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ON THE CHARACTERIZATION, EXISTENCE AND UNIQUENESS OF STEADY SOLUTIONS TO THE HYDROSTATIC EULER EQUATIONS IN A NOZZLE

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arXiv 2023年

作者： Leung, Wang Shing Wong, Tak Kwong Xie, Chunjing Department of Mathematics Temple University 1805 N. Broad Street PhiladelphiaPA19122 United States Department of mathematics The University of Hong Kong Pokfulam Hong Kong School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing CMA-Shanghai Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

Incompressible Euler flows in narrow domains, in which the horizontal length scale is much larger than other scales, play an important role in applications, and their leading-order behavior can be described by the hydrostatic Euler equations. In this paper, we show that steady solutions of the hydrostatic Euler equations in an infinite strip strictly away from stagnation must be shear flows. Furthermore, we prove the existence, uniqueness, and asymptotic behavior of global steady solutions to the hydrostatic Euler equations in general nozzles. In terms of stream function formulation, the hydrostatic Euler equations can be written as a degenerate elliptic equation, for which the Liouville type theorem in a strip is a consequence of the analysis for the second order ordinary differential equation (ODE). The analysis on the associated ODE also helps determine the far field behavior of solutions in general nozzles, which plays an important role in guaranteeing the equivalence of stream function formulation. One of the key ingredients for the analysis on flows in a general nozzle is a new transformation, which combines a change of variable and an Euler-Lagrange transformation. With the aid of this new transformation, the solutions in the new coordinates enjoy explicit representations so that the regularity with respect to the horizontal variable can be gained in a clear way. Copyright © 2023, The Authors. All rights reserved.

关键词： Nozzles

When Adversarial Example Attacks Meet Vertical Federated Learning

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When Adversarial Example Attacks Meet Vertical Federated Lea...

Symposia and Workshops on Ubiquitous, Autonomic and Trusted computing, UIC-ATC

作者： Dan Meng Zhihui Fu Chao Kong Yue Qi Guitao Cao OPPO Research Institute Shenzhen China School of Computer and Information Anhui Polytechnic University Wuhu China Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai China MoE Engineering Research Center of SH/HW Co-design Technology and Application ECNU Shanghai China

Federated learning (FL) is proposed to enable efficient machine learning while protecting the privacy of user data. In non-federated scenarios, machine learning models are vulnerable to adversarial attacks. The attacker can construct elaborate adversarial examples, which can greatly reduce the performance of the victim model. It is worth exploring how FL models differ from traditional models in face of complex adversarial attacks. We are also curious about the robustness of different FL modeling methods against adversarial attacks, providing suggestions for selecting suitable FL models in practical applications. Consequently, we perform adversarial example attacks on vertical federated learning and design experiments to study how vertical federated models perform under adversarial example attacks. The simulation results show that federated models are more robust than non-federated models. Besides, in vertical federation learning, decision trees and XGBoost are much more robust than logistic regression and neural networks.

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Unifying Farkas lemma and S-lemma: New theory and applications in nonquadratic nonconvex optimization

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arXiv 2021年

作者： Yang, Meijia Xia, Yong Wang, Shu School of Mathematics and Physics University of Science and Technology Beijing Beijing100083 China State Key Laboratory of Software Development Environment LMIB of the Ministry of Education School of Mathematics and System Sciences Beihang University Beijing100191 China Institute of Computational Mathematics and Scientific/Engineering Computing State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

We unify nonlinear Farkas lemma and S-lemma to a generalized alternative theorem for nonlinear nonconvex system. It provides fruitful applications in globally solving nonconvex non-quadratic optimization problems via ... 详细信息

关键词： Quadratic programming

Global Stability and Optimal Control of Epidemics in Heterogeneously Structured Populations Exhibiting Adaptive Behaviour

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SSRN

SSRN 2023年

作者： Liu, Lixiang Chen, Shanshan Small, Michael Moore, Jack Murdoch Shang, Keke Department of Computer Science School of Electronic and Electrical Engineering Shanghai University of Engineering Science Shanghai201620 China Complex Systems Group Department of Mathematics and Statistics The University of Western Australia Perth6009 Australia Mineral Resources Commonwealth Scientific and Industrial Research Organisation Kensington6151 Australia MOE Key Laboratory of Advanced Micro-Structured Materials School of Physics Science and Engineering Tongji University Shanghai200092 China Computational Communication Collaboratory Nanjing University Nanjing210093 China

During the outbreak of infectious diseases, individual always make some adaptive response to avoid infected the diseases. In this paper, we introduce SIRS model on scale-free networks that take into account behavioral memory and time delay to depict individuals’ adaptive feedback, which is better characterize the actual spread of epidemics. We address uniform persistence and find that the model has the sharp threshold property, that is, for the basic reproduction number less than one, the disease-free equilibrium is globally asymptotically stable, while for the basic reproduction number is above one, the endemic equilibrium is globally stable. We further analyze the effects of two control strategies (the vaccination of susceptible people and treatment of infected people) on epidemic dynamics by optimal control strategy. The existence and uniqueness of the optimal control strategy are obtained. Finally, we perform some stochastic network simulations that yield quantitative agreement with the deterministic mean-field approach. The final results show that the effect of time delay does not change the basic reproduction number, but it plays an important role in the process of disease transmission. The behavioral memory is able to affect the basic reproduction number, and it has important and positive implications for disease transmission and control. The work of this paper can provide a theoretical basis and reference for the prediction and prevention of infectious diseases. © 2023, The Authors. All rights reserved.

关键词： Diseases

Splitting Method for Stochastic Navier-Stokes Equations

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arXiv 2025年

作者： Zhu, Jie Zhu, Yujun Ming, Ju Gunzburger, Max D. School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China Department of Scientific Computing Florida State University TallahasseeFL32304 United States

This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS component and a stochastic equation. We rigorously analyze the proposed splitting method from the perspectives of equivalence, stability, existence and uniqueness of the solution. We also propose a modified splitting scheme, which simplified the stochastic equation by omitting its nonlinear terms. A detailed analysis of the solution properties for this modified approach is provided. Additionally, we discuss the statistical errors with both the original splitting format and the modified scheme. Our theoretical and numerical studies demonstrate that the equivalent splitting scheme exhibits significantly enhanced stability compared to the original stochastic NS equations, enabling more effective handling of nonlinear characteristics. Several numerical experiments were performed to compare the statistical errors of the splitting method and the modified splitting method. Notably, the deterministic NS equation in the splitting method does not require repeated solving, and the stochastic equation in the modified scheme is free of nonlinear terms. These features make the modified splitting method particularly advantageous for large-scale computations, as it significantly improves computational efficiency without compromising accuracy. Copyright © 2025, The Authors. All rights reserved.

关键词： Navier Stokes equations

Spiking Neural Networks for Temporal Processing: Status Quo and Future Prospects

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arXiv 2025年

作者： Ma, Chenxiang Chen, Xinyi Li, Yanchen Yang, Qu Wu, Yujie Li, Guoqi Pan, Gang Tang, Huajin Tan, Kay Chen Wu, Jibin Department of Data Science and Artificial Intelligence The Hong Kong Polytechnic University Hong Kong Department of Computing The Hong Kong Polytechnic University Hong Kong Department of Electrical and Computer Engineering National University of Singapore 119077 Singapore Institute of Automation Chinese Academy of Sciences Beijing100045 China State Key Laboratory of Brain-Machine Intelligence College of Computer Science and Technology MOE Frontier Science Center for Brain Science and Brain-Machine Integration Zhejiang University Hangzhou310027 China

Temporal processing is fundamental for both biological and artificial intelligence systems, as it enables the comprehension of dynamic environments and facilitates timely responses. Spiking Neural Networks (SNNs) excel in handling such data with high efficiency, owing to their rich neuronal dynamics and sparse activity patterns. Given the recent surge in the development of SNNs, there is an urgent need for a comprehensive evaluation of their temporal processing capabilities. In this paper, we first conduct an in-depth assessment of commonly used neuromorphic benchmarks, revealing critical limitations in their ability to evaluate the temporal processing capabilities of SNNs. To bridge this gap, we further introduce a benchmark suite consisting of three temporal processing tasks characterized by rich temporal dynamics across multiple timescales. Utilizing this benchmark suite, we perform a thorough evaluation of recently introduced SNN approaches to elucidate the current status of SNNs in temporal processing. Our findings indicate significant advancements in recently developed spiking neuron models and neural architectures regarding their temporal processing capabilities, while also highlighting a performance gap in handling long-range dependencies when compared to state-of-the-art non-spiking models. Finally, we discuss the key challenges and outline potential avenues for future research. Copyright © 2025, The Authors. All rights reserved.

关键词： Spatio-temporal data

Two-dimensional ferromagnetic superlattices

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National Science Review 2020年第4期7卷 745-754页

作者： Shanshan Liu Ke Yang Wenqing Liu Enze Zhang Zihan Li Xiaoqian Zhang Zhiming Liao Wen Zhang Jiabao Sun Yunkun Yang Han Gao Ce Huang Linfeng Ai Ping Kwan Johnny Wong ANDrew Thye Shen Wee Alpha T.N'Diaye Simon A.Morton Xufeng Kou Jin Zou Yongbing Xu Hua Wu Faxian Xiu State Key Laboratory of Surface Physics and Department of Physics Fudan University Institute for Nanoelectronic Devices and Quantum Computing Fudan University Laboratory for Computational Physical Sciences (MOE) Fudan University Department of Electronic Engineering Royal Holloway University of London School of Electronic Science and Engineering Nanjing University Materials Engineering The University of Queensland Department of Physics National University of Singapore Centre for Advanced 2D Materials and Graphene Research Centre National University of Singapore Lawrence Berkeley National Laboratory School of Information Science and Technology Shanghai Tech University Centre for Microscopy and Microanalysis The University of Queensland Collaborative Innovation Center of Advanced Microstructures

Mechanically exfoliated two-dimensional ferromagnetic materials(2 D FMs) possess long-range ferromagnetic order and topologically nontrivial skyrmions in few layers. However, because of the dimensionality effect, such few-layer systems usually exhibit much lower Curie temperature(TC) compared to their bulk counterparts. It is therefore of great interest to explore effective approaches to enhance their TC, particularly in wafer-scale for practical applications. Here, we report an interfacial proximity-induced high-TC2 D FM FeGe Te(FGT) via A-type antiferromagnetic material Cr Sb(CS) which strongly couples to FGT. A superlattice structure of(FGT/CS)n, where n stands for the period of FGT/CS heterostructure, has been successfully produced with sharp interfaces by molecular-beam epitaxy on 2-inch wafers. By performing elemental specific X-ray magnetic circular dichroism(XMCD) measurements, we have unequivocally discovered that TCof 4-layer FeGeTecan be significantly enhanced from 140 K to230 K because of the interfacial ferromagnetic coupling. Meanwhile, an inverse proximity effect occurs in the FGT/CS interface, driving the interfacial antiferromagnetic Cr Sb into a ferrimagnetic state as evidenced by double-switching behavior in hysteresis loops and the XMCD spectra. Density functional theory calculations show that the Fe-Te/Cr-Sb interface is strongly FM coupled and doping of the spin-polarized electrons by the interfacial Cr layer gives rise to the TCenhancement of the FeGeTefilms, in accordance with our XMCD measurements. Strikingly, by introducing rich Fe in a 4-layer FGT/CS superlattice, TCcan be further enhanced to near room temperature. Our results provide a feasible approach for enhancing the magnetic order of few-layer 2 D FMs in wafer-scale and render opportunities for realizing realistic ultra-thin spintronic devices.

关键词： 2D ferromagnetic material room temperature 2-inch Fe3GeTe2 film wafers proximity effect (Fe3GeTe2/CrSb)nsuperlattice

RTStitch: Real-time Stitching of High-resolution PCB Images *

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RTStitch: Real-time Stitching of High-resolution PCB Images ...

IEEE International Conference on Systems, Man and Cybernetics

作者： Wenbin Yang Xianzhong Liu Shanghai Key Laboratory of Trustworthy Computing School of Software Engineering East China Normal University Shanghai China Software/Hardware Co-design Engineering Research Center MoE School of Software Engineering East China Normal University Shanghai China

ISBN: (纸本)9781665442084

In the Automatic Optical Inspection (AOI) system, it is necessary to stitch high-resolution Printed Circuit Board (PCB) partial images in real time to obtain a panoramic image. However, the proportion of the overlapping area of these images is usually relatively small, and there are few feature points in the overlap area of some images. Traditional image stitching algorithms are not effective in processing such images, and it is difficult to meet the requirements of real-time stitching. Therefore, we propose RTStitch, a method specially used for real-time stitching of high-resolution PCB images in AOI systems. We divide the images into two categories. An image with a large change in the pixel gray value of the first column in the overlapping area is the first type of image, otherwise, it is the second type of image. We use different methods to obtain a relatively accurate maximum overlap position for these two types of images. Besides, we propose a new method of selecting template images, then perform template matching to obtain horizontal and vertical errors. We focus on the areas where the gray level changes drastically in the overlapping area to improve the accuracy of the registration. Our experimental results show that for the first type of image, RTStitch improves the registration accuracy by more than 2%, while for the second type of image, the registration accuracy is improved by more than 10%. And more than doubled the stitching speed. Moreover, RTStitch can meet the high-precision and real-time requirements of the AOI system.

关键词： Splicing Conferences Printed circuits Cameras Real-time systems Automatic optical inspection Image stitching

Fate and Bioavailability of Fluoroquinolone Antibiotics in the Phytoremediation Process Assessed by Plants and Dgt

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SSRN

SSRN 2023年

作者： Chen, Jun Liu, Shuang-Shuang Wu, Qiong Huang, Wei-Jie Yang, Fang Wang, Yi-Jie He, Lu-Xi Ying, Guang-Guo Chen, Wen-Long Chen, Chang-Er Guangdong Provincial Engineering Technology Research Center for Life and Health of River and Lake Key Laboratory of Water Security Guarantee in Guangdong-Hong Kong-Marco Greater Bay Area of Ministry of Water Resources Key Laboratory of the Pearl River Estuary Regulation and Protection of Ministry of Water Resources Pearl River Water Resource Research Institute Guangzhou510611 China Guangdong Provincial Key Laboratory of Fishery Ecology and Environment Scientific Observing and Experimental Station of South China Sea Fishery Resource and Environment Ministry of Agriculture and Rural Affairs South China Sea Fisheries Research Institute Chinese Academy of Fishery Sciences Guangzhou510300 China Environmental Research Institute School of Environment Guangdong Provincial Key Laboratory of Chemical Pollution and Environmental Safety MOE Key Laboratory of Environmental Theoretical Chemistry South China Normal University Guangzhou510006 China

Phytoremediation is considered an effective technology for the remediation of antibiotic-contaminated waters, yet the underlying mechanism remains poorly understood. Hence, the possibility and means of phytoremediation of fluoroquinolone antibiotics (FQs) by different wetland plants were investigated in this study. The phytoremediation rates of ΣFQs were 46- 69%, and the rhizosphere microorganism degradation (accounting for 90 - 93%) dominated the FQs removal compared with plant uptake and hydrolysis. The dissipation of FQs in the hydroponic system followed the first-order kinetic model. The uptake and rhizosphere biodegradation of FQs for Cyperus papyrus are significantly higher than other plants, indicating that plant species is a critical factor affecting the phytoremediation efficiency. The distribution of FQs in plant tissues followed the root > stem > leaf sequence, suggesting that FQs are more concentrated in roots than in aboveground tissues. Negative correlations between DGT-derived and root concentrations imply that these wetland plants take up the FQs mainly via active transport mechanism (requiring some vectors maybe via the exudates), while the process of root-to-stem transfer and upward transport belongs to passive transport, which mainly depends on transpiration. These results facilitated our understanding of the phytoremediation processes and better its application in the future. © 2023, The Authors. All rights reserved.

关键词： Biodegradation