arXiv subjects

Na Zhao

Publications and source records attributed to Na Zhao.

88 records · Page 5Linked to original sources

arXiv2021

Static-Dynamic Co-Teaching for Class-Incremental 3D Object Detection

Deep learning-based approaches have shown remarkable performance in the 3D object detection task. However, they suffer from a catastrophic performance drop on the originally trained classes when incrementally learning new classes without revisiting the old data. This "catastrophic forgetting" phenomenon impedes the deployment of 3D object detection approaches in real-world scenarios, where continuous learning systems are needed. In this paper, we study the unexplored yet important class-incremental 3D object detection problem and present the first solution - SDCoT, a novel static-dynamic co-teaching method. Our SDCoT alleviates the catastrophic forgetting of old classes via a static teacher, which provides pseudo annotations for old classes in the new samples and regularizes the current model by extracting previous knowledge with a distillation loss. At the same time, SDCoT consistently learns the underlying knowledge from new data via a dynamic teacher. We conduct extensive experiments on two benchmark datasets and demonstrate the superior performance of our SDCoT over baseline approaches in several incremental learning scenarios.

cs.CV↗

arXiv2021

WEM: A Node Importance Algorithm in Weighted Networks

In view of the node importance in weighted networks, weighted expected method (WEM), was proposed in this paper, which take an advantages of uncertain graph algorithm. First, a weight processing method is proposed based on the relationship between the weight of edges and the intensity of contact between nodes, and the calculation method of the contribution of the weight of edges to the node importance is defined, even if there are two converse situations in the reality. Then, because of the use of dynamic programming method, which reduces the complexity of computational time to a linear level, WEM will be more suitable for the calculation in large weighted networks. Owning to its features of calculating, WEM can, to the greatest extent, ensure a precise order of node essential scores for each node. The node connectivity experiment and SIR simulation experiment show that the WEM has higher accuracy and relatively low time complexity.

cs.SI↗

arXiv2021

Global Calderón--Zygmund theory for parabolic $p$-Laplacian system: the case $1<p\leq \frac{2n}{n+2}$

The aim of this paper is to establish global Calderón--Zygmund theory to parabolic $p$-Laplacian system: $$ u_t -\operatorname{div}(|\nabla u|^{p-2}\nabla u) = \operatorname{div} (|F|^{p-2}F)~\text{in}~Ω\times (0,T)\subset \mathbb{R}^{n+1}, $$ proving that $$F\in L^q\Rightarrow \nabla u\in L^q,$$ for any $q>\max\{p,\frac{n(2-p)}{2}\}$ and $p>1$. Acerbi and Mingione \cite{Acerbi07} proved this estimate in the case $p>\frac{2n}{n+2}$. In this article we settle the case $1<p\leq \frac{2n}{n+2}$. We also treat systems with discontinuous coefficients having small BMO (bounded mean oscillation) norm.

math.AP↗

arXiv2021

Few-shot 3D Point Cloud Semantic Segmentation

Many existing approaches for 3D point cloud semantic segmentation are fully supervised. These fully supervised approaches heavily rely on large amounts of labeled training data that are difficult to obtain and cannot segment new classes after training. To mitigate these limitations, we propose a novel attention-aware multi-prototype transductive few-shot point cloud semantic segmentation method to segment new classes given a few labeled examples. Specifically, each class is represented by multiple prototypes to model the complex data distribution of labeled points. Subsequently, we employ a transductive label propagation method to exploit the affinities between labeled multi-prototypes and unlabeled points, and among the unlabeled points. Furthermore, we design an attention-aware multi-level feature learning network to learn the discriminative features that capture the geometric dependencies and semantic correlations between points. Our proposed method shows significant and consistent improvements compared to baselines in different few-shot point cloud semantic segmentation settings (i.e., 2/3-way 1/5-shot) on two benchmark datasets. Our code is available at https://github.com/Na-Z/attMPTI.

cs.CV↗

arXiv2021

Scalable Estimation and Inference with Large-scale or Online Survival Data

With the rapid development of data collection and aggregation technologies in many scientific disciplines, it is becoming increasingly ubiquitous to conduct large-scale or online regression to analyze real-world data and unveil real-world evidence. In such applications, it is often numerically challenging or sometimes infeasible to store the entire dataset in memory. Consequently, classical batch-based estimation methods that involve the entire dataset are less attractive or no longer applicable. Instead, recursive estimation methods such as stochastic gradient descent that process data points sequentially are more appealing, exhibiting both numerical convenience and memory efficiency. In this paper, for scalable estimation of large or online survival data, we propose a stochastic gradient descent method which recursively updates the estimates in an online manner as data points arrive sequentially in streams. Theoretical results such as asymptotic normality and estimation efficiency are established to justify its validity. Furthermore, to quantify the uncertainty associated with the proposed stochastic gradient descent estimator and facilitate statistical inference, we develop a scalable resampling strategy that specifically caters to the large-scale or online setting. Simulation studies and a real data application are also provided to assess its performance and illustrate its practical utility.

stat.ME↗

arXiv2021

SESS: Self-Ensembling Semi-Supervised 3D Object Detection

The performance of existing point cloud-based 3D object detection methods heavily relies on large-scale high-quality 3D annotations. However, such annotations are often tedious and expensive to collect. Semi-supervised learning is a good alternative to mitigate the data annotation issue, but has remained largely unexplored in 3D object detection. Inspired by the recent success of self-ensembling technique in semi-supervised image classification task, we propose SESS, a self-ensembling semi-supervised 3D object detection framework. Specifically, we design a thorough perturbation scheme to enhance generalization of the network on unlabeled and new unseen data. Furthermore, we propose three consistency losses to enforce the consistency between two sets of predicted 3D object proposals, to facilitate the learning of structure and semantic invariances of objects. Extensive experiments conducted on SUN RGB-D and ScanNet datasets demonstrate the effectiveness of SESS in both inductive and transductive semi-supervised 3D object detection. Our SESS achieves competitive performance compared to the state-of-the-art fully-supervised method by using only 50% labeled data. Our code is available at https://github.com/Na-Z/sess.

cs.CV↗

arXiv2020

Decay and vanishing of some D-solutions of the Navier-Stokes equations

An old problem since Leray \cite{Le:1} asks whether homogeneous D solutions of the 3 dimensional Navier-Stokes equation in $\mathbb{R}^3$ or some noncompact domains are 0. In this paper, we give a positive solution to the problem in two special cases: (1) when the solution is axially symmetric and periodic in the vertical variable; (2) full 3 dimensional slab case $\mathbb{R}^2 \times [0, 1]$ with Dirichlet boundary condition. Other partial results are also presented. The paper is self contained comparing with the first part \cite{CPZ:1} although the general idea is related.

math.AP↗

arXiv2020

Lowest Degree Decomposition of Complex Networks

The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network science, which allow us to better conduct successful social advertisements, immunize a network against epidemics, discover drug target candidates and essential proteins, and prevent cascading breakdowns in power grids, financial markets and ecological systems. Inspired by the nested nature of real networks, we propose a decomposition method where at each step the nodes with the lowest degree are pruned. We have strictly proved that this so-called lowest degree decomposition (LDD) is a subdivision of the famous k-core decomposition. Extensive numerical analyses on epidemic spreading, synchronization and nonlinear mutualistic dynamics show that the LDD can more accurately find out the most influential spreaders, the most efficient controllers and the most vulnerable species than k-core decomposition and other well-known indices. The present method only makes use of local topological information, and thus has high potential to become a powerful tool for network analysis.

physics.soc-ph↗

arXiv2019

Short-time detection of QRS complexes using dual channels 1 based on U-Net and bidirectional long short-term memory

Cardiovascular disease is associated with high rates of morbidity and mortality, and can be reflected by 19 abnormal features of electrocardiogram (ECG). Detecting changes in the QRS complexes in ECG 20 signals is regarded as a straightforward, noninvasive, inexpensive, and preliminary diagnosis approach 21 for evaluating the cardiac health of patients. Therefore, detecting QRS complexes in ECG signals must 22 be accurate over short times. However, the reliability of automatic QRS detection is restricted by all 23 kinds of noise and complex signal morphologies. In this study, we proposed a new algorithm for 24 short-time detection of QRS complexes using dual channels based on U-Net and bidirectional long 25 short-term memory. First, a proposed preprocessor with mean filtering and discrete wavelet transform 26 was initially applied to remove different types of noise. Next the signal was transformed and 27 annotations were relabeled. Finally, a method combining U-Net and bidirectional long short-term 28 memory with dual channels was used for the short-time detection of QRS complexes. The proposed 29 algorithm was trained and tested using 44 ECG records from the MIT-BIH arrhythmia database. It 30 achieved, on average, high values for detection sensitivity (99.56%), positive predictivity (99.72%), 31 and accuracy (99.28%) on the test set, indicating an improvement compared to algorithms reported in 32 the literature.

eess.SP↗

arXiv2019

Identifying significant edges via neighborhood information

Heterogeneous nature of real networks implies that different edges play different roles in network structure and functions, and thus to identify significant edges is of high value in both theoretical studies and practical applications. We propose the so-called second-order neighborhood (SN) index to quantify an edge's significance in a network. We compare SN index with many other benchmark methods based on 15 real networks via edge percolation. Results show that the proposed SN index outperforms other well-known methods.

physics.soc-ph↗

arXiv2019

Automatic Detection of ECG Abnormalities by using an Ensemble of Deep Residual Networks with Attention

Heart disease is one of the most common diseases causing morbidity and mortality. Electrocardiogram (ECG) has been widely used for diagnosing heart diseases for its simplicity and non-invasive property. Automatic ECG analyzing technologies are expected to reduce human working load and increase diagnostic efficacy. However, there are still some challenges to be addressed for achieving this goal. In this study, we develop an algorithm to identify multiple abnormalities from 12-lead ECG recordings. In the algorithm pipeline, several preprocessing methods are firstly applied on the ECG data for denoising, augmentation and balancing recording numbers of variant classes. In consideration of efficiency and consistency of data length, the recordings are padded or truncated into a medium length, where the padding/truncating time windows are selected randomly to sup-press overfitting. Then, the ECGs are used to train deep neural network (DNN) models with a novel structure that combines a deep residual network with an attention mechanism. Finally, an ensemble model is built based on these trained models to make predictions on the test data set. Our method is evaluated based on the test set of the First China ECG Intelligent Competition dataset by using the F1 metric that is regarded as the harmonic mean between the precision and recall. The resultant overall F1 score of the algorithm is 0.875, showing a promising performance and potential for practical use.

cs.LG↗

arXiv2019

PS^2-Net: A Locally and Globally Aware Network for Point-Based Semantic Segmentation

In this paper, we present the PS^2-Net -- a locally and globally aware deep learning framework for semantic segmentation on 3D scene-level point clouds. In order to deeply incorporate local structures and global context to support 3D scene segmentation, our network is built on four repeatedly stacked encoders, where each encoder has two basic components: EdgeConv that captures local structures and NetVLAD that models global context. Different from existing start-of-the-art methods for point-based scene semantic segmentation that either violate or do not achieve permutation invariance, our PS^2-Net is designed to be permutation invariant which is an essential property of any deep network used to process unordered point clouds. We further provide theoretical proof to guarantee the permutation invariance property of our network. We perform extensive experiments on two large-scale 3D indoor scene datasets and demonstrate that our PS2-Net is able to achieve state-of-the-art performances as compared to existing approaches.

cs.CV↗

arXiv2018

A Liouville type theorem for axially symmetric $D$-solutions to steady Navier-Stokes Equations

We study axially symmetric $D$-solutions of three dimensional steady Navier-Stokes equations. We prove that if the velocity $u$ decays like $|x'|^{-(\frac{2}{3})^+}$ uniformly for $z$, or the vorticity $ω$ decays like $|x'|^{-(\frac{5}{3})^+}$ uniformly for $z$, then $u$ vanishes. Here $|x'|$ denotes the distance to the axis.

math.AP↗

arXiv2017

Sharp one component regularity for Navier-Stokes

We consider the conditional regularity of mild solution $v$ to the incompressible Navier-Stokes equations in three dimensions. Let $e \in \mathbb{S}^2$ and $0 < T^\ast < \infty$. J. Chemin and P. Zhang \cite{CP} proved the regularity of $v$ on $(0,T^\ast]$ if there exists $p \in (4, 6)$ such that $$\int_0^{T^\ast}\|v\cdot e\|^p_{\dot{H}^{\frac{1}{2}+\frac{2}{p}}}dt < \infty.$$ J. Chemin, P. Zhang and Z. F. Zhang \cite{CPZ} extended the range of $p$ to $(4, \infty)$. In this article we settle the case $p \in [2, 4]$. Our proof also works for the case $p \in (4,\infty)$.

math.AP↗

arXiv2017

A Novel Quantum Image Compression Method Based on JPEG

Quantum image processing has been a hot topic. The first step of it is to store an image into qubits, which is called quantum image preparation. Different quantum image representations may have different preparation methods. In this paper, we use GQIR (the generalized quantum image representation) to represent an image, and try to decrease the operations used in preparation, which is also known as quantum image compression. Our compression scheme is based on JPEG (named from its inventor: the Joint Photographic Experts Group) --- the most widely used method for still image compression in classical computers. We input the quantized JPEG coefficients into qubits and then convert them into pixel values. Theoretical analysis and experimental results show that the compression ratio of our scheme is obviously higher than that of the previous compression method.

quant-ph↗

arXiv2017

Improved Liouville theorems for axially symmetric Navier-Stokes equations

In this paper, we consider the Liouville property for ancient solutions of the incompressible Navier-Stokes equations. In 2D and the 3D axially symmetric case without swirl, we prove sharp Liouville theorems for smooth ancient mild solutions: velocity fields $v$ are constants if vorticity fields satisfy certain condition and $v$ are sublinear with respect to spatial variables, and we also give counterexamples when $v$ are linear with respect to spatial variables. The condition which vorticity fields need to satisfy is $\lim\limits_{|x|\rightarrow +\infty}|w(x,t)|=0$ and $\lim\limits_{r\rightarrow +\infty}\frac{|w|}{\sqrt{x_1^2+x_2^2}}=0$ uniformly for all $t\in(-\infty,0)$ in 2D and 3D axially symmetric case without swirl, respectively. In the case when solutions are axially symmetric with nontrivial swirl, we prove that if $Γ=rv_θ\in L^\infty_tL^p_x(\mathbb{R}^3\times(-\infty,0))$ where $1\leq p<\infty$, then bounded ancient mild solutions are constants.

math.AP↗