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A minimal descriptor of an ancestral recombinations graph

BMC BIOINFORMATICS 2011年第1期12卷 1-17页

作者： Parida, Laxmi Palamara, Pier Francesco Javed, Asif IBM T J Watson Res Computat Genom Yorktown Hts NY 10598 USA Columbia Univ New York NY USA

Background: Ancestral Recombinations Graph (ARG) is a phylogenetic structure that encodes both duplication events, such as mutations, as well as genetic exchange events, such as recombinations: this captures the (genetic) dynamics of a population evolving over generations. Results: In this paper, we identify structure-preserving and samples-preserving core of an ARG G and call it the minimal descriptor ARG of G. Its structure-preserving characteristic ensures that all the branch lengths of the marginal trees of the minimal descriptor ARG are identical to that of G and the samples-preserving property asserts that the patterns of genetic variation in the samples of the minimal descriptor ARG are exactly the same as that of G. We also prove that even an unbounded G has a finite minimal descriptor, that continues to preserve certain (graph-theoretic) properties of G and for an appropriate class of ARGs, our estimate (Eqn 8) as well as empirical observation is that the expected reduction in the number of vertices is exponential. Conclusions: Based on the definition of this lossless and bounded structure, we derive local properties of the vertices of a minimal descriptor ARG, which lend itself very naturally to the design of efficient sampling algorithms. We further show that a class of minimal descriptors, that of binary ARGs, models the standard coalescent exactly (Thm 6).

关键词： Leaf Node Random Graph sampling algorithm Outgoing Edge Incoming Edge

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Polynomial time samplable distributions

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JOURNAL OF COMPLEXITY 1999年第4期15卷 557-574页

作者： Yamakami, T Univ Toronto Dept Comp Sci Toronto ON M5S 3G4 Canada

This paper studies the complexity of the polynomial-time samplable (P-samplable) distributions, which can be approximated within an exponentially small Factor by sampling algorithms in time polynomial in the length of their outputs. The paper shows that common assumptions in complexity theory yield the separation of polynomial-time samplable distributions from the polynomial-lime computable distributions with respect to polynomial domination, average-polynomial domination, polynomial equivalence, and average-polynomial equivalence. (C) 1999 Academic Press.

关键词： average-case complexity sampling algorithm domination condition strong one-way functions

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An improved model combining knowledge graph and GCN for PLM knowledge recommendation

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SOFT COMPUTING 2024年第6期28卷 5557-5575页

作者： Tong, Guoxiang Li, Deyun Liu, Xuemei Univ Shanghai Sci & Technol Sch Opt Elect & Comp Engn Shanghai 200093 Peoples R China Tongji Univ Sch Mech Engn Shanghai 200092 Peoples R China

Faced with the challenges of intelligently managing the entire product lifecycle, traditional management techniques no longer meet the complex demands of modern enterprises. To address it, we employ an ontology modeling method based on a multidimensional view of product information for a knowledge graph, culminating in a comprehensive PLM knowledge system. To better serve PLM users, we propose an intelligent recommendation model based on context and user behavior for knowledge recommendations. This model seamlessly integrates the knowledge storage structure, user preference attributes, and the rich semantics of the knowledge graph. To improve the recommendation capability of the model, we design an improved multi-hop neighbor node sampling algorithm and use a graph convolutional neural network to quantify the target user preference attributes layer by layer. After a series of rigorous validation experiments, our method consistently outperformed competing models across key performance metrics, such as accuracy and recall, underscoring its efficacy and practicality in knowledge recommendation within PLM systems.

关键词： Product lifecycle management Recommendation model Knowledge graph sampling algorithm

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Constructing hierarchical Archimedean copulas with Levy subordinators

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JOURNAL OF MULTIVARIATE ANALYSIS 2010年第6期101卷 1428-1433页

作者： Hering, Christian Hofert, Marius Mai, Jan-Frederik Scherer, Matthias Tech Univ Munich HVB Stiftungsinst Finanzmath D-85748 Garching Germany Univ Ulm Inst Number Theory & Probabil Theory D-89081 Ulm Germany

A probabilistic interpretation for hierarchical Archimedean copulas based on Levy subordinators is given. Independent exponential random variables are divided by group-specific Levy subordinators which are evaluated at a common random time. The resulting random vector has a hierarchical Archimedean survival copula. This approach suggests an efficient sampling algorithm and allows one to easily construct several new parametric families of hierarchical Archimedean copulas. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Hierarchical Archimedean copulas Levy subordinators sampling algorithm

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A fast algorithm to sample the number of vertexes and the area of the random convex hull on the unit square

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COMPUTATIONAL STATISTICS 2014年第5期29卷 1187-1205页

作者： Ng, Chi Tim Lim, Johan Lee, Kyeong Eun Yu, Donghyeon Choi, Sujung Chonnam Natl Univ Dept Stat Kwangju 500757 South Korea Seoul Natl Univ Dept Stat Seoul 151747 South Korea Kyoungpook Natl Univ Dept Stat Taegu 702701 South Korea Univ Texas SW Med Ctr Dallas Dept Clin Sci Dallas TX 75390 USA Ulsan Univ Sci & Technol Sch Technol Management Ulsan 689798 South Korea

We propose an algorithm to sample the area of the smallest convex hull containing sample points uniformly distributed over unit square. To do it, we introduce a new coordinate system for the position of vertexes and re-write joint distribution of the number of vertexes and their locations in the new coordinate system. The proposed algorithm is much faster than existing procedure and has a computational complexity on the order of , where is the number of vertexes. Using the proposed algorithm, we numerically investigate the asymptotic behavior of functionals of the random convex hull. In addition, we apply it to finding pairs of stocks where the returns are dependent on each other on the New York Stock Exchange.

关键词： Area Convex hull Pairwise dependence sampling algorithm Uniform distribution Unit square Vertexes

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Remarks on some misconceptions about unequal probability sampling without replacement

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COMPUTER SCIENCE REVIEW 2023年 47卷

作者： Tille, Yves Univ Neuchatel Inst Stat Bellevaux 51 CH-2000 Neuchatel Switzerland

Before computer scientists became interested in unequal probability sampling methods, they were widely studied by survey statisticians. We show that sometimes the same sampling methods have been proposed again without reference to existing methods. We also show that methods that are not correct and that were widely discussed in the 1950s are being proposed again. We review the most common errors and misunderstandings about these methods. (c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Entropy Inclusion probability Poisson sampling sampling algorithm Weighted sampling

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Calculating the interaction index of a fuzzy measure: A polynomial approach based on sampling

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FUZZY SETS AND SYSTEMS 2023年 466卷

作者： Gutierrez, Inmaculada Castro, Javier Gomez, Daniel Espinola, Rosa Univ Complutense Madrid Fac Stat Madrid Spain Univ Complutense Madrid Inst Evaluac Sanitaria Madrid Spain

In this paper we address the problem of fuzzy measures index calculation. On the basis of fuzzy sets, Murofushi and Soneda proposed an interaction index to deal with the relations between two individuals. This index was later extended in a common frame-work by Grabisch. Both indices are fundamental in the literature of fuzzy measures. Nevertheless, the corresponding calculation still presents a highly complex problem for which no approximation solution has been proposed yet. Then, using a representation of the Shapley based on orders, here we suggest an alternative calculation of the interaction index, both for the simple case of pairs of individuals, and for the more complex situation in which any set could be considered. This alternative representation facilitates the handling of these indices. Moreover, we draw on this representation to define two polynomial methods based on sampling to estimate the interaction index, as well as a method to approximate the generalized version of it. We provide some computational results to test the goodness of the proposed algorithms.& COPY;2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Fuzzy measures Interaction Index Interaction representation Shapley value sampling algorithm

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Trajectory tracking in 2D under fuzzy controller with variable sampling

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Journal of Electrical Systems and Information Technology 2015年第3期2卷 338-346页

作者： Ján Cigánek

The paper deals with an effective approach of the robust controller design based on the fuzzy logic, and algorithms for variable sampling of trajectory points to improve the control performance of trajectory tracking. The proposed controller design and sampling algorithms are verified in the case study of the selected mechatronic system. All presented results are reached in co-simulation of two different modeling environments, Matlab-Simulink and MSC Adams. MSC Adams is used for the dynamics of the mechatronic system and Matlab-Simulink for the control part of the co-simulation, respectively.

关键词： Control system Co-simulation Fuzzy logic Mechatronic system sampling algorithm Trajectory tracking

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Polynomial time perfect sampler for discretized Dirichlet distribution

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Workshop on the Grammer of Technology Development

作者： Matsui, Tomomi Kijima, Shuji Univ Tokyo Dept Math Informat Grad Sch Informat Sci & Technol Bunkyo Ku Tokyo 1138656 Japan

ISBN: (纸本)9784431752318

In this paper, we propose a perfect (exact) sampling algorithm according to a discretized Dirichlet distribution. The Dirichlet distribution appears as prior and posterior distribution for the multinomial distribution in many statistical methods in bioinformatics. Our algorithm is a monotone coupling from the past algorithm, which is a Las Vegas type randomized algorithm. We propose a new Markov chain whose limit distribution is a discretized Dirichlet distribution. Our algorithm simulates transitions of the chain O(n(3) In Delta) times where n is the dimension (the number of parameters) and 1/Delta is the grid size for discretization. Thus the obtained bound does not depend on the magnitudes of parameters. In each transition, we need to sample a random variable according to a discretized beta distribution (2-dimensional Dirichlet distribution). To show the polynomiality, we employ the path coupling method carefully and show that our chain is rapidly mixing.

关键词： coupling from the past (CFTP) Dirichlet distribution Markov chain Monte Carlo path coupling sampling algorithm

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On a characterization of ordered pivotal sampling

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BERNOULLI 2012年第4期18卷 1320-1340页

作者： Chauvet, Guillaume Crest Ensai F-35170 Bruz France

When auxiliary information is available at the design stage, samples may be selected by means of balanced sampling. Deville and Tillie proposed in 2004 a general algorithm to perform balanced sampling, named the cube method. In this paper, we are interested in a particular case of the cube method named pivotal sampling, and first described by Deville and Tine in 1998. We show that this sampling algorithm, when applied to units ranked in a fixed order, is equivalent to Deville's systematic sampling, in the sense that both algorithms lead to the same sampling design. This characterization enables the computation of the second-order inclusion probabilities for pivotal sampling. We show that the pivotal sampling enables to take account of an appropriate ordering of the units to achieve a variance reduction, while limiting the loss of efficiency if the ordering is not appropriate.

关键词： balanced sampling cube method design effect sampling algorithm second order inclusion probabilities unequal probabilities

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