29,963 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
Loop Spaces and Connections
We examine the geometry of loop spaces in derived algebraic geometry and
extend in several directions the well known connection between rotation of
loops and the de Rham differential. Our main result, a categorification of the
geometric description of cyclic homology, relates S^1-equivariant quasicoherent
sheaves on the loop space of a smooth scheme or geometric stack X in
characteristic zero with sheaves on X with flat connection, or equivalently
D_X-modules. By deducing the Hodge filtration on de Rham modules from the
formality of cochains on the circle, we are able to recover D_X-modules
precisely rather than a periodic version. More generally, we consider the
rotated Hopf fibration Omega S^3 --> Omega S^2 --> S^1, and relate Omega
S^2-equivariant sheaves on the loop space with sheaves on X with arbitrary
connection, with curvature given by their Omega S^3-equivariance.Comment: Revised versio
Derived Algebraic Geometry
This text is a survey of derived algebraic geometry. It covers a variety of
general notions and results from the subject with a view on the recent
developments at the interface with deformation quantization.Comment: Final version. To appear in EMS Surveys in Mathematical Science
Algebraic K-theory of quasi-smooth blow-ups and cdh descent
We construct a semi-orthogonal decomposition on the category of perfect
complexes on the blow-up of a derived Artin stack in a quasi-smooth centre.
This gives a generalization of Thomason's blow-up formula in algebraic K-theory
to derived stacks. We also provide a new criterion for descent in Voevodsky's
cdh topology, which we use to give a direct proof of Cisinski's theorem that
Weibel's homotopy invariant K-theory satisfies cdh descent.Comment: 24 pages; to appear in Annales Henri Lebesgu
- …