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Threshold group testing with consecutive positives

DISCRETE APPLIED MATHEMATICS 2014年 169卷 68-72页

作者： Chang, Huilan Tsai, Yi-Lin Natl Univ Kaohsiung Dept Appl Math Kaohsiung 811 Taiwan

Threshold group testing introduced by Damaschke (2006) is a generalization of classical group testing where a group test yields a positive (negative) outcome if it contains at least u (at most!) positive items, and an arbitrary outcome for otherwise. Motivated by applications to DNA sequencing, group testing with consecutive positives has been proposed by Balding and Torney (1997) and Colbourn (1999) where n items are linearly ordered and up to d positive items are consecutive in the order. In this paper, we introduce threshold-constrained group tests to group testing with consecutive positives. We prove that all positive items can be identified in [log(2)(n/u-1)] + 2[log(2)(u+2)] +log(2)(u+ 1)]-2 tests for the gap-free case (u = l+1) while the information-theoretic lower bound is [log(2) n(d- u+1)]-1 when n >= d+u-2 and for u = 1 the best adaptive algorithm provided by Juan and Chang (2008) takes at most rlog2 ni rlog2 di tests. We further show that the case with a gap (u > l + 1) can be dealt with by the subroutines used to conquer the gap-free case. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Group testing sequential algorithm Threshold Consecutive positives

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A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2007年第4期13卷 337-351页

作者： Sbihi, Abdelkader Univ Lancaster Sch Management Optimisat Res Ctr Lancaster LA1 4YX England

In this paper, we propose an optimal algorithm for the Multiple-choice Multidimensional Knapsack Problem MMKP. The main principle of the approach is twofold: (i) to generate an initial feasible solution as a starting lower bound, and (ii) at different levels of the search tree to determine an intermediate upper bound obtained by solving an auxiliary problem called MMKPaux and perform the strategy of fixing items during the exploration. The approach which we develop is of best-first search strategy. The method was able to optimally solve the MMKP. The performance of the exact algorithm is evaluated on a set of small and medium instances, some of them are extracted from the literature and others are randomly generated. This algorithm is parallelizable and it is one of its important feature.

关键词： combinatorial optimization branch and bound sequential algorithm Knapsack

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Direct and inverse solutions with non-Fourier effect on the irregular shape

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2010年第13-14期53卷 2685-2693页

作者： Wang, Chi-Chang Feng Chia Univ Dept Mech & Comp Aided Engn Taichung 40724 Taiwan

This study used the finite element method with linear least-squares error method to construct a simple non-iterative inverse operation procedure, for solving non-Fourier heat transfer effect in irregular geometry. Numerical validation indicated that, irregular geometry would enhance heat wave reflection and thus make temperature distribution more complex, moreover, non-Fourier heat transfer has limited heat wave propagation speed, heat information fails to be reflected in time at measure point of the other side, hence, inverse operation difficulty increases. However, sequential algorithm constructed by this study is able to estimate unknown boundary condition correctly and efficiently at every instant by only one array operation in successive time steps. In addition, by measuring a few future time temperatures, the sensitivity of estimated result to measurement error can be effectively reduced as well. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Inverse non-Fourier effect heat conduction sequential algorithm Irregular shape Linear least-squares error method Finite element method Non-iterative

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Kernel reconstruction learning

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NEUROCOMPUTING 2023年 522卷 1-10页

作者： Wu, Yun Xiong, Shifeng Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China Chinese Acad Sci Acad Math & Syst Sci NCMIS KLSC Beijing Peoples R China

This paper proposes a class of kernel interpolation-based methods, called kernel reconstruction learning, for solving machine learning problems. Kernel reconstruction learning uses kernel interpolators to recon-struct the unknown functions, which are needed to estimate in the problem, with estimated function val-ues at selected knots. It can be applied to any learning problem that involves function estimation. We prove a reconstruction representer theorem, which indicates that conventional kernel methods, including kernel ridge regression, kernel support vector machine, and kernel logistic regression, can be viewed as special cases of kernel reconstruction learning. Furthermore, kernel reconstruction learning provides new algorithms for large datasets. The kernel reconstruction vector machine, kernel reconstruction logistic regression, and kernel reconstruction density estimation are discussed in detail. With appropriate imple-mentations, they are shown to have higher prediction/estimation accuracy and/or less computational cost than popular kernel methods.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Kernel method Representer theorem Interpolation Classification Density estimation sequential algorithm

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Minimal average cost of searching for a counterfeit coin: Restricted model

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DISCRETE APPLIED MATHEMATICS 2006年第14期154卷 1996-2009页

作者： Liu, Wen An Ma, Hong Yong Henan Normal Univ Coll Math & Informat Sci Xinxiang 453007 Peoples R China

The following restricted model of coin-weighing problem is considered: there is a heavier coin in a set of n coins, n-1 of which are good coins having the same weight. The test device is a two-arms balance scale and each test-set is of the form A : B with vertical bar A vertical bar = vertical bar B vertical bar <= e, where e >= 1 is a given integer. We present an optimal sequential algorithm requiring the minimal average cost of weighings when the probability distribution on the coin set is uniform distribution. (c) 2006 Elsevier B.V. All rights reserved.

关键词： coin-weighing problem sequential algorithm average cost Huffman tree

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Joint Albedo Estimation and Pose Tracking from Video

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2013年第7期35卷 1674-1689页

作者： Taheri, Sima Sankaranarayanan, Aswin C. Chellappa, Rama Univ Maryland Dept Elect & Comp Engn College Pk MD 20742 USA Rice Univ Dept Elect & Comp Engn Houston TX 77251 USA Univ Maryland Dept Elect & Comp Engn Ctr Automat Res College Pk MD 20742 USA

The albedo of a Lambertian object is a surface property that contributes to an object's appearance under changing illumination. As a signature independent of illumination, the albedo is useful for object recognition. Single image-based albedo estimation algorithms suffer due to shadows and non-Lambertian effects of the image. In this paper, we propose a sequential algorithm to estimate the albedo from a sequence of images of a known 3D object in varying poses and illumination conditions. We first show that by knowing/estimating the pose of the object at each frame of a sequence, the object's albedo can be efficiently estimated using a Kalman filter. We then extend this for the case of unknown pose by simultaneously tracking the pose as well as updating the albedo through a Rao-Blackwellized particle filter (RBPF). More specifically, the albedo is marginalized from the posterior distribution and estimated analytically using the Kalman filter, while the pose parameters are estimated using importance sampling and by minimizing the projection error of the face onto its spherical harmonic subspace, which results in an illumination-insensitive pose tracking algorithm. Illustrations and experiments are provided to validate the effectiveness of the approach using various synthetic and real sequences followed by applications to unconstrained, video-based face recognition.

关键词： Albedo pose tracking spherical harmonics sequential algorithm Kalman filter Rao-Blackwellized particle filter intrinsic image statistics

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Estimation of time-varying heat sources through inversion of a low order model built with the Modal Identification Method from in-situ temperature measurements

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2010年第1-3期53卷 206-219页

作者： Girault, M. Videcoq, E. Petit, D. ENSMA CNRS Lab Etud Therm UMR 6608 F-86961 Futuroscope France LMEE F-91020 Evry France

An approach using an experimentally built low-order model is proposed for the estimation of time-varying heat sources. In a first step, a low order dynamical system of equations, linking up temperatures at a set of specific points to heat sources strengths, is identified from experimental data using the Modal Identification Method. In a second step, the low order model is used to efficiently solve the transient inverse problem for the estimation of heat sources intensities from temperature measurements. The proposed approach is illustrated with an experimental set-up involving thermal diffusion with convective and radiative boundary conditions. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Nonlinear heat transfer Reduced model Experimental identification Inverse problem sequential algorithm Future time steps

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Kernel methods for clustering:: Competitive learning and c-means

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INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 2006年第4期14卷 481-493页

作者： Inokuchi, Ryo Miyamoto, Sadaaki Univ Tsukuba Doctoral Program Risk Engn Tsukuba Ibaraki 3058573 Japan Univ Tsukuba Dept Risk Engn Tsukuba Ibaraki 3058573 Japan

Recently kernel methods in support vector machines have widely been used in machine learning algorithms to obtain nonlinear models. Clustering is an unsupervised learning method which divides whole data set into subgroups, and popular clustering algorithms such as c-means are employing kernel methods. Other kernel-based clustering algorithms have been inspired from kernel c-means. However, the formulation of kernel c-means has a high computational complexity. This paper gives an alternative formulation of kernel-based clustering algorithms derived from competitive learning clustering. This new formulation obviously uses sequential updating or on-line learning to avoid high computational complexity. We apply kernel methods to related algorithms: learning vector quantization and self-organizing map. We moreover consider kernel methods for sequential c-means and its fuzzy version by the proposed formulation.

关键词： competitive learning clustering c-means learning vector quantization self-organizing map kernel method sequential algorithm

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Resolution of linear inverse forced convection problems using model reduction by the Modal Identification Method: application to turbulent flow in parallel-plate duct

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2004年第17-18期47卷 3909-3925页

作者： Girault, M Petit, D Univ Poitiers Lab Etud Therm CNRS UMR 6608ENSMA F-86961 Futuroscope France

Inverse Heat Convection Problems have received attention only recently. They usually involve the use of a high order model corresponding to the spatial discretization of the domain. In this numerical study, the possibility to quickly solve such a problem with a low order model is analysed. The proposed method can be applied to any forced convection problem, whatever the geometry, as far as it is linear. Starting from a Detailed Model (DM) of the system, the Modal Identification Method is applied to build a Reduced Model (RM), which can be used to solve the inverse problem. The inversion procedure is sequential and requires no iterations. The function specification method is used to stabilize the inverse problem. An illustrative application is given. Turbulent forced convection is considered, with a hydrodynamically fully developed, thermally developing, incompressible, turbulent flow of a newtonian and constant property fluid inside a parallel-plate duct. Axial conduction in the flow is neglected. Two wall heat flux densities, varying with time, are estimated from the knowledge of simulated transient temperature measurements inside the fluid. When solving the inverse problem with RM instead of DM, a drastic reduction of computing time is obtained (with a reduction factor up to 11,000 in the present study), without significant loss of accuracy. Effects of functional form of the unknowns, sensors number and position, measurement error, on the accuracy of estimates are examined. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： forced convection modal identification Reduced Model inverse method estimation of boundary conditions sequential algorithm Future Time Steps

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Size-invariant four-scan Euclidean distance transformation

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PATTERN RECOGNITION 1998年第11期31卷 1761-1766页

作者： Shih, FY Liu, JJ New Jersey Inst Technol Dept Comp & Informat Sci Comp Vis Lab Newark NJ 07102 USA

Distance transform (DT)((1)) is used to convert a binary image that consists of object (foreground) and nonobject (background) pixels into another image in which each object pixel has a value corresponding to the minimum distance from the background by a predefined distance function. The Euclidean distance is more accurate than the others, such as city-black, chessboard and chamfer, but it takes more computational time due to its nonlinearity. By using the relative X and Y coordinates computed from the object pixel to the source mapping pixel of its neighbors as well as correction of particular cases, the Euclidean distance transformation (EDT) can be correctly obtained in just four scans of an image. In other words, the new algorithm achieves the computational complexity of EDT to be linear to the size of an image. (C) 1998 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

关键词： distance transform Euclidean distance image processing recursive algorithm sequential algorithm skeletonization

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