements Research Articles

Quadrilateral Barycentric Basis Functions for Surface Integral Equations

A framework for solving surface integral equation on quadrilateral, triangular, and mixed quadrilateral-triangular meshes is presented. The initial meshes are represented in terms of quadrilateral barycentric meshes (QBMs), which are obtained by partitioning each initial quadrilateral and triangle into four and three barycentric quadrilaterals, respectively. Quadrilateral barycentric basis functions (QBBFs) are defined on QBMs. The QBBFs serve a dual role. First, they allow defining primary basis functions (PBFs), which are well suited for representing surface currents on quadrilateral, triangular, and mixed meshes. Second, the QBBFs are used to define dual basis function (DBFs), which are natural for using in conjunction with Calderon multiplicative preconditioners (CMPs). These QBBFs, PBFs, and DBFs result in a substantial reduction in the number of nonzero elements in the sparse projection matrices for PBFs and DBFs as well as reduction of unknowns and quadrature points. When these PBFs and DBFs are used in CMPs, they reduce the number of iterations and eliminate the dense mesh breakdown of the surface electric field integral equation. Numerical examples demonstrate the efficiency of using the introduced QBBFs with associated PBFs and DBFs for solving electromagnetic surface electric field integral equations on quadrilateral, triangular, and mixed meshes.

Joint Beamforming and Antenna Subarray Formation for MIMO Cognitive Radios

The antenna subarray formation (ASF) is a promising technique for multiple-input multiple-output (MIMO) receiver. For MIMO cognitive radio systems, we propose a joint beamforming and ASF scheme in this letter which maximizes the cognitive achievable capacity subject to the peak transmit power constraint at the secondary transmitter, peak interference power constraint at the primary receiver, and the limited number of nonzero elements in the ASF matrix. To solve the joint optimization problem, we propose a relax-and-recover scheme. Simulation results have shown that the proposed scheme outperforms the conventional antenna selection scheme.

Pathological Equivalents of Fully-Differential Active Devices for Symbolic Nodal Analysis

The use of pathological elements (i.e., nullators, norators, and the voltage mirror-current mirror pair) as universal active elements opens up the possibility to model the behavior of active devices with either differential features or input-output multiples, in order to be used in analysis tasks of linear(ized) analog circuits. This brief tries on the modeling this class of active devices, which is carried out by considering the impedance characteristics along with the behavior equation of each active device, the kind of signal to be processed and by applying the pathological element properties. In order to obtain a more realistic model, not only parasitic elements associated to the input-output terminals of each active device are considered, but the tracking errors of voltage and current differential followers modeled with grounded pathological elements and admittances are also included. Due to that the gain and tracking errors are finites and of limited bandwidth, a two-pole model is used for each of them in order to include their contributions on the symbolic expressions computed. Because the behavior of fully-differential amplifiers is modeled with grounded pathological elements, a standard nodal analysis can be performed. This imply that not only the size of the admittance matrix is smaller than those generated by applying modified nodal analysis (MNA) method, for instance, but also the number of nonzero elements and the generation of cancellation-terms are both reduced. As a result, the computational complexity during the solution of the system of equations is reduced when recursive determinant-expansion techniques are applied. Examples are described and compared with the MNA method, in order to show the usefulness of the proposed models to compute fully-symbolic small-signal characteristics of analog circuits containing fully-differential active devices and/or with input-output multiples.

Sparsity aware consistent and high precision variable selection

Variable selection is fundamental while dealing with sparse signals that contain only a few number of nonzero elements. This is the case in many signal processing areas extending from high-dimensional statistical modeling to sparse signal estimation. This paper explores a new and efficient approach to model a system with underlying sparse parameters. The idea is to get the noisy observations and estimate the minimum number of underlying parameters with acceptable estimation accuracy. The main challenge is due to the non-convex optimization problem to be solved. The reconstruction stage deals with some suitable objective function in order to estimate the original sparse signal by performing variable selection procedure. This paper introduces a suitable objective function in order to simultaneously recover the true support of the underlying sparse signal while still achieving an acceptable estimation error. It is shown that the proposed method performs the best variable selection compared to the other algorithms, while approaching the lowest least mean squared error in almost all the cases.

Pólya convertibility problem for symmetric matrices

We investigate symmetric (0, 1) matrices on which the permanent is convertible to the determinant by assigning ± signs to their entries. In particular, we obtain several quantitative bounds for the number of nonzero elements of such matrices, including the analog of Gibson’s theorem for symmetric matrices.

An efficient classification approach for large-scale mobile ubiquitous computing

Context classification is at the center of user-centric ubiquitous computing that targets the provision of personalized services based on expressed preferences and interests. Classification of context for Mobile Ubiquitous Computing (MUC), where there are high volumes of data and users place large demands on a context-aware system, must be effective and efficient in computational terms. The Sequential Minimal Optimization (SMO) based SVMTorch is widely used for text classification; it is however inefficient for MUC-oriented context analysis due to: (1) a low classification speed caused by inefficient matrix multiplication, and (2) the inability to classify multi-label data.In this paper, we propose an efficient classification approach to improve and extend the SVMTorch. Firstly, we propose a semi-sparse algorithm to speed up vector/matrix multiplication which lies at the core of the SVMTorch-based classification approaches. Theoretically, to multiply two vectors (i.e., a selected vector and a trained vector) with m and n non-zero elements respectively, the traditional SVMTorch needs O(m+n) time while our semi-sparse algorithm requires only O(n) time, where n is the number of non-zero elements in the trained vector. Secondly, we extend the functions of the traditional SVMTorch approach which is limited to the classification of single-label data, to support multi-class multi-label classification. Finally, we parallelize the improved SVMTorch which incorporates the semi-spares algorithm and function extensions to access multi-core processor and cluster systems to further improve the effectiveness and efficiency of the classification process. The experimental results demonstrate that our proposed solution significantly improves the performance and capability of the traditional SVMTorch. The results support the conclusion that the larger training and testing data sets are, the more improvement our solution brings to the effectiveness and efficiency of the context classification. This conclusion is verified in a Chinese web page classifier developed based on the solution presented in this paper.

Synthetic aperture radar imaging pulses

In our work we have demonstrated how techniques that are used to compute fast back-projections can be used in f1 norm regularized LS-based algorithms to make them computationally feasible. The motivation of f1 norm regularization is to promote sparsity in the SAR image where image sparsity is the number of non-zero elements directly in the SAR image or the SAR image projected onto a basis; e.g., a wavelet basis.

Greedy Sparse RLS

Starting from the orthogonal (greedy) least squares method, we build an adaptive algorithm for finding online sparse solutions to linear systems. The algorithm belongs to the exponentially windowed recursive least squares (RLS) family and maintains a partial orthogonal factorization with pivoting of the system matrix. For complexity reasons, the permutations that bring the relevant columns into the first positions are restrained mainly to interchanges between neighbors at each time moment. The storage scheme allows the computation of the exact factorization, implicitly working on indefinitely long vectors. The sparsity level of the solution, i.e., the number of nonzero elements, is estimated using information theoretic criteria, in particular Bayesian information criterion (BIC) and predictive least squares. We present simulations showing that, for identifying sparse time-varying FIR channels, our algorithm is consistently better than previous sparse RLS methods based on the -norm regularization of the RLS criterion. We also use our sparse greedy RLS algorithm for computing linear predictions in a lossless audio coding scheme and obtain better compression than MPEG4 ALS using an RLS-LMS cascade.

Compressive Sensing Based on Deterministic Sparse Toeplitz Measurement Matrices with Random Pitch

Selecting an appropriate measurement matrix is one of the key points of compressive sensing.Due to randomly introducing zero elements into these matrices to form sparse Toeplitz matrices with random pitch,the number of random independent variables can be reduced to 1/2 and 1/16 less than that of original Toeplitz matrices,the number of nonzero elements can also be reduced significantly,which is conducive to data transmission and storage.Simulation results show that the reconstructions of sparse Toeplitz measurement matrices with random pitch are better than Gaussian and original Toeplitz matrices.Moreover,the time of reconstruction is only about 15% to 40% of the time of Gauss and general Toeplitz reconstruction.

Sparsistency and rates of convergence in large covariance matrix estimation

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications, sparsity priori may occur on the covariance matrix, its inverse or its Cholesky decomposition. We study these three sparsity exploration problems under a unified framework with a general penalty function. We show that the rates of convergence for these problems under the Frobenius norm are of order (s(n) log p(n)/n)(1/2), where s(n) is the number of nonzero elements, p(n) is the size of the covariance matrix and n is the sample size. This explicitly spells out the contribution of high-dimensionality is merely of a logarithmic factor. The conditions on the rate with which the tuning parameter λ(n) goes to 0 have been made explicit and compared under different penalties. As a result, for the L(1)-penalty, to guarantee the sparsistency and optimal rate of convergence, the number of nonzero elements should be small: sn'=O(pn) at most, among O(pn2) parameters, for estimating sparse covariance or correlation matrix, sparse precision or inverse correlation matrix or sparse Cholesky factor, where sn' is the number of the nonzero elements on the off-diagonal entries. On the other hand, using the SCAD or hard-thresholding penalty functions, there is no such a restriction.

Effect of joint spatial correlation on the diversity performance of space-time block codes

We characterize the effect of joint spatial correlation on the diversity performance of multiple-input multiple-output (MIMO) systems. The joint spatial correlation is structured by the coupling matrix whose elements determine the average power coupling between the transmit and receive eigenmodes. We first derive the closed-form expression for the exact symbol error probability (SEP) of orthogonal space-time block codes over jointly correlated MIMO Rayleigh-fading channels. We then show that the achievable diversity order is equal to the number of nonzero elements of the power coupling matrix and establish the Schur monotonicity theorems on the SEP and the effective fading figure as a functional of elements of the power coupling matrix.

Wavelet Reconstruction of Nonuniformly Sampled Signals

For the reconstruction of a nonuniformly sampled signal based on its noisy observations, we propose a level dependent l1 penalized wavelet reconstruction method. The LARS/Lasso algorithm is applied to solve the Lasso problem. The data adaptive choice of the regularization parameters is based on the AIC and the degrees of freedom is estimated by the number of nonzero elements in the Lasso solution. Simulation results conducted on some commonly used 1_D test signals illustrate that the proposed method possesses good empirical properties.

Condensing timetables with target date divisible by each instructor’s number of class hours

Initial data required to construct a school timetable which can be represented as amatrix with a constant number of nonzero elements in each row and a constant set of elements in each column are considered. Conditions are determined under which this matrix can be transformed so that the sets of elements in each row and each column are preserved and the nonzero elements in every row are consecutive.

Parallel LSQR Algorithms Used in Seismic Tomography

AbstractThis paper addresses the LSQR algorithms used in earthquake travel time tomography. We keep the epicenter terms in the equation for regional events, and then use orthogonal projection method to eliminate the epicenter terms; for tele‐events, the classic smoothing process is used. The number of non‐zero elements in partial derivative matrix is increased a couple of times because of the orthogonal projection and smoothing process. For a large scale inversion problem, the amount of non‐zero elements can be dozens of Gigabytes or hundreds of Gigabytes. The huge amount of memory requirement becomes the bottle neck of LSQR algorithms. To solve this problem, we studied the distribution property of non‐zero elements in partial derivative matrix , designed an efficient data structure for the sparse matrix, used a distributed memory and computation scheme for matrix computation, and implemented it on a multi‐processor super computer. We derived an estimation formula of parallel efficiency and tested two real tomography models.

A Frisch-Newton Algorithm for Sparse Quantile Regression

Recent experience has shown that interior-point methods using a log barrier approach are far superior to classical simplex methods for computing solutions to large parametric quantile regression problems. In many large empirical applications, the design matrix has a very sparse structure. A typical example is the classical fixed-effect model for panel data where the parametric dimension of the model can be quite large, but the number of non-zero elements is quite small. Adopting recent developments in sparse linear algebra we introduce a modified version of the Frisch-Newton algorithm for quantile regression described in Portnoy and Koenker[28]. The new algorithm substantially reduces the storage (memory) requirements and increases computational speed. The modified algorithm also facilitates the development of nonparametric quantile regression methods. The pseudo design matrices employed in nonparametric quantile regression smoothing are inherently sparse in both the fidelity and roughness penalty components. Exploiting the sparse structure of these problems opens up a whole range of new possibilities for multivariate smoothing on large data sets via ANOVA-type decomposition and partial linear models.

Implicit nonstaggered finite‐difference time‐domain method

AbstractA new, unconditionally stable, implicit nonstaggered finite‐difference time‐domain (INS‐FDTD) method is introduced. This method is more efficient than the (unconditionally stable) finite‐element time‐domain (FETD) method with brick elements because the number of nonzero elements in the system matrix is reduced. A numerical‐dispersion analysis is provided as well. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 317–319, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20809

An improved compact 2-D finite-difference frequency-domain method for guided wave structures

An improved compact two-dimensional (2-D) finite-difference frequency-domain method is presented to determine the dispersion characteristics of guided wave structures. Eigenvalue equations that contain only two transverse electric field components are derived from Maxwell's differential equations. Compared to the traditional 2-D FDFD containing four or six field components, both the order and number of nonzero elements of the coefficient matrix are reduced simultaneously. The method is verified by two application examples.

Analysis of truncated periodic array using two-stage wavelet-packet transformations for impedance matrix compression

A novel method of moments procedure is applied to the problem of scattering by metallic truncated periodic arrays. In such problems, the induced current shows localized behavior within the unit cell and at the same time exhibits cell-to-cell periodicity. In order to select a set of expansion functions that may account for such behavior, a two-stage basis transformation, of which the first stage is an ordinary wavelet transformation performed independently on each unit-cell, has been applied to a pulse basis. The resultant basis functions at the first stage are regrouped and retransformed to reveal the periodicity of their coefficients. Expansion functions are then iteratively selected from this newly constructed basis to form a compressed impedance matrix. The compression ratios obtained in this manner are higher than the compression ratio achieved using a basis constructed via an ordinary single-stage wavelet transformation, where compression is the ratio between the number of nonzero elements in the matrix used to solve the problem and the number of elements in the original matrix. An even higher compression is attained by considering, in addition, functions that reveal array-end related features and iteratively selecting the expansion from an overcomplete dictionary.

On lowest density MDS codes

Let F/sub q/ denote the finite field GF(q) and let h be a positive integer. MDS (maximum distance separable) codes over the symbol alphabet F/sub q//sup b/ are considered that are linear over F/sub q/ and have sparse ("low-density") parity-check and generator matrices over F/sub q/ that are systematic over F/sub q//sup b/. Lower bounds are presented on the number of nonzero elements in any systematic parity-check or generator matrix of an F/sub q/-linear MDS code over F/sub q//sup b/, along with upper bounds on the length of any MDS code that attains those lower bounds. A construction is presented that achieves those bounds for certain redundancy values. The building block of the construction is a set of sparse nonsingular matrices over F/sub q/ whose pairwise differences are also nonsingular. Bounds and constructions are presented also for the case where the systematic condition on the parity-check and generator matrices is relaxed to be over F/sub q/, rather than over F/sub q//sup b/.

State Space Orderings for Gauss--Seidel in Markov Chains Revisited

States of a Markov chain may be reordered to reduce the magnitude of the subdominant eigenvalue of the Gauss--Seidel (GS) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the GS splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semiconvergent. On the other hand, there are semiconvergent state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. Moreover, a version of the Cuthill--McKee algorithm may be used to order the states of a Markov chain so that Property-R is satisfied. The computational complexity of the ordering algorithm is less than that of a single GS iteration. In doing all this, the aim is to gain insight into (faster) converging orderings.