3,175 research outputs found
Width of the confinement-induced resonance in a quasi-one-dimensional trap with transverse anisotropy
We theoretically study the width of the s-wave confinement-induced resonance
(CIR) in quasi-one-dimensional atomic gases under tunable transversely
anisotropic confinement. We find that the width of the CIR can be tuned by
varying the transverse anisotropy. The change in the width of the CIR can
manifest itself in the position of the discontinuity in the interaction energy
density, which can be probed experimentally.Comment: 6 pages, 3 figures, update references, published versio
Optimal False Discovery Control of Minimax Estimator
In the analysis of high dimensional regression models, there are two
important objectives: statistical estimation and variable selection. In
literature, most works focus on either optimal estimation, e.g., minimax
error, or optimal selection behavior, e.g., minimax Hamming loss. However in
this study, we investigate the subtle interplay between the estimation accuracy
and selection behavior. Our result shows that an estimator's error rate
critically depends on its performance of type I error control. Essentially, the
minimax convergence rate of false discovery rate over all rate-minimax
estimators is a polynomial of the true sparsity ratio. This result helps us to
characterize the false positive control of rate-optimal estimators under
different sparsity regimes. More specifically, under near-linear sparsity, the
number of yielded false positives always explodes to infinity under worst
scenario, but the false discovery rate still converges to 0; under linear
sparsity, even the false discovery rate doesn't asymptotically converge to 0.
On the other side, in order to asymptotically eliminate all false discoveries,
the estimator must be sub-optimal in terms of its convergence rate. This work
attempts to offer rigorous analysis on the incompatibility phenomenon between
selection consistency and rate-minimaxity observed in the high dimensional
regression literature
A Novel Method for the Absolute Pose Problem with Pairwise Constraints
Absolute pose estimation is a fundamental problem in computer vision, and it
is a typical parameter estimation problem, meaning that efforts to solve it
will always suffer from outlier-contaminated data. Conventionally, for a fixed
dimensionality d and the number of measurements N, a robust estimation problem
cannot be solved faster than O(N^d). Furthermore, it is almost impossible to
remove d from the exponent of the runtime of a globally optimal algorithm.
However, absolute pose estimation is a geometric parameter estimation problem,
and thus has special constraints. In this paper, we consider pairwise
constraints and propose a globally optimal algorithm for solving the absolute
pose estimation problem. The proposed algorithm has a linear complexity in the
number of correspondences at a given outlier ratio. Concretely, we first
decouple the rotation and the translation subproblems by utilizing the pairwise
constraints, and then we solve the rotation subproblem using the
branch-and-bound algorithm. Lastly, we estimate the translation based on the
known rotation by using another branch-and-bound algorithm. The advantages of
our method are demonstrated via thorough testing on both synthetic and
real-world dataComment: 10 pages, 7figure
Corrosion mechanism and evaluation of anodized magnesium alloys
The corrosion of anodized Mg alloys is investigated by means of immersion, salt spray, polarization curve, AC electrochemical impedance spectroscopy (EIS), SEM and optical microscopy analyses. Based on the blocking, retarding and passivating effects of an anodized coating on corrosion of Mg alloys, a corrosion model is proposed to illustrate the corrosion reaction at the coating/substrate interface in coating through-pores. It is found that EIS can sensitively respond to the occurrence of corrosion in anodized Mg alloys and reflect the protection performance of anodized coatings, which may be used as an in situ method of monitoring corrosion for anodized Mg alloys
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