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If n ≥ d + 2, then the Cayley-Menger matrix is singular, namely |M p0,..., p n- 1)| = 0. Now consider the refinement problem for a network with a K4 underlying graph (complete graph with four vertices) with a set of measured internode distances.
The present work is dedicated to the polytomy refinement problem.
The polytomy refinement problem is motivated by the problem of correcting gene trees.
Decoupling the contig refinement problem from the assembly process removes the burden of re-implementing a positional reassembly process for each assembler.
We formalize the contig refinement problem and present an algorithm for positional reassembly that relies on the positional de Bruijn graph.
We formulate the contig refinement problem in a similar manner; that is, as finding a string that explains all occuring positional k-mers.
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In addition to the refinement problems associated with pseudo symmetry, these structures are also more challenging simply as a result of size.
In a pair of earlier papers the author showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes for MHD.
Dayan and Hinton originally suggested that a self-refinement problem can be tackled by EM to avoid gradient computation [33].
Minimum NAD polytomy refinement (MinNADref) problem: Input: A polytomy G and a species tree S ; Output: In the set H (G ) of all refinements of G, a refinement H with the minimum number of NAD nodes.
From the crystallisation itself and sample handling, to structure solution and refinement, specific problems due to larger molecules are discussed.
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