Jian Sun

TL;DR: Rank ordered-based object image clustering may facilitate robust clustering of digital images as discussed by the authors, where the rank order distance for each pairing of object images by normalizing the asymmetric distances of corresponding object images is obtained.

Abstract: In the paper, we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5]. Our result shows that if a geometric hexagonal triangulation of the plane is PL conformal to the regular hexagonal triangulation and all inner angles are in [δ, π/2 − δ] for any constant δ > 0, then it is the regular hexagonal triangulation. This partially solves a conjecture of Luo [4]. The proof uses the concept of quasi-harmonic functions to unfold the properties of the mesh. ∗Mathematical Sciences Center, Tsinghua University, Beijing 100084 China. Email: mike890505@gmail.com. †Department of Computer Science, Stony Brook University, New York 11794 USA. Email: gu@cs.stonybrook.edu. ‡Mathematical Sciences Center, Tsinghua University, Beijing 100084 China. Email: jsun@math.tsinghua.edu.cn. 1 ar X iv :1 30 6. 36 30 v1 [ m at h. G T ] 1 6 Ju n 20 13

TL;DR: HyperAdam as discussed by the authors combines the idea of learning to optimize and traditional Adam optimizer, which is the state-of-the-art for various network training, such as multilayer perceptron, CNN and LSTM.

TL;DR: Hyper-GAN as mentioned in this paper proposes a unified Hyper-GAN model for cross-contrast image translation, which consists of a pair of hyper-encoder and hyper-decoder to first map from the source contrast to a common feature space, and then further map to the target contrast image.

TL;DR: In this paper, the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5] was considered, and it was shown that for any constant δ > 0, the polygonal mesh is PL conformal to the regular hexagonal triangle.