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Given a real number $q$ and a star body in the $n$-dimensional Euclidean space, the generalized dual curvature measure of a convex body was introduced by Lutwak-Yang-Zhang [43]. The corresponding generalized dual Minkowski problem is studied in this paper. By using variational methods, we solve the generalized dual Minkowski problem for $q<0$, and the even generalized dual Minkowski problem for $0\leq q\leq1$. We also obtain a sufficient condition for the existence of solutions to the even generalized dual Minkowski problem for $1

Deep Active Learning (DAL) has been advocated as a promising method to reduce labeling costs in supervised learning. However, existing evaluations of DAL methods are based on different settings, and their results are controversial. To tackle this issue, this paper comprehensively evaluates 19 existing DAL methods in a uniform setting, including traditional fully-\underline{s}upervised \underline{a}ctive \underline{l}earning (SAL) strategies and emerging \underline{s}emi-\underline{s}upervised \underline{a}ctive \underline{l}earning (SSAL) techniques. We have several non-trivial findings. First, most SAL methods cannot achieve higher accuracy than random selection. Second, semi-supervised training brings significant performance improvement compared to pure SAL methods. Third, performing data selection in the SSAL setting can achieve a significant and consistent performance improvement, especially with abundant unlabeled data. Our findings produce the following guidance for practitioners: one should (i) apply SSAL early and (ii) collect more unlabeled data whenever possible, for better model performance.

The dual Minkowski problem in the two-dimensional plane is studied in this paper. By combining the theoretical analysis and numerical estimation of an integral with parameters, we find the number of solutions to this problem for the constant dual curvature case when $04$ is also obtained. As an application, a result on the uniqueness and nonuniqueness of solutions to the $L_p$-Alexandrov problem is obtained for $p<0$., Comment: The first time we submitted this paper for publication is June 4, 2022. We noticed the paper H. Li & Y. Wan [29] submitted to arXiv on September 29, 2022. The method and result in our Section 3 are also obtained in [29]. Due to non-monotonicity, the paper [29] does not solve the uniqueness problem for 3

In this paper, a generalization of the $L_{p}$-Christoffel-Minkowski problem is studied. We consider an anisotropic curvature flow and derive the long-time existence of the flow. Then under some initial data, we obtain the existence of smooth solutions to this problem for $c=1$., Comment: arXiv admin note: substantial text overlap with arXiv:2011.11408

Deep learning (DL) has achieved unprecedented success in a variety of tasks. However, DL systems are notoriously difficult to test and debug due to the lack of explainability of DL models and the huge test input space to cover. Generally speaking, it is relatively easy to collect a massive amount of test data, but the labeling cost can be quite high. Consequently, it is essential to conduct test selection and label only those selected "high quality" bug-revealing test inputs for test cost reduction. In this paper, we propose a novel test prioritization technique that brings order into the unlabeled test instances according to their bug-revealing capabilities, namely TestRank. Different from existing solutions, TestRank leverages both intrinsic attributes and contextual attributes of test instances when prioritizing them. To be specific, we first build a similarity graph on test instances and training samples, and we conduct graph-based semi-supervised learning to extract contextual features. Then, for a particular test instance, the contextual features extracted from the graph neural network (GNN) and the intrinsic features obtained with the DL model itself are combined to predict its bug-revealing probability. Finally, TestRank prioritizes unlabeled test instances in descending order of the above probability value. We evaluate the performance of TestRank on a variety of image classification datasets. Experimental results show that the debugging efficiency of our method significantly outperforms existing test prioritization techniques.

In this paper, the $\mathit{L}_{\mathit{p}}$-dual Minkowski problem of Monge-Amp\`ere type were studied for different $\mathit{p}$ and $\mathit{q}$. Some new nonuniqueness results were obtained for the range $\mathit{p}\le\mathit{q}-\mathit{n}+1$, $\mathit{p}\lt\mathit{q}-\lambda_{1}(\mathit{n},\mathit{k})$ and $\mathit{f}\equiv1$, where $\lambda_{1}(\mathit{n},\mathit{k})$ is the best constant of the Poincar\'e inequality on $\mathbb{S}^{n-1}$ with k-symmetricity. The second part of this paper is devoted to prove some new nonexistence results for the supercritical range $\mathit{p}\leq-\mathit{q}, \mathit{q}\geq\mathit{n}$ on all dimensional spaces. The key ingredient of our proof was based on a generalization of Chou-Wang identity for $\mathit{q}=\mathit{n}$, $\mathit{p}$=$-\mathit{q}$ to a full range of $(\mathit{p},\mathit{q})$.

In this paper, we consider a fully nonlinear curvature flow of a convex hypersurface in the Euclidean n-space. This flow involves k-th elementary symmetric function for principal curvature radii and a function of support function. Under some appropriate assumptions, we prove the long-time existence and convergence of this flow. As an application, we give the existence of smooth solutions to the Orlicz-Christoffel-Minkowski problem., Comment: 19 pages. arXiv admin note: text overlap with arXiv:2005.02376

In this paper we study the dual Orlicz-Minkowski problem, which is a generalization of the dual Minkowski problem in convex geometry. By considering a geometric flow involving Gauss curvature and functions of normal vectors and radial vectors, we obtain a new existence result of smooth even solutions to this problem for smooth even measures., Comment: arXiv admin note: text overlap with arXiv:2005.02376

In this paper a generalized Gauss curvature flow about a convex hypersurface in the Euclidean $n$-space is studied. This flow is closely related to the Orlicz-Minkowski problem, which involves Gauss curvature and a function of support function. Under some appropriate assumptions, we prove the long-time existence and convergence of this flow. As a byproduct, two existence results of solutions to the even Orlicz-Minkowski problem are obtained, one of which improves the known result., Comment: 19 pages. arXiv admin note: text overlap with arXiv:2001.08862

In this paper the dual Orlicz-Minkowski problem, a generalization of the $L_p$ dual Minkowski problem, is studied. By studying a flow involving the Gauss curvature and support function, we obtain a new existence result of solutions to this problem for smooth measures., Comment: Accepted by Transactions of the American Mathematical Society

In this paper, we use the modified potential well method to study the long time behaviors of solutions to the heat flow of H-system in a bounded smooth domain of $R^2$. Global existence and finite time blowup of solutions are proved when the initial energy is in three cases. When the initial energy is low or critical, we not only give a threshold result for the global existence and blowup of solutions, but also obtain the decay rate of the $L^2$ norm for global solutions. When the initial energy is high, sufficient conditions for the global existence and blowup of solutions are also provided. We extend the recent results which were obtained in [12].

Deep learning has become the de-facto computational paradigm for various kinds of perception problems, including many privacy-sensitive applications such as online medical image analysis. No doubt to say, the data privacy of these deep learning systems is a serious concern. Different from previous research focusing on exploiting privacy leakage from deep learning models, in this paper, we present the first attack on the implementation of deep learning models. To be specific, we perform the attack on an FPGA-based convolutional neural network accelerator and we manage to recover the input image from the collected power traces without knowing the detailed parameters in the neural network. For the MNIST dataset, our power side-channel attack is able to achieve up to 89% recognition accuracy.

Machine learning systems based on deep neural networks, being able to produce state-of-the-art results on various perception tasks, have gained mainstream adoption in many applications. However, they are shown to be vulnerable to adversarial example attack, which generates malicious output by adding slight perturbations to the input. Previous adversarial example crafting methods, however, use simple metrics to evaluate the distances between the original examples and the adversarial ones, which could be easily detected by human eyes. In addition, these attacks are often not robust due to the inevitable noises and deviation in the physical world. In this work, we present a new adversarial example attack crafting method, which takes the human perceptual system into consideration and maximizes the noise tolerance of the crafted adversarial example. Experimental results demonstrate the efficacy of the proposed technique., Comment: Adversarial example attacks, Robust and Imperceptible, Human perceptual system, Neural Networks