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linear dynamical system over Finite Distributive Lattice

Journal of Donghua University(English Edition) 2021年第3期38卷 264-271页

作者： DENG Aiping GONG Xiaoyue MA Hongcai College of Science Donghua University Shanghai 201620 China

A finite dynamical system(FDS)over a lattice L is a pair(S(L),f),where S(L)is a left-L module and f is a mapping from S into *** phase space of(S(L),f)is a digraph whose vertex set is S(L)and there is an arc from x to y if y=f(x).Let L be a finite distributive lattice,A an n×n matrix over L,and f(x)=*** structure of the phase space of the FDS(Ln,f)is *** number of limit cycles in the phase space of(Ln,f)is described in Möbius *** phase spaces of some invertible,nilpotent,and idempotent FDS(Ln,f)are characterized explicitly.

关键词： finite distributive lattice linear dynamical system phase space limit cycle rooted in-tree

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Predicting state transitions in the transcriptome and metabolome using a linear dynamical system model

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BMC BIOINFORMATICS 2007年第1期8卷 1-10页

作者： Morioka, Ryoko Kanaya, Shigehiko Hirai, Masami Y. Yano, Mitsuru Ogasawara, Naotake Saito, Kazuki RIKEN Plant Sci Ctr Kanagawa Japan Nara Inst Sci & Technol Grad Sch Informat Sci Dept Bioinformat & Genom Nara Japan Chiba Univ Grad Sch Pharmaceut Sci Dept Mol Biol & Biotechnol Inage Ku Chiba Japan

Background: Modelling of time series data should not be an approximation of input data profiles, but rather be able to detect and evaluate dynamical changes in the time series data. Objective criteria that can be used to evaluate dynamical changes in data are therefore important to filter experimental noise and to enable extraction of unexpected, biologically important information. Results: Here we demonstrate the effectiveness of a Markov model, named the linear dynamical system, to simulate the dynamics of a transcript or metabolite time series, and propose a probabilistic index that enables detection of time-sensitive changes. This method was applied to time series datasets from Bacillus subtilis and Arabidopsis thaliana grown under stress conditions;in the former, only gene expression was studied, whereas in the latter, both gene expression and metabolite accumulation. Our method not only identified well-known changes in gene expression and metabolite accumulation, but also detected novel changes that are likely to be responsible for each stress response condition. Conclusion: This general approach can be applied to any time-series data profile from which one wishes to identify elements responsible for state transitions, such as rapid environmental adaptation by an organism.

关键词： Time Series Data Anthocyanin Biosynthesis Lysogeny Broth linear dynamical system Accumulation Profile

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Compressive Privacy for a linear dynamical system

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2020年 15卷 895-910页

作者： Song, Yang Wang, Chong Xiao Tay, Wee Peng Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

We consider a linear dynamical system in which the state vector consists of both public and private states. One or more sensors make measurements of the state vector and sends information to a fusion center, which performs the final state estimation. To achieve an optimal tradeoff between the utility of estimating the public states and protection of the private states, the measurements at each time step are linearly compressed into a lower dimensional space. Under the centralized setting where all measurements are collected by a single sensor, we propose an optimization problem and an algorithm to find the best compression matrix. Under the decentralized setting where measurements are made separately at multiple sensors, each sensor optimizes its own local compression matrix. We propose methods to separate the overall optimization problem into multiple sub-problems that can be solved locally at each sensor. We consider the cases where there is no message exchange between the sensors;and where each sensor takes turns to transmit messages to the other sensors. Simulations and empirical experiments demonstrate the efficiency of our proposed approach in allowing the fusion center to estimate the public states with good accuracy while preventing it from estimating the private states accurately.

关键词： Inference privacy compressive privacy parameter privacy linear dynamical system Kalman filter

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Upper Bounds of the Deviations in linear dynamical system with Bounded Disturbances

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AUTOMATION AND REMOTE CONTROL 2020年第9期81卷 1702-1710页

作者： Kvinto, Ya, I Khlebnikov, M., V Russian Acad Sci Trapeznikov Inst Control Sci Moscow Russia

A practically significant effect of a surge occurrences in linear dynamical systems under nonzero initial conditions is explored. The linear dynamical system subjected to unknown-but-bounded exogenous disturbances is considered. Using the apparatus of linear matrix inequalities and the invariant ellipsoids concept, the estimations of the upper bounds of the trajectories deviations are obtained, and an approach is suggested to the feedback design that minimizes the deviations. The efficacy of the approach proposed is illustrated on numerical examples.

关键词： linear dynamical system trajectories deviations bounded exogenous disturbances LMIs invariant ellipsoids

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Off-Line and On-Line Vigilance Estimation Based on linear dynamical system and Manifold Learning

Off-Line and On-Line Vigilance Estimation Based on Linear Dy...

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32nd Annual International Conference of the IEEE Engineering-in-Medicine-and-Biology-Society (EMBC 10)

作者： Shi, Li-Chen Lu, Bao-Liang Shanghai Jiao Tong Univ Ctr Brain Like Comp & Machine Intelligence Dept Comp Sci & Engn Shanghai 200240 Peoples R China

ISBN: (纸本)9781424441242

For many human machine interaction systems, to ensure work safety, the techniques for continuously estimating the vigilance of operators are highly desirable. Up to now, various methods based on electroencephalogram (EEG) are proposed to solve this problem. However, most of them are static methods and are based on supervised learning strategy. The main deficiencies of the existing methods are that the label information is hard to get and the time dependency of vigilance changes are ignored. In this paper, we introduce the dynamic characteristics of vigilance changes into vigilance estimation and propose a novel model based on linear dynamical system and manifold learning techniques to implement off-line and on-line vigilance estimation. In this model, both spatial information of EEG and temporal information of vigilance changes are used. The label information what we need is merely to know which EEG indices are important for vigilance estimation. Experimental results show that the mean off-line and on-line correlation coefficients between estimated vigilance level and local error rate in second-scale without being averaged are 0.89 and 0.83, respectively.

关键词： EEG spatial information continuous operator vigilance estimation electroencephalogram electroencephalography human-machine interaction systems learning (artificial intelligence) linear dynamical system manifold learning medical signal processing neurophysiology occupational health off line vigilance estimation on line vigilance estimation vigilance change temporal information

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UNKNOWN SIGNAL DETECTION IN linear dynamical system NOISE 29

UNKNOWN SIGNAL DETECTION IN LINEAR DYNAMICAL SYSTEM NOISE

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IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP)

作者： Ford, Gabriel Hu, Timothy Bucci, Donald Foster, Benjamin Lockheed Martin Adv Technol Labs Cherry Hill NJ 08002 USA

ISBN: (纸本)9781728108247

A machine learning approach to detecting unknown signals in time-correlated noise is presented. In the proposed approach, a linear dynamical system (LDS) model is trained to represent the background noise via expectation-maximization (EM). The negative log-likelihood (NLL) of test data under the learned background noise LDS is computed via the Kalman filter recursions, and an unknown signal is detected if the NLL exceeds a threshold. The proposed detection scheme is derived as a generalized likelihood ratio test (GLRT) for an unknown deterministic signal in LDS noise. In simple additive white Gaussian noise (AWGN), the proposed scheme reduces to an energy detector. However, experimental results on a wireless software defined radio (SDR) testbed demonstrate that the proposed scheme substantially outperforms energy detection in a time-correlated noise background.

关键词： Signal detection Kalman filter linear dynamical system expectation-maximization generalized likelihood ratio test

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FAST DYNAMIC MRI USING linear dynamical system MODEL 41

FAST DYNAMIC MRI USING LINEAR DYNAMICAL SYSTEM MODEL

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41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Singh, Vimal Tewfik, Ahmed H. Univ Texas Austin Elect & Comp Engn Dept Austin TX 78712 USA

ISBN: (纸本)9781479999880

Imaging of physiological functions using magnetic resonance imaging is limited due its slow data acquisition speed. Previously various techniques based on data sharing in the spatiotemporal k-space or sparse recovery methods have been proposed to increase imaging speeds in dynamic MRI. This paper presents a novel formulation for fast dynamic MRI which combines the generic linear dynamical system based spatiotemporal model with sparse recovery techniques. Specifically, the formulation uses a known prior time-evolution model for the physiological function implicitly and enforces the model errors (innovations) to be sparse. The preliminary results of dynamic MRI recovery experiments on an in-vivo myocardial perfusion dataset show that the proposed approach preserves details like edges and fine structures in recovered images better than previous k-space data-sharing and sparse recovery techniques individually.

关键词： MRI linear dynamical system Compressed Sensing Sparse Innovations

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On the Invariance of Trajectories Under Perturbations in linear Dynamic Control systems

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Journal of Mathematical Sciences (United States) 2025年第1期288卷 92-105页

作者： Zubova, S.P. Raetskaya, E.V. Trung, Le Hay Voronezh State University Voronezh Russian Federation G. F. Morozov Voronezh State Forest Engineering University Voronezh Russian Federation Da Nang University of Science and Education Da Nang Viet Nam

For a linear, nonstationary, completely controllable dynamical system with multipoint conditions on the state, we consider a problem on the independence of the state (trajectory) of the system of external perturbations and possible changes in the parameters of the system (internal perturbations). The problem is to construct a control for the perturbed system under which the state of the perturbed system is identical to the state of the unperturbed system. We compare controls for the unperturbed and perturbed systems at the same states of the systems. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

关键词： 34H05 blocking cascade decomposition method control invariance linear dynamical system perturbation

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linear dynamical systems approach for human action recognition with dual-stream deep features

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APPLIED INTELLIGENCE 2022年第1期52卷 452-470页

作者： Du, Zhouning Mukaidani, Hiroaki Hiroshima Univ Grad Sch Adv Sci & Engn 1-4-1 Kagamiyama Higashihiroshima Hiroshima 7398527 Japan

Human action recognition with a dual-stream architecture using linear dynamical systems (LDSs) approach is discussed in this paper. First, a slice process is established to extract original slices from video sequences. Two slicing methods are adopted to subtract or reserve the remaining frames in the video sequences. By applying background subtraction to adjacent frames of the original slices, difference slices are also expressed. To capture the spatial component of the background and difference expressed in each slice simultaneously, a framework based on pre-trained convolutional neural networks (CNNs) is introduced for dual-stream deep feature extraction. Subsequently, LDSs are established to model the timing relationship between adjacent slices and obtain the temporal component of the background and difference features, which are expressed as linear dynamical background feature (LD-BF) and linear dynamical difference feature (LD-DF). Practical experiments were conducted to demonstrate the effectiveness and robustness of the proposed approach using different datasets. Specifically, our experiments were conducted on the UCF50, UCF101, and hmdb51 datasets. The impact of retaining various principal component analysis (PCA) feature dimensions and distinct slicing methods in terms of detail recognition were evaluated. In particular, combining LD-BF with LD-DF under appropriate feature dimensions and slicing methods further improved the accuracy for the UCF50, UCF101, and hmdb51 datasets. In addition, the computational cost of the feature extraction process was evaluated to illustrate the efficiency of the proposed approach. The experimental results show that the proposed approach is competitive with state-of-the-art approaches in the three datasets.

关键词： Human action recognition linear dynamical system Dual-stream deep features Background subtraction

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Dynamic mode decomposition based on expectation-maximization algorithm for simultaneous system identification and denoising

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MECHANICAL systemS AND SIGNAL PROCESSING 2025年 223卷

作者： Iwasaki, Yuto Sasaki, Yasuo Nagata, Takayuki Kaneko, Sayumi Nonomura, Taku Tohoku Univ Grad Sch Engn Dept Aerosp Engn 6-6-01 Aramaki Aza AobaAoba Ku Sendai Miyagi 9808579 Japan

The present study proposes a novel dynamic mode decomposition (DMD) that can simultaneously estimate the reduced-order model, the original signal, and the system/observation noise model only from the noisy data. An expectation-maximization (EM)-algorithm DMD (EMDMD) combines DMD and the parameter adjustment of the linear dynamical system (LDS) based on the EM algorithm. The initial parameters based on the linearity of the reduced-order data are set by using DMD. Subsequently, the log-likelihood of the complete data is maximized by adjusting the LDS parameters while separating the noise. The proposed algorithm is applied to the benchmark data of the short-fat and tall-skinny data matrices with different noise and the time-series velocity fields of the flow around a circular cylinder and the separated flow around an airfoil. The performance of EMDMD in terms of system identification and noise separation from the noisy data is evaluated, and the EMDMD shows the highest system identification and noise separation performance in all data.

关键词： Dynamic mode decomposition Expectation-maximization algorithm linear dynamical system system identification Denoising

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