40247854
Fast iterative and preconditioning methods for linear and non-linear systems
Apparatus for unloading a top unloading mine car that is mounted to pivot about a horizontal axis extending along one side of the base of the mine car includes a hoist chain detachably connected to the mine car at the side opposite the pivotal axis. The hoist chain extends upwardly over a pulley mounted on a positioning crank arm. The pulley moves on rotation of the crank arm from a position substantially vertically above the connection means when the mine car is in an upright position to a position above the pivotal axis. The hoist chain continues around a pulley mounted on a drive crank arm and then to an attachment of restricted mobility. The drive crank arm and the positioning crank arm are rotated in a single direction by drive means which are adapted to rotate the drive crank arm at twice the angular velocity of the positioning crank arm. On rotation of the crank arms the hoist chain rotates the top unloading car past the axis of rotation to dump the contents of the car and returns the car to the upright position. In a preferred embodiment, the attachment of restricted mobility of the hoist chain is a differential pulley. A compensating chain runs from the differential pulley over an idler pulley to a connection on the positioning arm to adjust the effective length of the hoist chain.
21847139
An Analysis of Sparse Approximate Inverse Preconditioners for Boundary Integral Equations
Preconditioning techniques for dense linear systems arising from singular boundary integral equations are described and analyzed. A particular class of approximate inverse based preconditioners related to the mesh neighbor methods is known to be efficient. This paper shows that it is an operator splitting preconditioner and clusters eigenvalues for the normal equation matrix thus ensuring a fast convergence of the conjugate gradient normal method. Clustering of the eigenvalues of the preconditioned matrix and fast convergence of the generalized minimal residual method are also observed. For the type of problems considered, we demonstrate a crucial connection between two essential features of eigenvalue clustering for a sparse preconditioner---approximate inversion for a small cluster radius and operator splitting for a small cluster size. Experimental results from several boundary integral equations are presented.
15785287
A Nonlinear Multigrid Method for Total Variation Minimization from Image Restoration
Abstract
Image restoration has been an active research topic and variational formulations are particularly effective in high quality recovery. Although there exist many modelling and theoretical results, available iterative solvers are not yet robust in solving such modeling equations. Recent attempts on developing optimisation multigrid methods have been based on first order conditions. Different from this idea, this paper proposes to use piecewise linear function spanned subspace correction to design a multilevel method for directly solving the total variation minimisation. Our method appears to be more robust than the primal-dual method (Chan et al., SIAM J. Sci. Comput. 20(6), 1964–1977, 1999) previously found reliable. Supporting numerical results are presented.

3879090
On A Recursive Schur Preconditioner For Iterative Solution Of A Class Of Dense Matrix Problems
There are currently several distinct preconditioning methods for dense matrices based on applying a wavelet transform to obtain a matrix with a large number of small entries. A sparse preconditioner for this transformed matrix can be formed by setting to zero entries that are assumed to be unimportant. The effectiveness of the preconditioner depends on retaining the most important entries and on ensuring that they are positioned conveniently within the transformed matrix. In this paper we present a new, recursive preconditioning strategy that takes into account more of the significant entries without greatly increasing cost and outperforms existing methods in certain cases.
25215706
On Two Variants of an Algebraic Wavelet Preconditioner
A recursive method of constructing preconditioning matrices for the nonsymmetric stiffness matrix in a wavelet basis is proposed for solving a class of integral and differential equations. It is based on a level-by-level application of the wavelet scales decoupling the different wavelet levels in a matrix form just as in the well-known nonstandard form. The result is a powerful iterative method with built-in preconditioning leading to two specific algebraic multilevel iteration algorithms: one with an exact Schur preconditioning and the other with an approximate Schur preconditioning. Numerical examples are presented to illustrate the efficiency of the new algorithms.
12726286
Fast Multilevel Algorithm for a Minimization Problem in Impulse Noise Removal
An effective 2-phase method for removing impulse noise was recently proposed. Its phase 1 identifies noisy pixel candidates by using median-type filters. Then in phase $2$, it restores only the noisy pixel candidates by some variational methods. The resulting method can handle salt-and-pepper noise and random-valued impulse noise at a level as high as 90% and 60%, respectively. The aim of this paper is to generalize a fast multilevel method for Gaussian denoising to solving the minimization problem arising in phase $2$ of the 2-phase method. The multilevel algorithm gives better images than standard optimization methods such as the Newton method or the conjugate gradient method. Also it can handle more general regularization functionals than the smooth ones previously considered. Supporting numerical experiments on two-dimensional gray-scale images are presented.
16722943
The Euclidean Orienteering Problem Revisited
We consider the rooted orienteering problem: Given a set $P$ of $n$ points in the plane, a starting point $r \in P$, and a length constraint $B$, one needs to find a path starting from $r$ that visits as many points of $P$ as possible and of length not exceeding $B$. We present a $(1-\varepsilon)$-approximation algorithm for this problem that runs in $n^{O(1/\varepsilon)}$ time; the computed path visits at least $ (1-\varepsilon)k_{\mathrm{opt}}$ points of $P$, where $k_{\mathrm{opt}}$ is the number of points visited by an optimal solution. This is the first polynomial time approximation scheme for this problem. The algorithm also works in higher dimensions.
14878951
The orienteering problem in the plane revisited
We consider the <i>orienteering problem</i>: Given a set <i>P</i> of <i>n</i> points in the plane, a starting point <i>r</i> ∈ <i>P</i>, and a length constraint <i>B</i>, one needs to find a tour starting at <i>r</i> that visits as many points of <i>P</i> as possible and of length not exceeding <i>B</i>. We present a (1−ε)-approximation algorithm for this problem that runs in <i>n</i><sup><i>O</i>(1/ε)</sup> time, and visits at least (1−ε)<i>k</i><sub>opt</sub> points of <i>P</i>, where <i>k</i><sub>opt</sub> is the number of points visited by the optimal solution. This is the first polynomial time approximation scheme (PTAS) for this problem. The algorithm also works in higher dimensions.
9478736
HuMiTar: A sequence-based method for prediction of human microRNA targets
BackgroundMicroRNAs (miRs) are small noncoding RNAs that bind to complementary/partially complementary sites in the 3' untranslated regions of target genes to regulate protein production of the target transcript and to induce mRNA degradation or mRNA cleavage. The ability to perform accurate, high-throughput identification of physiologically active miR targets would enable functional characterization of individual miRs. Current target prediction methods include traditional approaches that are based on specific base-pairing rules in the miR's seed region and implementation of cross-species conservation of the target site, and machine learning (ML) methods that explore patterns that contrast true and false miR-mRNA duplexes. However, in the case of the traditional methods research shows that some seed region matches that are conserved are false positives and that some of the experimentally validated target sites are not conserved.ResultsWe present HuMiTar, a computational method for identifying common targets of miRs, which is based on a scoring function that considers base-pairing for both seed and non-seed positions for human miR-mRNA duplexes. Our design shows that certain non-seed miR nucleotides, such as 14, 18, 13, 11, and 17, are characterized by a strong bias towards formation of Watson-Crick pairing. We contrasted HuMiTar with several representative competing methods on two sets of human miR targets and a set of ten glioblastoma oncogenes. Comparison with the two best performing traditional methods, PicTar and TargetScanS, and a representative ML method that considers the non-seed positions, NBmiRTar, shows that HuMiTar predictions include majority of the predictions of the other three methods. At the same time, the proposed method is also capable of finding more true positive targets as a trade-off for an increased number of predictions. Genome-wide predictions show that the proposed method is characterized by 1.99 signal-to-noise ratio and linear, with respect to the length of the mRNA sequence, computational complexity. The ROC analysis shows that HuMiTar obtains results comparable with PicTar, which are characterized by high true positive rates that are coupled with moderate values of false positive rates.ConclusionThe proposed HuMiTar method constitutes a step towards providing an efficient model for studying translational gene regulation by miRs.
618005
Online conflict-free coloring for halfplanes, congruent disks, and axis-parallel rectangles
We present randomized algorithms for online conflict-free coloring (CF in short) of points in the plane, with respect to halfplanes, congruent disks, and nearly-equal axis-parallel rectangles. In all three cases, the coloring algorithms use O(log n) colors, with high probability.
 We also present a deterministic algorithm for online CF coloring of points in the plane with respect to nearly-equal axis-parallel rectangles, using O(log3n) colors. This is the first efficient (i.e, using polylog(n) colors) deterministic online CF coloring algorithm for this problem.
16132278
A constant factor approximation algorithm for k-median clustering with outliers
We consider the k-median clustering with outliers problem: Given a finite point set in a metric space and parameters k and m, we want to remove m points (called outliers), such that the cost of the optimal k-median clustering of the remaining points is minimized. We present the first polynomial time constant factor approximation algorithm for this problem.