15,854 research outputs found
Weak Decays of Doubly Heavy Baryons: Multi-body Decay Channels
The newly-discovered decays into the , but the experimental data has indicated that this decay is not
saturated by any two-body intermediate state. In this work, we analyze the
multi-body weak decays of doubly heavy baryons , ,
, , and , in particular the
three-body nonleptonic decays and four-body semileptonic decays. We classify
various decay modes according to the quark-level transitions and present an
estimate of the typical branching fractions for a few golden decay channels.
Decay amplitudes are then parametrized in terms of a few SU(3) irreducible
amplitudes. With these amplitudes, we find a number of relations for decay
widths, which can be examined in future.Comment: 47pages, 1figure. arXiv admin note: substantial text overlap with
arXiv:1707.0657
Forward-Backward Greedy Algorithms for General Convex Smooth Functions over A Cardinality Constraint
We consider forward-backward greedy algorithms for solving sparse feature
selection problems with general convex smooth functions. A state-of-the-art
greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to
solve a large number of optimization problems, thus it is not scalable for
large-size problems. The FoBa-gdt algorithm, which uses the gradient
information for feature selection at each forward iteration, significantly
improves the efficiency of FoBa-obj. In this paper, we systematically analyze
the theoretical properties of both forward-backward greedy algorithms. Our main
contributions are: 1) We derive better theoretical bounds than existing
analyses regarding FoBa-obj for general smooth convex functions; 2) We show
that FoBa-gdt achieves the same theoretical performance as FoBa-obj under the
same condition: restricted strong convexity condition. Our new bounds are
consistent with the bounds of a special case (least squares) and fills a
previously existing theoretical gap for general convex smooth functions; 3) We
show that the restricted strong convexity condition is satisfied if the number
of independent samples is more than where is the
sparsity number and is the dimension of the variable; 4) We apply FoBa-gdt
(with the conditional random field objective) to the sensor selection problem
for human indoor activity recognition and our results show that FoBa-gdt
outperforms other methods (including the ones based on forward greedy selection
and L1-regularization)
Geodesic Distance Function Learning via Heat Flow on Vector Fields
Learning a distance function or metric on a given data manifold is of great
importance in machine learning and pattern recognition. Many of the previous
works first embed the manifold to Euclidean space and then learn the distance
function. However, such a scheme might not faithfully preserve the distance
function if the original manifold is not Euclidean. Note that the distance
function on a manifold can always be well-defined. In this paper, we propose to
learn the distance function directly on the manifold without embedding. We
first provide a theoretical characterization of the distance function by its
gradient field. Based on our theoretical analysis, we propose to first learn
the gradient field of the distance function and then learn the distance
function itself. Specifically, we set the gradient field of a local distance
function as an initial vector field. Then we transport it to the whole manifold
via heat flow on vector fields. Finally, the geodesic distance function can be
obtained by requiring its gradient field to be close to the normalized vector
field. Experimental results on both synthetic and real data demonstrate the
effectiveness of our proposed algorithm
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