26,095 research outputs found

### The $z$-matching problem on bipartite graphs

The $z$-matching problem on bipartite graphs is studied with a local
algorithm. A $z$-matching ($z \ge 1$) on a bipartite graph is a set of matched
edges, in which each vertex of one type is adjacent to at most $1$ matched edge
and each vertex of the other type is adjacent to at most $z$ matched edges. The
$z$-matching problem on a given bipartite graph concerns finding $z$-matchings
with the maximum size. Our approach to this combinatorial optimization are of
two folds. From an algorithmic perspective, we adopt a local algorithm as a
linear approximate solver to find $z$-matchings on general bipartite graphs,
whose basic component is a generalized version of the greedy leaf removal
procedure in graph theory. From an analytical perspective, in the case of
random bipartite graphs with the same size of two types of vertices, we develop
a mean-field theory for the percolation phenomenon underlying the local
algorithm, leading to a theoretical estimation of $z$-matching sizes on
coreless graphs. We hope that our results can shed light on further study on
algorithms and computational complexity of the optimization problem.Comment: 15 pages, 3 figure

### gap: Genetic Analysis Package

A preliminary attempt at collecting tools and utilities for genetic data as an R package called gap is described. Genomewide association is then described as a specific example, linking the work of Risch and Merikangas (1996), Long and Langley (1997) for family-based and population-based studies, and the counterpart for case-cohort design established by Cai and Zeng (2004). Analysis of staged design as outlined by Skol et al. (2006) and associate methods are discussed. The package is flexible, customizable, and should prove useful to researchers especially in its application to genomewide association studies.

### Understanding for flavor physics in the lepton sector

In this paper, we give a model for understanding flavor physics in the lepton
sector--mass hierarchy among different generations and neutrino mixing pattern.
The model is constructed in the framework of supersymmetry, with a family
symmetry $S4*U(1)$. There are two right-handed neutrinos introduced for seesaw
mechanism, while some standard model(SM) gauge group singlet fields are
included which transforms non-trivially under family symmetry. In the model,
each order of contributions are suppressed by $\delta \sim 0.1$ compared to the
previous one. In order to reproduce the mass hierarchy, $m_\tau$ and
$\sqrt{\Delta m_{atm}^2}$, $m_\mu$ and $\sqrt{\Delta m_{sol}^2}$ are obtained
at leading-order(LO) and next-to-leading-order(NLO) respectively, while
electron can only get its mass through
next-to-next-to-next-to-leading-order(NNNLO) contributions. For neutrino mixing
angels, $\theta_{12}, \theta_{23}, \theta_{13}$ are $45^\circ, 45^\circ, 0$
i.e. Bi-maximal mixing pattern as first approximation, while higher order
contributions can make them consistent with experimental results. As
corrections for $\theta_{12}$ and $\theta_{13}$ originate from the same
contribution, there is a relation predicted for them
$\sin{\theta_{13}}=\displaystyle
\frac{1-\tan{\theta_{12}}}{1+\tan{\theta_{12}}}$. Besides, deviation from
$\displaystyle \frac{\pi}{4}$ for $\theta_{23}$ should have been as large as
deviation from 0 for $\theta_{13}$ if it were not the former is suppressed by a
factor 4 compared to the latter.Comment: version to appear in Phys. Rev.

### On the four-zero texture of quark mass matrices and its stability

We carry out a new study of quark mass matrices $M^{}_{\rm u}$ (up-type) and
$M^{}_{\rm d}$ (down-type) which are Hermitian and have four zero entries, and
find a new part of the parameter space which was missed in the previous works.
We identify two more specific four-zero patterns of $M^{}_{\rm u}$ and
$M^{}_{\rm d}$ with fewer free parameters, and present two toy flavor-symmetry
models which can help realize such special and interesting quark flavor
structures. We also show that the texture zeros of $M^{}_{\rm u}$ and
$M^{}_{\rm d}$ are essentially stable against the evolution of energy scales in
an analytical way by using the one-loop renormalization-group equations.Comment: 33 pages, 4 figures, minor comments added, version to appear in Nucl.
Phys.

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