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AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems

RADIO SCIENCE 1996年第5期31卷 1225-1251页

作者： Bleszynski, E Bleszynski, M Jaroszewicz, T ROCKWELL INT CORP CTR SCITHOUSAND OAKSCA 91360 MONOPOLE RES LOS ANGELESCA 90064 ROCKWELL INT CORP N AMER AIRCRAFTLOS ANGELESCA

We describe basic elements and implementation of the adaptive integral method (AIM): a fast iterative integral-equation solver applicable to large-scale electromagnetic scattering and radiation problems. As compared to the conventional method of moments, the AIM solver provides (for typical geometries) significantly reduced storage and solution time already for problems involving 2,000 unknowns. This reduction is achieved through a compression of the impedance matrix, split into near-field and far-field components. The near-field component is computed by using the Galerkin method employing a set of N arbitrary basis functions. The far-field matrix elements are calculated by using the Galerkin method as well, with a set of N auxiliary basis functions. The auxiliary basis functions are constructed as superpositions of pointlike current elements located on uniformly spaced Cartesian grid nodes and are required to reproduce, with a prescribed accuracy, the far field generated by the original basis functions. Algebraically, the resulting near-field component of the impedance matrix is sparse, while its far-field component is a product of two sparse matrices and a three-level Toeplitz matrix. These Toeplitz properties are exploited, by using discrete fast Fourier transforms, to carry out matrix-vector multiplications with O(N(3/2)logN) and O(NlogN) serial complexities for surface and volumetric scattering problems, respectively. The corresponding storage requirements are O(N-3/2) and O(N). In the domain-decomposed parallelized implementation of the solver, with the number Np of processors equal to the number of domains, the total memory required in surface problems is reduced to O(N-3/2/N-p(1/2)). The speedup factor in matrix-vector multiplication is equal to the number of processors N-p. We present a detailed analysis of the errors introduced by the use of the auxiliary basis functions in computing far-field impedance matrix elements. We also discuss the algorithm comple

关键词： primary element METHOD OF MOMENTS algorithmic complexity Galerkin method Solvers speedup factor near-field Storage requirements basis functions far-field field component Integral Methods Electromagnetic scattering impedance matrix

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Field programmable gate array-based fault-tolerant hysteresis current control for AC machine drives

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IET ELECTRIC POWER APPLICATIONS 2012年第3期6卷 181-189页

作者： Berriri, H. Naoaur, W. Bahri, I. Slama-Belkhodja, I. Monmasson, E. Univ Tunis El Manar Dept Elect Engn ENIT LSE Tunis Tunisia Univ Cergy Pontoise Dept Elect Engn SATIE IUP GEII F-95031 Cergy Pontoise France

This study presents a field programmable gate array (FPGA) implementation of a simple fault-tolerant control that ensures continuous operation of hysteresis current controlled AC machine drives under faulty current sensor. The adopted control requires the use of three current sensors and is available for three-phase isolated neutral systems. The third current sensor allows the faulty current sensor detection and isolation based on analytical redundancy that provides residuals with well-defined thresholds. The control is reconfigured in case of faulty current measurement and operation continuity is performed using the remaining two healthy sensors. The main interest of using FPGAs to implement such controllers is the very important reduction of execution time delay in spite of algorithm complexity. As a result, a high sampling frequency can be used and the residual thresholds can be accurately defined even for the experimental set-up. Numerous experimental results are given to illustrate the efficiency of FPGA-based solutions to achieve efficient and reliable fault-tolerant hysteresis current control of AC machine drives.

关键词： AC machines Fault tolerance Hysteresis Current sensors algorithmic complexity Field programmable gate arrays Current control Field programmable

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Structure space of Bayesian networks is dramatically reduced by subdividing it in sub-networks

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2015年 287卷 48-62页

作者： Bouhamed, Heni Masmoudi, Afif Lecroq, Thierry Rebai, Ahmed Sfax Univ Ctr Biotechnol Sfax Bioinformat Unit Sfax Tunisia Sfax Univ Lab Stat & Probabil Sfax Tunisia Univ Rouen LITIS EA 4108 F-76821 Mont St Aignan France

Currently, Bayesian Networks (BNs) have become one of the most complete, self-sustained and coherent formalisms used for knowledge acquisition, representation and application through computer systems. However, learning of BNs structures from data has been shown to be an NP-hard problem. It has turned out to be one of the most exciting challenges in machine learning. In this context, the present work's major objective lies in setting up a further solution conceived to be a remedy for the intricate algorithmic complexity imposed during the learning of BN-structure with a massively-huge data backlog. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Bayesian network Structure learning Modeling algorithmic complexity

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Folded Hasse diagrams of combined traces

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INFORMATION PROCESSING LETTERS 2014年第4期114卷 208-216页

作者： Mikulski, Lukasz Koutny, Maciej Newcastle Univ Sch Comp Sci Newcastle Upon Tyne NE1 7RU Tyne & Wear England Nicolaus Copernicus Univ Fac Math & Comp Sci Torun Poland

To represent concurrent behaviours one can use concepts originating from language theory, including traces and comtraces. Traces can express notions such as concurrency and causality, whereas comtraces can also capture weak causality and simultaneity. This paper is concerned with the development of efficient data structures and algorithms for manipulating comtraces. We introduce and investigate folded Hasse diagrams of comtraces which generalise Hasse diagrams defined for partial orders and traces. We also develop an efficient on-line algorithm for deriving Hasse diagrams from language theoretic representations of comtraces. Finally, we briefly discuss how folded Hasse diagrams could be used to implement efficiently some basic operations on comtraces. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Comtrace Trace Hasse diagram Stratified order structure Partial order Concurrency Causality Weak causality Independence algorithmic complexity Petri net Inhibitor arc

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A computationally intractable problem on simplicial complexes

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COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS 1996年第2期6卷 85-98页

作者： Egecioglu, O Gonzalez, TF UNIV CALIF SANTA BARBARA DEPT COMP SCI SANTA BARBARA CA 93106 USA

We analyze the problem of computing the minimum number er(C) of internal simplexes that need to be removed from a simplicial 2-complex C so that the remaining complex can be nulled by deleting a sequence of external simplexes. We show that the decision version of this problem is NP-complete even when C is embeddable in 3-dimensional space. Since the Betti numbers of C can be computed in polynomial time, this implies that there is no polynomial time computable formula for er(C) in terms of the Betti numbers of the complex, unless P = NP. The problem can be solved in linear time for 1-complexes (graphs). Our reduction can also be used to show that the corresponding approximation problem is at least as difficult as the one for the minimum cardinality vertex cover, and what is worse, as difficult as the minimum set cover problem. Thus simple heuristics may generate solutions that are arbitrarily far from optimal.

关键词： simplicial complex collapsing Betti number algorithmic complexity vertex cover approximation algorithm

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On the realisability of double-cross matrices by polylines in the plane

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JOURNAL OF COMPUTER AND SYSTEM SCIENCES 2017年 86卷 117-135页

作者： Kuijpers, Bart Moelans, Bart UHasselt Hasselt Univ AgoralaanGebouw D B-3590 Diepenbeek Belgium Transnat Univ Limburg Databases & Theoret Comp Sci Res Grp AgoralaanGebouw D B-3590 Diepenbeek Belgium Unleashed Kemp Steenweg 309Box 1 B-3500 Hasselt Belgium

We study a decision problem, that emerges from the area of spatial reasoning. This decision problem concerns the description of polylines in the plane by means of their double-cross matrix. In such a matrix, the relative position of each pair of line segments in a polyline is expressed by means of a 4-tuple over {-, 0,+}. However, not any such matrix of 4-tuples is the double-cross matrix of a polyline. This gives rise to the decision problem: given a matrix of such 4-tuples, decide whether it is the double-cross matrix of a polyline. This problem is decidable, but it is NP-hard. In this paper, we give polynomial-time algorithms for the cases where consecutive line segments in a polyline make angles that are multiples of 90 degrees or 45 degrees and for the case where, apart from an input matrix, the successive angles of a polyline are also given as input. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Spatial reasoning Double-cross calculus Qualitative description of polylines Computational algebraic geometry algorithmic complexity

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GALLAI'S THEOREM FOR LIST COLORING OF DIGRAPHS

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SIAM JOURNAL ON DISCRETE MATHEMATICS 2011年第1期25卷 170-180页

作者： Harutyunyan, Ararat Mohar, Bojan Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada

A classical theorem of Gallai states that in every graph that is critical for k-colorings, the vertices of degree k-1 induce a tree-like graph whose blocks are either complete graphs or cycles of odd length. We provide a generalization to colorings and list colorings of digraphs, where some new phenomena arise. In particular, the problem of list coloring digraphs with the lists at each vertex v having min{d(+)(upsilon), d(-)(upsilon)} colors turns out to be NP-hard.

关键词： digraph coloring dichromatic number list coloring Gallai tree algorithmic complexity NP-complete critical digraph

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Orderings of uniquely colorable hypergraphs

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DISCRETE APPLIED MATHEMATICS 2007年第11期155卷 1395-1407页

作者： Bujtas, Csilla Tuza, Zsolt Univ Pannonia Dept Comp Sci H-8200 Veszprem Hungary Hungarian Acad Sci Inst Comp & Automat Budapest Hungary

For a mixed hypergraph H = (X, W, D), where L and D are set systems over the vertex set X, a coloring is a partition of X into color classes' such that every C is an element of L meets some class in more than one vertex, and every D is an element of D has a nonempty intersection with at least two classes. A vertex-order x(1), x(2),..., x(n) on X (n = vertical bar X vertical bar) is uniquely colorable if the subhypergraph induced by {x(j) : 1 <= j <= i} has precisely one coloring, for each i (1 <= i <= n). We prove that it is NP-complete to decide whether a mixed hypergraph admits a uniquely colorable vertex-order, even if the input is restricted to have just one coloring. On the other hand, via a characterization theorem it can be decided in linear time whether a given color-sequence belongs to a mixed hypergraph in which the uniquely colorable vertex-order is unique. (c) 2007 Elsevier B.V. All rights reserved.

关键词： algorithmic complexity mixed hypergraph uniquely colourable vertex-order

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Speed-up of DNA melting algorithm with complete nearest neighbor properties

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BIOPOLYMERS 2003年第3期70卷 364-376页

作者： Tostesen, E Liu, F Jenssen, TK Hovig, E Norwegian Radium Hosp Dept Tumor Biol N-0310 Oslo Norway PubGene AS N-0319 Oslo Norway

We describe an optimized algorithm, which is faster and more accurate compared to previously described algorithms, for computing the statistical mechanics of denaturation of nucleic acid sequences according to the classical Poland-Scheraga type of model. Nearest neighbor thermodynamics has been included in a complete and general way, by rigorously treating nearest neighbor interactions, helix end interactions, and isolated base-pairs. This avoids the simplifications of previous approaches and achieves full generality and controllability with respect to thermodynamic modeling. The algorithm computes subchain partition functions by recursion, from which various quantitative aspects of the melting process are easily derived, for example the base-pairing probability profiles. The algorithm represents an optimization with respect to algorithmic complexity of the partition function algorithm of Yeramian et al. (Biopolymers 1990, 30, 481-497): we reduce the computation time for a base-pairing probability profile from O(N-2) to O(N), where N is the sequence length. This speed-up comes in addition to the speed-up due to a multiexponential approximation of the loop entropy factor as introduced by Fixman and Freire(22) and applied by Yeramian et al.(25) The speed-up, however, is independent of the multiexponential approximation and reduces time from O(N-3) to O(N-2) in the exact case. A method for representing very large numbers is described, which avoids numerical overflow in the partition Junctions for genomic length sequences. In addition to calculating the standard base-pairing probability profiles, we propose to use the algorithm to calculate various other probabilities (loops, helices, tails) for a more direct view of the melting regions and their positions and sizes. This can provide a better understanding of the physics of denaturation and the biology of genomes. (C) 2003 Wiley Periodicals, Inc.

关键词： DNA melting hybridization helix-coil transition Poland-Scheraga nearest neighbor thermodynamic parameters format end interactions algorithmic complexity loop entropy factor genomic sequences partition function numerical overflow matrix multiplication recursion base-pairing probability loop probability domains

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BROADCASTING ALGORITHM IN COMPUTER-NETWORKS - ACCUMULATIVE DEPTH

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IEE PROCEEDINGS-E COMPUTERS AND DIGITAL TECHNIQUES 1990年第6期137卷 427-432页

作者： RIVERA, FF PLATA, O ZAPATA, EL Department of Electronics Faculty of Physics University of Santiago Santiago de Compostela Spain

We introduce the concept of accumulative depth of a node in a computer network. By utilising this concept as a criterion in the assignment of weights to the nodes of the network, we develop an efficient algorithm (NOBF) to calculate a near-optimal broadcasting figure (a broadcast with a near-minimal transmission delay) in arbitrary point-to-point computer networks. Static and dynamic assignments of weights have been considered. We analyse the efficiency of the algorithm based on accumulative depth as a function of the transmission delay and the algorithmic complexity.

关键词： point-to-point computer networks NOBF algorithmic complexity computer networks accumulative depth transmission delay efficient algorithm near-optimal broadcasting figure Computer networks and techniques Computer communications computational complexity

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