New numerical procedures are proposed to solve the symmetric matrix polynomial equation A(T)(-s) X(s) + X-T(-s) A(s)= 2B(s) that is frequently encountered in control and signal processing. An interpolation approach is...
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New numerical procedures are proposed to solve the symmetric matrix polynomial equation A(T)(-s) X(s) + X-T(-s) A(s)= 2B(s) that is frequently encountered in control and signal processing. An interpolation approach is presented that takes full advantage of symmetry properties and leads to an equivalent reduced-size linear system of equations. It results in a simple and general characterization of all solutions of expected column degrees. Several new theoretical results concerning stability theory and reduced Sylvester resultant matrices are also developed and used to conclude a priori on the existence of a solution. By means of numerical experiments, it is shown that our algorithms are more efficient than older methods and, namely, appear to be numerically reliable. (C) 1998 Elsevier Science Ltd. All rights reserved.
The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered backprojection (FBP) for X-ray computed tomography (CT) and the invers...
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The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered backprojection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform for magnetic resonance imaging (MRI), based on simple mathematical models for the imaging systems. These methods are typically fast, but have suboptimal properties such as poor resolution-noise tradeoff for CT. A second type is iterative reconstruction methods based on more complete models for the imaging system physics and, where appropriate, models for the sensor statistics. These iterative methods improved image quality by reducing noise and artifacts. The U.S. Food and Drug Administration (FDA)-approved methods among these have been based on relatively simple regularization models. A third type of methods has been designed to accommodate modified data acquisition methods, such as reduced sampling in MRI and CT to reduce scan time or radiation dose. These methods typically involve mathematical image models involving assumptions such as sparsity or low rank. A fourth type of methods replaces mathematically designed models of signals and systems with data-driven or adaptive models inspired by the field of machine learning. This article focuses on the two most recent trends in medical image reconstruction: methods based on sparsity or low-rank models and data-driven methods based on machine learning techniques.
The repeated median line estimator is a highly robust method for fitting a regression line to a set of n data points in the plane. In this paper, we consider the problem of updating the estimate after a point is remov...
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The repeated median line estimator is a highly robust method for fitting a regression line to a set of n data points in the plane. In this paper, we consider the problem of updating the estimate after a point is removed from or added to the data set. This problem occurs, e.g., in statistical online monitoring, where the computational effort is often critical. We present a deterministic algorithm for the update working in O(n) time and O(n(2)) space. (C) 2003 Elsevier B.V. All rights reserved.
In many applications like verification or combinatorial optimization, ordered binary decision diagrams (OBDDs) are used as a representation or data structure for Boolean functions. efficient algorithms exist for the i...
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In many applications like verification or combinatorial optimization, ordered binary decision diagrams (OBDDs) are used as a representation or data structure for Boolean functions. efficient algorithms exist for the important operations on OBDDs, and many functions can be represented in reasonable size if a good variable ordering is chosen. In general, it is NP-hard to compute optimal or near-optimal variable orderings, and already simple classes of Boolean functions contain functions whose OBDD size is exponential for each variable ordering. For the class of Boolean functions representable by fan-in 2 read-once formulas the structure of optimal variable orderings is described, leading to a linear time algorithm for the construction of optimal variable orderings and the size of the corresponding OBDD. Moreover, it is proved that the hardest read-once formula has an OBDD size of order n(beta) where beta = log(4)(3 + root 5) < 1.1943. (C) 2000 Elsevier Science B.V. All rights reserved.
Primer Approximation Multiplex PCR (PAMP) is a recently introduced experimental technique for detecting large-scale cancer genome lesions such as inversions and deletions from heterogeneous samples containing a mixtur...
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Primer Approximation Multiplex PCR (PAMP) is a recently introduced experimental technique for detecting large-scale cancer genome lesions such as inversions and deletions from heterogeneous samples containing a mixture of cancer and normal cells. In this chapter we will first review previous solutions for the problem of selecting sets of PAMP primers that minimize detection failure probability and subsequently review our approach based on integer programming formulations for inversion and deletion detections.
Consider an m-machine production line for processing identical parts served by a mobile robot. The problem is to find the minimum cycle time for 2-cyclic schedules, in which exactly two parts enter and two parts leave...
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Consider an m-machine production line for processing identical parts served by a mobile robot. The problem is to find the minimum cycle time for 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. This work treats a special case of the 2-cyclic robot scheduling problem when the robot route is given and the operation durations are to be chosen from prescribed intervals. The problem was previously proved to be polynomially solvable in O(m(8)log m) time. This paper proposes an improved algorithm with reduced complexity O(m(4)). (C) 2010 Elsevier B.V. All rights reserved.
Two efficient algorithms are presented that, for a given linear system Ax = b , eliminate equations that are non-zero multiples of other equations. The second algorithm runs in linear time when the entries of A are +1...
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Two efficient algorithms are presented that, for a given linear system Ax = b , eliminate equations that are non-zero multiples of other equations. The second algorithm runs in linear time when the entries of A are +1, −1 or 0.
Using a linear time many-one reduction from the problem TOTAL DOMINATING SET to the problem DOMINATING SET we show how to obtain efficient algorithms to compute a minimum cardinality total dominating set on a variety ...
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Using a linear time many-one reduction from the problem TOTAL DOMINATING SET to the problem DOMINATING SET we show how to obtain efficient algorithms to compute a minimum cardinality total dominating set on a variety of graph classes, among them permutation graphs, dually chordal graphs and k-polygon graphs. (C) 1997 Elsevier Science B.V.
Two forms of Friedland's separate bias estimation algorithm with U-D factorization of the covariance matrices are provided. Each is suited to implementation in a particular computing environment. (We consider MATL...
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Two forms of Friedland's separate bias estimation algorithm with U-D factorization of the covariance matrices are provided. Each is suited to implementation in a particular computing environment. (We consider MATLAB and compiled computer languages.) We reduce the computation time substantially, primarily at the time propagation stage, by using a separated bias formulation, while retaining the desirable numerical properties of the U-D factorization. The perecentage reduction typically increases with ratio of bias state dimension to dynamic state dimension. A numerical evaluation is given for the MATLAB algorithm.
In this paper, we show that every chordal graph with n vertices and m edges admits an additive 4-spanner with at most 2n - 2 edges and an additive 3-spanner with at most O(n log n) edges. This significantly improves r...
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In this paper, we show that every chordal graph with n vertices and m edges admits an additive 4-spanner with at most 2n - 2 edges and an additive 3-spanner with at most O(n log n) edges. This significantly improves results of Peleg and Schaffer from [Graph Spanners, J Graph Theory 13 (1989) 99-116]. Our spanners are additive and easier to construct. An additive 4-spanner can be constructed in linear time while an additive 3-spanner is constructable in O(m log n) time. Furthermore, our method can be extended to graphs with largest induced cycles of length k. Any such graph admits an additive (k + 1)-spanner with at most 2n - 2 edges which is constructable in O(n k + m) time. (c) 2005 Elsevier B.V. All rights reserved.
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