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Cluster perturbation theory. XI. Excitation-energy series using a variational excitation-energy function

JOURNAL OF CHEMICAL PHYSICS 2025年第2期162卷 024114页

作者： Hillers-Bendtsen, Andreas Erbs Johansen, Magnus Bukhave von Buchwald, Theo Juncker Mikkelsen, Kurt V. Olsen, Jeppe Jorgensen, Poul Helgaker, Trygve Univ Copenhagen Dept Chem Univ Pk 5 DK-2100 Copenhagen O Denmark Tech Univ Denmark DTU Chem Kemitorvet Bldg 206 DK-2800 Lyngby Denmark Aarhus Univ Dept Chem Langelandsgade 140 DK-8000 Aarhus C Denmark Univ Oslo Hylleraas Ctr Quantum Mol Sci Dept Chem POB 1033 Blindern N-0315 Oslo Norway

Traditionally, excitation energies in coupled-cluster (CC) theory have been calculated by solving the CC Jacobian eigenvalue equation. However, based on our recent work [J & oslash;rgensen et al., Sci. Adv. 10, eadn3454 (2024)], we propose a reformulation of the calculation of excitation energies where excitation energies are determined as a conventional molecular property. To this end, we introduce an excitation-energy function that depends on the CC Jacobian and the right and left eigenvectors for the Jacobian eigenvalue problem. This excitation-energy function is variational with respect to the right and left eigenvectors but not with respect to the cluster amplitudes. Instead, the cluster amplitudes satisfy the cluster-amplitude equations, and we set up an excitation-energy Lagrangian by adding to the excitation-energy function the cluster-amplitude equations with an undetermined multiplier for each cluster-amplitude constraint. The excitation-energy Lagrangian is variational in all its parameters. Based on the variational property of the Lagrangian, we have determined two quadratically convergent excitation-energy series: the total-order cluster-perturbation (tCP) and variational cluster-perturbation (vCP) excitation-energy series. Calculations of the excitation energies of three small molecules have shown that the vCP series is to be preferred over the tCP series. The test calculations have been carried out for CPS(D) expansions [targeting the CC singles-and-doubles (CCSD) wave function from the CC singles wave function] and the CPSD(T) expansion [targeting the CC singles-doubles-triples (CCSDT) wave function from the CCSD wave function]. For the S(D) and SD(T) orbital excitation space calculations, we obtain in the second vCP iteration excitation energies with a mean deviation from CCSD excitation energies of about 0.04 eV for the S(D) orbital spaces, and for the SD(T) orbital space calculation, we obtain a mean deviation from the CCSDT excitation energies of

关键词： eigenvalues and eigenfunctions

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Accelerated Convergence Method for Flow Field Based on DMD-POD Combined Reduced-Order Optimization Model

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IEEE ACCESS 2025年 13卷 10340-10355页

作者： Li, Jianhui Huang, Jun Sun, Yahui Li, Guoqiang SouthWest Univ Sci & Technol Sch Mfg Sci & Engn Mianyang 621010 Sichuan Peoples R China Southwest Univ Sci & Technol Sch Comp Sci & Technol Mianyang 621010 Sichuan Peoples R China

This work presents a novel acceleration method that achieves more efficient convergence of steady-state flow fields. This method involves conducting dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) model reduction on the field snapshots. Subsequently, the residual of the reduced-order model is optimized in the POD modal space to obtain a more accurate solution. This optimized solution is then used as the initial field, and the solver continues iterating until the residual converges. Taking full advantage of both DMD and POD, the proposed approach removes the interference of high-frequency oscillatory flow components and concentrates on the main energy components. This effectively overcomes the problems of slow convergence and residual jumps caused by system stiffness, thereby accelerating the convergence process. The results show that for linear equations, the proposed method achieves a significant acceleration, with a convergence speed five times faster than traditional numerical methods. For the nonlinear Burgers equation, the proposed method also reduces the number of convergence steps by nearly 70%. Additionally, the performance of the proposed accelerated convergence method was further validated through the complex flow around a high-dimensional dual ellipsoid.

关键词： Convergence Iterative methods Extrapolation Steady-state eigenvalues and eigenfunctions Accuracy Numerical models Stability analysis Smoothing methods Power system stability Computational fluid dynamics combined reduced order model accelerated convergence method

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Rethinking Variational Bayes in Community Detection From Graph Signal Perspective

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2025年第5期37卷 2903-2917页

作者： Cheng, Junwei Tang, Yong He, Chaobo Feng, Pengxing Han, Kunlin Guan, Quanlong South China Normal Univ Sch Comp Sci Guangzhou 510000 Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong 999077 Peoples R China Jinan Univ Sch Informat Sci & Technol Guangzhou 510000 Peoples R China Univ Southern Calif Comp Sci Dept Los Angeles CA 90089 USA

Methods based on variational bayes theorytare widely used to detect community structures in networks. In recent years, many related methods have emerged that provide valuable insights into variational bayes theory. Remarkably, a fundamental assumption remains incomprehensible. Variational bayes-based methods typically employ a posterior distribution that follows a gaussian distribution to approximate the unknown prior distribution. However, the complexity and irregularity of node distributions in real-world networks prompt us to consider what characteristics of network information are suitable for the posterior distribution. Mathematically, inappropriate low- and high-frequency signals in expectation inference and variance inference can intensify the adverse effects of community distortion and ambiguity. To analysis these two phenomena and propose reasonable countermeasures, we conduct an empirical study. It is found that appropriately compressing low-frequency signals during expectation inference and amplifying high-frequency signals during variance inference are effective strategies. Based on these two strategies, this paper proposes a novel variational bayes plug-in, namely VBPG, to boost the performance of existing variational bayes-based community detection methods. Specifically, we modulate the frequency signals during expectation and variance inference to generate a new gaussian distribution. This strategy improves the fitting accuracy between the posterior distribution and the unknown true distribution without altering the modules of existing methods. The comprehensive experimental results validate that methods using VBPG achieve competitive performance improvements in most cases.

关键词： Bayes methods Gaussian distribution Distortion Frequency modulation Data mining Symmetric matrices Matrix decomposition Electronic mail eigenvalues and eigenfunctions Signal reconstruction Variational bayes community detection graph signal process graph neural networks graph filters

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Slow dynamical modes from static averages

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JOURNAL OF CHEMICAL PHYSICS 2025年第12期162卷 124108页

作者： Devergne, Timothee Kostic, Vladimir Pontil, Massimiliano Parrinello, Michele Italian Inst Technol Atomist Simulat Genoa Italy Italian Inst Technol Computat Stat & Machine Learning Genoa Italy Univ Novi Sad Dept Math & Informat Novi Sad Serbia UCL AI Ctr Dept Comp Sci London England

In recent times, efforts have been made to describe the evolution of a complex system not through long trajectories but via the study of probability distribution evolution. This more collective approach can be made practical using the transfer operator formalism and its associated dynamics generator. Here, we reformulate in a more transparent way the result of Devergne et al. [Adv. Neural Inform. Process. Syst. 37, 75495-75521 (2024)] and show that the lowest eigenfunctions and eigenvalues of the dynamics generator can be efficiently computed using data easily obtainable from biased simulations. We also show explicitly that the long time dynamics can be reconstructed by using the spectral decomposition of the dynamics operator.

关键词： eigenvalues and eigenfunctions

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A Variational Rayleigh-Ritz Method for Modeling H -Plane Bend Rectangular Waveguides

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2025年第1期73卷 482-493页

作者： Rosa, Guilherme S. Ribeiro, Raul O. Simionato, Eligia Penchel, Rafael A. Sao Paulo State Univ Unesp Sch Engn BR-01049010 Sao Joaoda Da Boa Vista SP Brazil Fed Ctr Technol Educ Celso Suckow da Fonseca CEFET Dept Elect Engn BR-20271110 Rio De Janeiro Brazil

This article introduces a novel variational formula for modeling waveguides with uniformly curved longitudinal axes. Using the Rayleigh-Ritz method, we analyze the electromagnetic fields in H -plane bend rectangular waveguides. In addition, we present a Galerkin method solution (GMS) for discretizing the associated vector Helmholtz equation within a local curved coordinate system. The proposed methodologies are validated through comparison with analytical results and a Galerkin-based solution from the literature across several representative scenarios. The rate of convergence, with respect to the number of expansion terms in the Rayleigh-Ritz method solution (RRMS), is observed to be faster than that in Galerkin-based solutions, while requiring comparable computational times. Furthermore, we explore the impact of both dielectric and conduction losses via the Rayleigh-Ritz method, aspects previously unattainable with analytical methods.

关键词： Electromagnetic waveguides Rectangular waveguides Method of moments Vectors Microwave theory and techniques Geometry eigenvalues and eigenfunctions Curved rectangular waveguide Galerkin method Rayleigh-Ritz method variational solution

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Fault Diagnosis of Wind Turbines Based on Improved Dynamic Network Marker

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IEEE ACCESS 2025年 13卷 2474-2485页

作者： Pan, Zesheng Fang, Ruiming Wei, Tingyu Shang, Rongyan Peng, Changqing Huaqiao Univ Sch Informat Sci & Engn Xiamen 361021 Peoples R China

With the rapid increase in the installed capacity of wind power in China, early warning and identification of defects in wind turbine units has become crucial for the healthy development of the wind power industry. This paper proposes a comprehensive fault warning method for the entire wind turbine unit that is distinct from most current methods that focus solely on partial components. It addresses the complex coupling between various monitoring data from the supervisory control and data acquisition system and the internal defects of the unit. Utilizing a sample covariance matrix and the dynamic network marker theory, the method integrates diverse data inputs to predict potential failures. Case validation reveals that this approach maintains robustness across different operating conditions, issues warnings approximately 6 hours and 40 minutes before faults occur, and effectively identifies fault types. This capability is beneficial for initiative maintenance and rational planning of maintenance schedules in wind turbines.

关键词： Covariance matrices eigenvalues and eigenfunctions Training Signal processing algorithms Real-time systems Predictive models Power system stability Monitoring Long short term memory Feature extraction Fault detection fault diagnosis network theory predictive maintenance renewable energy systems supervisory control and data acquisition wind power

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Distributed Practical Bipartite Output Consensus for Heterogeneous Multi-Agent Systems With Actuator Attacks and External Disturbances Under Edge-Based Event-Triggered Mechanism

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IEEE ACCESS 2025年 13卷 43259-43274页

作者： Lv, Chunhui Cai, Yuliang Su, Hanguang He, Qiang Liaoning Univ Coll Math & Stat Shenyang 110036 Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Peoples R China Northeastern Univ Coll Med & Biol Informat Engn Shenyang 110169 Peoples R China

This study presents an edge-based event-triggered control method to address the practical bipartite output consensus problem for heterogeneous multi-agent systems (MASs) under actuator attacks and external disturbances. Initially, a fully distributed edge-triggered compensator is introduced to efficiently observe the bipartite state of the leader. Zeno behavior is then eliminated for each agent. To address the negative consequences caused by actuator attacks, a distributed state predictor is designed. And a distributed resilient controller is proposed to mitigate the effects of actuator attacks and external disturbances, ensuring practical bipartite output consensus. Finally, the effectiveness of the approach is validated through a numerical example and a comparative example. Compared to existing methods, the proposed approach offers four key advantages: it removes dependence on global topology, eliminates continuous communication, and supports signed communication topologies;it reduces unnecessary communication through an edge-based event-triggered mechanism;it introduces a distributed state predictor to handle actuator attacks and complex external disturbances, improving robustness;and the resilient control strategy ensures practical consensus, providing a more practical and robust solution.

关键词： Actuators Event detection Multi-agent systems Protocols Topology System dynamics Numerical models eigenvalues and eigenfunctions Couplings Vectors Edge-triggered control fully distributed actuator attacks resilient control external disturbances

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Necessary and Sufficient Conditions for Controllability and Essential Controllability of Directed Circle and Tree Graphs

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IEEE-CAA JOURNAL OF AUTOMATICA SINICA 2025年第4期12卷 694-704页

作者： Qu, Jijun Ji, Zhijian Wang, Jirong Liu, Yungang Qingdao Univ Inst Complex Sci Coll Automat Qingdao 266075 Peoples R China Shandong Key Lab Ind Control Technol Qingdao 266075 Peoples R China Qingdao Univ Coll Mech & Elect Engn Qingdao 266075 Peoples R China Shandong Univ Sch Control Sci & Engn Jinan 250061 Peoples R China

The multi-agent controllability is intrinsically affected by the network topology and the selection of leaders. A focus of exploring this problem is to uncover the relationship between the eigenspace of Laplacian matrix and network topology. For strongly connected directed circle graphs, we elaborate how the zero entries in the left eigenvectors of Laplacian matrix L arise. The topologies arising from left eigenvectors with zero entries are filtered to construct essentially controllable directed circle graphs regardless of the choice of leaders. We propose two methods for constructing a substantial quantity of essentially controllable graphs, with a focus on utilizing essentially controllable circle graphs as the foundation. For a special directed graph-OT tree, the controllability is shown to be related with its substructure-paths. This promotes the establishment of a sufficient and necessary condition for controllability. Finally, a method is presented to check the controllable subspace by identifying the left eigenvectors and generalized left eigenvectors.

关键词： Controllability Multi-agent systems Topology Network topology eigenvalues and eigenfunctions Tree graphs Vectors Sufficient conditions Laplace equations Directed graphs Circle graphs controllability controllable subspace essential controllability tree graphs

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Direction of Arrival Estimation Based on AR Modeling in the Presence of Colored Noise

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IEEE ACCESS 2025年 13卷 62427-62433页

作者： Bakhshandeh Babarsad, Sina Mahmoudi, Alimorad Namjoo, Ehsan Shahid Chamran Univ Ahvaz Fac Engn Dept Elect Engn Ahvaz *** Iran

This paper investigates the problem of estimating the direction of arrival considering colored noise at the sensors. To this aim, we model the recieved signal at each time instant with an AR system with rank equal to the number of sources and we simultaneously estimated signal and noise parameters by solving a quadratic eigenvalue problem. Simulation results demonstrate that utilizing root mean square error as the accuracy metric, the proposed method outperforms existing subspace-based approaches, particularly when the targets are close to eachother.

关键词： Noise Direction-of-arrival estimation Sensors Colored noise Maximum likelihood estimation Transforms Signal processing algorithms Multiple signal classification eigenvalues and eigenfunctions White noise AR modeling colored noise DOA estimation subspace-based methods

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Fully Distributed Event-Triggered Security Control for DC Microgrids Subject to DoS Attacks

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IEEE TRANSACTIONS ON SMART GRID 2025年第2期16卷 929-941页

作者： Xiao, Feng Liu, Yu Zhang, Xiaodan Wei, Bo North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewable Beijing 102206 Peoples R China North China Elect Power Univ Sch Control & Comp Engn Beijing 102206 Peoples R China

As the application of distributed DC microgrids becomes more and more widespread, their voltage restoration and current sharing that cannot be guaranteed simultaneously due to droop control have received a lot of attention. In this paper, we propose a new adaptive safety control strategy with an event-triggering mechanism to reduce the communication burden. The current sharing of the distributed generation units is guaranteed while bus voltage deviations are eliminated. The control objectives are well achieved even under DoS attacks. Moreover, the controller and the triggering mechanism are designed to be scalable without the bus voltage sampling and any global information. The stability of the control system is proved by the Lyapunov theory, and Zeno behavior is also strictly ruled out. Finally, the simulation results illustrate the validity of the proposed approach.

关键词： Voltage control Microgrids Denial-of-service attack Control systems Observers Event detection eigenvalues and eigenfunctions Power system stability Laplace equations Decentralized control DoS attacks event-triggered control DC microgrids current sharing voltage restoration

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