111,497 research outputs found
Fast solving of Weighted Pairing Least-Squares systems
This paper presents a generalization of the "weighted least-squares" (WLS),
named "weighted pairing least-squares" (WPLS), which uses a rectangular weight
matrix and is suitable for data alignment problems. Two fast solving methods,
suitable for solving full rank systems as well as rank deficient systems, are
studied. Computational experiments clearly show that the best method, in terms
of speed, accuracy, and numerical stability, is based on a special {1, 2,
3}-inverse, whose computation reduces to a very simple generalization of the
usual "Cholesky factorization-backward substitution" method for solving linear
systems
Vortex dynamos
We investigate the kinematic dynamo properties of interacting vortex tubes. These flows are of great importance in geophysical and astrophysical fluid dynamics: for a large range of systems, turbulence is dominated by such coherent structures. We obtain a dynamically consistent 2(2)-(1)-dimensional velocity field of the form (u(x, y, t), upsilon(x, y, t), w(x, y, t)) by solving the z-independent Navier-Stokes equations in the presence of helical forcing. This system naturally forms vortex tubes via an inverse cascade. It has chaotic Lagrangian properties and is therefore a candidate for fast dynamo action. The kinematic dynamo properties of the flow are calculated by determining the growth rate of a small-scale seed field. The growth rate is found to have a complicated dependence on Reynolds number Re and magnetic Reynolds number Rm, but the flow continues to act as a dynamo for large Re and Rm. Moreover the dynamo is still efficient even in the limit Re much greater than Rm, providing Rm is large enough, because of the formation of coherent structures
Developing and applying heterogeneous phylogenetic models with XRate
Modeling sequence evolution on phylogenetic trees is a useful technique in
computational biology. Especially powerful are models which take account of the
heterogeneous nature of sequence evolution according to the "grammar" of the
encoded gene features. However, beyond a modest level of model complexity,
manual coding of models becomes prohibitively labor-intensive. We demonstrate,
via a set of case studies, the new built-in model-prototyping capabilities of
XRate (macros and Scheme extensions). These features allow rapid implementation
of phylogenetic models which would have previously been far more
labor-intensive. XRate's new capabilities for lineage-specific models,
ancestral sequence reconstruction, and improved annotation output are also
discussed. XRate's flexible model-specification capabilities and computational
efficiency make it well-suited to developing and prototyping phylogenetic
grammar models. XRate is available as part of the DART software package:
http://biowiki.org/DART .Comment: 34 pages, 3 figures, glossary of XRate model terminolog
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