Estimates of the gaps between consecutive eigenvalues of Laplacian

By the calculation of the gap of the consecutive eigenvalues of $\Bbb S^n$ with standard metric, using the Weyl's asymptotic formula, we know the order of the upper bound of this gap is $k^{\frac{1}{n}}.$ We conjecture that this order is also right for general Dirichlet problem of the Laplace operator, which is optimal if this conjecture holds, obviously. In this paper, using new method, we solve this conjecture in the Euclidean space case intrinsically. We think our method is valid for the case of general Riemannian manifolds and give some examples directly.Comment: 15 page

Robust Visual Tracking Revisited: From Correlation Filter to Template Matching

In this paper, we propose a novel matching based tracker by investigating the relationship between template matching and the recent popular correlation filter based trackers (CFTs). Compared to the correlation operation in CFTs, a sophisticated similarity metric termed "mutual buddies similarity" (MBS) is proposed to exploit the relationship of multiple reciprocal nearest neighbors for target matching. By doing so, our tracker obtains powerful discriminative ability on distinguishing target and background as demonstrated by both empirical and theoretical analyses. Besides, instead of utilizing single template with the improper updating scheme in CFTs, we design a novel online template updating strategy named "memory filtering" (MF), which aims to select a certain amount of representative and reliable tracking results in history to construct the current stable and expressive template set. This scheme is beneficial for the proposed tracker to comprehensively "understand" the target appearance variations, "recall" some stable results. Both qualitative and quantitative evaluations on two benchmarks suggest that the proposed tracking method performs favorably against some recently developed CFTs and other competitive trackers.Comment: has been published on IEEE TI

Conceal an entrance by means of superscatterer

By using the novel property of the rectangular superscatterer, we propose a design which can conceal an entrance from electromagnetic wave detection. Such a superscatterer is realized by coating a negative index material shell on a perfect electrical conductor rectangle cylinder. The results are numerically confirmed by full-wave simulations both in the far-field and near-field.Comment: 10 pages, 4 figure