8,048 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
High Order Asymptotic Preserving DG-IMEX Schemes for Discrete-Velocity Kinetic Equations in a Diffusive Scaling
In this paper, we develop a family of high order asymptotic preserving
schemes for some discrete-velocity kinetic equations under a diffusive scaling,
that in the asymptotic limit lead to macroscopic models such as the heat
equation, the porous media equation, the advection-diffusion equation, and the
viscous Burgers equation. Our approach is based on the micro-macro
reformulation of the kinetic equation which involves a natural decomposition of
the equation to the equilibrium and non-equilibrium parts. To achieve high
order accuracy and uniform stability as well as to capture the correct
asymptotic limit, two new ingredients are employed in the proposed methods:
discontinuous Galerkin spatial discretization of arbitrary order of accuracy
with suitable numerical fluxes; high order globally stiffly accurate
implicit-explicit Runge-Kutta scheme in time equipped with a properly chosen
implicit-explicit strategy. Formal asymptotic analysis shows that the proposed
scheme in the limit of epsilon -> 0 is an explicit, consistent and high order
discretization for the limiting equation. Numerical results are presented to
demonstrate the stability and high order accuracy of the proposed schemes
together with their performance in the limit
Charge-impurity-induced Majorana fermions in topological superconductors
We study numerically Majorana fermions (MFs) induced by a charged impurity in
topological superconductors. It is revealed from the relevant Bogoliubov-de
Gennes equations that (i) for quasi-one dimensional systems, a pair of MFs are
bounded at the two sides of one charge impurity and well separated; and (ii)
for a two dimensional square lattice, the charged-impurity-induced MFs are
similar to the known pair of vortex-induced MFs, in which one MF is bounded by
the impurity while the other appears at the boundary. Moreover, the
corresponding local density of states is explored, demonstrating that the
presence of MF states may be tested experimentally.Comment: 5 pages, 5 figure
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