Results in Control and Optimization最新文献_第2页

Deep learning based 3D residual convolutional and Multi-Head Attention (3D-RMA) for lip-reading 基于深度学习的三维残差卷积和多头注意唇读算法

IF 3.2

Results in Control and Optimization Pub Date : 2025-09-01 DOI: 10.1016/j.rico.2025.100608

Archana Chaudhari , Masuk Abdullah , Vivek Deshpande , Tushar Zanke , Samrudhi Wath , Snehashish Mulgir , Stuti Jagtap

{"title":"Deep learning based 3D residual convolutional and Multi-Head Attention (3D-RMA) for lip-reading","authors":"Archana Chaudhari , Masuk Abdullah , Vivek Deshpande , Tushar Zanke , Samrudhi Wath , Snehashish Mulgir , Stuti Jagtap","doi":"10.1016/j.rico.2025.100608","DOIUrl":"10.1016/j.rico.2025.100608","url":null,"abstract":"<div><div>Lip reading, an essential yet intricate facet of communication, has seen notable progress through the application of advanced deep learning techniques. This research introduces a deep learning-based lip-reading model that integrates Conv3D layers, Multi-Head Attention mechanisms, Bidirectional LSTMs, and a Dense output layer, combined with a custom Connectionist Temporal Classification (CTC) loss function. Our comprehensive data preprocessing pipeline extracts video frames, normalizes pixel values, and converts textual alignments into numerical tokens, enabling effective model integration. The model architecture is carefully structured to capture spatiotemporal features, with Conv3D layers addressing spatial information, while Multi-Head Attention mechanisms and Bidirectional LSTMs effectively manage temporal dependencies. Residual connections and Max-Pooling layers are incorporated to enhance feature extraction and abstraction, supporting improved performance. The use of Layer Normalization and Dropout layers contributes to stable learning and mitigates overfitting. Through extensive training and evaluation, our model demonstrates a 96% accuracy rate in decoding lip movements and predicting corresponding words. The implementation of the CTC loss function allows for effective handling of variable-length sequences, further contributing to the model’s performance. This research provides a technically sound approach to lip reading, contributing to the advancement of visual speech recognition and offering potential benefits for communication accessibility among individuals with hearing impairments.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"20 ","pages":"Article 100608"},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamics of pest control model using natural enemy and refugia plant 利用天敌和避难植物防治害虫模型的动态

IF 3.2

Results in Control and Optimization Pub Date : 2025-08-18 DOI: 10.1016/j.rico.2025.100607

Muhammad Luthfi , Agus Suryanto , Isnani Darti , Farah Aini Abdullah

{"title":"Dynamics of pest control model using natural enemy and refugia plant","authors":"Muhammad Luthfi , Agus Suryanto , Isnani Darti , Farah Aini Abdullah","doi":"10.1016/j.rico.2025.100607","DOIUrl":"10.1016/j.rico.2025.100607","url":null,"abstract":"<div><div>In this study, we introduce a pest control model that describes the interaction among pests, natural enemies (predators), and refugia plants, incorporating intraspecific competition within the predator population. Predators interact mutually with refugia plants to maintain their presence in agricultural areas, enhancing their control of the pest population. On the other hand, heightened intraspecific competition for two key resources, nectar and pests, may encourage predators to migrate and exploit new resources. The non-negativity and boundedness of the solutions are shown to ensure that the proposed model is biologically feasible. We perform dynamic analysis to identify all potential equilibrium points and examine their local and global stability characteristics. The model has seven equilibrium points. However, only three of them are conditionally stable. The pest-free equilibrium point is stable under certain conditions, indicating that the pest population may be effectively controlled. Furthermore, we show that our system exhibits a Hopf bifurcation. Finally, we confirm our analytical results through some numerical simulations.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"20 ","pages":"Article 100607"},"PeriodicalIF":3.2,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144866640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamical analysis of time delay effects on the stability of a harvested predator-prey system with a general Holling type response 时滞对具有一般Holling型响应的捕获捕食系统稳定性影响的动力学分析

IF 3.2

Results in Control and Optimization Pub Date : 2025-08-10 DOI: 10.1016/j.rico.2025.100603

Odhiambo Francis

引用次数: 0

Hybrid Hunger Games Search optimization using a neural networks approach applied to UAVs 混合饥饿游戏搜索优化的神经网络方法应用于无人机

IF 3.2

Results in Control and Optimization Pub Date : 2025-07-28 DOI: 10.1016/j.rico.2025.100599

Nadia Samantha Zuñiga-Peña , Salatiel Garcia-Nava , Norberto Hernandez-Romero , Juan Carlos Seck-Touh-Mora

{"title":"Hybrid Hunger Games Search optimization using a neural networks approach applied to UAVs","authors":"Nadia Samantha Zuñiga-Peña , Salatiel Garcia-Nava , Norberto Hernandez-Romero , Juan Carlos Seck-Touh-Mora","doi":"10.1016/j.rico.2025.100599","DOIUrl":"10.1016/j.rico.2025.100599","url":null,"abstract":"<div><div>Optimization methods like population-based algorithms are valuable when applied to multidimensional and nonlinear problems. Many engineering problems, such as controller parameterization, can be addressed using population-based algorithms since these parameters are usually found through essays, resulting in high time and resource consumption. Population-based algorithms need to define the range within which the search for the best solution is performed, known as the search space. However, due to the nonlinear nature of the systems to which these controllers are applied, there is no certainty about the search space that must be defined. This study proposes a hybrid optimization strategy that couples the Hunger Games Search (HGS) metaheuristic with an unsupervised Self Organizing Map, Kohonen Neural Network, to improve trajectory-tracking control of unmanned aerial vehicles (UAVs) transporting cable suspended loads. In the proposed NNHGS, the HGS algorithm seeks the controller gains that minimize Root Mean Square tracking Error (RMSE). At the same time, the neural network continuously reshapes the search intervals according to the evolving tracking performance. By expanding the exploration into parameter regions beyond the initial bounds, the NNHGS finds high-quality solutions that standard HGS excludes. The simulation results obtained with a Super Twisting Sliding Mode Controller (STSMC) show a reduction in the final tracking error from RMSE=0.0480 with HGS to RMSE = 0.0204 by NNHGS, along with enhanced disturbance rejection and rapid adaptation to parameter changes. These gains highlight the suitability of this method for real-world missions such as logistics, disaster relief, or remote inspection, where UAVs must remain stable under uncertain or parameter-varying conditions.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"20 ","pages":"Article 100599"},"PeriodicalIF":3.2,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144738354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal control and cost-effectiveness analysis of Q-fever transmission dynamics in livestock and humans 家畜和人之间q热传播动力学的最优控制和成本-效果分析

IF 3.2

Results in Control and Optimization Pub Date : 2025-07-28 DOI: 10.1016/j.rico.2025.100601

Nkuba Nyerere , Verediana M. Mbalilo

{"title":"Optimal control and cost-effectiveness analysis of Q-fever transmission dynamics in livestock and humans","authors":"Nkuba Nyerere , Verediana M. Mbalilo","doi":"10.1016/j.rico.2025.100601","DOIUrl":"10.1016/j.rico.2025.100601","url":null,"abstract":"<div><div>Q-fever, caused by the zoonotic bacterium <em>Coxiella burnetii</em>, remains a significant global health concern due to its complex transmission dynamics involving livestock, humans, and the environment. This study develops a comprehensive mathematical model to investigate the spread of Q-fever and assess the effectiveness of five distinct control strategies targeting both human and animal populations. The model incorporates key epidemiological factors, including environmental contamination, which plays a critical role in sustaining indirect transmission. Numerical simulations and cost-effectiveness analysis reveal that early, coordinated, and sustained interventions are vital for effective disease control. In particular, the combination of livestock vaccination, gradual culling of seropositive animals, and public health education, emerged as the most cost-effective, achieving elimination in humans within two years, symptomatic livestock within three years, and asymptomatic livestock within four years. In the absence of interventions, the model predicts exponential disease spread, with Q-fever persisting for over six years in livestock and up to four years in humans, further fueled by environmental reservoirs. Across all scenarios, human infections are more quickly eliminated than those in livestock, highlighting the challenge of clearing environmental and animal reservoirs. These findings underscore the importance of integrated, long-term strategies that address direct and indirect transmission routes, combining animal health management, environmental decontamination, and public awareness to prevent endemicity and mitigate the health and economic burden of Q-fever.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"20 ","pages":"Article 100601"},"PeriodicalIF":3.2,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144725030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal control for system of stochastic differential equations with Lévy jumps 具有lsamvy跃变的随机微分方程系统的最优控制

IF 3.2

Results in Control and Optimization Pub Date : 2025-07-28 DOI: 10.1016/j.rico.2025.100600

Md. Abdullah Bin Masud, Mostak Ahmed

{"title":"Optimal control for system of stochastic differential equations with Lévy jumps","authors":"Md. Abdullah Bin Masud, Mostak Ahmed","doi":"10.1016/j.rico.2025.100600","DOIUrl":"10.1016/j.rico.2025.100600","url":null,"abstract":"<div><div>We have addressed the challenge of designing robust vaccination and quarantine strategies in the presence of uncertainty and random perturbations, particularly in epidemic scenarios such as COVID-19. To realistically model the dynamics of disease spread, we develop a stochastic Susceptible–Infected–Recovered (SIR) model that incorporates both Brownian motion to capture continuous, small-scale fluctuations and Lévy jumps to represent rare events. This jump effectively captures key features of real-world epidemics, such as superspreading events, the sudden emergence of new variants, and mass gatherings, which are not captured by Poisson noise or Markov jumps. The model includes time-dependent vaccination and isolation control strategies under parameter uncertainty. We solve the optimal control problem using Pontryagin’s Maximum Principle and perform numerical simulations to assess the influence of different noise sources on infection dynamics and control performance. The results show that the incorporation of Lévy jumps significantly affects epidemic outcomes. In the case of negative Lévy jumps (representing sudden quarantine or lockdown), the maximum number of infected individuals is reduced by approximately 13.4%, and the total control cost is reduced by 31.9%. The positive jump significantly amplifies infection peaks and alters optimal control paths, underscoring its critical role in epidemic modeling. The findings highlight the need to incorporate jump-driven stochasticity when designing adaptive and resilient vaccination policies in the face of extreme and unpredictable epidemic events.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"20 ","pages":"Article 100600"},"PeriodicalIF":3.2,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

High-temperature performance evaluation of sustainable date palm fiber concrete with activated carbon: An MCDM and Weibull analysis approach 可持续椰枣纤维混凝土的高温性能评价：MCDM和Weibull分析方法

IF 3.2

Results in Control and Optimization Pub Date : 2025-07-24 DOI: 10.1016/j.rico.2025.100602

Musa Adamu , Yasser E. Ibrahim , Ashwin Raut

{"title":"High-temperature performance evaluation of sustainable date palm fiber concrete with activated carbon: An MCDM and Weibull analysis approach","authors":"Musa Adamu , Yasser E. Ibrahim , Ashwin Raut","doi":"10.1016/j.rico.2025.100602","DOIUrl":"10.1016/j.rico.2025.100602","url":null,"abstract":"<div><div>This study explores the optimization and performance evaluation of date palm fiber (DPF) reinforced concrete containing powdered activated carbon (PAC) subjected to high temperatures. Multi-criteria decision-making (MCDM) and Weibull distribution analyses were used to analyse the concrete’s properties. Weight loss and residual compressive strength at 300 °C, 600 °C, and 900 °C were measured. The concrete mixes were designed with varying DPF (0 %, 1 %, 2 %, and 3 %) and PAC (0 %, 1 %, 2 %, and 3 % by cement weight). Performance evaluation included compressive strength, workability, water absorption, and mass loss were measured. The EDAS method identified Mix M1D1P (1 % DPF, 1 % PAC) as the best-performing mix composition. The optimal mix demonstrated high compressive strength (54.13 MPa), residual strength at 800 °C (25.17 MPa), and low mass loss (9.84 %), making it suitable for high-temperature applications. The MCDM results revealed that mixes with moderate PAC content (1 %) outperformed those with excessive DPF and PAC due to reduced porosity and enhanced strength retention. Statistical reliability was verified through Weibull distribution, with high degree of correlation (R² = 0.981) for the residual strength at 600 °C. The findings underscore the potential of DPF as a sustainable fiber that enhances thermal stability and mechanical performance while supporting eco-friendly construction practices. This study advances smart concrete technology by providing a systematic framework for material selection and optimization, paving the way for durable and sustainable high-performance concrete applications. The findings in this study also explores its practical applications in structural and thermal barrier systems, offering functional foresight for civil engineering and sustainable construction practices.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"20 ","pages":"Article 100602"},"PeriodicalIF":3.2,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An accurate MINLP formulation for selecting conductors in three-phase asymmetric networks: A computational implementation in the Julia software 用于选择三相非对称网络导体的精确MINLP公式：Julia软件中的计算实现

Results in Control and Optimization Pub Date : 2025-07-18 DOI: 10.1016/j.rico.2025.100596

Brandon Cortés-Caicedo , Oscar Danilo Montoya

{"title":"An accurate MINLP formulation for selecting conductors in three-phase asymmetric networks: A computational implementation in the Julia software","authors":"Brandon Cortés-Caicedo , Oscar Danilo Montoya","doi":"10.1016/j.rico.2025.100596","DOIUrl":"10.1016/j.rico.2025.100596","url":null,"abstract":"<div><div>The increasing global demand for electricity, driven by population growth and technological advancements, has necessitated the expansion of power generation, transmission, and distribution systems. Consequently, grid operators are focused on redesigning networks to enhance energy supply efficiency, with special emphasis on selecting conductors for unbalanced three-phase systems to minimize costs. This paper introduces a computational implementation of a mathematical model in the complex variable domain, addressing the conductor selection problem. The primary aim is to offer a comprehensive tutorial that guides readers through the formulation of three-phase power flow in distribution networks and the computational implementation of the conductor selection problem in both single-hour and multi-period scenarios using the Julia programming language. The mathematical models were implemented and solved using the <span>JuMP</span> optimization environment alongside the <span>Bonmin</span> solver. Validation was performed on academic test systems with different network configurations to assess the impact of conductor selection under balanced and unbalanced operating conditions. The results confirm that the proposed exact optimization methodology outperforms metaheuristic algorithms commonly found in the literature, achieving lower total costs and improved computational efficiency.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"20 ","pages":"Article 100596"},"PeriodicalIF":0.0,"publicationDate":"2025-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robust switching control design for matrix second order systems: Application to robotic cane platform 矩阵二阶系统的鲁棒切换控制设计：在机器人手杖平台上的应用

Results in Control and Optimization Pub Date : 2025-07-16 DOI: 10.1016/j.rico.2025.100597

Ivan Yupanqui, Macarena Vilca, Renzo Mendoza, Alain Chupa, Diego Arce, Jesús Alan Calderón, Bryan Bastidas, Miguel Badillo

{"title":"Robust switching control design for matrix second order systems: Application to robotic cane platform","authors":"Ivan Yupanqui, Macarena Vilca, Renzo Mendoza, Alain Chupa, Diego Arce, Jesús Alan Calderón, Bryan Bastidas, Miguel Badillo","doi":"10.1016/j.rico.2025.100597","DOIUrl":"10.1016/j.rico.2025.100597","url":null,"abstract":"<div><div>This paper addresses the switching control design problem for a class of nonlinear matrix second-order systems that characterize the dynamics of robotic and multibody systems. These systems are inherently characterized by significant nonlinearities and are subject to uncertainties, parameter variations, and external disturbances, which pose substantial challenges for control design. Analytical solutions for such control problems are often intractable, necessitating the use of numerical optimization techniques. This study presents sufficient conditions, derived from Lyapunov stability theory, for synthesizing switching feedback controllers that ensure system stability with guaranteed <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance. The approach leverages the Linear Parameter Varying (LPV) representation of the nonlinear dynamics through Takagi–Sugeno (T-S) modeling methodology. The proposed stability conditions are formulated as Linear Matrix Inequalities (LMIs), enabling efficient computation using standard convex optimization software. Comprehensive simulation studies demonstrate that the proposed switching control strategy, applicable to a broad class of nonlinear matrix second-order systems, significantly outperforms conventional weighted gain-scheduling approaches in terms of feasibility regions and <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> performance indices. Experimental validation on a robotic cane platform confirms the practical effectiveness of the proposed methodology, achieving nice dynamic performance and robust disturbance rejection capabilities.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"20 ","pages":"Article 100597"},"PeriodicalIF":0.0,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Customer satisfaction in peer-to-peer lending platforms: A text mining and sentiment analysis approach p2p借贷平台的客户满意度：文本挖掘和情感分析方法

IF 3.2

Results in Control and Optimization Pub Date : 2025-07-11 DOI: 10.1016/j.rico.2025.100598

Sarasanabelli Prasanna Kumari , Ali B.M. Ali , Madhusmita Mohanty , Bibhuti Bhusan Dash , Muhammad Rafiq , Sachi Nandan Mohanty , Iskandar Shernazarov , Nashwan Adnan Othman , Nadia Batool

{"title":"Customer satisfaction in peer-to-peer lending platforms: A text mining and sentiment analysis approach","authors":"Sarasanabelli Prasanna Kumari , Ali B.M. Ali , Madhusmita Mohanty , Bibhuti Bhusan Dash , Muhammad Rafiq , Sachi Nandan Mohanty , Iskandar Shernazarov , Nashwan Adnan Othman , Nadia Batool","doi":"10.1016/j.rico.2025.100598","DOIUrl":"10.1016/j.rico.2025.100598","url":null,"abstract":"<div><div>This study examines customer experience and satisfaction with peer-to-peer (P2P) lending platforms in India by analyzing user-generated online reviews. Despite the rapid expansion of India’s P2P lending market, few studies have analyzed consumer feedback to evaluate platform performance. To address this gap, 11,000 customer reviews were scraped from nine leading Indian P2P platforms. Text mining and sentiment analysis techniques, specifically Frequency Analysis, Convergence of Iterated Correlations (CONCOR) cluster analysis, and Exploratory Factor Analysis (EFA) were employed to extract latent satisfaction drivers. The analysis identified key experience drivers such as customer support, loan processing speed, usability, and fraud-related concerns. EFA distilled these into three underlying satisfaction factors: Positive Experiences and Core Functionalities, Customer Support and Overall Experience, and Efficiency in Application Interaction. The study reveals India-specific insights into digital lending behavior and provides targeted recommendations for improving platform trust, responsiveness, and financial accessibility, essential to user retention and financial inclusion in India’s evolving FinTech ecosystem.</div></div>","PeriodicalId":34733,"journal":{"name":"Results in Control and Optimization","volume":"20 ","pages":"Article 100598"},"PeriodicalIF":3.2,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144828521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0