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JOURNAL OF algorithmS 1996年第3期21卷 598-617页

作者： Zhou, X Nakano, S Nishizeki, T TOHOKU UNIV GRAD SCH INFORMAT SCIDEPT SYST INFORMAT SCISENDAIMIYAGI 98077JAPAN

Many combinatorial problems can be efficiently solved for partial k-trees (graphs of treewidth bounded by k). The edge-coloring problem is one of the well-known combinatorial problems for which no efficient algorithms were previously known, except a polynomial-time algorithm of very high complexity. This paper gives a linear-time sequential algorithm and an optimal parallel algorithm which find an edge-coloring of a given partial k-tree with the minimum number of colors for fixed k. (C) 1996 Academic Press, Inc.

关键词： Decomposable graphs algorithms colored graph Parallel algorithms sequential algorithm Color algorithms

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Estimating Heavy-Tail Exponents Through Max Self-Similarity

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第3期57卷 1615-1636页

作者： Stoev, Stilian A. Michailidis, George Taqqu, Murad S. Univ Michigan Dept Stat Ann Arbor MI 48109 USA Boston Univ Dept Math Boston MA 02215 USA

In this paper, a novel approach to the problem of estimating the heavy-tail exponent alpha > 0 of a distribution is proposed. It is based on the fact that block-maxima of size m scale at a rate m(1/alpha) for independent, as well as for a number of dependent data. This scaling rate can be captured well by the max-spectrum plot of the data that leads to regression based estimators for alpha . Consistency and asymptotic normality of these estimators is established for independent data under mild conditions on the behavior of the tail of the distribution. The proposed estimators have an important computational advantage over existing methods;namely, they can be calculated and updated sequentially in an on-line fashion without having to store the entire data set. Practical issues on the automatic selection of tuning parameters for the estimators and corresponding confidence intervals are also addressed. Extensive numerical simulations show that the proposed method is competitive for both small and large sample sizes, robust to contaminants and continues to work under the presence of substantial amount of dependence. The proposed estimators are used to illustrate the close connection between long-range dependence and heavy tails over an Internet traffic trace.

关键词： Block-maxima Frechet distribution heavy-tail exponent hill plot sequential algorithm

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Decomposition methods for differentiable optimization problems over Cartesian product sets

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 1998年第1期9卷 5-42页

作者： Patriksson, M Univ Washington Dept Math Seattle WA 98195 USA

This paper presents a unified analysis of decomposition algorithms for continuously differentiable optimization problems defined on Cartesian products of convex feasible sets. The decomposition algorithms are analyzed using the framework of cost approximation algorithms. A convergence analysis is made for three decomposition algorithms: a sequential algorithm which extends the classical Gauss-Seidel scheme, a synchronized parallel algorithm which extends the Jacobi method, and a partially asynchronous parallel algorithm. The analysis validates inexact computations in both the subproblem and line search phases, and includes convergence rate results. The range of feasible step lengths within each algorithm is shown to have a direct correspondence to the increasing degree of parallelism and asynchronism, and the resulting usage of more outdated information in the algorithms.

关键词： Cartesian product sets decomposition cost approximation sequential algorithm parallel processing partially asynchronous algorithms

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Inverse estimation of temperature boundary conditions with irregular shape of gas tank

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2010年第21-22期53卷 4651-4662页

作者： Lin, David T. W. Wang, Chi-Chang Yang, Ching-Yu Li, Jen-Chieh Feng Chia Univ Dept Mech & Comp Aided Engn Taichung 40724 Taiwan Natl Univ Tainan Inst Mechatron Syst Engn Tainan 700 Taiwan Natl Kaohsiung Univ Appl Sci Dept Mold & Die Engn Kaohsiung 807 Taiwan

To broaden the application of inverse estimation, the purpose of this study is to estimate the unknown temperature boundary condition of the complex or irregular shape, like the high pressure gas tank. An inverse algorithm based on the sequential method and the concept of future time combined with the finite-element method is proposed to solve the two dimensional irregular shape heat conduction problems. Special features about the proposed method are that the stiffness matrix of the irregular shape can be solved from the finite-element method and used by the inverse algorithm. The estimated results are quite accurate with the consideration of future time in the different measured errors, the various sensor's number and the sensor location. These results show that the proposed method is an accurate, sturdy, and efficient method for solving several realistic applications. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Inverse heat conduction Gas tank Irregular shape sequential algorithm Future time

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Layer-Wise Learning Strategy for Nonparametric Tensor Product Smoothing Spline Regression and Graphical Models

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JOURNAL OF MACHINE LEARNING RESEARCH 2019年第1期20卷 1-38页

作者： Tan, Kean Ming Lu, Junwei Zhang, Tong Liu, Han Univ Michigan Dept Stat Ann Arbor MI 48109 USA Harvard TH Chan Sch Publ Hlth Dept Biostat Boston MA 02115 USA Hong Kong Univ Sci & Technol Dept Math Dept Comp Sci & Engn Clear Water Bay Hong Kong Peoples R China Northwestern Univ Dept Elect Engn & Comp Sci Evanston IL 60208 USA

Nonparametric estimation of multivariate functions is an important problem in statistical machine learning with many applications, ranging from nonparametric regression to nonparametric graphical models. Several authors have proposed to estimate multivariate functions under the smoothing spline analysis of variance (SSANOVA) framework, which assumes that the multivariate function can be decomposed into the summation of main effects, two-way interaction effects, and higher order interaction effects. However, existing methods are not scalable to the dimension of the random variables and the order of interactions. We propose a LAyer-wiSE leaRning strategy (LASER) to estimate multivariate functions under the SSANOVA framework. The main idea is to approximate the multivariate function sequentially starting from a model with only the main effects. Conditioned on the support of the estimated main effects, we estimate the two-way interaction effects only when the corresponding main effects are estimated to be non-zero. This process is continued until no more higher order interaction effects are identified. The proposed strategy provides a data-driven approach for estimating multivariate functions under the SSANOVA framework. Our proposal yields a sequence of estimators. To study the theoretical properties of the sequence of estimators, we establish the notion of post-selection persistency. Extensive numerical studies are performed to evaluate the performance of LASER.

关键词： Persistency nonparametric regression nonparametric graphical models sequential algorithm model selection

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A two-dimensional mathematical model of non-linear dual-sorption of percutaneous drug absorption

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BIOMEDICAL ENGINEERING ONLINE 2005年第1期4卷 1-15页

作者： George, K. Brunel Univ Sch Informat Syst Comp & Math Dept Math Sci Uxbridge UB8 3PH Middx England Univ Delhi Aditi Coll Delhi 110039 India Civil & Computat Engn Ctr Sch Engn Swansea SA2 8PP W Glam Wales

Background: Certain drugs, for example scopolamine and timolol, show non-linear kinetic behavior during permeation process. This non-linear kinetic behavior is due to two mechanisms;the first mechanism being a simple dissolution producing mobile and freely diffusible molecules and the second being an adsorption process producing non-mobile molecules that do not participate in the diffusion process. When such a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, C, the donor concentration. The present paper studies the effect of the parameter value, C, when the region of the contact of the skin with drug, is a line segment on the skin surface. To confirm that dual-sorption process gives an explanation to non-linear kinetic behavior, the characteristic features that are used in one-dimensional models are (1) prolongation of half-life if the plot of flux versus time are straight lines soon after the vehicle removal, (2) the decrease in half-life with increase in donor concentration. This paper introduces another feature as a characteristic to confirm that dual-sorption model gives an explanation to the non-linear kinetic behavior of the drug. This new feature is "the prolongation of half-life is not a necessary feature if the plots of drug flux versus time is a non-linear curve, soon after the vehicle removal". Methods: From biological point of view, a drug absorption model is said to be nonlinear if the sorption isotherm is non-linear. When a model is non-linear the relationship between lag-time and donor concentration is non-linear and the lag time decreases with increase in donor concentration. A two-dimensional dual-sorption model is developed for percutaneous absorption of a drug, which shows non-linear kinetic behavior in the permeation process. This model may be used when the diffusion of the drug in the direction parallel to the

关键词： Concentration Profile Timolol Time Level sequential algorithm Drug Kinetic

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Inverse method in simultaneously estimate internal heat generation and root temperature of the T-shaped fin

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INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER 2010年第9期37卷 1312-1320页

作者： Wang, Chi-Chang Yang, Ching-Yu Feng Chia Univ Dept Mech & Comp Aided Engn Taichung 40724 Taiwan Natl Kaohsiung Univ Appl Sci Dept Mold & Die Engn Kaohsiung 807 Taiwan

This study employed the finite element method and rearranged the matrix to establish an inverse operation without iteration, in order to simultaneously estimate the internal heat generation and root temperature of the T-shaped fin. The results of numerical validation showed that the optimized the T-shaped fin has a good effect because of better efficiency of heat transfer. Regardless of the configurations, the estimation of internal heat generation is obviously affected by the measurement error. Nevertheless, the measurement of temperature in future time can reduce sensitivity of internal heat generation and root temperature to the measurement error. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Inverse heat conduction T-shaped fin sequential algorithm Future time Linear last-squares error method Finite element method

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Target scattering estimation in clutter with polarization optimization

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EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2015年第1期2015卷 1页

作者： Cheng, Xu Shi, Longfei Chang, Yuliang Li, Yongzhen Wang, Xuesong Natl Univ Def Technol Coll Elect Sci & Engn State Key Lab Complex Electromagnet Environm Effe Changsha 410073 Hunan Peoples R China

In this paper, we propose an adaptive waveform polarization method for the estimation of target scattering matrix in the presence of clutter. The proposed sequential algorithm, based on the concept of sequential minimum mean square error (MSE) estimation, to determine the coefficients of the scattering matrix, guarantees the convergence and the resulting computational complexity is linear with the number of iterations. The effectiveness of the proposed method is validated through numerical results, underlining the performance improvement given by joint transmission and reception (Tx/Rx) polarization optimization for the scalar system. Also, the results show that the vector system with transmission polarization optimization provides a comparative performance as the scalar measurement system employing joint Tx/Rx polarization optimization. Less computation burden highlights the advantage of the former mode.

关键词： Radar polarization Minimum MSE estimation sequential algorithm Waveform design Scattering matrix

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AN 0(LOG-N) PARALLEL algorithm FOR STRONG CONNECTIVITY AUGMENTATION PROBLEM

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1987年第3-4期22卷 187-197页

作者： CHAUDHURI, P Department of Electronics and Electrical Communication Engineering Indian Institute of Technology Kharagpur 721302 India

A synchronised parallel algorithm for the strong connectivity augmentation problem is presented. Its depth is 0(logn) using 0(n3) processors on a concurrent read, concurrent write parallel random access machine.

关键词： Parallel algorithm sequential algorithm strong connectivity augmentation CRCW PRAM time complexity GT:algorithm SD:G.1.0 F.2.2

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Efficient multiphysics modelling with adaptive grid refinement using a MPFA method

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COMPUTATIONAL GEOSCIENCES 2014年第5期18卷 625-636页

作者： Faigle, Benjamin Helmig, Rainer Aavatsmark, Ivar Flemisch, Bernd Univ Stuttgart IWS Dept Hydromech & Modelling Hydrosyst D-70529 Stuttgart Germany Univ Bergen CIPR N-5007 Bergen Norway

A sequential solution procedure is used to simulate compositional two-phase flow in porous media. We employ a multiphysics concept that adapts the numerical complexity locally according to the underlying processes to increase efficiency. The framework is supplemented by a local refinement of the simulation grid. To calculate the fluxes on such grids, we employ a combination of the standard two-point flux approximation and a multipoint flux approximation where the grid is refined. This is then used to simulate a large-scale example related to underground CO2 storage.

关键词： Adaptive mesh refinement Compressible two-phase flow Porous media sequential algorithm

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