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Multiple model tracking algorithms based on neural network and multiple process noise soft switching 被引量:2
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作者 NieXiaohua 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第6期1227-1232,共6页
A multiple model tracking algorithm based on neural network and multiple-process noise soft-switching for maneuvering targets is presented.In this algorithm, the"current"statistical model and neural network are runn... A multiple model tracking algorithm based on neural network and multiple-process noise soft-switching for maneuvering targets is presented.In this algorithm, the"current"statistical model and neural network are running in parallel.The neural network algorithm is used to modify the adaptive noise filtering algorithm based on the mean value and variance of the"current"statistical model for maneuvering targets, and then the multiple model tracking algorithm of the multiple processing switch is used to improve the precision of tracking maneuvering targets.The modified algorithm is proved to be effective by simulation. 展开更多
关键词 maneuvering target current statistical model neural network multiple model algorithm.
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A distributed algorithm for signal coordination of multiple agents with embedded platoon dispersion model
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作者 别一鸣 王殿海 +1 位作者 马东方 朱自博 《Journal of Southeast University(English Edition)》 EI CAS 2011年第3期311-315,共5页
In order to reduce average arterial vehicle delay, a novel distributed and coordinated traffic control algorithm is developed using the multiple agent system and the reinforce learning (RL). The RL is used to minimi... In order to reduce average arterial vehicle delay, a novel distributed and coordinated traffic control algorithm is developed using the multiple agent system and the reinforce learning (RL). The RL is used to minimize average delay of arterial vehicles by training the interaction ability between agents and exterior environments. The Robertson platoon dispersion model is embedded in the RL algorithm to precisely predict platoon movements on arteries and then the reward function is developed based on the dispersion model and delay equations cited by HCM2000. The performance of the algorithm is evaluated in a Matlab environment and comparisons between the algorithm and the conventional coordination algorithm are conducted in three different traffic load scenarios. Results show that the proposed algorithm outperforms the conventional algorithm in all the scenarios. Moreover, with the increase in saturation degree, the performance is improved more significantly. The results verify the feasibility and efficiency of the established algorithm. 展开更多
关键词 multiple agents signal coordination reinforce learning platoon dispersion model
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Maneuvering target tracking using threshold interacting multiple model algorithm
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作者 徐迈 山秀明 徐保国 《Journal of Southeast University(English Edition)》 EI CAS 2005年第4期440-444,共5页
To avoid missing track caused by the target maneuvers in automatic target tracking system, a new maneuvering target tracking technique called threshold interacting multiple model (TIMM) is proposed. This algorithm i... To avoid missing track caused by the target maneuvers in automatic target tracking system, a new maneuvering target tracking technique called threshold interacting multiple model (TIMM) is proposed. This algorithm is based on the interacting multiple model (IMM) method and applies a threshold controller to improve tracking accuracy. It is also applicable to other advanced algorithms of IMM. In this research, we also compare the position and velocity root mean square (RMS) errors of TIMM and IMM algorithms with two different examples. Simulation results show that the TIMM algorithm is superior to the traditional IMM alzorithm in estimation accuracy. 展开更多
关键词 maneuvering target tracking Kalman filter interacting multiple model (IMM) threshold interacting multiple model (TIMM)
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Interacting Multiple Model Algorithm with the Unscented Particle Filter (UPF) 被引量:9
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作者 邓小龙 谢剑英 倪宏伟 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2005年第4期366-371,共6页
Combining interacting multiple model (IMM) and unscented particle filter (UPF), a new multiple model filtering algorithm is presented. Multiple models can be adapted to targets' high maneu- vering. Particle filte... Combining interacting multiple model (IMM) and unscented particle filter (UPF), a new multiple model filtering algorithm is presented. Multiple models can be adapted to targets' high maneu- vering. Particle filter can be used to deal with the nonlinear or non-Gaussian problems and the unscented Kalman filter (UKF) can improve the approximate accuracy. Compared with other interacting multiple model algorithms in the simulations, the results demonstrate the validity of the new filtering method. 展开更多
关键词 interacting multiple model UPF UKF nonlinear/non-Gaussian
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Hierarchical interacting multiple model algorithm based on improved current model 被引量:4
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作者 Xianghua Wang Xinyu Yang +1 位作者 Zheng Qin Huijie Yang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第6期961-967,共7页
Interacting multiple models is the hotspot in the research of maneuvering target models at present. A hierarchical idea is introduced into IMM algorithm. The method is that the whole models are organized as two levels... Interacting multiple models is the hotspot in the research of maneuvering target models at present. A hierarchical idea is introduced into IMM algorithm. The method is that the whole models are organized as two levels to co-work, and each cell model is an improved "current" statistical model. In the improved model, a kind of nonlinear fuzzy membership function is presented to get over the limitation of original model, which can not track weak maneuvering target precisely. At last, simulation experiments prove the efficient of the novel algorithm compared to interacting multiple model and hierarchical interacting multiple model based original "current" statistical model in tracking precision. 展开更多
关键词 target tracking "current" statistical model multiple model hierarchical.
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Multiple constraints-based QoS multicast routing: model and algorithms 被引量:4
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作者 SunBaolin LiLayuan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第1期187-193,共7页
Constraint-based multicast routing, which aims at identifying a path that satisfies a set of quality of service (QoS) constraints, has became a very important research issue in the areas of networks and distributed sy... Constraint-based multicast routing, which aims at identifying a path that satisfies a set of quality of service (QoS) constraints, has became a very important research issue in the areas of networks and distributed systems. In general, multi-constrained path selection with or without optimization is a NP-complete problem that can not be exactly solved in polynomial time. Hence, accurate constraints-based routing algorithms with a fast running time are scarce, perhaps even non-existent. The expected impact of such a constrained-based routing algorithm has resulted in the proposal of numerous heuristics and a few exact QoS algorithms. This paper aims to give a thorough, concise and fair evaluation of the most important multiple constraint-based QoS multicast routing algorithms known today, and it provides a descriptive overview and simulation results of these multi-constrained routing algorithms. 展开更多
关键词 multicast routing algorithm multiple constraints QoS routing NP-complete.
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Data Fusion Algorithm for Multi-Sensor Dynamic System Based on Interacting Multiple Model 被引量:3
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作者 陈志锋 蔡云泽 《Journal of Shanghai Jiaotong university(Science)》 EI 2015年第3期265-272,共8页
This paper presents a data fusion algorithm for dynamic system with multi-sensor and uncertain system models. The algorithm is mainly based on Kalman filter and interacting multiple model(IMM). It processes crosscorre... This paper presents a data fusion algorithm for dynamic system with multi-sensor and uncertain system models. The algorithm is mainly based on Kalman filter and interacting multiple model(IMM). It processes crosscorrelated sensor noises by using augmented fusion before model interacting. And eigenvalue decomposition is utilized to reduce calculation complexity and implement parallel computing. In simulation part, the feasibility of the algorithm was tested and verified, and the relationship between sensor number and the estimation precision was studied. Results show that simply increasing the number of sensor cannot always improve the performance of the estimation. Type and number of sensors should be optimized in practical applications. 展开更多
关键词 MULTI-SENSOR cross-correlated noises augmented fusion interacting multiple model(IMM)
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An Algorithm of the Adaptive Grid and Fuzzy Interacting Multiple Model 被引量:4
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作者 Yuan Zhang Chen Guo +2 位作者 Hai Hu Shubo Liu Junbo Chu 《Journal of Marine Science and Application》 2014年第3期340-345,共6页
This paper studies the algorithm of the adaptive grid and fuzzy interacting multiple model (AGFIMM) for maneuvering target tracking, while focusing on the problems of the fixed structure multiple model (FSMM) algo... This paper studies the algorithm of the adaptive grid and fuzzy interacting multiple model (AGFIMM) for maneuvering target tracking, while focusing on the problems of the fixed structure multiple model (FSMM) algorithm's cost-efficiency ratio being not high and the Markov transition probability of the interacting multiple model (IMM) algorithm being difficult to determine exactly. This algorithm realizes the adaptive model set by adaptive grid adjustment, and obtains each model matching degree in the model set by fuzzy logic inference. The simulation results show that the AGFIMM algorithm can effectively improve the accuracy and cost-efficiency ratio of the multiple model algorithm, and as a result is suitable for enineering apolications. 展开更多
关键词 maneuvering target tracking adaptive grid fuzzy logicinference variable structure multiple model adaptive grid andfuzzy interacting multiple model (AGFIMM) interacting multiplemodel (IMM)
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An Optimization Algorithm Employing Multiple Metamodels and Optimizers 被引量:2
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作者 Yoel Tenne 《International Journal of Automation and computing》 EI CSCD 2013年第3期227-241,共15页
Modern engineering design optimization often relies on computer simulations to evaluate candidate designs, a setup which results in expensive black-box optimization problems. Such problems introduce unique challenges,... Modern engineering design optimization often relies on computer simulations to evaluate candidate designs, a setup which results in expensive black-box optimization problems. Such problems introduce unique challenges, which has motivated the application of metamodel-assisted computational intelligence algorithms to solve them. Such algorithms combine a computational intelligence optimizer which employs a population of candidate solutions, with a metamodel which is a computationally cheaper approximation of the expensive computer simulation. However, although a variety of metamodels and optimizers have been proposed, the optimal types to employ are problem dependant. Therefore, a priori prescribing the type of metamodel and optimizer to be used may degrade its effectiveness. Leveraging on this issue, this study proposes a new computational intelligence algorithm which autonomously adapts the type of the metamodel and optimizer during the search by selecting the most suitable types out of a family of candidates at each stage. Performance analysis using a set of test functions demonstrates the effectiveness of the proposed algorithm, and highlights the merit of the proposed adaptation approach. 展开更多
关键词 Expensive optimization problems computational intelligence adaptive algorithms METAmodelLING model selection.
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A Multiple Model Approach to Modeling Based on LPF Algorithm 被引量:2
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作者 Li, N. Li, S. Xi, Y. 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2001年第3期64-70,共7页
Input-output data fitting methods are often used for unknown-structure nonlinear system modeling. Based on model-on-demand tactics, a multiple model approach to modeling for nonlinear systems is presented. The basic i... Input-output data fitting methods are often used for unknown-structure nonlinear system modeling. Based on model-on-demand tactics, a multiple model approach to modeling for nonlinear systems is presented. The basic idea is to find out, from vast historical system input-output data sets, some data sets matching with the current working point, then to develop a local model using Local Polynomial Fitting (LPF) algorithm. With the change of working points, multiple local models are built, which realize the exact modeling for the global system. By comparing to other methods, the simulation results show good performance for its simple, effective and reliable estimation. 展开更多
关键词 algorithmS Computer simulation Data structures Input output programs Mathematical models Parameter estimation POLYNOMIALS
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Multiple QoS modeling and algorithm in computational grid 被引量:1
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作者 Li Chunlin Feng Meilai Li Layuan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2007年第2期412-417,共6页
Multiple QoS modeling and algorithm in grid system is considered. Grid QoS requirements can be formulated as a utility function for each task as a weighted sum of its each dimensional QoS utility functions. Multiple Q... Multiple QoS modeling and algorithm in grid system is considered. Grid QoS requirements can be formulated as a utility function for each task as a weighted sum of its each dimensional QoS utility functions. Multiple QoS constraint resource scheduling optimization in computational grid is distributed to two subproblems: optimization of grid user and grid resource provider. Grid QoS scheduling can be achieved by solving sub problems via an iterative algorithm. 展开更多
关键词 QoS modeling Computational grid Scheduling algorithm.
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A solution of UAV localization problem using an interacting multiple nonlinear fuzzy adaptive H_(∞)models filter algorithm 被引量:3
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作者 Elzoghby MOSTAFA Li FU +1 位作者 Arafa IBRAHIM.I. Arif USMAN 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2019年第4期978-990,共13页
The purpose of this research is to improve the robustness of the autonomous system in order to improve the position and velocity estimation of an Unmanned Aerial Vehicle(UAV).Therefore, new integrated SINS/GPS navigat... The purpose of this research is to improve the robustness of the autonomous system in order to improve the position and velocity estimation of an Unmanned Aerial Vehicle(UAV).Therefore, new integrated SINS/GPS navigation scheme based on Interacting Multiple Nonlinear Fuzzy Adaptive H_∞ Models(IMM-NFAH_∞) filtering technique for UAV is presented. The proposed IMM-NFAH_∞ strategy switches between two different Nonlinear Fuzzy Adaptive H_∞(NFAH_∞) filters and each NFAH_∞ filter is based on different fuzzy logic inference systems. The newly proposed technique takes into consideration the high order Taylor series terms and adapts the nonlinear H_∞ filter based on different fuzzy inference systems via adaptive filter bounds(di),along with disturbance attenuation parameter c. Simulation analysis validates the performance of the proposed algorithm, and the comparison with nonlinear H_∞(NH_∞) filter and that with different NFAH_∞ filters demonstrate the effectiveness of UAV localization utilizing IMM-NFAH_∞ filter. 展开更多
关键词 Interacting multiple models Integrated navigation system Multi-mode estimation Nonlinear fuzzy adaptive filter Sensor data fusion UAV localization
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A novel maneuvering multi-target tracking algorithm based on multiple model particle filter in clutters 被引量:2
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作者 胡振涛 Pan Quan Yang Feng 《High Technology Letters》 EI CAS 2011年第1期19-24,共6页
To solve the problem of strong nonlinear and motion model switching of maneuvering target tracking system in clutter environment, a novel maneuvering multi-target tracking algorithm based on multiple model particle fi... To solve the problem of strong nonlinear and motion model switching of maneuvering target tracking system in clutter environment, a novel maneuvering multi-target tracking algorithm based on multiple model particle filter is presented in this paper. The algorithm realizes dynamic combination of multiple model particle filter and joint probabilistic data association algorithm. The rapid expan- sion of computational complexity, caused by the simple combination of the interacting multiple model algorithm and particle filter is solved by introducing model information into the sampling process of particle state, and the effective validation and utilization of echo is accomplished by the joint proba- bilistic data association algorithm. The concrete steps of the algorithm are given, and the theory analysis and simulation results show the validity of the method. 展开更多
关键词 maneuvering multi-target tracking multiple model particle filter interacting multiple model IMM) joint probabilistic data association
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Directional Modulation Based on a Quantum Genetic Algorithm for a Multiple-Reflection Model 被引量:1
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作者 Yuwei Huang Xiubo Chen +2 位作者 Kaiguo Yuan Jianyi Zhang Biao Liu 《Computers, Materials & Continua》 SCIE EI 2020年第9期1771-1783,共13页
Directional modulation is one of the hot topics in data security researches.To fulfill the requirements of communication security in wireless environment with multiple paths,this study takes into account the factors o... Directional modulation is one of the hot topics in data security researches.To fulfill the requirements of communication security in wireless environment with multiple paths,this study takes into account the factors of reflections and antenna radiation pattern for directional modulation.Unlike other previous works,a novel multiple-reflection model,which is more realistic and complex than simplified two-ray reflection models,is proposed based on two reflectors.Another focus is a quantum genetic algorithm applied to optimize antenna excitation in a phased directional modulation antenna array.The quantum approach has strengths in convergence speed and the globe searching ability for the complicated model with the large-size antenna array and multiple paths.From this,a phased directional modulation transmission system can be optimized as regards communication safety and improve performance based on the constraint of the pattern of the antenna array.Our work can spur applications of the quantum evolutionary algorithm in directional modulation technology,which is also studied. 展开更多
关键词 Directional modulation quantum genetic algorithm phased antenna array multiple reflection
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Optimal Planning of Multiple PV-DG in Radial Distribution Systems Using Loss Sensitivity Analysis and Genetic Algorithm
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作者 A. Elkholy 《Journal of Power and Energy Engineering》 2025年第2期1-22,共22页
This paper introduces an optimized planning approach for integrating photovoltaic as distributed generation (PV-DG) into the radial distribution power systems, utilizing exhaustive load flow (ELF), loss sensitivity fa... This paper introduces an optimized planning approach for integrating photovoltaic as distributed generation (PV-DG) into the radial distribution power systems, utilizing exhaustive load flow (ELF), loss sensitivity factor (LSF), genetic algorithms (GA) methods, and numerical method based on LSF. The methodology aims to determine the optimal allocation and sizing of multiple PV-DG to minimize power loss through time series power flow analysis. An approach utilizing continuous sensitivity analysis is developed and inherently leverages power flow and loss equations to compute LSF of all buses in the system towards employing a dynamic PV-DG model for more accurate results. The algorithm uses a numerical grid search method to optimize PV-DG placement in a power distribution system, focusing on minimizing system losses. It combines iterative analysis, sensitivity assessment, and comprehensive visualization to identify and present the optimal PV-DG configurations. The present-ed algorithms are verified through co-simulation framework combining MATLAB and OpenDSS to carry out analysis for 12-bus radial distribution test system. The proposed numerical method is compared with other algorithms, such as ELF, LSF methods, and Genetic Algorithms (GA). Results show that the proposed numerical method performs well in comparison with LSF and ELF solutions. 展开更多
关键词 Photovoltaic Systems Distributed Generation multiple Allocation and Sizing Power Losses Radial Distribution System Genetic algorithm
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Adaptive Multi-Learning Cooperation Search Algorithm for Photovoltaic Model Parameter Identification
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作者 Xu Chen Shuai Wang Kaixun He 《Computers, Materials & Continua》 2025年第10期1779-1806,共28页
Accurate and reliable photovoltaic(PV)modeling is crucial for the performance evaluation,control,and optimization of PV systems.However,existing methods for PV parameter identification often suffer from limitations in... Accurate and reliable photovoltaic(PV)modeling is crucial for the performance evaluation,control,and optimization of PV systems.However,existing methods for PV parameter identification often suffer from limitations in accuracy and efficiency.To address these challenges,we propose an adaptive multi-learning cooperation search algorithm(AMLCSA)for efficient identification of unknown parameters in PV models.AMLCSA is a novel algorithm inspired by teamwork behaviors in modern enterprises.It enhances the original cooperation search algorithm in two key aspects:(i)an adaptive multi-learning strategy that dynamically adjusts search ranges using adaptive weights,allowing better individuals to focus on local exploitation while guiding poorer individuals toward global exploration;and(ii)a chaotic grouping reflection strategy that introduces chaotic sequences to enhance population diversity and improve search performance.The effectiveness of AMLCSA is demonstrated on single-diode,double-diode,and three PV-module models.Simulation results show that AMLCSA offers significant advantages in convergence,accuracy,and stability compared to existing state-of-the-art algorithms. 展开更多
关键词 Photovoltaic model parameter identification cooperation search algorithm adaptive multiple learning chaotic grouping reflection
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TERIME:An Improved RIME Algorithm With Enhanced Exploration and Exploitation for Robust Parameter Extraction of Photovoltaic Models
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作者 Shi-Shun Chen Yu-Tong Jiang +1 位作者 Wen-Bin Chen Xiao-Yang Li 《Journal of Bionic Engineering》 2025年第3期1535-1556,共22页
Parameter extraction of photovoltaic(PV)models is crucial for the planning,optimization,and control of PV systems.Although some methods using meta-heuristic algorithms have been proposed to determine these parameters,... Parameter extraction of photovoltaic(PV)models is crucial for the planning,optimization,and control of PV systems.Although some methods using meta-heuristic algorithms have been proposed to determine these parameters,the robustness of solutions obtained by these methods faces great challenges when the complexity of the PV model increases.The unstable results will affect the reliable operation and maintenance strategies of PV systems.In response to this challenge,an improved rime optimization algorithm with enhanced exploration and exploitation,termed TERIME,is proposed for robust and accurate parameter identification for various PV models.Specifically,the differential evolution mutation operator is integrated in the exploration phase to enhance the population diversity.Meanwhile,a new exploitation strategy incorporating randomization and neighborhood strategies simultaneously is developed to maintain the balance of exploitation width and depth.The TERIME algorithm is applied to estimate the optimal parameters of the single diode model,double diode model,and triple diode model combined with the Lambert-W function for three PV cell and module types including RTC France,Photo Watt-PWP 201 and S75.According to the statistical analysis in 100 runs,the proposed algorithm achieves more accurate and robust parameter estimations than other techniques to various PV models in varying environmental conditions.All of our source codes are publicly available at https://github.com/dirge1/TERIME. 展开更多
关键词 Photovoltaic modeling RIME algorithm Optimization problems Meta-heuristic algorithms STABILITY
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An algorithm for quantifying filopodia of multiple cells with weak fluorescence signal
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作者 Muyang Hao Hongcong Zheng +3 位作者 Xiaoyan Wang Qing Ye Renqun Liu Yimei Huang 《Journal of Innovative Optical Health Sciences》 2025年第6期55-67,共13页
Filopodia function as cellular sensors,detecting the microenvironment and directing cell migration.They play a crucial role in cancer metastasis.Quantifying the filopodia characteristics of cancer cells is a prerequis... Filopodia function as cellular sensors,detecting the microenvironment and directing cell migration.They play a crucial role in cancer metastasis.Quantifying the filopodia characteristics of cancer cells is a prerequisite for studying the complex role of filopodia in cancer cell metastasis.Several algorithms have been developed,yet most of these algorithms are typically suited for extracting filopodia from individual cells.This paper aims to develop an independent algorithm(MC-FiloAssay)for quantifying filopodia in multi-cell environments.The filopodia of nasopharyngeal carcinoma cells(CNE2 and 5-8F)and normal nasopharyngeal epithelial cells(NP69)were quantified with MC-FiloAssay.A linear regression analysis comparing filopodia lengths measured by MC-FiloAssay and manual annotation yielded a coefficient of determination(R^(2)=0.99),indicating high accuracy in multi-cell filopodia extraction.Furthermore,MC-FiloAssay outperforms existing algorithms under low signal conditions and in multi-cell fields of view.Analysis of CNE2 cells at different confluences revealed that confluence does not affect filopodia length or width but influences filopodia density.Additionally,significant differences were observed between CNE2 and the other two cell lines(5-8 F and NP69):CNE2 filopodia were longer,thinner,and more densely distributed.These results demonstrate that MCFiloAssay is a robust tool for multi-cell filopodia quantification. 展开更多
关键词 FILOPODIA cancer metastasis multiple cells quantification algorithm nasopharyngeal carcinoma
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Multifactor diagnostic model of converter energy consumption based on K-means algorithm and its application
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作者 Fei-xiang Dai Guang Chen +3 位作者 Xiang-jun Bao Gong-guo Liu Lu Zhang Xiao-jing Yang 《Journal of Iron and Steel Research International》 2025年第8期2359-2369,共11页
To address the challenge of identifying the primary causes of energy consumption fluctuations and accurately assessing the influence of various factors in the converter unit of an iron and steel plant,the focus is pla... To address the challenge of identifying the primary causes of energy consumption fluctuations and accurately assessing the influence of various factors in the converter unit of an iron and steel plant,the focus is placed on the critical components of material and heat balance.Through a thorough analysis of the interactions between various components and energy consumptions,six pivotal factors have been identified—raw material composition,steel type,steel temperature,slag temperature,recycling practices,and operational parameters.Utilizing a framework based on an equivalent energy consumption model,an integrated intelligent diagnostic model has been developed that encapsulates these factors,providing a comprehensive assessment tool for converter energy consumption.Employing the K-means clustering algorithm,historical operational data from the converter have been meticulously analyzed to determine baseline values for essential variables such as energy consumption and recovery rates.Building upon this data-driven foundation,an innovative online system for the intelligent diagnosis of converter energy consumption has been crafted and implemented,enhancing the precision and efficiency of energy management.Upon implementation with energy consumption data at a steel plant in 2023,the diagnostic analysis performed by the system exposed significant variations in energy usage across different converter units.The analysis revealed that the most significant factor influencing the variation in energy consumption for both furnaces was the steel grade,with contributions of−0.550 and 0.379. 展开更多
关键词 Equivalent energy consumption model Intelligent diagnostic model K-means clustering algorithm Online system Energy management
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Extinction and Optimal Control of Stochastic Epidemic Model with Multiple Vaccinations and Time Delay
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作者 YANG Rujie QIU Hong JU Xuewei 《数学理论与应用》 2025年第2期110-121,共12页
In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and co... In this paper,based on the SVIQR model we develop a stochastic epidemic model with multiple vaccinations and time delay.Firstly,we prove the existence and uniqueness of the global positive solution of the model,and construct suitable functions to obtain sufficient conditions for disease extinction.Secondly,in order to effectively control the spread of the disease,appropriate control strategies are formulated by using optimal control theory.Finally,the results are verified by numerical simulation. 展开更多
关键词 Stochastic epidemic model multiple vaccinations Extinction of disease Isolation delay Optimal control
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