Mohammad Fardad;Elham Mohammadzadeh Mianji;Gabriel-Miro Muntean;Irina Tal
{"title":"Permissioned Distributed Ledgers-Based Cooperative Decentralized Vehicular Edge Computing for Secure and Efficient Task Computation","authors":"Mohammad Fardad;Elham Mohammadzadeh Mianji;Gabriel-Miro Muntean;Irina Tal","doi":"10.1109/TITS.2026.3703872","DOIUrl":"https://doi.org/10.1109/TITS.2026.3703872","url":null,"abstract":"With the rapid advancement of the Internet of Vehicles (IoV), computationally intensive applications, like autonomous driving, pose significant challenges to the limited onboard resources of Connected and Autonomous Vehicles (CAVs). While Vehicular Edge Computing (VEC) offers relief by offloading tasks to nearby edge servers, challenges such as centralization, scalability, and security remain unresolved, particularly in the dynamic environment of IoV. In this paper, we introduce Permissioned Distributed Ledgers (PDL)-based Cooperative Decentralized Vehicular Edge Computing (PDL-CoDeVEC), a multi-layer framework that integrates PDLs into IoV networks to enhance the energy efficiency, scalability, security, and privacy of vehicular task computation. To address efficient computational decision-making, we conduct an in-depth analysis of the latency and energy consumption associated with both local and offloaded task processing. We then formulate the task computation decision-making problem as a utility maximization problem. The utility function is designed to balance the energy/computation-complexity trade-off of vehicular tasks. By maximizing the aggregated utility function, the system achieves optimal decision-making for task computation. To realize this goal, we propose a decentralized Multi-Agent Deep Reinforcement Learning (MADRL) algorithm, named Multi-Agent Cooperative TAsk Coordination (MACTAC). MACTAC enables CAVs to independently make intelligent decisions while benefiting from shared learning during the training phase. Through extensive simulations, we show that our MACTAC algorithm substantially improves aggregated utility over existing methods, enabling CAVs to complete tasks on time without compromising task completion rates, while maintaining effective scalability.","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"12819-12834"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11595261","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149097900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reinforcement Learning for Freeway Lane-Change Regulation via Connected Vehicles","authors":"Ke Sun;Huan Yu","doi":"10.1109/TITS.2026.3722245","DOIUrl":"https://doi.org/10.1109/TITS.2026.3722245","url":null,"abstract":"Lane change decision-making is a complex task due to intricate vehicle-vehicle and vehicle-infrastructure interactions. Existing algorithms for lane-change control often depend on vehicles with a certain level of autonomy (e.g., autonomous or connected autonomous vehicles), which limits their applicability under low penetration rates of automated vehicles. To address this issue, this study proposes a lane-change regulation framework using multi-agent reinforcement learning (MARL) to improve freeway traffic efficiency via connected vehicles. Specifically, lane-change regulation signals (e.g., ‘left change allowed” or ‘right change disallowed”) are computed at a traffic management center and then broadcast to connected vehicles. Thus, human-driven vehicles remain uncontrolled, while connected vehicles follow the received regulation signals. Compared to vehicle-level maneuver control, this approach reduces communication and positioning requirements, avoids direct trajectory intervention, and can accommodate different levels of connectivity and autonomy. To further bridge the gap between theoretical macroscopic analysis and microscopic simulations, the proposed framework combines a microscopic simulation environment and a macroscopic lane-grid representation. The microscopic simulator is used to generate vehicle-level trajectories and execute the realized traffic dynamics, while the macroscopic framework aggregates microscopic vehicle information into lane-grid states, enabling low-cost control at the grid-agent level. Based on a multi-lane macroscopic traffic model represented by partial differential equations (PDEs), lane changes are interpreted as source-term exchanges between adjacent lanes, which can be regulated by the proposed lane-change regulation signals. Our model is evaluated in varied traffic scenarios and demand conditions using microscopic simulation. Experimental results demonstrate that the method improves overall traffic efficiency with limited additional energy consumption while maintaining driving safety.","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"12129-12141"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149097905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cheng Zhang;Hai Wang;Long Chen;Yicheng Li;Yingfeng Cai
{"title":"HybridFusion: A Universal Multimodal Data Fusion Framework for 3-D Detection and Tracking","authors":"Cheng Zhang;Hai Wang;Long Chen;Yicheng Li;Yingfeng Cai","doi":"10.1109/TITS.2026.3722557","DOIUrl":"https://doi.org/10.1109/TITS.2026.3722557","url":null,"abstract":"Environment perception based on multimodal data fusion is crucial for the development of autonomous driving (AD) technology. However, the existing fusion-based detection and tracking methods often struggle to efficiently utilize the multimodal complementary information. This limitation can significantly impact the safety of autonomous vehicles (AVs), especially in complex traffic scenarios and adverse weather conditions. To address this issue, this work proposes a universal multimodal data fusion framework called HybridFusion for 3-D object detection and tracking tasks. Specifically, a novel Modal-Specific Feature Interaction Strategy (MSFIS) is introduced within the detection algorithm. The strategy complementarily fuses multimodal features while preserving the potential information from individual modalities. Furthermore, a Motion-Appearance Coupling Driven Data Association Strategy (MACD-DAS) is incorporated into the tracking algorithm. The strategy comprehensively processes spatial motion information and multimodal appearance features, effectively reducing the uncertainty in state prediction and feature matching. Extensive experiments were conducted on View-of-Delft (VoD) and K-Radar datasets. The experimental results demonstrate that the proposed HybridFusion significantly improves the performance of multimodal detection and tracking algorithms in complex traffic scenes and adverse weather conditions. The demo is available at <uri>https://youtu.be/el_5jtxDO2I</uri>","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"12027-12042"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149097889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Anticipatory Driving Maneuver for Safety and Comfort: Temporal Graph Cross Attention-Based Front Vehicle Trajectory Prediction","authors":"Hyunsik Min;Gyeongseon Baek;Yeeun Kim;Byeongjoon Noh","doi":"10.1109/TITS.2026.3703652","DOIUrl":"https://doi.org/10.1109/TITS.2026.3703652","url":null,"abstract":"Advanced autonomous driving (AD) systems must move beyond reactive collision avoidance and support anticipatory maneuver planning that preserves ride comfort, traffic flow stability, and user trust. In interactive traffic environments, proactively anticipating front-vehicle behavior is particularly important for maintaining near-term ego stability and comfort under realistic sensing constraints. This study proposes a vision-only front-vehicle trajectory prediction framework that constructs ego-centered spatiotemporal graphs from forward-facing monocular dashcam video and forecasts future trajectories using a Temporal Graph Cross Attention (TGCA) mechanism. TGCA selectively emphasizes interaction-critical vehicles by capturing temporally aligned behavior patterns across consecutive frames. The proposed framework was validated through real-world dashcam experiments on an in-house dataset and a curated public CoVLA benchmark subset, together with traffic-simulation-based evaluations. Across both datasets, the model achieved a 5-s prediction MAE of approximately 0.09. In downstream simulations using cut-in as a representative interaction-critical lane-change scenario, the framework reduced high-risk events with time-to-collision (TTC) below 1.5 s by 82% and lowered average delay by about 11%. These results suggest that front-vehicle trajectory prediction can provide a practical foundation for prediction-driven anticipatory driving in future AD systems operating under realistic sensing constraints.","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"12737-12750"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149096968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jia Hu;Zhexi Lian;Haoran Wang;Zihan Zhang;Ruoxi Qian;Duo Li;Jaehyun So
{"title":"Anti-Bullying Adaptive Cruise Control: A Proactive Right-of-Way Protection Approach","authors":"Jia Hu;Zhexi Lian;Haoran Wang;Zihan Zhang;Ruoxi Qian;Duo Li;Jaehyun So","doi":"10.1109/TITS.2026.3723562","DOIUrl":"https://doi.org/10.1109/TITS.2026.3723562","url":null,"abstract":"Adaptive Cruise Control (ACC) systems have been widely commercialized in recent years. However, existing ACC systems remain vulnerable to close-range cut-ins, a behavior that resembles “road bullying”. To address this issue, this research proposes an Anti-bullying Adaptive Cruise Control (AACC) approach under a vehicle-cloud cooperation scheme. To handle diverse “road bullying” cut-in scenarios smoothly, the proposed approach first leverages an online Inverse Optimal Control (IOC)-based algorithm for individual driving style identification in the cloud. Then, based on Stackelberg competition, a game-theoretic-based motion planning framework is presented in which the identified individual driving styles are utilized to formulate cut-in vehicles’ reaction functions. By integrating such reaction functions into the ego vehicle’s motion planning, the cloud could consider cut-in vehicles’ all possible reactions to find optimal right-of-way protection maneuvers for the ego vehicle. To the best of our knowledge, this research is the first to model vehicles’ interaction dynamics and develop an interactive planner that adapts to various cut-in vehicle driving styles. Simulation results show that the proposed approach can prevent “road bullying” cut-ins and be adaptive to different cut-in vehicles’ driving styles. Compared with the traditional ACC, the proposed approach can improve safety and comfort by up to 79.8% and 20.8%. The driving efficiency is improved by up to 17.32% in traffic flow. Increasing the penetration rate of cloud-connected EVs improves lane-average speed by up to 1.36 km/h, demonstrating traffic-flow-level benefits. Furthermore, the proposed approach can support real-time field implementation by ensuring less than 50 milliseconds computation time in nearly all cases.","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"12079-12095"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149097101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Observer-Based Adaptive Estimation for Time Delay Hyperbolic PDE Systems With Application to Traffic Dynamics","authors":"Yong Qin;Ning Xu;Xudong Zhao;Guangdeng Zong;Ben Niu","doi":"10.1109/TITS.2026.3706736","DOIUrl":"https://doi.org/10.1109/TITS.2026.3706736","url":null,"abstract":"This paper presents the design of a Luenberger-type adaptive boundary observer for a class of linear hyperbolic partial differential equation models describing traffic dynamics. The observer enables online joint estimation of the traffic flow system state and unknown parameter using boundary measurement data. By integrating swapping transformations with adaptive parameter update law, the observer effectively reconstructs the traffic state and identifies parameter, mitigating traffic oscillations and congestion propagation. A Lyapunov-based stability analysis demonstrates that the estimation errors for both the state and parameters converge exponentially to a bounded residual set, provided the observer gain satisfies a specific linear matrix inequality. The effectiveness of the proposed design is validated using real-world traffic data from the NGSIM US 101 dataset.","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"12661-12671"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149097310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"STELLAR: Spatio-Temporal Tensor Completion via Low-Rankness and Smoothness of Difference Features for Traffic Data Imputation","authors":"Kaijie Wang;Zai Yang;Hailin Wang","doi":"10.1109/TITS.2026.3706346","DOIUrl":"https://doi.org/10.1109/TITS.2026.3706346","url":null,"abstract":"Low-rank matrix/tensor completion methods have attracted growing interest in traffic data imputation. These approaches leverage the low-rank structure and spatio-temporal smoothness of traffic measurements. However, most existing methods model these properties separately and combine them in a linear manner. This simplification overlooks the interdependencies between low-rank structure and smoothness, potentially degrading imputation quality. To address this issue, we propose a method termed STELLAR (<inline-formula> <tex-math>$boldsymbol {s}$ </tex-math></inline-formula>patio-<bold><i>te</i></b>mporal tensor comp<inline-formula> <tex-math>$boldsymbol {l}$ </tex-math></inline-formula>etion via <inline-formula> <tex-math>$boldsymbol {l}$ </tex-math></inline-formula>ow-r<inline-formula> <tex-math>$boldsymbol {a}$ </tex-math></inline-formula>nkness and smoothness of diffe<inline-formula> <tex-math>$boldsymbol {r}$ </tex-math></inline-formula>ence features), which fuses global low-rankness and local spatio-temporal smoothness of traffic data in a unified manner. Specifically, we impose the nuclear norm on the difference features after three spatio-temporal difference transformations of the traffic tensor, thereby simultaneously quantifying the low-rankness and smoothness. This results in a convex formulation of STELLAR that is efficiently solved via the alternating direction method of multipliers (ADMM). We prove the global convergence of STELLAR to an optimal solution of the associated convex problem. Extensive experiments on real-world traffic datasets demonstrate that STELLAR outperforms many state-of-the-art methods while maintaining competitive computational efficiency. In particular, on the Seattle traffic dataset, STELLAR achieves up to an 11.1% reduction in root mean square error (RMSE) over the suboptimal baseline. The STELLAR code is available at <uri>https://github.com/IAmEzreal/STELLAR.git</uri>","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"12672-12686"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149097311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Two-Stage Stochastic Program for Scheduling Bus Service Under Demand Uncertainty","authors":"Wei Huang;Shichu Rong;Yingying Lin;Jiemin Xie;Yilin Chen","doi":"10.1109/TITS.2026.3706587","DOIUrl":"https://doi.org/10.1109/TITS.2026.3706587","url":null,"abstract":"To improve the reliability of public transport (PT) service, this paper develops a PT operating mode considering both regular and flexible services. Flexible bus services are introduced to accommodate demand that cannot be served by regular operations under demand uncertainty. A two-stage stochastic program is proposed to jointly optimize the service design decisions (i.e., stop allocation and service headway) and vehicle scheduling decisions. To solve the problem efficiently, the concept of service reliability (SR) is introduced to reformulate the coupled two-stage problem into two independently tractable subproblems. An SR-based gradient solution framework integrating fixed-point structure and branch-and-price is developed to efficiently obtain a high-quality solution. The proposed model and the SR-based approach are evaluated on both a toy service line and a real bus line in Shenzhen, China. The effects of demand variability on different costs of the transit system are further analyzed. Numerical results show that the proposed SR-based approach can effectively balance service design and operational adjustments to reduce the expected total system cost under demand uncertainty.","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"12265-12278"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149097322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shirui Tian;Huilong Pi;Mingxing Duan;Zhuo Tang;Kenli Li
{"title":"FDOD: A Novel Few-Shot Small Object Detection Framework Using Fractional Fourier Transform and Differentiation","authors":"Shirui Tian;Huilong Pi;Mingxing Duan;Zhuo Tang;Kenli Li","doi":"10.1109/TITS.2026.3707002","DOIUrl":"https://doi.org/10.1109/TITS.2026.3707002","url":null,"abstract":"Few-shot small object detection poses a pivotal challenge in enhancing object recognition accuracy for autonomous driving. Limited by the scarcity of training samples, it struggles with inadequate semantic features and generalization capabilities across scales and domains. To address this, this paper introduces an efficient and lightweight Fractional Fourier Transform (FrFT) and Fractional Differentiation (FD) optimization for small object detection, abbreviated as FDOD, comprising four modules: meta-learning-based feature extraction, FrFT and FD optimization-based feature enhancement, alignment fine-tuning, and small object prediction. Firstly, a shared backbone network is employed to extract features from support and query samples; Secondly, the FrFT and FD optimization-based module is designed to decompose object features into phase and amplitude components, thereby enhancing the semantic representation of low-resolution small objects, and an FD optimization problem is formulated to dynamically optimize frequency-domain features, the combination of the two enables amplify non local textures and enhance edges in frequency bands for small object detection with few samples, and improving cross scale generalization ability; Thirdly, an adaptive attention-guided feature alignment strategy is adopted to refine the inter-class feature discrimination between support and query samples; Finally, an object bounding box is generated through the prediction head. We conducted extensive experiments on public datasets to validate FDOD. The experimental results show that its mean accuracy precision is improved by 11.7% and 8.6%, respectively, compared to the current leading model on PASCALVOC and MS-COCO, especially on small object samples such as pedestrians and bicycles, where the accuracy is improved significantly. At the same time, it demonstrated an efficient adaptive capability on KITTI, with a computational efficiency of <inline-formula> <tex-math>$mathrm {1.33times }$ </tex-math></inline-formula> that of the current leading model.","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"13011-13023"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149097393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Systematic Review of Driver Behavior Studies to Improve Road Safety and Eco-Sustainability","authors":"Vittorio Nicolosi;Maria Augeri;Lella Liana Imbriani;Giuseppe Cappelli;Marco Mameli;Sepideh Shiralizadeh","doi":"10.1109/TITS.2026.3717478","DOIUrl":"https://doi.org/10.1109/TITS.2026.3717478","url":null,"abstract":"Road safety and environmental pollution are two major issues in road transportation. Driver behavior, understood as a set of events (accelerations, braking, pedal use, lane changes, speed, etc.) describing driving styles and driver states, is central to both reducing crash risks and achieving environmental sustainability. Improving behavior through profiling, feedback, technological support (e.g., ADAS), and incentive schemes can both save lives and reduce fuel consumption and greenhouse gas emissions. This dual benefit makes it a crucial topic for governments, insurers, fleet managers, and automotive engineers. This paper presents a Systematic Literature Review (SLR) aimed at describing the state of knowledge on the classification of driving styles. It examines the different forms of driver behavior, along with the study types, data sources, datasets, features, preprocessing methods, and artificial intelligence algorithms employed to classify such behaviors and assess their effectiveness. Based on the reviewed studies, the goal is to support future experiments and the development of new behavioral models for driver assistance and autonomous driving systems, enhancing both safety and environmental performance. The main novelty of this study lies in its comprehensive and updated perspective on driver behavior research. Unlike previous reviews, which were often limited to naturalistic studies or specific data collection tools, this work considers a wider range of approaches, including naturalistic studies, site-based observations, and driving simulator experiments. Furthermore, the review is updated through 2024 and includes a large number of papers, providing broader and more comprehensive insights.","PeriodicalId":13416,"journal":{"name":"IEEE Transactions on Intelligent Transportation Systems","volume":"27 10","pages":"11912-11928"},"PeriodicalIF":9.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149097367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}