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On optimal boundary control of ericksen-leslie system in dimension two

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arXiv 2018年

作者： Qiao, L.I.U. Wang, Changyou Zhang, Xiaotao Zhou, Jianfeng Key Laboratory of High Performance Computing and Stochastic Information Processing College of Mathematics & Statistics Hunan Normal Univ. Changsha Hunan410081 China Department of Mathematics Purdue Univ. West LafayetteIN47907 United States School of Mathematical Sciences Fudan Univ. Shanghai200433 China School of Mathematical Sciences Xiamen Univ. Xiamen Fujian361005 China

In this paper, we consider the boundary value problem of a simplified Ericksen-Leslie system in dimension two with non-slip boundary condition for the velocity field u and time-dependent boundary condition for the director field d of unit length. For such a system, we first establish the existence of a global weak solution that is smooth away from finitely many singular times, then establish the existence of a unique global strong solution that is smooth for t > 0 under the assumption that the image of boundary data is contained in the hemisphere S2+. Finally, we apply these theorems to the problem of optimal boundary control of the simplified Ericksen-Leslie system and show both the existence and a necessary condition of an optimal boundary *** Codes 35B65, 35Q35 Copyright © 2018, The Authors. All rights reserved.

关键词： Nematic liquid crystals

Towards good practices on building effective CNN baseline model for person re-identification

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arXiv 2018年

作者： XIONG, FU XIAO, YANG CAO, ZHIGUO GONG, KAICHENG FANG, ZHIWEN ZHOU, JOEY TIANYI National Key Laboratory of Science and Technology on Multi-Spectral Information Processing School of Automation Huazhong University of Science and Technology School of Energy and Mechanical-electronic Engineering Hunan University of Humanities Science and Technology Loudi China Institute of High Performance Computing A STAR Singapore

Person re-identification is indeed a challenging visual recognition task due to the critical issues of human pose variation, human body occlusion, camera view variation, etc. To address this, most of the state-of-theart approaches are proposed based on deep convolutional neural network (CNN), being leveraged by its strong feature learning power and classification boundary fitting capacity. Although the vital role towards person re-identification, how to build effective CNN baseline model has not been well studied yet. To answer this open question, we propose 3 good practices in this paper from the perspectives of adjusting CNN architecture and training procedure. In particular, they are adding batch normalization after the global pooling layer, executing identity categorization directly using only one fully-connected, and using Adam as optimizer. The extensive experiments on 3 widely-used benchmark datasets demonstrate that, our propositions essentially facilitate the CNN baseline model to achieve the state-of-the-art performance without any other highlevel domain knowledge or low-level technical trick. Copyright © 2018, The Authors. All rights reserved.

关键词： Domain Knowledge

Action recognition for depth video using multi-view dynamic images

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arXiv 2018年

作者： Xiao, Yang Chen, Jun Wang, Yancheng Cao, Zhiguo Zhou, Joey Tianyi Bai, Xiang National Key Laboratory of Science and Technology on Multi-spectral Information Processing School of Automation Huazhong University of Science and Technology Wuhan Hubei430074 China Institute of High Performance Computing A*STAR Singapore School of Electronic Information and Communications Huazhong University of Science and Technology Wuhan Hubei430074 China

Dynamic imaging is a recently proposed action description paradigm for simultaneously capturing motion and temporal evolution information, particularly in the context of deep convolutional neural networks (CNNs). Compared with optical flow for motion characterization, dynamic imaging exhibits superior efficiency and compactness. Inspired by the success of dynamic imaging in RGB video, this study extends it to the depth domain. To better exploit three-dimensional (3D) characteristics, multi-view dynamic images are proposed. In particular, the raw depth video is densely projected with respect to different virtual imaging viewpoints by rotating the virtual camera within the 3D space. Subsequently, dynamic images are extracted from the obtained multi-view depth videos and multi-view dynamic images are thus constructed from these images. Accordingly, more view-tolerant visual cues can be involved. A novel CNN model is then proposed to perform feature learning on multi-view dynamic images. Particularly, the dynamic images from different views share the same convolutional layers but correspond to different fully connected layers. This is aimed at enhancing the tuning effectiveness on shallow convolutional layers by alleviating the gradient vanishing problem. Moreover, as the spatial occurrence variation of the actions may impair the CNN, an action proposal approach is also put forth. In experiments, the proposed approach can achieve state-of-the-art performance on three challenging datasets. Copyright © 2018, The Authors. All rights reserved.

关键词： Convolution

Quasi-periodic solutions for differential equations with an elliptic-type degenerate equilibrium point under small perturbations

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arXiv 2017年

作者： Li, Xuemei Shang, Zaijiu Key Laboratory of High Performance Computing and Stochastic Information Processing Department of Mathematics Hunan Normal University Changsha Hunan410081 Institute of Mathematics Amss Chinese Academy of Science Beijing100080 China

This work focuses on the existence of quasi-periodic solutions for ordinary and delay differential equations (ODEs and DDEs for short) with an elliptic-type degenerate equilibrium point under quasi-periodic perturbations. We prove that under appropriate hypotheses there exist quasi-periodic solutions for perturbed ODEs and DDEs near the equilibrium point for most parameter values, then apply these results to the delayed van der Pol's oscillator with zero-Hopf singularity. Copyright © 2017, The Authors. All rights reserved.

关键词： Ordinary differential equations

An application of nakayama functor in representation stability theory

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arXiv 2017年

作者： Gan, Wee Liang Li, Liping Xi, Changchang Department of Mathematics University of California RiversideCA92521 United States Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education College of Mathematics and Computer Science Hunan Normal University Changsha Hunan410081 China School of Mathematical Sciences Capital Normal University Beijing100048 China

Using the Nakayama functor, we construct an equivalence from a Serre quotient category of a category of finitely generated modules to a category of finite-dimensional modules. We then apply this result to the categories FIG and VIq, and answer positively an open question of Nagpal on representation stability theory. Copyright © 2017, The Authors. All rights reserved.

关键词： Algebra

Cross-view Asymmetric Metric Learning for Unsupervised Person Re-identification

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arXiv 2017年

作者： Yu, Hong-Xing Wu, Ancong Zheng, Wei-Shi School of Data and Computer Science Sun Yat-sen University China School of Electronics and Information Technology Sun Yat-sen University China Key Laboratory of Machine Intelligence and Advanced Computing Ministry of Education China Collaborative Innovation Center of High Performance Computing NUDT China Guangdong Key Laboratory of Big Data Analysis and Processing Guangzhou China

While metric learning is important for Person reidentification (RE-ID), a significant problem in visual surveillance for cross-view pedestrian matching, existing metric models for RE-ID are mostly based on supervised learning that requires quantities of labeled samples in all pairs of camera views for training. However, this limits their scalabilities to realistic applications, in which a large amount of data over multiple disjoint camera views is available but not labelled. To overcome the problem, we propose unsupervised asymmetric metric learning for unsupervised RE-ID. Our model aims to learn an asymmetric metric, i.e., specific projection for each view, based on asymmetric clustering on cross-view person images. Our model finds a shared space where view-specific bias is alleviated and thus better matching performance can be achieved. Extensive experiments have been conducted on a baseline and five large-scale RE-ID datasets to demonstrate the effectiveness of the proposed model. Through the comparison, we show that our model works much more suitable for unsupervised RE-ID compared to classical unsupervised metric learning models. We also compare with existing unsupervised REID methods, and our model outperforms them with notable margins. Specifically, we report the results on large-scale unlabelled RE-ID dataset, which is important but unfortunately less concerned in literatures. Copyright © 2017, The Authors. All rights reserved.

关键词： Machine learning

Boundedness of parammetric Marcinkiewicz integrals on weighted Hardy spaces

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Applied Mathematics(A Journal of Chinese Universities) 2015年第3期30卷 253-262页

作者： SHI Xian-liang SUN Jie College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) Hunan Normal University

In this paper, several new results on the boundedness of parammetric Marcinkiewicz integrals on the weighted Hardy spaces and the weak weighted Hardy spaces are established.

关键词： parammetric Marcinkiewicz integral weight function weighted Hardy space weak weighted Hardy space

Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials

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Advances in Applied Mathematics and Mechanics 2015年第6期7卷 796-817页

作者： Jiangxing Wang Ziqing Xie Chuanmiao Chen Key Laboratory of High Performance Computing and Stochastic Information Processing College of Mathematics and Computer ScienceHunan Normal UniversityChangsha 410081China

An implicit discontinuous Galerkin method is introduced to solve the timedomain Maxwell’s equations in *** Maxwell’s equations in metamaterials are represented by integral-differential *** scheme is based on discontinuous Galerkin method in spatial domain and Crank-Nicolson method in temporal *** fully discrete numerical scheme is proved to be unconditionally *** polynomial of degree at most p is used for spatial approximation,our scheme is verified to converge at a rate of O(τ^(2)+h^(p)+1/2).Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

关键词： Maxwell’s equations metamaterials fully disctete DG method L2-stability L2-error estimate.

On-Line Scheduling for Jobs with Arbitrary Release Times on Parallel Related Uniform Machines

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Intelligent information Management 2016年第4期8卷 98-102页

作者： Xiayan Cheng Rongheng Li Yunxia Zhou Department of Mathematics Hunan First Normal University Changsha China Department of Mathematics Key Laboratory of High Performance Computing and Stochastic Information Processing Hunan Normal University Changsha China Department of Computer Hunan Normal University Changsha China

A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.

关键词： Online Scheduling Uniform Machine Competitive Ratio Approximation Algorithm