17,292 research outputs found
The classification of two-loop integrand basis in pure four-dimension
In this paper, we have made the attempt to classify the integrand basis of
all two-loop diagrams in pure four-dimension space-time. Our classification
includes the topology of two-loop diagrams which determines the structure of
denominators, and the set of numerators under different kinematic
configurations of external momenta by using Gr\"{o}bner basis method. In our
study, the variety defined by setting all propagators to on-shell has played an
important role. We discuss the structure of variety and how it splits to
various irreducible branches when external momenta at each corner of diagrams
satisfy some special kinematic conditions. This information is crucial to the
numerical or analytical fitting of coefficients for integrand basis in
reduction process.Comment: 52 pages, 9 figures. v2 reference added, v3 published versio
Constraints on absolute neutrino Majorana mass from current data
We present new constraints on the neutrino Majorana masses from the current
data of neutrinoless double beta decay and neutrino flavour mixing. With the
latest results of progresses from various isotopes, including
the recent calculations of the nuclear matrix elements, we find that the
strongest constraint of the effective Majorana neutrino mass is from the
data of the EXO-200 and KamLAND-Zen collaborations. Further
more, by combining the experimental data with the neutrino
mixing parameters from new analyses, we get the mass upper limits of neutrino
mass eigenstates and flavour eigenstates and suggest several relations among
these neutrino masses.Comment: 6 latex pages, 2 figures. Final version for publication in "The
Universe
Form Factor and Boundary Contribution of Amplitude
The boundary contribution of an amplitude in the BCFW recursion relation can
be considered as a form factor involving boundary operator and unshifted
particles. At the tree-level, we show that by suitable construction of
Lagrangian, one can relate the leading order term of boundary operators to some
composite operators of N=4 super-Yang-Mills theory, then the computation of
form factors is translated to the computation of amplitudes. We compute the
form factors of these composite operators through the computation of
corresponding double trace amplitudes.Comment: 38 pages, 6 figure
Accelerated Linearized Bregman Method
In this paper, we propose and analyze an accelerated linearized Bregman (ALB)
method for solving the basis pursuit and related sparse optimization problems.
This accelerated algorithm is based on the fact that the linearized Bregman
(LB) algorithm is equivalent to a gradient descent method applied to a certain
dual formulation. We show that the LB method requires
iterations to obtain an -optimal solution and the ALB algorithm
reduces this iteration complexity to while requiring
almost the same computational effort on each iteration. Numerical results on
compressed sensing and matrix completion problems are presented that
demonstrate that the ALB method can be significantly faster than the LB method
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