1,856 research outputs found
A note on Berezin-Toeplitz quantization of the Laplace operator
Given a Hodge manifold, it is introduced a self-adjoint operator on the space
of endomorphisms of the global holomorphic sections of the polarization line
bundle. Such operator is shown to approximate the Laplace operator on functions
when composed with Berezin-Toeplitz quantization map and its adjoint up to an
error which tends to zero when taking higher powers of the polarization line
bundle
Scalar curvature and asymptotic Chow stability of projective bundles and blowups
The holomorphic invariants introduced by Futaki as obstruction to the
asymptotic Chow semistability are studied by an algebraic-geometric point of
view and are shown to be the Mumford weights of suitable line bundles on the
Hilbert scheme. These invariants are calculated in two special cases. The first
is a projective bundle over a curve of genus at least two, and it is shown that
it is asymptotically Chow polystable (with every polarization) if and only the
underlying vector bundle is slope polystable. This proves a conjecture of
Morrison with the extra assumption that the involved polarization is
sufficiently divisible. Moreover it implies that a projective bundle is
asymptotically Chow polystable (with every polarization) if and only if it
admits a constant scalar curvature Kaehler metric. The second case is a
manifold blown-up at points, and new examples of asymptotically Chow unstable
constant scalar curvature Kaehler classes are given.Comment: 15 page
PIntron: a Fast Method for Gene Structure Prediction via Maximal Pairings of a Pattern and a Text
Current computational methods for exon-intron structure prediction from a
cluster of transcript (EST, mRNA) data do not exhibit the time and space
efficiency necessary to process large clusters of over than 20,000 ESTs and
genes longer than 1Mb. Guaranteeing both accuracy and efficiency seems to be a
computational goal quite far to be achieved, since accuracy is strictly related
to exploiting the inherent redundancy of information present in a large
cluster. We propose a fast method for the problem that combines two ideas: a
novel algorithm of proved small time complexity for computing spliced
alignments of a transcript against a genome, and an efficient algorithm that
exploits the inherent redundancy of information in a cluster of transcripts to
select, among all possible factorizations of EST sequences, those allowing to
infer splice site junctions that are highly confirmed by the input data. The
EST alignment procedure is based on the construction of maximal embeddings that
are sequences obtained from paths of a graph structure, called Embedding Graph,
whose vertices are the maximal pairings of a genomic sequence T and an EST P.
The procedure runs in time linear in the size of P, T and of the output.
PIntron, the software tool implementing our methodology, is able to process in
a few seconds some critical genes that are not manageable by other gene
structure prediction tools. At the same time, PIntron exhibits high accuracy
(sensitivity and specificity) when compared with ENCODE data. Detailed
experimental data, additional results and PIntron software are available at
http://www.algolab.eu/PIntron
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