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Low Rank and Structured Modeling of High-Dimensional Vector Autoregressions

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2019年第5期67卷 1207-1222页

作者： Basu, Sumanta Li, Xianqi Michailidis, George Cornell Univ Dept Stat Sci Ithaca NY 14850 USA Harvard Med Sch Massachusetts Gen Hosp Athinoula A Martinos Ctr Biomed Imaging Boston MA 02115 USA Univ Florida Dept Stat Gainesville FL 32611 USA Univ Florida Dept Comp & Informat Sci Gainesville FL 32611 USA Univ Florida Dept Engn Gainesville FL 32611 USA Univ Florida Informat Inst Gainesville FL 32611 USA

Network modeling of high-dimensional time series data is a key learning task due to its widespread use in a number of application areas, including macroeconomics, finance, and neuroscience. While the problem of sparse modeling based on vector autoregressive models (VAR) has been investigated in depth in the literature, more complex network structures that involve low rank and group sparse components have received considerably less attention, despite their presence in data. Failure to account for low-rank structures results in spurious connectivity among the observed time series, which may lead practitioners to draw incorrect conclusions about pertinent scientific or policy questions. In order to accurately estimate a network of Granger causal interactions after accounting for latent effects, we introduce a novel approach for estimating low-rank and structured sparse high-dimensional VAR models. We introduce a regularized framework involving a combination of nuclear norm and lasso (or group lasso) penalties. Subsequently, we establish nonasymptotic probabilistic upper bounds on the estimation error rates of the low-rank and the structured sparse components. We also introduce a fast estimation algorithm and finally demonstrate the performance of theproposed modeling framework over standard sparse VAR estimates through numerical experiments on synthetic and real data.

关键词： Lasso group lasso nuclear norm low rank vector autoregression probabilistic bounds identifiability fast algorithm

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fast inter-prediction algorithm based on motion vector information for high efficiency video coding

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EURASIP JOURNAL ON IMAGE AND VIDEO PROCESSING 2018年第1期2018卷 1页

作者： Lin, Kao-Min Lin, Jie-Ru Chen, Mei-Juan Yeh, Chia-Hung Lee, Cheng-An Natl Dong Hwa Univ Dept Elect Engn Hualien Taiwan Natl Taiwan Normal Univ Dept Elect Engn Taipei Taiwan Natl Sun Yat Sen Univ Dept Elect Engn Kaohsiung Taiwan

High Efficiency Video Coding (HEVC/H.265) is the latest international video coding standard, which achieves better compression ratio and supports higher resolution than Advanced Video Coding (H.264/AVC). However, HEVC/H.265 increases the computational burden. To reduce the coding complexity of the HEVC encoder, this paper proposes a fast inter-prediction algorithm to speed up coding time. We collect the average rate-distortion costs (RD-cost) of Skip modes and Merge modes to accelerate prediction unit (PU) mode decisions. In addition, we also acquire and analyze the motion vector range from Merge modes and Inter 2N x 2N modes to decide whether to execute Merge and advanced motion vector prediction (AMVP) of other PUs. The experimental results show that the proposed algorithm provides 48.54% time saving on average in random-access configuration and maintains good rate-distortion performance and video quality at the same time. The proposed algorithm also outperforms previous works.

关键词： High efficiency video coding fast algorithm Motion vector range Merge mode Advanced motion vector prediction (AMVP) Inter-prediction

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The Linear Noise Approximation for Spatially Dependent Biochemical Networks

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BULLETIN OF MATHEMATICAL BIOLOGY 2019年第8期81卷 2873-2901页

作者： Lotstedt, Per Uppsala Univ Dept Informat Technol Div Comp Sci SE-75105 Uppsala Sweden

An algorithm for computing the linear noise approximation (LNA) of the reaction-diffusion master equation (RDME) is developed and tested. The RDME is often used as a model for biochemical reaction networks. The LNA is derived for a general discretization of the spatial domain of the problem. If M is the number of chemical species in the network and N is the number of nodes in the discretization in space, then the computational work to determine approximations of the mean and the covariances of the probability distributions is proportional to M2N2 in a straightforward implementation. In our LNA algorithm, the work is proportional to M2N. Since N usually is larger than M, this is a significant reduction. The accuracy of the approximation in the algorithm is estimated analytically and evaluated in numerical experiments.

关键词： Linear noise approximation Spatially dependent fast algorithm

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An H2N2 Interpolation for Caputo Derivative with Order in (1,2) and Its Application to Time-Fractional Wave Equations in More Than One Space Dimension

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JOURNAL OF SCIENTIFIC COMPUTING 2020年第2期83卷 38-38页

作者： Shen, Jinye Li, Changpin Sun, Zhi-zhong Southeast Univ Sch Math Nanjing 210096 Peoples R China Shanghai Univ Dept Math Shanghai 200444 Peoples R China

In this paper, a new derived method is developed for a known numerical differential formula of the Caputo fractional derivative of order gamma is an element of(1,2) (Li and Zeng in Numerical methods for fractional calculus. Chapman & Hall/CRC numerical analysis and scientific computing, CRC Press, Boca Raton, 2015) by means of the quadratic interpolation polynomials, and a concise expression of the truncation error is given. This new method will be called as the H2N2 method because of the application of the quadratic Hermite and Newton interpolation polynomials. A finite difference scheme with a second order accuracy in space and a (3-gamma)-th order accuracy in time based on the H2N2 method is constructed for the initial boundary value problem of time-fractional wave equations. The stability and convergence of the difference scheme are proved. Furthermore, in order to increase computational efficiency, using the sum-of-exponentials to approximate the kernel t(1-gamma), a fast difference scheme is presented. The problem with weak regularity at the initial time is also discussed with the help of the graded meshes. At each time level, the difference scheme is solved with a fast Poisson solver. Numerical results show the effectiveness of the two difference schemes and confirm our theoretical analysis.

关键词： Fractional wave equation Caputo derivative fast algorithm Difference scheme fast Poisson solver Convergence

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Fokker-Planck equation driven by asymmetric Levy motion

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2019年第2期45卷 787-811页

作者： Wang, Xiao Shang, Wenpeng Li, Xiaofan Duan, Jinqiao Huang, Yanghong Henan Univ Sch Math & Stat Kaifeng 475004 Peoples R China IIT Dept Appl Math Chicago IL 60616 USA Univ Manchester Sch Math Manchester M13 9PL Lancs England

Non-Gaussian Levy noises are present in many models for understanding underlining principles of physics, finance, biology, and more. In this work, we consider the Fokker-Planck equation (FPE) due to one-dimensional asymmetric Levy motion, which is a non-local partial differential equation. We present an accurate numerical quadrature for the singular integrals in the non-local FPE and develop a fast summation method to reduce the order of the complexity from O(J(2)) to O (J log J) in one time step, where J is the number of unknowns. We also provide conditions under which the numerical schemes satisfy maximum principle. Our numerical method is validated by comparing with exact solutions for special cases. We also discuss the properties of the probability density functions and the effects of various factors on the solutions, including the stability index, the skewness parameter, the drift term, the Gaussian and non-Gaussian noises, and the domain size.

关键词： Fokker-Planck equations Non-Gaussian noises Asymmetric alpha-stable Levy motion Non-local partial differential equation fast algorithm

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The fast Detection and Identification algorithm of Optical Fiber Intrusion Signals

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algorithmS 2018年第9期11卷 129-129页

作者： Sheng, Zhiyong Qu, Dandan Zhang, Yuan Yang, Dan North China Univ Technol Sch Elect & Informat Engn Beijing 100144 Peoples R China

With the continuous development of optical fiber sensing technology, the Optical Fiber Pre-Warning System (OFPS) has been widely used in various fields. The OFPS identifies the type of intrusion based on the detected vibration signal to monitor the surrounding environment. Aiming at the real-time requirements of OFPS, this paper presents a fast algorithm to accelerate the detection and recognition processing of optical fiber intrusion signals. The algorithm is implemented in an embedded system that is composed of a digital signal processor (DSP). The processing flow is divided into two parts. First, the dislocation processing method is adopted for the sum processing of original signals, which effectively improves the real-time performance. The filtered signals are divided into two parts and are parallel processed by two DSP boards to save time. Then, the data is input into the identification module for feature extraction and classification. Experiments show that the algorithm can effectively detect and identify the optical fiber intrusion signals. At the same time, it accelerates the processing speed and meets the real-time requirements of OFPS for detection and identification.

关键词： OFPS fast algorithm real-time performance feature extraction

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The algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment

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SENSORS 2020年第5期20卷 1353-1353页

作者： Pan, Chao Lv, Zhicheng Hua, Xia Li, Hongyan Hubei Univ Econ Sch Informat & Commun Engn Wuhan 430205 Peoples R China Wuhan Inst Technol Sch Elect & Informat Engn Wuhan 430205 Peoples R China

Normalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between the inner-product in cross-correlation and a first-order moment. Then digital normalized cross-correlation is transformed into a new calculation formula that mainly includes a first-order moment. Finally, by using a fast algorithm for first-order moment, we can compute the first-order moment in this new formula rapidly, and thus develop a fast algorithm for normalized cross-correlation, which contributes to that arbitrary-length digital normalized cross-correlation being performed by a simple procedure and less multiplications. Furthermore, as the algorithm for the first-order moment can be implemented by systolic structure, we design a systolic array for normalized cross-correlation with a seldom multiplier, in order for its fast hardware implementation. The proposed algorithm and systolic array are also improved for reducing their addition complexity. The comparisons with some algorithms and structures have shown the performance of the proposed method.

关键词： normalized cross-correlation fast algorithm first-order moment systolic array multiplication complexity

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STABILITY AND ERROR ANALYSIS FOR A SECOND-ORDER fast APPROXIMATION OF THE ONE-DIMENSIONAL SCHRODINGER EQUATION UNDER ABSORBING BOUNDARY CONDITIONS

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2018年第6期40卷 A4083-A4104页

作者： Li, Buyang Zhang, Jiwei Zheng, Chunxiong Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China Wuhan Univ Sch Math & Stat Hubei Key Lab Computat Sci Wuhan 430072 Hubei Peoples R China Tsinghua Univ Dept Math Sci Beijing Peoples R China

A second-order Crank-Nicolson finite difference method, integrating a fast approximation of an exact discrete absorbing boundary condition, is proposed for solving the one-dimensional Schrodinger equation in the whole space. The fast approximation is based on Gaussian quadrature approximation of the convolution coefficients in the discrete absorbing boundary conditions. It approximates the time convolution in the discrete absorbing boundary conditions by a system of O(log(2) N) ordinary differential equations at each time step, where N denotes the total number of time steps. Stability and an error estimate are presented for the numerical solutions given by the proposed fast algorithm. Numerical experiments are provided, which agree with the theoretical results and show the performance of the proposed numerical method.

关键词： Schrodinger equation absorbing boundary condition fast algorithm Gaussian quadrature stability error estimate

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IMPROVE THE HEVC algorithm COMPLEXITY BASED ON THE VISUAL PERCEPTION

IMPROVE THE HEVC ALGORITHM COMPLEXITY BASED ON THE VISUAL PE...

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IEEE International Conference on Consumer Electronics (ICCE)

作者： Lee, Pei-Jun Bui, Trong-An Yao, Sham-Ru Natl Chi Nan Univ Dept Elect Engn Nantou County Taiwan

ISBN: (纸本)9781538679104

The visual perception, we want to mention here is the three visual methods in image processing. It is Just Noticeable Difference (JND), Luminance Histogram Bin Variation and Edge Detection. Based on these three methods, we reduce CU (coding unit) splitting coding time. In addition, we use the previous edge detection data to reduce the candidate of PU mode. HEVC (high-efficiency video coding), as the latest video coding standard, can achieve up to 50%-bit rate saving while maintaining the same subjective quality compared to H.264/AVC. However, HEVC takes very high computational complexity. In this research, we will combine two methods of CU splitting and PU mode deciding to improve this problem. Experimental results show that the proposed algorithm can achieve about 36.25% encoder time saving on average with 0.123dB PSNR loss while result in negligible BD-Bitrate loss compared with HM 16.0 (HEVC test model).

关键词： CU splitting PU mode deciding visual perception fast algorithm video coding

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A fast acoustic emission beamforming localization method based on Hilbert curve

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2019年 133卷 106291-000页

作者： He, Tian Tai, Junfei Shan, Yingchun Wang, Xiaoran Liu, Xiandong Beihang Univ Sch Transportat Sci & Engn Beijing 100191 Peoples R China

The low efficiency of the acoustic emission (AE) beamforming localization method in large-scale structural monitoring seriously restricts its application in practice. The Hilbert curve is introduced to improve the computational efficiency of AE beamforming method in this paper. Firstly, the Hilbert curve is introduced to traverse the monitored area, and quickly capture the approximate position of the AE source based on Beamforming. Then, the 'Nine-Four bisection' method is proposed to overcome the boundary problem in region division. Finally, the Hilbert curve-beamforming method (HCBF) is verified by simulation and experiment data. The results show that, the presented method not only greatly improves the computational efficiency, but also maintains the original localization accuracy and reliability. It creates a prerequisite for the further promotion and development of the beamforming method in the field of AE source localization in large-scale structural health monitoring. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Acoustic emission Beamforming Hilbert curve Damage localization fast algorithm

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