DIANet: Dense-and-Implicit Attention Network

Attention networks have successfully boosted the performance in various vision problems. Previous works lay emphasis on designing a new attention module and individually plug them into the networks. Our paper proposes a novel-and-simple framework that shares an attention module throughout different network layers to encourage the integration of layer-wise information and this parameter-sharing module is referred as Dense-and-Implicit-Attention (DIA) unit. Many choices of modules can be used in the DIA unit. Since Long Short Term Memory (LSTM) has a capacity of capturing long-distance dependency, we focus on the case when the DIA unit is the modified LSTM (refer as DIA-LSTM). Experiments on benchmark datasets show that the DIA-LSTM unit is capable of emphasizing layer-wise feature interrelation and leads to significant improvement of image classification accuracy. We further empirically show that the DIA-LSTM has a strong regularization ability on stabilizing the training of deep networks by the experiments with the removal of skip connections or Batch Normalization in the whole residual network. The code is released at https://github.com/gbup-group/DIANet

New Real-Variable Characterizations of Musielak-Orlicz Hardy Spaces

Let $\varphi: {\mathbb R^n}\times [0,\infty)\to[0,\infty)$ be such that $\varphi(x,\cdot)$ is an Orlicz function and $\varphi(\cdot,t)$ is a Muckenhoupt $A_\infty({\mathbb R^n})$ weight. The Musielak-Orlicz Hardy space $H^{\varphi}(\mathbb R^n)$ is defined to be the space of all $f\in{\mathcal S}'({\mathbb R^n})$ such that the grand maximal function $f^*$ belongs to the Musielak-Orlicz space $L^\varphi(\mathbb R^n)$. Luong Dang Ky established its atomic characterization. In this paper, the authors establish some new real-variable characterizations of $H^{\varphi}(\mathbb R^n)$ in terms of the vertical or the non-tangential maximal functions, or the Littlewood-Paley $g$-function or $g_\lambda^\ast$-function, via first establishing a Musielak-Orlicz Fefferman-Stein vector-valued inequality. Moreover, the range of $\lambda$ in the $g_\lambda^\ast$-function characterization of $H^\varphi(\mathbb R^n)$ coincides with the known best results, when $H^\varphi(\mathbb R^n)$ is the classical Hardy space $H^p(\mathbb R^n)$, with $p\in (0,1]$, or its weighted variant.Comment: J. Math. Anal. Appl. (to appear

Range-based attacks on links in random scale-free networks

$Range$ and $load$ play keys on the problem of attacking on links in random scale-free (RSF) networks. In this Brief Report we obtain the relation between $range$ and $load$ in RSF networks analytically by the generating function theory, and then give an estimation about the impact of attacks on the $efficiency$ of the network. The analytical results show that short range attacks are more destructive for RSF networks, and are confirmed numerically. Further our results are consistent with the former literature (Physical Review E \textbf{66}, 065103(R) (2002))