parametric complexity is a central concept in Minimum Description Length (MDL) model selection. In practice it often turns out to be infinite, even for quite simple models Such as the Poisson and geometric families. I...
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parametric complexity is a central concept in Minimum Description Length (MDL) model selection. In practice it often turns out to be infinite, even for quite simple models Such as the Poisson and geometric families. In such cases, MDL model selection as based on NML and Bayesian inference based on Jeffreys' prior cannot be used. Several ways to resolve this problem have been proposed. We conduct experiments to compare and evaluate their behaviour on small sample sizes. We find interestingly poor behaviour for the plug-in predictive code;a restricted NML model performs quite well but it is questionable if the results validate its theoretical motivation. A Bayesian marginal distribution with Jeffreys' prior can still be used if one sacrifices the first observation to make a proper posterior;this approach turns out to be most dependable. (c) 2005 Elsevier Inc. All rights reserved.
Cai and Schieber (1997) proved that bipartite graphs plus one edge can be recognized in linear time. We extend their result to bipartite graphs plus two edges. Our algorithm works on a depth-first-search spanning tree...
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Cai and Schieber (1997) proved that bipartite graphs plus one edge can be recognized in linear time. We extend their result to bipartite graphs plus two edges. Our algorithm works on a depth-first-search spanning tree. This gives, as a byproduct, also a simplified solution to the one-edge case. It is a notoriously open question whether recognizing bipartite graphs plus k edges is a fixed-parameter tractable problem. The present result might support the affirmative conjecture. (C) 2002 Elsevier Science B.V. All rights reserved.
We address the MAX MIN VERTEX COVER problem, which is the maximization version of the well studied MIN INDEPENDENT DOMINATING SET problem, known to be NP-hard and highly inapproximable in polynomial time. We present t...
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We address the MAX MIN VERTEX COVER problem, which is the maximization version of the well studied MIN INDEPENDENT DOMINATING SET problem, known to be NP-hard and highly inapproximable in polynomial time. We present tight approximation results for this problem on general graphs, namely a polynomial approximation algorithm which guarantees an n(-1/2) approximation ratio, while showing that unless P = NP, the problem is inapproximable within ratio ns(epsilon-(1/2)) for any strictly positive epsilon. We also analyze the problem on various restricted classes of graphs, on which we show polynomiality or constant-approximability of the problem. Finally, we show that the problem is fixed-parameter tractable with respect to the size of an optimal solution, to treewidth and to the size of a maximum matching. (C) 2014 Elsevier B.V. All rights reserved.
Scaffolding, the problem of ordering and orienting contigs, typically using paired-end reads, is a crucial step in the assembly of high-quality draft genomes. Even as sequencing technologies and mate-pair protocols ha...
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ISBN:
(纸本)9783642200359
Scaffolding, the problem of ordering and orienting contigs, typically using paired-end reads, is a crucial step in the assembly of high-quality draft genomes. Even as sequencing technologies and mate-pair protocols have improved significantly, scaffolding programs still rely on heuristics, with no guarantees on the quality of the solution. In this work, we explored the feasibility of an exact solution for scaffolding and present a first tractable solution for this problem (Opera). We also describe a graph contraction procedure that allows the solution to scale to large scaffolding problems and demonstrate this by scaffolding several large real and synthetic datasets. In comparisons with existing scaffolders, Opera simultaneously produced longer and more accurate scaffolds demonstrating the utility of an exact approach. Opera also incorporates an exact quadratic programming formulation to precisely compute gap sizes (Availability: http://***/projects/operasf/).
We construct a family of planar graphs {G(n)}(n >= 4), where G(n) has n vertices including a source vertex s, a sink vertex t, and edge weights that change linearly with a parameter lambda such that, as lambda vari...
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ISBN:
(纸本)9781728149523
We construct a family of planar graphs {G(n)}(n >= 4), where G(n) has n vertices including a source vertex s, a sink vertex t, and edge weights that change linearly with a parameter lambda such that, as lambda varies in (-infinity, +infinity), the piece-wise linear cost of the shortest path from s to t has n(Omega)(log n) pieces. This shows that lower bounds obtained by Carstensen (1983) and Mulmuley & Shah (2001) for general graphs also hold for planar graphs, refuting a conjecture of Nikolova (2009). Gusfield (1980) and Dean (2009) showed that the number of pieces for every n-vertex graph with linear edge weights is n(log n+O(1)). We generalize this result in two ways. (i) If the edge weights vary as a polynomial of degree at most d, then the number of pieces is n(log n+(alpha(n)+O(1))d), where alpha(n) is the inverse Ackermann function. (ii) If the edge weights are linear forms of three parameters, then the number of pieces, appropriately defined for R-3, is n((log n)2 + O(log n)).
Abstract This paper adressed nonlinear system identification problem using Volterra models. First, an approach is established to identify Volterra models using “Plant-friendly” input sequence with define properties....
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Abstract This paper adressed nonlinear system identification problem using Volterra models. First, an approach is established to identify Volterra models using “Plant-friendly” input sequence with define properties. Second, we focus on the parametric complexity problem. As a solution, Volterra kernels are projected onto Laguerre basis resulting a reduced Volterra-Laguerre models. The efficiency of the proposed approach is illustrated according to a real system : the Two Tank System.
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