26,386 research outputs found
Maximum Smoothed Likelihood Component Density Estimation in Mixture Models with Known Mixing Proportions
In this paper, we propose a maximum smoothed likelihood method to estimate
the component density functions of mixture models, in which the mixing
proportions are known and may differ among observations. The proposed estimates
maximize a smoothed log likelihood function and inherit all the important
properties of probability density functions. A majorization-minimization
algorithm is suggested to compute the proposed estimates numerically. In
theory, we show that starting from any initial value, this algorithm increases
the smoothed likelihood function and further leads to estimates that maximize
the smoothed likelihood function. This indicates the convergence of the
algorithm. Furthermore, we theoretically establish the asymptotic convergence
rate of our proposed estimators. An adaptive procedure is suggested to choose
the bandwidths in our estimation procedure. Simulation studies show that the
proposed method is more efficient than the existing method in terms of
integrated squared errors. A real data example is further analyzed
Branching ratios and direct CP asymmetries in decays
We study the two-body hadronic decays, where () denotes a
pseudoscalar (vector) meson, in the factorization-assisted
topological-amplitude approach proposed in our previous work. This approach is
based on the factorization of short-distance and long-distance dynamics into
Wilson coefficients and hadronic matrix elements of four-fermion operators,
respectively, with the latter being parametrized in terms of several
nonperturbative quantities. We further take into account the -
mixing effect, which improves the global fit to the branching ratios involving
the and mesons. Combining short-distance dynamics associated
with penguin operators and the hadronic parameters determined from the global
fit to branching ratios, we predict direct asymmetries. In particular, the
direct asymmetries in the , , and decays are found to be of , which can be
observed at the LHCb or future Belle II experiment. We also predict the
asymmetry observables of some neutral meson decays.Comment: 16 pages, 2 figure
Perturbative QCD study of decays to a pseudoscalar meson and a tensor meson
We study two-body hadronic decays, with being a light
pseudoscalar (tensor) meson, in the perturbative QCD approach. The CP-averaged
branching ratios and the direct CP asymmetries of the modes are
predicted, where is the difference between the strange numbers of
final and initial states. We also define and calculate experimental observables
for the modes under the mixing, including CP
averaged branching ratios, time-integrated CP asymmetries, and the CP
observables , and . Results are compared to the ones in the literature, and to the ones, which indicate
considerable U-spin symmetry breaking. Our work provides theoretical
predictions for the decays for the first time, some of which will
be potentially measurable at future experiments.Comment: 6 pages, 1 figur
Multifractal analysis of weighted networks by a modified sandbox algorithm
Complex networks have attracted growing attention in many fields. As a
generalization of fractal analysis, multifractal analysis (MFA) is a useful way
to systematically describe the spatial heterogeneity of both theoretical and
experimental fractal patterns. Some algorithms for MFA of unweighted complex
networks have been proposed in the past a few years, including the sandbox (SB)
algorithm recently employed by our group. In this paper, a modified SB
algorithm (we call it SBw algorithm) is proposed for MFA of weighted
networks.First, we use the SBw algorithm to study the multifractal property of
two families of weighted fractal networks (WFNs): "Sierpinski" WFNs and "Cantor
dust" WFNs. We also discuss how the fractal dimension and generalized fractal
dimensions change with the edge-weights of the WFN. From the comparison between
the theoretical and numerical fractal dimensions of these networks, we can find
that the proposed SBw algorithm is efficient and feasible for MFA of weighted
networks. Then, we apply the SBw algorithm to study multifractal properties of
some real weighted networks ---collaboration networks. It is found that the
multifractality exists in these weighted networks, and is affected by their
edge-weights.Comment: 15 pages, 6 figures. Accepted for publication by Scientific Report
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