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A novel high-precision non-classical method to solve fractional rheology and viscoelastic vibration: linear computational complexity and experimental verification

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2025年 315卷

作者： Liu, Tian-Ming Chen, Yan-Mao Liu, Ji-Ke Liu, Qi-Xian Sun Yat Sen Univ Dept Mech Shenzhen Campus66 Gongchang Rd Shenzhen 518107 Guangdong Peoples R China

The theory of fractional calculus can precisely depict the non-integer order characteristics of materials, especially when it comes to predicting viscoelastic behaviors such as rheology and viscoelastic damping. Despite the marked superiority of fractional calculus in the realm of viscoelastic material modeling, its numerical processing encounters numerous challenges. This is because traditional computational methods for handling such problems must deal with a large amount of historical data, thus leading to low efficiency. Moreover, existing non-classical methods typically find it arduous to simultaneously take into account both computational accuracy and efficiency. In light of the aforementioned issues, this study presents an innovative non-classical computational approach. Through the implementation of the piecewise processing strategy, this study effectively addresses the inherent limitation of weak algebraic decay in the infinite state representation associated with non-classical methods. This innovative approach not only achieves a substantial improvement in computational accuracy but also maintains an efficient linear computational complexity, thereby striking an optimal balance between precision and computational efficiency. This method has been successfully applied to the solution of multi- component fractional viscoelastic constitutive equations and verified through experiments. Furthermore, based on the nonlocal strain gradient theory and the fractional-order constitutive relation, the nonlinear motion equation of the fractional viscoelastic nanobeam is derived. Comparative analyses of the vibration responses of the linear and nonlinear models are conducted, revealing the nonlinear viscoelastic damping characteristics of the system. The research outcomes indicate that this method is applicable to addressing fractional viscoelastic mechanics problems and holds the potential to extend to a broader category of fractional differential equations, being capabl

关键词： Fractional calculus Interval decomposition Infinite state expression Interpolation quadrature Exponential decay linear computational complexity

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Exhaustively Identifying Cross -Linked Peptides with a linear computational complexity

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JOURNAL OF PROTEOME RESEARCH 2017年第10期16卷 3942-3952页

作者： Yu, Fengchao Li, Ning Yu, Weichuan Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Hong Kong Hong Kong Peoples R China Hong Kong Univ Sci & Technol Div Life Sci Hong Kong Hong Kong Peoples R China Hong Kong Univ Sci & Technol Div Biomed Engn Hong Kong Hong Kong Peoples R China

Chemical cross-linking coupled to mass spectrometry is a powerful tool to study protein protein interactions and protein conformations. Two linked peptides are ionized and fragmented to produce a tandem mass spectrum. In such an experiment, a tandem mass spectrum contains ions from two peptides. The peptide identification problem becomes a peptide peptide pair identification problem. Currently, most tools do not search all possible pairs due to the quadratic time complexity. Consequently, missed findings are unavoidable. In our previous work, we developed a tool named ECL to search all pairs of peptides exhaustively. Unfortunately, it is very slow due to the quadratic computational complexity, especially when the database is large. Furthermore, ECL uses a score function without statistical calibration, while researchers1-3 have proposed that it is inappropriate to directly compare uncalibrated scores because different spectra have different random score distributions. Here we propose an advanced version of ECL, named ECL2. It achieves a linear time and space complexity by taking advantage of the additive property of a score function. It can search a data set containing tens of thousands of spectra against a database containing thousands of proteins in a few hours. Comparison with other five state-of-the-art tools shows that ECL2 is much faster than pLink, StavroX, ProteinProspector, and ECL. Kojak is the only one that is faster than ECL2, but Kojak does not exhaustively search all possible peptide pairs. The comparison shows that ECL2 has the highest sensitivity among the state-of-the-art tools. The experiment using a large-scale in vivo cross-linking data set demonstrates that ECL2 is the only tool that can find the peptide-spectrum matches (PSMs) passing the false discovery rate/q-value threshold. The result illustrates that the exhaustive search and a well-calibrated score function are useful to find PSMs from a huge search space.

关键词： cross-linked peptides identification linear computational complexity exhaustive database search

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A Third Order Fast Sweeping Method with linear computational complexity for Eikonal Equations

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JOURNAL OF SCIENTIFIC COMPUTING 2015年第1期62卷 198-229页

作者： Wu, Liang Zhang, Yong-Tao Univ Notre Dame Dept Appl & Computat Math & Stat Notre Dame IN 46556 USA

Fast sweeping methods are a class of efficient iterative methods for solving steady state hyperbolic PDEs. They utilize the Gauss-Seidel iterations and alternating sweeping strategy to cover a family of characteristics of the hyperbolic PDEs in a certain direction simultaneously in each sweeping order. The first order fast sweeping method for solving Eikonal equations (Zhao in Math Comput 74:603-627, 2005) has linear computational complexity, namely, the computational cost is where is the number of grid points of the computational mesh. Recently, a second order fast sweeping method with linear computational complexity was developed in Zhang et al. (SIAM J Sci Comput 33:1873-1896, 2011). The method is based on a discontinuous Galerkin (DG) finite element solver and causality indicators which guide the information flow directions of the nonlinear Eikonal equations. How to extend the method to higher order accuracy is still an open problem, due to the difficulties of solving much more complicated local nonlinear systems and calculations of local causality information. In this paper, we extend previous work and develop a third order fast sweeping method with linear computational complexity for solving Eikonal equations. A novel approach is designed for capturing the causality information in the third order DG local solver. Numerical experiments show that the method has third order accuracy and a linear computational complexity.

关键词： Fast sweeping methods Discontinuous Galerkin methods High order accuracy linear computational complexity Static Hamilton-Jacobi equations Eikonal equations

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Neuromorphic Vision Restoration Network for Advanced Driver Assistance System

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IEEE TRANSACTIONS ON CONSUMER ELECTRONICS 2024年第1期70卷 3658-3668页

作者： Xie, Dirui Xiao, He Hu, Xiaofang Zhou, Yue Zhou, Guangdong Duan, Shukai Southwest Univ Coll Artificial Intelligence Chongqing 400715 Peoples R China

Adverse weather conditions severely impact the environmental perception capabilities of the Advanced Driver Assistance System (ADAS). However, it is difficult to deploy these high-performance Transformers for image restoration on resources constrained ADAS platform. Recently, the rapid development of neuromorphic computing systems (NSC), based on fast in-memory computing, provides an ideal and feasible solution to it. Combining Transformers and NSC faces challenges due to the high complexity and outliers of Softmax attention. Moreover, existing image restoration networks are mostly designed for a single task and lack generalization. To address these issues, we propose a neuromorphic-computing-friendly linear Sparse Transformer (LSFormer) with linear computational complexity. The LSFormer achieves advanced image restoration performance compared to Softmax attention Transformers. Meanwhile, we propose the implementation scheme based on neuromorphic computing systems, reducing the deployment complexity at the edge. We evaluate LSFormer on multiple image restoration tasks including low-light image enhancement, image deraining, and dehazing. The results demonstrates that the performance of LSFormer outperforms state-of-the-art (SOTA) networks. Furthermore, the comparison between existing hardware implementations of Softmax attention and our proposed scheme using various metrics validates the feasibility and superiority of our proposed scheme.

关键词： Neuromorphic computing vision Transformer advanced driver assistance system image restoration linear computational complexity

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A novel dual-criterion framework for change point detection

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STATISTICS & PROBABILITY LETTERS 2024年 211卷

作者： Zhang, Qiang Chengdu Univ Sch Comp Sci 2025 Chengluo Ave Chengdu 610106 Sichuan Peoples R China

In this work, we introduce a dual-criterion framework for change-point detection. This innovative approach intuitively facilitates the simultaneous determination of both the number and locations of change points, while effectively identifying and excluding outliers. Numerous onedimensional criterion-based change point detection methods can be generalized and integrated within this novel framework.

关键词： Change point detection Dual-criterion framework Complex data sequence linear computational complexity

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Large-Scale Multi-View Clustering via Fast Essential Subspace Representation Learning

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IEEE SIGNAL PROCESSING LETTERS 2022年 29卷 1893-1897页

作者： Zheng, Qinghai Fuzhou Univ Coll Comp & Data Sci Fuzhou 350108 Peoples R China

Large-scale Multi-View Clustering (LMVC) is a hot research problem in the fields of signal processing and machine learning, and many anchor-based multi-view subspace clustering algorithms are proposed in recent years. However, most existing methods usually concentrate on the issue of reducing the time cost and ignore the exploration of the complementary information during the clustering process. To this end, we propose a Fast Essential Subspace Representation Learning (FESRL) method for large-scale multi-view subspace clustering. Specifically, FESRL introduces the orthogonal transformation to investigate both the complementary and consensus information across multiple views. The essential subspace representation can be learned in a linear time cost. Experiments conducted on several benchmark datasets illustrate the competitiveness of the proposed method.

关键词： Signal processing algorithms Optimization Costs Representation learning Time complexity Clustering algorithms Convergence Large-scale multi-view subspace clustering linear computational complexity

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Robust joint design of transmit waveform and receive filter for MIMO radar space-time adaptive processing with signal-dependent interferences

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IET RADAR SONAR AND NAVIGATION 2017年第8期11卷 1321-1332页

作者： Wang, Yuxi Li, Wei Sun, Qilu Huang, Guoce Air Force Engn Univ Informat & Nav Coll Xian 710077 Shaanxi Peoples R China

This study deals with the problem of joint design of multiple-input-multiple-output (MIMO) radar transmit waveform and receive filter in the presence of signal-dependent interferences. To enhance the detection performance of a slow moving target, MIMO radar space-time adaptive technology is adapted. Considering the issue of imprecise knowledge about target's Doppler frequency and direction, the worst-case output signal-to-interference-plus-noise ratio over the uncertainty set of target steering vector is set as figure of merit. Furthermore, due to the non-linear power amplifier and the fact that transmit antenna may be out of work, constraints of peak-to-average power ratio and transmit power for each transmit antenna are taken into account. As to the resulted hard problem, some suitable mathematical transformations are performed and a novel sequential optimisation procedure combined with semi-definite relaxation, Charnes-Cooper transform and Lagrange duality method is developed to tackle the non-convex joint design problem. Randomisation procedure is utilised to synthesise the final transmit waveform and receive filter. The computational complexity is linear with the numbers of iterations and trials of the randomisation. The convergence of the devised algorithm is analysed and numerical results in a variety of scenarios are provided to demonstrate the effectiveness of the proposed algorithm.

关键词： radar signal processing nonconvex robust joint design problem nonlinear power amplifier final transmit waveform multiple-input-multiple-output radar transmit waveform linear computational complexity robust joint design target steering vector Optimisation techniques output signal-to-interference-plus-noise ratio transmit antenna MIMO radar space-time adaptive processing randomisation procedure sequential optimisation procedure signal-dependent interferences receive filter Radar equipment, systems and applications Signal detection transmitting antennas Filtering methods in signal processing target Doppler frequency peak-to-average power ratio concave programming space-time adaptive processing power amplifiers radar antennas slow-moving target detection performance Charnes-Cooper transform Single antennas MIMO radar space-time adaptive technology Lagrange duality method transmit waveform computational complexity Amplifiers semidefinite relaxation radar detection transmit power filtering theory MIMO radar

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Modeling Spatial Extremes via Ensemble-of-Trees of Pairwise Copulas

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第3期65卷 571-586页

作者： Yu, Hang Uy, Wayne Isaac T. Dauwels, Justin Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Cornell Univ Ctr Appl Math Ithaca NY 14850 USA Nanyang Technol Univ Sch Phys & Math Sci Singapore 639798 Singapore

Assessing the risk of extreme events in a spatial domain, such as hurricanes, floods, and droughts, presents a unique significance in practice. Unfortunately, the existing extreme-value statistical models are typically not feasible for practical large-scale problems. Graphical models, on the other hand, are capable of handling sizable number of variables, but have yet to be explored in the realm of extreme-value analysis. To bridge the gap, an extreme-value graphical model is introduced in this paper, i.e., an ensemble-of-trees of pairwise copulas (ETPC). In the proposed graphical model, extreme-value marginal distributions are stitched together by means of a pairwise copulas, which in turn are the building blocks of the ensemble of trees. Novel linear-complexity stochastic gradient-based algorithms are then developed for learning the ETPC model and inferring missing data. As a result, the ETPC model is applicable to extreme-value problems with thousands of variables. It can be proven that, under mild conditions, the ETPC model exhibits the favorable property of tail-dependence between an arbitrary pair of sites (variables);consequently, the model is able to reliably capture statistical dependence between extreme values at different sites. Experimental results for both synthetic and real data demonstrate the advantages of the ETPC model in modeling fitting, imputation, and computational efficiency.

关键词： Extreme events pairwise copulas graphical models ensemble of trees stochastic gradient log-determinant linear computational complexity tail dependence

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Rational cubic clipping with linear complexity for computing roots of polynomials

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APPLIED MATHEMATICS AND COMPUTATION 2016年 273卷 1051-1058页

作者： Chen, Xiao-diao Ma, Weiyin Hangzhou Dianzi Univ Sch Comp Hangzhou Zhejiang Peoples R China City Univ Hong Kong Dept MBE Hong Kong Hong Kong Peoples R China

Many problems in computer aided geometric design and computer graphics can be turned into a root-finding problem of polynomial equations. Among various clipping methods, the ones based on the Bernstein-Bezier form have good numerical stability. One of such clipping methods is the k-clipping method, where k = 2, 3 and often called a cubic clipping method when k = 3. It utilizes 0(n(2)) time to find two polynomials of degree k bounding the given polynomial f(t) of degree n, and achieves a convergence rate of k + 1 for a single root. The roots of the bounding polynomials of degree k are then used for bounding the roots of f(t). This paper presents a rational cubic clipping method for finding two bounding cubics within 0(n) time, which can achieve a higher convergence rate 5 than that of 4 of the previous cubic clipping method. When the bounding cubics are obtained, the remaining operations are the same as those of previous cubic clipping method. Numerical examples show the efficiency and the convergence rate of the new method. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Approximation order Fast cubic clipping method Root-finding Convergence rate linear computational complexity

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Dynamic construction of an antidictionary with linear complexity

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THEORETICAL COMPUTER SCIENCE 2014年 526卷 108-119页

作者： Ota, Takahiro Fukae, Hirotada Morita, Hiroyoshi Nagano Prefectural Inst Technol Dept Comp & Syst Engn Ueda Nagano 3861211 Japan Shikoku Polytech Coll Elect Informat Technol Dept Kochi 7815232 Japan Univ Electrocommun Grad Sch Informat Syst Chofu Tokyo 1828585 Japan

An antidictionary is in particular useful for data compression. Static construction algorithms of antidictionaries with linear complexity have been proposed. However, the construction algorithms do not work in a dynamic manner with linear complexity. In this paper, we propose a dynamic construction algorithm of an antidictionary with linear complexity. The proposed algorithm uses two linear construction algorithms of suffix trees proposed by Weiner and Ukkonen, individually. It is proved that the proposed algorithm works with linear complexity. Moreover, its effectiveness is demonstrated by simulation results. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Antidictionary Incremental construction linear computational complexity Suffix tree Data compression

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