1,622 research outputs found
A family of tree-based generators for bubbles in directed graphs
6sìopenBubbles are pairs of internally vertex-disjoint (s, t)-paths in a directed graph. In de Bruijn graphs built from reads of RNA and DNA data, bubbles represent interesting biological events, such as alternative splicing (AS) and allelic differences
(SNPs and indels). However, the set of all bubbles in a de Bruijn graph built from real data is usually too large to be efficiently enumerated and analysed in practice. In particular, despite significant research done in this area, listing bubbles still remains the main bottleneck for tools that detect AS events in a reference-free context. Recently, in the concept of a bubble generator was introduced as a way for obtaining a compact representation of the bubble space of a graph. Although this bubble generator was quite effective in finding AS events, preliminary experiments showed that it is about 5 times slower than state-of-art methods. In this paper we propose a new family of bubble generators which improve substantially on previous work: bubble generators in this new family are about two orders of magnitude faster and are still able to achieve similar precision in identifying AS events. To highlight the practical value of our new bubble generators, we also report some experimental results on real datasets.openAcuña, Vicente; Soares de Lima, Leandro Ishi; Italiano, Giuseppe F.; Pepè Sciarria, Luca; Sagot, Marie-France; Sinaimeri, BlerinaAcuña, Vicente; Soares de Lima, Leandro Ishi; Italiano, Giuseppe F.; Pepè Sciarria, Luca; Sagot, Marie-France; Sinaimeri, Blerin
A Family of Tree-Based Generators for Bubbles in Directed Graphs
International audienceBubbles are pairs of internally vertex-disjoint (s, t)-paths in a directed graph. In de Bruijn graphs built from reads of RNA and DNA data, bubbles represent interesting biological events, such as alternative splicing (AS) and allelic differences (SNPs and indels). However, the set of all bubbles in a de Bruijn graph built from real data is usually too large to be efficiently enumerated and analysed in practice. In particular, despite significant research done in this area, listing bubbles still remains the main bottleneck for tools that detect AS events in a reference-free context. Recently, in [1] the concept of a bubble generator was introduced as a way for obtaining a compact representation of the bubble space of a graph. Although this generator was quite effective in finding AS events, preliminary experiments showed that it is about 5 times slower than state-of-art methods. In this paper we propose a new family of bubble generators which improve substantially on the previous generator: generators in this new family are about two orders of magnitude faster and are still able to achieve similar precision in identifying AS events. To highlight the practical value of our new generators, we also report some experimental results on a real dataset
Simplicial and Cellular Trees
Much information about a graph can be obtained by studying its spanning
trees. On the other hand, a graph can be regarded as a 1-dimensional cell
complex, raising the question of developing a theory of trees in higher
dimension. As observed first by Bolker, Kalai and Adin, and more recently by
numerous authors, the fundamental topological properties of a tree --- namely
acyclicity and connectedness --- can be generalized to arbitrary dimension as
the vanishing of certain cellular homology groups. This point of view is
consistent with the matroid-theoretic approach to graphs, and yields
higher-dimensional analogues of classical enumerative results including
Cayley's formula and the matrix-tree theorem. A subtlety of the
higher-dimensional case is that enumeration must account for the possibility of
torsion homology in trees, which is always trivial for graphs. Cellular trees
are the starting point for further high-dimensional extensions of concepts from
algebraic graph theory including the critical group, cut and flow spaces, and
discrete dynamical systems such as the abelian sandpile model.Comment: 39 pages (including 5-page bibliography); 5 figures. Chapter for
forthcoming IMA volume "Recent Trends in Combinatorics
ASC: A stream compiler for computing with FPGAs
Published versio
Scattering amplitudes in gauge theories with and without supersymmetry
This thesis aims at providing better understanding of the perturbative
expansion of gauge theories with and without supersymmetry. At tree level, the
BCFW recursion relations are analyzed with respect to their validity for
general off-shell objects in Yang-Mills theory, which is a significant step
away from their established zone of applicability. Unphysical poles constitute
a new potential problem in addition to the boundary behavior issue, common to
the on-shell case as well. For an infinite family of massive fermion currents,
both obstacles are shown to be avoided under the certain conditions, which
provides a natural recursion relation. At one loop, scattering amplitudes can
be calculated from unitarity cuts through their expansion into known scalar
integrals with free coefficients. A powerful method to obtain these
coefficients, namely spinor integration, is discussed and rederived in a
somewhat novel form. It is then used to compute analytically the infinite
series of one-loop gluon amplitudes in N = 1 super-Yang-Mills theory with
exactly three negative helicities. The final part of this thesis concerns the
intriguing relationship between gluon and graviton scattering amplitudes, which
involves a beautiful duality between the color and kinematic content of gauge
theories. This BCJ duality is extended to include particles in the fundamental
representation of the gauge group, which is shown to relieve the restriction of
the BCJ construction to factorizable gravities and thus give access to
amplitudes in generic (super-)gravity theories.Comment: 111 pages, PhD thesis defended on 12/09/201
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