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

Feature Extraction and Fusion Using Deep Convolutional Neural Networks for Face Detection

This paper proposes a method that uses feature fusion to represent images better for face detection after feature extraction by deep convolutional neural network (DCNN). First, with Clarifai net and VGG Net-D (16 layers), we learn features from data, respectively; then we fuse features extracted from the two nets. To obtain more compact feature representation and mitigate computation complexity, we reduce the dimension of the fused features by PCA. Finally, we conduct face classification by SVM classifier for binary classification. In particular, we exploit offset max-pooling to extract features with sliding window densely, which leads to better matches of faces and detection windows; thus the detection result is more accurate. Experimental results show that our method can detect faces with severe occlusion and large variations in pose and scale. In particular, our method achieves 89.24% recall rate on FDDB and 97.19% average precision on AFW