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Qian Zhang

Publications and source records attributed to Qian Zhang.

At least 289 records · Page 16Linked to original sources

Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system

In this paper, we consider the quasilinear Schrödinger system in $\mathbb R^{N}$($N\geq3$): $$\left\{\begin{align} &-Δu+ A(x)u-\frac{1}{2}\triangle(u^{2})u=\frac{2α}{α+β}|u|^{α-2}u|v|^β,\\ &-Δv+ Bv-\frac{1}{2}\triangle(v^{2})v=\frac{2β}{α+β}|u|^α|v|^{β-2}v,\end{align}\right. $$ where $α,β>1$, $2<α+β<\frac{4N}{N-2}$,$B>0$ is a constant. By using a constrained minimization on Nehari-Pohožaev set, for any given integer $s\geq2$, we construct a non-radially symmetrical nodal solution with its $2s$ nodal domains.

math.AP↗

Ground states solution of Nehari-Pohožaev type for periodic quasilinear Schrödinger system

This paper is concerned with a quasilinear Schrödinger system in $\mathbb R^{N}$ $$\left\{\aligned &-Δu+A(x)u-\frac{1}{2}\triangle(u^{2})u=\frac{2α}{α+β}|u|^{α-2}u|v|^β,\\ &-Δv+B(x)v-\frac{1}{2}\triangle(v^{2})v=\frac{2β}{α+β}|u|^α|v|^{β-2}v,\\ & u(x)\to 0\ \hbox{and}\quad v(x)\to 0\ \hbox{as}\ |x|\to \infty,\endaligned\right. $$ where $α,β>1$ and $2<α+β<\frac{4N}{N-2}$ ($N \geq 3$). $A(x)$ and $B(x)$ are two periodic functions. By minimization under a convenient constraint and concentration-compactness lemma, we prove the existence of ground states solution. Our result covers the case of $α+β\in(2,4)$ which seems to be the first result for coupled quasilinear Schrödinger system in the periodic situation.

math.AP↗

Existence of nontrivial solutions to a fourth-order Kirchhoff type elliptic equation with critical exponent

In this paper, a critical fourth-order Kirchhoff type elliptic equation with a subcritical perturbation is studied. The main feature of this problem is that it involves both a nonlocal coefficient and a critical term, which bring essential difficulty for the proof of the existence of weak solutions. When the dimension of the space is smaller than or equals to $7$, the existence of weak solution is obtained by combining the Mountain Pass Lemma with some delicate estimate on the Talenti's functions. When the dimension of the space is larger than or equals to $8$, the above argument no longer works. By introducing an appropriate truncation on the nonlocal coefficient, it is shown that the problem admits a nontrivial solution under appropriate conditions on the parameter.

math.AP↗

Existence of ground state solution of Nehari-Pohožaev type for a quasilinear Schrödinger system

This paper is concerned with the following quasilinear Schrödinger system in the entire space $\mathbb R^{N}$($N\geq3$): $$\left\{\begin{align} &-Δu+A(x)u-\frac{1}{2}\triangle(u^{2})u = \frac{2α}{α+β}|u|^{α-2}u|v|^β,\\ &-Δv+Bv-\frac{1}{2}\triangle(v^{2})v=\frac{2β}{α+β}|u|^α|v|^{β-2}v.\end{align}\right. $$ By establishing a suitable constraint set and studying related minimization problem, we prove the existence of ground state solution for $α,β>1$, $2<α+β<\frac{4N}{N-2}$. Our results can be looked on as a generalization to results by Guo and Tang (Ground state solutions for quasilinear Schrödinger systems, J. Math. Anal. Appl. 389 (2012) 322).

math.AP↗

Evaluating Strong Idempotence of Image Codec

In this paper, we first propose the concept of strong idempotent codec based on idempotent codec. The idempotence of codec refers to the stability of codec to re-compression. Similarly, we define the strong idempotence of codec as the stability of codec to multiple quality re-compression, which is an important feature of codec in the context of cloud transcoding. We provide a detailed example of strong idempotent codec with known source distribution. Further, we formalize a testing protocol to evaluate the strong idempotence of image codec. And finally, we evaluate the strong idempotence of current image codecs, including traditional codec and recent neural codec. Experimental results show that current image codecs are not stable to multi-round re-compression with different qualities, even if they are close to idempotent.

cs.MM↗

Nonconforming finite elements for the Brinkman and $-\text{curl}Δ\text{curl}$ problems on cubical meshes

We propose two families of nonconforming elements on cubical meshes: one for the $-\text{curl}Δ\text{curl}$ problem and the other for the Brinkman problem. The element for the $-\text{curl}Δ\text{curl}$ problem is the first nonconforming element on cubical meshes. The element for the Brinkman problem can yield a uniformly stable finite element method with respect to the parameter $ν$. The lowest-order elements for the $-\text{curl}Δ\text{curl}$ and the Brinkman problems have 48 and 30 degrees of freedom, respectively. The two families of elements are subspaces of $H(\text{curl};Ω)$ and $H(\text{div};Ω)$, and they, as nonconforming approximation to $H(\text{gradcurl};Ω)$ and $[H^1(Ω)]^3$, can form a discrete Stokes complex together with the Lagrange element and the $L^2$ element.

math.NA↗

DPSNN: A Differentially Private Spiking Neural Network with Temporal Enhanced Pooling

Privacy protection is a crucial issue in machine learning algorithms, and the current privacy protection is combined with traditional artificial neural networks based on real values. Spiking neural network (SNN), the new generation of artificial neural networks, plays a crucial role in many fields. Therefore, research on the privacy protection of SNN is urgently needed. This paper combines the differential privacy(DP) algorithm with SNN and proposes a differentially private spiking neural network (DPSNN). The SNN uses discrete spike sequences to transmit information, combined with the gradient noise introduced by DP so that SNN maintains strong privacy protection. At the same time, to make SNN maintain high performance while obtaining high privacy protection, we propose the temporal enhanced pooling (TEP) method. It fully integrates the temporal information of SNN into the spatial information transfer, which enables SNN to perform better information transfer. We conduct experiments on static and neuromorphic datasets, and the experimental results show that our algorithm still maintains high performance while providing strong privacy protection.

cs.NE↗

TinyDet: Accurate Small Object Detection in Lightweight Generic Detectors

Small object detection requires the detection head to scan a large number of positions on image feature maps, which is extremely hard for computation- and energy-efficient lightweight generic detectors. To accurately detect small objects with limited computation, we propose a two-stage lightweight detection framework with extremely low computation complexity, termed as TinyDet. It enables high-resolution feature maps for dense anchoring to better cover small objects, proposes a sparsely-connected convolution for computation reduction, enhances the early stage features in the backbone, and addresses the feature misalignment problem for accurate small object detection. On the COCO benchmark, our TinyDet-M achieves 30.3 AP and 13.5 AP^s with only 991 MFLOPs, which is the first detector that has an AP over 30 with less than 1 GFLOPs; besides, TinyDet-S and TinyDet-L achieve promising performance under different computation limitation.

cs.CV↗

OpenInst: A Simple Query-Based Method for Open-World Instance Segmentation

Open-world instance segmentation has recently gained significant popularitydue to its importance in many real-world applications, such as autonomous driving, robot perception, and remote sensing. However, previous methods have either produced unsatisfactory results or relied on complex systems and paradigms. We wonder if there is a simple way to obtain state-of-the-art results. Fortunately, we have identified two observations that help us achieve the best of both worlds: 1) query-based methods demonstrate superiority over dense proposal-based methods in open-world instance segmentation, and 2) learning localization cues is sufficient for open world instance segmentation. Based on these observations, we propose a simple query-based method named OpenInst for open world instance segmentation. OpenInst leverages advanced query-based methods like QueryInst and focuses on learning localization cues. Notably, OpenInst is an extremely simple and straightforward framework without any auxiliary modules or post-processing, yet achieves state-of-the-art results on multiple benchmarks. Specifically, in the COCO$\to$UVO scenario, OpenInst achieves a mask AR of 53.3, outperforming the previous best methods by 2.0 AR with a simpler structure. We hope that OpenInst can serve as a solid baselines for future research in this area.

cs.CV↗

BoxTeacher: Exploring High-Quality Pseudo Labels for Weakly Supervised Instance Segmentation

Labeling objects with pixel-wise segmentation requires a huge amount of human labor compared to bounding boxes. Most existing methods for weakly supervised instance segmentation focus on designing heuristic losses with priors from bounding boxes. While, we find that box-supervised methods can produce some fine segmentation masks and we wonder whether the detectors could learn from these fine masks while ignoring low-quality masks. To answer this question, we present BoxTeacher, an efficient and end-to-end training framework for high-performance weakly supervised instance segmentation, which leverages a sophisticated teacher to generate high-quality masks as pseudo labels. Considering the massive noisy masks hurt the training, we present a mask-aware confidence score to estimate the quality of pseudo masks and propose the noise-aware pixel loss and noise-reduced affinity loss to adaptively optimize the student with pseudo masks. Extensive experiments can demonstrate the effectiveness of the proposed BoxTeacher. Without bells and whistles, BoxTeacher remarkably achieves 35.0 mask AP and 36.5 mask AP with ResNet-50 and ResNet-101 respectively on the challenging COCO dataset, which outperforms the previous state-of-the-art methods by a significant margin and bridges the gap between box-supervised and mask-supervised methods. The code and models will be available at https://github.com/hustvl/BoxTeacher.

cs.CV↗

Global stability of the Dirac-Klein-Gordon system in two and three space dimensions

In this paper we study global nonlinear stability for the Dirac-Klein-Gordon system in two and three space dimensions for small and regular initial data. In the case of two space dimensions, we consider the Dirac-Klein-Gordon system with a massless Dirac field and a massive scalar field, and prove global existence, sharp time decay estimates and linear scattering for the solutions. In the case of three space dimensions, we consider the Dirac-Klein-Gordon system with a mass parameter in the Dirac equation, and prove uniform (in the mass parameter) global existence, unified time decay estimates and linear scattering in the top order energy space.

math.AP↗

Global solutions of 2-D cubic Dirac equation with non-compactly supported data

We are interested in the cubic Dirac equation in two space dimensions. We establish the small data global existence and sharp pointwise decay results for general cubic nonlinearities without additional structure. We also prove the scattering of the Dirac equation for certain classes of nonlinearities. In all the above results we do not require the initial data to have compact support.

math.AP↗

Stability of a coupled wave-Klein-Gordon system with non-compactly supported initial data

In this paper we study global nonlinear stability for a system of semilinear wave and Klein-Gordon equations with quadratic nonlinearities. We consider nonlinearities of the type of wave-Klein-Gordon interactions where there are no derivatives on the wave component. The initial data are assumed to have a suitable polynomial decay at infinity, but are not necessarily compactly supported. We prove small data global existence, sharp pointwise decay estimates and linear scattering results for the solutions. We give a sufficient condition which combines the Sobolev norms of the nonlinearities on flat time slices outside the light cone and the norms of them on truncated hyperboloids inside the light cone, for the linear scattering of the solutions.

math.AP↗

Nonreciprocal slow or fast light in anti-$\mathcal{PT}$-symmetric optomechanics

Non-Hermitian systems with anti-parity-time ($\mathcal{APT}$) symmetry have revealed rich physics beyond conventional systems. Here, we study optomechanics in an $\mathcal{APT}$-symmetric spinning resonator and show that, by tuning the rotating speed to approach the exceptional point (EP) or the non-Hermitian spectral degeneracy, nonreciprocal light transmission with a high isolation ratio can be realized. Accompanying this process, nonreciprocal group delay or advance is also identified in the vicinity of EP. Our work sheds new light on manipulating laser propagation with optomechanical EP devices and, in a broader view, can be extended to explore a wide range of $\mathcal{APT}$-symmetric effects, such as $\mathcal{APT}$-symmetric phonon lasers, $\mathcal{APT}$-symmetric topological effects, and $\mathcal{APT}$-symmetric force sensing or accelerator.

quant-ph↗

Complex strengthening mechanisms in nanocrystalline Ni-Mo alloys revealed by a machine-learning interatomic potential

A nanocrystalline metal's strength increases significantly as its grain size decreases, a phenomenon known as the Hall-Petch relation. Such relation, however, breaks down when the grains become too small. Experimental studies have circumvented this problem in a set of Ni-Mo alloys by stabilizing the grain boundaries (GB). Here, using atomistic simulations with a machine learning-based interatomic potential (ML-IAP), we demonstrate that the inverse Hall-Petch relation can be correctly reproduced due to a change in the dominant deformation mechanism as the grain becomes small in the Ni-Mo polycrystals. It is found that the atomic von Mises strain can be significantly reduced by either solute doping and/or annealing for small-grain-size polycrystals, leading to the increased strength of the polycrystals. On the other hand, for large-grain-size polycrystals, annealing weakens the material due to the large atomic movements in GB regions. Over a broad range of grain size, the superposition of the solute and annealing effects on polycrystals enhances the strength of those with small grain size more than those with large ones, giving rise to the continuous strengthening at extremely small grain sizes. Overall, this study not only demonstrates the reliability of the ML-IAP, but also provides a comprehensive atomistic view of complex strengthening mechanisms in nanocrystals, opening up a new avenue to tailor their mechanical properties.

cond-mat.mtrl-sci↗

Deep-Learning Tool for Early Identifying Non-Traumatic Intracranial Hemorrhage Etiology based on CT Scan

Background: To develop an artificial intelligence system that can accurately identify acute non-traumatic intracranial hemorrhage (ICH) etiology based on non-contrast CT (NCCT) scans and investigate whether clinicians can benefit from it in a diagnostic setting. Materials and Methods: The deep learning model was developed with 1868 eligible NCCT scans with non-traumatic ICH collected between January 2011 and April 2018. We tested the model on two independent datasets (TT200 and SD 98) collected after April 2018. The model's diagnostic performance was compared with clinicians's performance. We further designed a simulated study to compare the clinicians's performance with and without the deep learning system augmentation. Results: The proposed deep learning system achieved area under the receiver operating curve of 0.986 (95% CI 0.967-1.000) on aneurysms, 0.952 (0.917-0.987) on hypertensive hemorrhage, 0.950 (0.860-1.000) on arteriovenous malformation (AVM), 0.749 (0.586-0.912) on Moyamoya disease (MMD), 0.837 (0.704-0.969) on cavernous malformation (CM), and 0.839 (0.722-0.959) on other causes in TT200 dataset. Given a 90% specificity level, the sensitivities of our model were 97.1% and 90.9% for aneurysm and AVM diagnosis, respectively. The model also shows an impressive generalizability in an independent dataset SD98. The clinicians achieve significant improvements in the sensitivity, specificity, and accuracy of diagnoses of certain hemorrhage etiologies with proposed system augmentation. Conclusions: The proposed deep learning algorithms can be an effective tool for early identification of hemorrhage etiologies based on NCCT scans. It may also provide more information for clinicians for triage and further imaging examination selection.

eess.IV↗

Deep Learning Approach to Predict Hemorrhage in Moyamoya Disease

Objective: Reliable tools to predict moyamoya disease (MMD) patients at risk for hemorrhage could have significant value. The aim of this paper is to develop three machine learning classification algorithms to predict hemorrhage in moyamoya disease. Methods: Clinical data of consecutive MMD patients who were admitted to our hospital between 2009 and 2015 were reviewed. Demographics, clinical, radiographic data were analyzed to develop artificial neural network (ANN), support vector machine (SVM), and random forest models. Results: We extracted 33 parameters, including 11 demographic and 22 radiographic features as input for model development. Of all compared classification results, ANN achieved the highest overall accuracy of 75.7% (95% CI, 68.6%-82.8%), followed by SVM with 69.2% (95% CI, 56.9%-81.5%) and random forest with 70.0% (95% CI, 57.0%-83.0%). Conclusions: The proposed ANN framework can be a potential effective tool to predict the possibility of hemorrhage among adult MMD patients based on clinical information and radiographic features.

cs.LG↗

Graph Neural Networks Intersect Probabilistic Graphical Models: A Survey

Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model real-world scenarios in compact graphical representations of distributions of variables. Graph Neural Networks (GNNs) are new inference methods developed in recent years and are attracting growing attention due to their effectiveness and flexibility in solving inference and learning problems over graph-structured data. These two powerful approaches have different advantages in capturing relations from observations and how they conduct message passing, and they can benefit each other in various tasks. In this survey, we broadly study the intersection of GNNs and PGMs. Specifically, we first discuss how GNNs can benefit from learning structured representations in PGMs, generate explainable predictions by PGMs, and how PGMs can infer object relationships. Then we discuss how GNNs are implemented in PGMs for more efficient inference and structure learning. In the end, we summarize the benchmark datasets used in recent studies and discuss promising future directions.

cs.AI↗