Ordering Of Rows Research Articles

Distributions of forest birds and butterflies in the Andaman islands, Bay of Bengal: nested patterns and processes

The distributional patterns of forest birds and butterflies in the Andaman islands, an oceanic chain located off SE Asia, were tested for nestedness. Both taxa were highly nested. Nestedness could be due to colonization or extinction processes, area or distance effects or nestedness of habitats. Nestedness in forest bird distributions were strongly influenced by area and habitat related factors. Habitats were significantly nested in all three island groups, however most strongly for the North Andamans. However forest bird distributions in the North Andamans, as indicated by row order in the packed matrix, was not correlated with habitat diversity, suggesting that habitat related factors alone cannot account for these patterns. Other causal influences could be passive sampling, where common and abundant species and habitats are more likely to have a widespread distribution than rare species and habitats. The nested subset pattern seen in two unrelated taxa suggests that the Andamans are extinction dominated and that the protection of forests on large islands is critical for the conservation of its biodiversity.

Remark on Algorithm 761

Several improvements to the estimation of partial derivatives in Algorithm 761 are presented. The problems corrected are (1) in the calculation of the probability weight in subroutine SDPD3P which may result in overflow, (2) in the calculation of final weight in subroutine SDPD3P which may result in overflow, (3) in the computation of a determinant in subroutine SDLEQN which is not necessary, and (4) in the computation of the condition number of a matrix in subroutine SDLEQN which generates very different results for matrices that differ only in row order.

Distribution of the Pb and Sb Atoms in the (Pb, Sb)S Layers of the Franckeite-Type Misfit Compound [(Pb, Sb)S]2.28NbS2 Examined by Scanning Tunneling and Atomic Force Microscopy

The distribution of the Pb and Sb atoms in the (Pb, Sb)S layers of the misfit compound [(Pb, Sb)S]2.28NbS2 was investigated by scanning tunneling microscopy (STM) and atomic force microscopy (AFM). This compound has NaCl-type MS (M=Pb, Sb) layers (Q-layers) alternating with NbS2 layers (H-layers) in which the Nb atoms are located in slightly distorted trigonal prism sites. Both the H- and Q-layers of [(Pb, Sb)S]2.28NbS2 were imaged by STM and AFM. The atomic-scale STM and AFM images were analyzed in terms of the partial and total electron density plots calculated for the Q- and H-layers. The STM images of the Q-layers allowed us to detect all the constitutive atoms of the Q-layers with a short-range ordering of pure Pb and Sb rows in the aQ modulation direction.

Reversing the row order for the row-by-row frontal method

The efficiency of the row-by-row frontal method for the solution of unsymmetric sparse linear systems of equations is dependent on the row ordering used. Numerical experience has shown us that it can be advantageous to reverse a given row ordering. We present two results on invariances under the reversal of the ordering and use real applications to illustrate the variations that can take place upon row reversal. Copyright © 2001 John Wiley & Sons, Ltd.

Sorting measurement queues to speed up the flow injection analysis mass spectrometry of combinatorial chemistry syntheses

A high-throughput flow injection analysis mass spectrometry system was developed for the purity estimation of multiple parallel combinatorial chemistry synthetic samples. Surreptitious inter-sample carry-over represents a threat to the accuracy of the purity estimates. The visualisation of carry-over in 96-well racks via a surveillance program was improved by introducing the automatic sorting of the intra-rack sample measurement queues. This was necessary as the logical arraying of building blocks by synthetic dispensing robots imparts an underlying row and/or column order to the 96-well racks, which complicates the estimation of carry-over. In a primary sorting step, the molecular weight difference between the expected synthetic products in consecutively measured wells was maximised; in a secondary sorting step, the consecutive measurement of wells with similar building blocks was minimised. Over four hundred samples drawn equally from five diverse combinatorial synthetic families were measured to explore the use of this two-stage sorting to ease the measurement of carry-over, and so to facilitate the optimisation of the flow injection analysis measurement duty cycle. Subsequently the duty cycle in daily use, of 168 s was reduced to 70 s, while maintaining the median inter-sample carry-over at levels below 1%.

Towards faster Givens rotations based power system state estimator

Numerically stable and computationally efficient power system state estimation (PSSE) algorithms are designed using an orthogonalization (QR decomposition) approach. They use Givens rotations for orthogonalization which enables sparsity exploitation during factorization of the large sparse augmented Jacobian. A priori row and column ordering is usually performed to reduce intermediate and and overall fills. Column ordering methods, usually based on minimum degree algorithm (MDA), have matured. However, there exists a significant scope for improving the quality of row ordering. This paper introduces a new row ordering technique for Givens rotations based power system state estimators. The proposed row processing method (VPAIR) requires a shift from conventionally used row oriented QR decomposition implementation to a column oriented QR decomposition implementation. It is demonstrated that, the proposed column oriented QR decomposition algorithm which uses MDA for column ordering and VPAIR for row ordering can lead to a much faster PSSE. These aspects are justified by simulations on large power systems.

Frontal solvers for process engineering: local row ordering strategies

The solution of chemical process simulation and optimization problems on today's high performance supercomputers requires algorithms that can take advantage of vector and parallel processing when solving the large, sparse matrices that arise. The frontal method can be highly efficient in this context due to its ability to make use of vectorizable dense matrix kernels on a relatively small frontal matrix in the innermost loop of the computation. However, the ordering of the rows in the coefficient matrix strongly affects size of the frontal matrix and thus the solution time. If a poor row ordering is used it may make the frontal method uncompetitive with other methods. We describe here a graph theoretical framework for identifying suitable row orderings that specifically addresses the issue of frontal matrix size. This leads to local, heuristic methods which aim to limit frontal matrix growth in the row and/or column dimensions. Results on a wide range of test problems indicate that improvements in frontal solver performance can often be obtained by the use of a restricted minimum column degree heuristic, which can be viewed as a variation of the minimum degree heuristic used in other contexts. Results also indicate that the natural unit-block structure of process simulation problems provides a quite reasonable ordering.

Improving the Run Time and Quality of Nested Dissection Ordering

When performing sparse matrix factorization, the ordering of matrix rows and columns has a dramatic impact on the factorization time. This paper describes an approach to the reordering problem that produces significantly better orderings than prior methods. The algorithm is a hybrid of nested dissection and minimum degree ordering, and combines an assortment of different algorithmic advances. New or improved algorithms are described for graph compression, multilevel partitioning, and separator improvement. When these techniques are combined, the resulting orderings average 39% better than minimum degree over a suite of test matrices, while requiring roughly 2.7 times the run time of Liu's multiple minimum degree.

Reliability of iterative linear equation solvers in chemical process simulation

For large-scale problems, it may be attractive to use iterative methods to solve the large, sparse, linear systems that arise in the equation-based approach to process simulation. This is because, as problem sizes grow, direct methods become extremely expensive in terms of both computation time and storage requirements. Iterative methods, however, may not be reliable for the indefinite and highly unsymmetric matrices encountered in a diverse multi-unit flowsheeting problem. An extensive computational study of the reliability of iterative linear solvers on such problems is presented here. Nine different iterative linear solvers are considered, in connection with incomplete factorization preconditioning. These are applied to a set of nine test problems. Results indicate that the ordering of rows and columns in the matrices is a crucial factor in determining the success with which iterative methods can be employed. Results also indicate that in general these multi-unit flowsheeting matrices are difficult to solve by iterative methods, and that, though there is certainly potential in the use of iterative methods, to realize this potential will require improvements in the reordering and/or preconditioning schemes used.

Row Ordering for a Sparse QR Decomposition

A new row ordering strategy based on pairing rows to minimize local fill-in is presented. The row ordering can be combined with most column ordering strategies to reduce computation, maintain sparsity, and solve rank deficient problems. Comparison of the new row pairing algorithm with Duff’s fixed pivot row ordering on a collection of sparse matrix test problems shows a median 47–71% reduction, depending on the column ordering, in floating point operations (flops) required for the QR decomposition. On a finite element application using nested domain decomposition for the column ordering, the new row ordering is competitive with the row ordering from nested domain decomposition.

Surface ordering of the molecular beam epitaxially grown GaAs(001)-2×4-As reconstruction

Our scanning tunneling microscopy (STM) and reflection high-energy electron diffraction (RHEED) showed that the intensity of the two-fourths fractional order feature in the RHEED pattern for the GaAs(001)-2×4 structure reflects the degree of ordering of the vacancy rows. The STM images show a high degree of surface ordering only when the RHEED produces nearly the equal intensity sharp streaks for all the fourfold fractional order diffraction. Two possible mechanisms are suggested to explain the observed STM-RHEED correlation.

On parallelism and convergence of incomplete LU factorizations

This paper discusses the effects of ordering on the speed of convergence to solutions for ILU preconditioned CGS methods. Two parallel ordering strategies are introduced and defined. They are reffered to as parallel block (PB( m)) and parallel diagonal (PD( m)) orderings, where m is a parameter related to the degree of parallelism. These two types of ordering are so defined that, depending on the value of m, PB( m) ordering will include row and four-color orderings, while PD( m) ordering will include diagonal and red-black orderings. These orderings are suitable to the execution of ILU preconditioned methods on mesh- or torus-connected parallel processors. Analytical and empirical studies are carried out, using 2D convection-diffusion model equations, to determine how the degree of parallelism affects the speed of convergence for these preconditioned methods.

Efficient algorithm for Weinberger array folding

Weinberger arrays (WAs) are an alternative to programmable logic arrays (PLAs) as a method of implementing combinational logic circuits. Column folding is a technique generally employed in PLAs to save the silicon area by implementing the circuit of two columns in the area of one. This paper describes an algorithm for folding Weinberger arrays. The algorithm performs column and row ordering and then column folding. The complexity of the algorithm is O(n 2). The algorithm has been tested extensively on WAs that were generated both for practical circuits and for numerous randomly generated ciruits. Experimental results are discussed.

Indentification of atmospheric organic sources using the carbon hollow tube-gas chromatography method and factor analysis

Atmospheric organics were sampled and analyzed by using the carbon hollow tube-gas chromatography method. Chromatograms from spice mixtures, cigarettes, and ambient air were analyzed. Principal factor analysis of row order chromatographic data produces factors which are eigenchromatograms of the components in the samples. Component sources are identified from the eigenchromatograms in all experiments and the individual eigenchromatogram corresponding to a particular source is determined in most cases. Organic sources in ambient air and in cigaretts are identified with 87% certainty. Analysis of clove cigarettes allows the determination of the relative amount of clove in different cigarettes. A new nondestructive quality control method using the hollow tube-gas chromatography analysis is discussed.

Transverse folding algorithm for PLAs

The letter reports a new concept for transverse folding of programmable logic arrays (PLAs). With the new definitions for the compatibility and foldability of rows (columns) of a column-folded (row-folded) PLA, the transverse compatibility-cum-foldability matrix (TCFM) is plotted. From the TCFM, a transverse folding matrix (TFM) is found, from which the row (column) folding pairs and the resulting ordering of rows and columns are obtained.

Row-ordering schemes for sparse givens transformations. II. implicit graph model

A new graph model is presented to study the row annihilation and row ordering problems in the QR decomposition of sparse matrices using Givens rotations. The graph-theoretic results obtained can be used to derive good row orderings for certain column orderings, such as width-1 and width-2 nested dissection orderings. This model is different from the bipartite-graph model introduced in [6]. We refer to the new model as implicit because the rows are not represented explicitly by nodes, in contrast to the bipartite-graph model, where the rows are represented by nodes in a bipartite graph.

Row-ordering schemes for sparse givens transformations. I. bipartite graph model

Let A be an m-by- n matrix, m⩾ n, and let P r and P c be permutation matrices of order m and n respectively. Suppose P rAP c is reduced to upper trapezoidal form ( R O ) using Givens rotations, where R is n by n and upper triangular. The sparsity structure of R depends only on P c . For a fixed P c , the number of arithmetic operations required to compute R depends on P r . In this paper, we consider row-ordering strategies which are appropriate when P c is obtained from nested-dissection orderings of A TA . Recently, it was shown that so-called “width-2” nested-dissection orderings of A TA could be used to simultaneously obtain good row and column orderings for A. In this series of papers, we show that the conventional (width-1) nested-dissection orderings can also be used to induce good row orderings. In this first paper, we analyze the application of Givens rotations to a sparse matrix A using a bipartite-graph model.

Ordering Schemes for Parallel Processing of Certain Mesh Problems

In this work, some ordering schemes for mesh points are presented which enable algorithms such as the Gauss–Seidel or SOR iteration to be performed efficiently for the nine-point operator finite difference method on computers consisting of a two-dimensional grid of processors. Convergence results are presented for the discretization of $u_{xx} + u_{yy} $ on a uniform mesh over a square, showing that the spectral radius of the iteration for these orderings is no worse than that for the standard row by row ordering of mesh points. Further applications of these mesh point orderings to network problems, more general finite difference operators, and picture processing problems are noted.

On Row and Column Orderings for Sparse Least Squares Problems

Let $P_1 $ and $P_2 $ be respectively $m \times m$ and $n \times n$ permutation matrices, with $m \geqq n$. Suppose the $m \times n$ sparse matrix $\bar A = P_1 AP_2 $ is reduced to upper trapezoidal form $\left[ {\begin{array}{*{20}c} R \\ 0 \\ \end{array} } \right]$ through the application of Givens rotations sequentially to the rows of $\bar A$. It is well known that the sparsity of R depends only on the choice of $P_2 $, but the choice of $P_1 $ can drastically affect the arithmetic required to compute R. In this paper we provide a mechanism for studying the connection between good row and good column orderings, along with a modified nested dissection algorithm for finding a good $P_2 $ which automatically induces a good $P_1 $. An analysis for a model problem is given, along with some experimental results.

Procrustean analysis of matrices with different row order

Procrustean analysis is extended here to the case where matrices have different row order. Using a definition system in the sense of facet theory, fitting transformations are determined for the set of centroids that represent common substantive equivalence classes of all or some matrices. The resulting operators are used to transform the original matrices. An index, δ, which is consistent with this approach expresses the goodness of fit.