On hypergraph Lagrangians

It is conjectured by Frankl and F\"uredi that the $r$-uniform hypergraph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-uniform hypergraphs with $m$ edges in \cite{FF}. Motzkin and Straus' theorem confirms this conjecture when $r=2$. For $r=3$, it is shown by Talbot in \cite{T} that this conjecture is true when $m$ is in certain ranges. In this paper, we explore the connection between the clique number and Lagrangians for $r$-uniform hypergraphs. As an implication of this connection, we prove that the $r$-uniform hypergraph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-uniform graphs with $t$ vertices and $m$ edges satisfying ${t-1\choose r}\leq m \leq {t-1\choose r}+ {t-2\choose r-1}-[(2r-6)\times2^{r-1}+2^{r-3}+(r-4)(2r-7)-1]({t-2\choose r-2}-1)$ for $r\geq 4.$Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1312.7529, arXiv:1211.7057, arXiv:1211.6508, arXiv:1311.140

Impact of Tropical Storm Bopha on the Intensity Change of Super Typhoon Saomai in the 2006 Typhoon Season

Super Typhoon Saomai (2006, 08W), which caused historical disaster in the landfall region, is the most powerful typhoon ever making landfall in Mainland China since 1949. The impact of Tropical Storm Bopha (2006, 10W) on Saomai is regarded as a binary tropical cyclone (TC) interaction. In order to quantify the influence of Bopha on the intensity of Saomai, a set of numerical experiments are performed by artificially modifying the intensity of Bopha in its initial conditions. It is shown that changing the intensity of Bopha has significant effects on simulating Saomai’s intensities, structures, and tracks. We find that moisture transport is a pivotal process of binary TC interaction. It is interesting that there are opposite effects by Bopha at different development stages of Saomai. The existence of Bopha and increasing its intensity would weaken Saomai at its intensifying stage while intensifying Saomai at its weakening stage. A possible explanation of these effects is the direction change of moisture transport from/to Saomai at its intensifying/weakening stages through the channel. It may suggest a significant relevance for operational intensity forecasts under active binary TC interaction

Hallucinating very low-resolution and obscured face images

Most of the face hallucination methods are designed for complete inputs. They will not work well if the inputs are very tiny or contaminated by large occlusion. Inspired by this fact, we propose an obscured face hallucination network(OFHNet). The OFHNet consists of four parts: an inpainting network, an upsampling network, a discriminative network, and a fixed facial landmark detection network. The inpainting network restores the low-resolution(LR) obscured face images. The following upsampling network is to upsample the output of inpainting network. In order to ensure the generated high-resolution(HR) face images more photo-realistic, we utilize the discriminative network and the facial landmark detection network to better the result of upsampling network. In addition, we present a semantic structure loss, which makes the generated HR face images more pleasing. Extensive experiments show that our framework can restore the appealing HR face images from 1/4 missing area LR face images with a challenging scaling factor of 8x.Comment: 20 pages, Submitted to Pattern Recognition Letter

Efficient Iris Localization via Optimization Model

Iris localization is one of the most important processes in iris recognition. Because of different kinds of noises in iris image, the localization result may be wrong. Besides this, localization process is time-consuming. To solve these problems, this paper develops an efficient iris localization algorithm via optimization model. Firstly, the localization problem is modeled by an optimization model. Then SIFT feature is selected to represent the characteristic information of iris outer boundary and eyelid for localization. And SDM (Supervised Descent Method) algorithm is employed to solve the final points of outer boundary and eyelids. Finally, IRLS (Iterative Reweighted Least-Square) is used to obtain the parameters of outer boundary and upper and lower eyelids. Experimental result indicates that the proposed algorithm is efficient and effective