The Experts below are selected from a list of 6648 Experts worldwide ranked by ideXlab platform
David Saad - One of the best experts on this subject based on the ideXlab platform.
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typical Kernel Size and number of sparse random matrices over galois fields a statistical physics approach
Physical Review E, 2008Co-Authors: Roberto C Alamino, David SaadAbstract:Using methods of statistical physics, we study the average number and Kernel Size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average Kernel Size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.
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Typical Kernel Size and number of sparse random matrices over Galois fields: a statistical physics approach.
Physical review. E Statistical nonlinear and soft matter physics, 2008Co-Authors: Roberto C Alamino, David SaadAbstract:Using methods of statistical physics, we study the average number and Kernel Size of general sparse random matrices over Galois fields GF(q) , with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q th complex roots of unity. This representation facilitates the derivation of the average Kernel Size of random matrices using the replica approach, under the replica-symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average numbers of random matrices for any general connectivity profile. We present numerical results for particular distributions.
Mark E Sorrells - One of the best experts on this subject based on the ideXlab platform.
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qtl analysis of Kernel Size and shape in two hexaploid wheat mapping populations
Field Crops Research, 2007Co-Authors: F Breseghello, Mark E SorrellsAbstract:Abstract Kernel Size and shape in wheat are important because of their relationship with yield and milling quality. This paper reports QTL analyses of Kernel morphology in two hexaploid wheat mapping populations, grown in NY and CA. Kernel morphology was evaluated through a new and improved method, combining measurements from two orthogonal pictures. Single marker regression showed that several genomic positions, scattered through the genome, were related to Kernel Size and shape, in both populations. The direction of allele effects was consistent between environments, although the LOD scores varied considerably. Composite interval mapping revealed QTLs on all seven homoeologous groups, considering both populations. For the QTLs detected through this method, the signal and magnitude of additive effects were similar between environments, indicating small QTL × environment interaction. In the population W7984 × Opata 85, the strongest signal was detected on the chromosome 5B, for Kernel length. In the population AC Reed × Grandin, the most important QTLs were detected on chromosome 2D, affecting the lateral dimensions of the Kernel. This study agreed with previous reports that the genetic control of Kernel length and width are largely independent. Additionally, it was shown that QTLs detected on different mapping populations, with identical evaluation methods, can be very distinct.
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association mapping of Kernel Size and milling quality in wheat triticum aestivum l cultivars
Genetics, 2006Co-Authors: F Breseghello, Mark E SorrellsAbstract:Association mapping is a method for detection of gene effects based on linkage disequilibrium (LD) that complements QTL analysis in the development of tools for molecular plant breeding. In this study, association mapping was performed on a selected sample of 95 cultivars of soft winter wheat. Population structure was estimated on the basis of 36 unlinked simple-sequence repeat (SSR) markers. The extent of LD was estimated on chromosomes 2D and part of 5A, relative to the LD observed among unlinked markers. Consistent LD on chromosome 2D was <1 cM, whereas in the centromeric region of 5A, LD extended for ∼5 cM. Association of 62 SSR loci on chromosomes 2D, 5A, and 5B with Kernel morphology and milling quality was analyzed through a mixed-effects model, where subpopulation was considered as a random factor and the marker tested was considered as a fixed factor. Permutations were used to adjust the threshold of significance for multiple testing within chromosomes. In agreement with previous QTL analysis, significant markers for Kernel Size were detected on the three chromosomes tested, and alleles potentially useful for selection were identified. Our results demonstrated that association mapping could complement and enhance previous QTL information for marker-assisted selection.
Roberto C Alamino - One of the best experts on this subject based on the ideXlab platform.
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typical Kernel Size and number of sparse random matrices over galois fields a statistical physics approach
Physical Review E, 2008Co-Authors: Roberto C Alamino, David SaadAbstract:Using methods of statistical physics, we study the average number and Kernel Size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average Kernel Size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.
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Typical Kernel Size and number of sparse random matrices over Galois fields: a statistical physics approach.
Physical review. E Statistical nonlinear and soft matter physics, 2008Co-Authors: Roberto C Alamino, David SaadAbstract:Using methods of statistical physics, we study the average number and Kernel Size of general sparse random matrices over Galois fields GF(q) , with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q th complex roots of unity. This representation facilitates the derivation of the average Kernel Size of random matrices using the replica approach, under the replica-symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average numbers of random matrices for any general connectivity profile. We present numerical results for particular distributions.
Iyad A. Kanj - One of the best experts on this subject based on the ideXlab platform.
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3-Hitting set on bounded degree hypergraphs: Upper and lower bounds on the Kernel Size
Discrete Mathematics Algorithms and Applications, 2015Co-Authors: Iyad A. Kanj, Fenghui ZhangAbstract:We study upper and lower bounds on the vertex-Kernel Size for the 3-HITTING SET problem on hypergraphs of degree at most 3, denoted 3-3-HS. We first show that, unless P = NP, 3-3-HS on 3-uniform hypergraphs does not have a vertex-Kernel of Size at most 35k/19 > 1.8421k. We then give a 4k - k0.2692 vertex-Kernel for 3-3-hs that is computable in time O(k2). We do not assume that the hypergraph is 3-uniform for the vertex-Kernel upper bound results. This result improves the upper bound of 4k on the vertex-Kernel Size for 3-3-HS, implied by the results of Wahlström.
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TAPAS - 3-Hitting set on bounded degree hypergraphs: upper and lower bounds on the Kernel Size
Theory and Practice of Algorithms in (Computer) Systems, 2011Co-Authors: Iyad A. Kanj, Fenghui ZhangAbstract:We study upper and lower bounds on the Kernel Size for the 3-HITTING SET problem on hypergraphs of degree at most 3, denoted 3- 3-hs.We first show that, unless P=NP, 3-3-hs on 3-uniform hypergraphs does not have a Kernel of Size at most 35k/19 > 1.8421k. We then give a 4k - k0.2692 Kernel for 3-3-hs that is computable in time O(k1.2692). This result improves the upper bound of 4k on the Kernel Size for 3- 3-hs, given by Wahlstrom. We also show that the upper bound results on the Kernel Size for 3-3-hs can be generalized to the 3-HS problem on hypergraphs of bounded degree Δ, for any integer-constant Δ > 3.
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parametric duality and Kernelization lower bounds and upper bounds on Kernel Size
SIAM Journal on Computing, 2007Co-Authors: Jianer Chen, Henning Fernau, Iyad A. KanjAbstract:Determining whether a parameterized problem is Kernelizable and has a small Kernel Size has recently become one of the most interesting topics of research in the area of parameterized complexity and algorithms. Theoretically, it has been proved that a parameterized problem is Kernelizable if and only if it is fixed-parameter tractable. Practically, applying a data reduction algorithm to reduce an instance of a parameterized problem to an equivalent smaller instance (i.e., a Kernel) has led to very efficient algorithms and now goes hand-in-hand with the design of practical algorithms for solving $\mathcal{NP}$-hard problems. Well-known examples of such parameterized problems include the vertex cover problem, which is Kernelizable to a Kernel of Size bounded by $2k$, and the planar dominating set problem, which is Kernelizable to a Kernel of Size bounded by $335k$. In this paper we develop new techniques to derive upper and lower bounds on the Kernel Size for certain parameterized problems. In terms of our lower bound results, we show, for example, that unless $\mathcal{P} = \mathcal{NP}$, planar vertex cover does not have a problem Kernel of Size smaller than $4k/3$, and planar independent set and planar dominating set do not have Kernels of Size smaller than $2k$. In terms of our upper bound results, we further reduce the upper bound on the Kernel Size for the planar dominating set problem to $67 k$, improving significantly the $335 k$ previous upper bound given by Alber, Fellows, and Niedermeier [J. ACM, 51 (2004), pp. 363-384]. This latter result is obtained by introducing a new set of reduction and coloring rules, which allows the derivation of nice combinatorial properties in the Kernelized graph leading to a tighter bound on the Size of the Kernel. The paper also shows how this improved upper bound yields a simple and competitive algorithm for the planar dominating set problem.
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parametric duality and Kernelization lower bounds and upper bounds on Kernel Size
Symposium on Theoretical Aspects of Computer Science, 2005Co-Authors: Jianer Chen, Henning Fernau, Iyad A. KanjAbstract:We develop new techniques to derive lower bounds on the Kernel Size for certain parameterized problems. For example, we show that unless $\mathcal{P}$=$\mathcal{NP}$, planar vertex cover does not have a problem Kernel of Size smaller than 4k/3, and planar independent set and planar dominating set do not have Kernels of Size smaller than 2k. We derive an upper bound of 67k on the problem Kernel for planar dominating set improving the previous 335k upper bound by Alber et al.
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STACS - Parametric duality and Kernelization: lower bounds and upper bounds on Kernel Size
STACS 2005, 2005Co-Authors: Jianer Chen, Henning Fernau, Iyad A. KanjAbstract:We develop new techniques to derive lower bounds on the Kernel Size for certain parameterized problems. For example, we show that unless $\mathcal{P}$=$\mathcal{NP}$, planar vertex cover does not have a problem Kernel of Size smaller than 4k/3, and planar independent set and planar dominating set do not have Kernels of Size smaller than 2k. We derive an upper bound of 67k on the problem Kernel for planar dominating set improving the previous 335k upper bound by Alber et al.
F Breseghello - One of the best experts on this subject based on the ideXlab platform.
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qtl analysis of Kernel Size and shape in two hexaploid wheat mapping populations
Field Crops Research, 2007Co-Authors: F Breseghello, Mark E SorrellsAbstract:Abstract Kernel Size and shape in wheat are important because of their relationship with yield and milling quality. This paper reports QTL analyses of Kernel morphology in two hexaploid wheat mapping populations, grown in NY and CA. Kernel morphology was evaluated through a new and improved method, combining measurements from two orthogonal pictures. Single marker regression showed that several genomic positions, scattered through the genome, were related to Kernel Size and shape, in both populations. The direction of allele effects was consistent between environments, although the LOD scores varied considerably. Composite interval mapping revealed QTLs on all seven homoeologous groups, considering both populations. For the QTLs detected through this method, the signal and magnitude of additive effects were similar between environments, indicating small QTL × environment interaction. In the population W7984 × Opata 85, the strongest signal was detected on the chromosome 5B, for Kernel length. In the population AC Reed × Grandin, the most important QTLs were detected on chromosome 2D, affecting the lateral dimensions of the Kernel. This study agreed with previous reports that the genetic control of Kernel length and width are largely independent. Additionally, it was shown that QTLs detected on different mapping populations, with identical evaluation methods, can be very distinct.
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association mapping of Kernel Size and milling quality in wheat triticum aestivum l cultivars
Genetics, 2006Co-Authors: F Breseghello, Mark E SorrellsAbstract:Association mapping is a method for detection of gene effects based on linkage disequilibrium (LD) that complements QTL analysis in the development of tools for molecular plant breeding. In this study, association mapping was performed on a selected sample of 95 cultivars of soft winter wheat. Population structure was estimated on the basis of 36 unlinked simple-sequence repeat (SSR) markers. The extent of LD was estimated on chromosomes 2D and part of 5A, relative to the LD observed among unlinked markers. Consistent LD on chromosome 2D was <1 cM, whereas in the centromeric region of 5A, LD extended for ∼5 cM. Association of 62 SSR loci on chromosomes 2D, 5A, and 5B with Kernel morphology and milling quality was analyzed through a mixed-effects model, where subpopulation was considered as a random factor and the marker tested was considered as a fixed factor. Permutations were used to adjust the threshold of significance for multiple testing within chromosomes. In agreement with previous QTL analysis, significant markers for Kernel Size were detected on the three chromosomes tested, and alleles potentially useful for selection were identified. Our results demonstrated that association mapping could complement and enhance previous QTL information for marker-assisted selection.
