107,969 research outputs found
Canonical, Stable, General Mapping using Context Schemes
Motivation: Sequence mapping is the cornerstone of modern genomics. However,
most existing sequence mapping algorithms are insufficiently general.
Results: We introduce context schemes: a method that allows the unambiguous
recognition of a reference base in a query sequence by testing the query for
substrings from an algorithmically defined set. Context schemes only map when
there is a unique best mapping, and define this criterion uniformly for all
reference bases. Mappings under context schemes can also be made stable, so
that extension of the query string (e.g. by increasing read length) will not
alter the mapping of previously mapped positions. Context schemes are general
in several senses. They natively support the detection of arbitrary complex,
novel rearrangements relative to the reference. They can scale over orders of
magnitude in query sequence length. Finally, they are trivially extensible to
more complex reference structures, such as graphs, that incorporate additional
variation. We demonstrate empirically the existence of high performance context
schemes, and present efficient context scheme mapping algorithms.
Availability and Implementation: The software test framework created for this
work is available from
https://registry.hub.docker.com/u/adamnovak/sequence-graphs/.
Contact: [email protected]
Supplementary Information: Six supplementary figures and one supplementary
section are available with the online version of this article.Comment: Submission for Bioinformatic
PDGA: The primal-dual genetic algorithm
Copyright @ 2003 IOS PressGenetic algorithms (GAs) are a class of search algorithms based on principles of natural evolution. Hence, incorporating mechanisms used in nature may improve the performance of GAs. In this paper inspired by the mechanisms of complementarity and dominance that broadly exist in nature, we present a new genetic algorithm — Primal-Dual Genetic Algorithm (PDGA). PDGA operates on a pair of chromosomes that are primal-dual to each other through the primal-dual mapping, which maps one to the other with a maximum distance away in a given distance space in genotype. The primal-dual mapping improves the exploration capacity of PDGA and thus its searching efficiency in the search space. To test the performance of PDGA, experiments were carried out to compare PDGA over traditional simple GA (SGA) and a peer GA, called Dual Genetic Algorithm (DGA), over a typical set of test problems. The experimental results demonstrate that PDGA outperforms both SGA and DGA on the test set. The results show that PDGA is a good candidate genetic algorithm
Newton's method, zeroes of vector fields, and the Riemannian center of mass
We present an iterative technique for finding zeroes of vector fields on
Riemannian manifolds. As a special case we obtain a ``nonlinear averaging
algorithm'' that computes the centroid of a mass distribution supported in a
set of small enough diameter D in a Riemannian manifold M. We estimate the
convergence rate of our general algorithm and the more special Riemannian
averaging algorithm. The algorithm is also used to provide a constructive proof
of Karcher's theorem on the existence and local uniqueness of the center of
mass, under a somewhat stronger requirement than Karcher's on D. Another
corollary of our results is a proof of convergence, for a fairly large open set
of initial conditions, of the ``GPA algorithm'' used in statistics to average
points in a shape-space, and a quantitative explanation of why the GPA
algorithm converges rapidly in practice. We also show that a mass distribution
in M with support Q has a unique center of mass in a (suitably defined) convex
hull of Q.Comment: 43 pages, 1 figur
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