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POINTWISE ESTIMATES FOR THE FUNDAMENTAL SOLUTIONS OF HIGHER ORDER SCHRÖDINGER EQUATIONS IN ODD DIMENSIONS I: LOW DIMENSIONAL CASE

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arXiv 2024年

In this paper, for any odd n and any integer m ≥ 1 with n tu(x, t) = ((−∆)m + V(x))u(x, t), t ∈ , x ∈ n, where V is a real-valued potential with certain decay. Let Pac(H) denote the projection onto the absolutely continuous spectrum space of H = (−∆)m + V, and assume that H has no positive embedded eigenvalue. Our main result says that e−itHPac(H) has integral kernel K(t, x, y) satisfying (Equation presented), where the constants C, h > 0, and h can be specified by m, n and the zero energy resonances of H. A similar result for smoothing operators like (Equation presented) is also given. One of the main novelties lies in a new and unified approach to obtain the asymptotic expansions of perturbed resolvents under various types of zero energy resonances. © 2024, CC0.

关键词： Schrodinger equation

A third-order discrete unified gas kinetic scheme for continuum and rarefied flows: Low-speed isothermal case

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arXiv 2017年

作者： Wu, Chen Shu, Chang Shi, Baochang Chen, Zhen State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore119260 Singapore School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

An efficient third-order discrete unified gas kinetic scheme (DUGKS) with efficiency is presented in this work for simulating continuum and rarefied flows. By employing two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third-order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation LBE based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second-order (or lower-order) of accuracy in time splitting scheme as in the conventional high-order Runge-Kutta (RK) based kinetic methods, the present method solves the original BE, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows. Copyright © 2017, The Authors. All rights reserved.

关键词： Boltzmann equation

Spiking Neural P Systems for Arithmetic Operations

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Spiking Neural P Systems for Arithmetic Operations

International Conference on Bio-Inspired computing: Theories and Applications, BICTA

作者： Xiangxiang Zeng Tao Song Linqiang Pan Xingyi Zhang Key Laboratory on Image Processing and Intelligent Control Department of Control Science and Engineering Huazhong University of Science and Technology Wuhan Hubei China Key Laboratory of Intelligent Computing and Signal Processing School of Computer Science and Technology Anhui University Hefei Anhui China

Recently, Gutierrez-Naranjo and Leporati considered performing basic arithmetic operations on a new class of bioinspired computing devices -- spiking neural P systems (for short, SN P systems). However, the binary encoding mechanism used in their research looks like the encoding approach in electronic circuits, instead of the style of spiking neurons (in usual SN P systems, information are encoded as the time interval between spikes). In this work, three SN P systems are constructed as adder, subtracter and multiplier, respectively. In these devices, a number is inputted to the system as the interval of time elapsed between two spikes received by input neuron, the result of a computation is the time between the moments when the output neuron spikes.

关键词： Neurons Tin Encoding Adders Educational institutions Generators Computational modeling

Adversarial Network Pruning by Filter Robustness Estimation

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Adversarial Network Pruning by Filter Robustness Estimation

International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Xinlu Zhuang Yunjie Ge Baolin Zheng Qian Wang Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education School of Cyber Science and Engineering Wuhan University Hubei China Alibaba Group Beijing China

Network pruning has been extensively studied in model compression to reduce neural networks’ memory, latency, and computation cost. However, the pruned networks still suffer from the threat posed by adversarial examples, limiting the broader application of the pruned networks in safety-critical applications. Previous studies maintain the robustness of the pruned networks by combining adversarial training and network pruning but ignore preserving the robustness at a high sparsity ratio in structured pruning. To address such a problem, we propose an effective filter importance criterion, Filter Robustness Estimation (FRE), to evaluate the importance of filters by estimating their contribution to the adversarial training loss. Empirical results show that our FRE-based Robustness-aware Filter Pruning (FRFP) outperforms the state-of-the-art methods by 12.19%∼37.01% of empirical robust accuracy on the CIFAR10 dataset with the VGG16 network at an extreme pruning ratio of 90%.

关键词： Training Limiting Costs Computational modeling Neural networks Estimation Signal processing algorithms

An Unconditionally Energy-Stable and Orthonormality-Preserving Iterative Scheme for the Kohn-Sham Gradient Flow Based Model

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arXiv 2023年

作者： Wang, Xiuping Chen, Huangxin Kou, Jisheng Sun, Shuyu Saudi Arabia School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and HighPerformance Scientific Computing Xiamen University Fujian Xiamen China Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province Shaoxing University Shaoxing China School of Mathematics and Statistics Hubei Engineering University Hubei Xiaogan China

We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in time but still continuous in space. The componentwise splitting iterative scheme changes one wave function at a time, similar to the Gauss-Seidel iteration for solving a linear equation system. At the time step n, the orthogonality of the wave function being updated to other wave functions is preserved by projecting the gradient of the Kohn-Sham energy onto the subspace orthogonal to all other wave functions known at the current time, while the normalization of this wave function is preserved by projecting the gradient of the Kohn-Sham energy onto the subspace orthogonal to this wave function at tn+1/2. The unconditional energy stability is nontrivial, and it comes from a subtle treatment of the two-electron integral as well as a consistent treatment of the two projections. Rigorous mathematical derivations are presented to show our proposed scheme indeed satisfies the desired properties. We then study the fully-discretized scheme, where the space is further approximated by a conforming finite element subspace. For the fully-discretized scheme, not only the preservation of orthogonality and normalization (together we called orthonormalization) can be quickly shown using the same idea as for the semi-discretized scheme, but also the highlight property of the scheme, i.e., the unconditional energy stability can be rigorously proven. The scheme allows us to use large time step sizes and deal with small systems involving only a single wave function during each iteration step. Several numerical experiments are performed to verify the theoretical analysis, where the number of iterations is indeed greatly reduced as compared to similar examples solved by the Kohn-Sham gradient flow based model in the literature. Copyright © 2023, The Aut

关键词： Wave functions

Intelligent and cooperative manufacturing planning

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International Journal of Manufacturing Research 2010年第1期5卷 39-57页

作者： Li, Wei Dong Gao, Liang Faculty of Engineering and Computing Coventry University Coventry United Kingdom State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and Engineering Huazhong University of Science and Technology Wuhan Hubei China Department of Industrial and Manufacturing System Engineering Huazhong University of Science and Technology China

In this research, several intelligent strategies have been developed to build up cooperative Process Planning and Scheduling (CPPS). Three game theory-based strategies have been introduced to analyse the cooperative integration of the two processes in a systematic way. To address the multiple constraints in the CPPS problem, a fuzzy logic-based Analytical Hierarchical Process (AHP) technique has been applied. In the meantime, modern heuristic algorithms have been developed and applied to the CPPS problem to identify optimal or near-optimal solutions from the vast search space efficiently. Experiments have been conducted and results show the objectives of the research have been achieved. Copyright © 2010 Inderscience Enterprises Ltd.

关键词： Heuristic algorithms

Image saliency and co-saliency detection by low-rank multiscale fusion

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Image saliency and co-saliency detection by low-rank multisc...

作者： Huang, Rui Feng, Wei Sun, Jizhou Zou, Yaobin College of Computer Science and Technology Civil Aviation University of China Tianjin300300 China Hubei Key Laboratory of Intelligent Vision Based Monitoring for Hydroelectric Engineering China Three Gorges University Yichang443003 China College of Intelligence and Computing School of Computer Science and Technology Tianjin University Tianjin300350 China Key Research Center for Surface Monitoring and Analysis of Cultural Relics State Administration of Cultural Heritage China

Saliency and co-saliency detection aim to distinguish conspicuous foreground objects from single and multiple images, thus are essential in many multimedia and vision applications. To achieve balanced efficiency and accuracy, most recent successful saliency detectors are based on superpixels. However, saliency detection with single-scale superpixel segmentation may fail in capturing intrinsic salient objects of complex natural scenes with small-scale high-contrast backgrounds. To tackle this problem, we present a simple strategy using multiscale superpixels to jointly detect salient object via low-rank optimisation. Specifically, we first build a multiscale superpixel pyramid and derive the corresponding saliency map by multimodal saliency features and priors at each single scale. Then, we use joint low-rank analysis of multiscale saliency maps to obtain a more reliable and adaptively-fused saliency map, which properly takes all scales saliency into account. We further propose a GMM generative co-saliency prior to enable the above approach to detect co-salient objects from multiple images. Extensive experiments on benchmark datasets validate the effectiveness and superiority of the proposed saliency and co-saliency detector over state-of-the-arts. Copyright © 2019 Inderscience Enterprises Ltd.

关键词： Object detection

Cloud-based remote control framework for unmanned surface vehicles ⁎

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IFAC-PapersOnLine 2020年第2期53卷 14564-14569页

作者： Zhao Wang Shaolong Yang Xianbo Xiang Antonio Vasilijević Nikola Mišković Ðula Nađ School of Naval Architecture and Ocean Engineering Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics (HUST) Wuhan 430074 PR China Laboratory for Underwater Systems and Technologies Faculty of Electrical Engineering and Computing University of Zagreb Zagreb Croatia

This paper proposes a cloud-based mission control framework for a fleet of unmanned vehicles. The framework enables easy remote access to fleet operations regardless of operator location. By leveraging cloud-based technologies the framework accomplishes scalable monitoring, remote control, data acquisition and sharing. While the front-end is applicable across mobile robotic systems, the back-end presented in this paper provides integration with the Robot Operating System (ROS); thus, enabling integration of various marine robotic agents based on the same robot framework. The proposed framework operation is demonstrated on the H2OmniX unmanned surface vehicles during trials in Biograd na Moru, Croatia.

关键词： remote control distributed control cloud-based control Robot Operating System

Further Investigations on Nonlinear Complexity of Periodic Binary Sequences

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arXiv 2024年

作者： Yuan, Qin Li, Chunlei Zeng, Xiangyong Helleseth, Tor He, Debiao Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University Hubei Wuhan430062 China Department of Informatics University of Bergen BergenN-5020 Norway Key Laboratory of Aerospace Information Security and Trusted Computing Ministry of Education School of Cyber Science and Engineering Wuhan University Hubei Wuhan430072 China

Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit relation between nonlinear complexities of finite-length binary sequences and their corresponding periodic sequences. Based on the relation, we propose two algorithms that can generate all periodic binary sequences with any prescribed nonlinear complexity. © 2024, CC BY.

关键词： Binary sequences