Underwater Networks Research Articles

Survey of AI-driven routing protocols in underwater acoustic networks for enhanced communication efficiency

The high-speed growth of undersea communication networks requires sophisticated routing protocols to deal with challenging underwater conditions including large latencies, limited bandwidths and varying topologies. In this paper, we examine the use of Artificial Intelligence (AI), Machine Learning (ML), Reinforcement Learning (RL) and fuzzy logic to optimize routing protocols for underwater networks. We provide a comprehensive survey of existing AI-based approaches, emphasizing their novelties and constraints underwater.To assess the efficiency of these AI-based routing protocols, we carry out extensive simulations across various underwater environments where metrics such as packet delivery ratio, energy consumption, end-to-end delay, and computational efficiency are focused on. The results reveal that AI-aided protocols excel over conventional methods particularly in situations involving complex environmental dynamics as well as resources limitation.However, there are practical implementation issues which must be solved before the real-world application of AI-based routing such as hardware constraints, concerns on energy usage , and scalability. This study provides valuable insights into the integration of AI technologies into underwater communication networks, paving the way for more reliable and efficient underwater operations. Our findings contribute to the growing body of knowledge in this field and offer a foundation for future advancements in underwater communication technologies.

Capacity analysis over fractional order Rayleigh fading channel under additive white generalized Gaussian noise

AbstractThis study presents an innovative fractional order Rayleigh fading model that can be used for channel capacity estimation in the presence of additive white generalized Gaussian noise. The proposed model assumes that the real and imaginary parts of channel gains are generalized Gaussian random variables, which makes it possible to consider the traditional Rayleigh fading model as a special case of fractional order Rayleigh fading. Compared to the Rayleigh model, the fractional order Rayleigh fading model offers a more precise representation of new real‐world communication, such as integrating terrestrial and underwater networks in sixth‐generation communications channels. The probability density function of the channel gain with additive white generalized Gaussian noise is analyzed here. Furthermore, the ergodic and outage capacities of the channel are determined, taking into account the assumption that the channel state information is only available at the receiver. The ergodic capacity is calculated using Meijer's G‐functions, resulting in a closed‐form expression. Numerical simulations demonstrate the superiority of the fractional order Rayleigh fading model over the Rayleigh channel. Moreover, the impact of ergodic and outage capacities under diverse channel characteristics is assessed.

Adaptive convolutional-LSTM neural network with NADAM optimization for intrusion detection in underwater IoT wireless sensor networks

Abstract Underwater IoT networks rely on sensor nodes to continuously monitor and collect real-time data from marine environments. The nodes in the underwater networks face security challenges in terms of intrusions. Intrusions are common in conventional wireless sensor networks as well as in underwater sensor networks. Intrusions like data tampering, node insertion, unauthorized access compromises the security and privacy of the network. The existing Intrusion Detection Systems (IDS) faces limitations while detecting intrusions in Underwater IoT Wireless Sensor Networks (UIoTWSN) due to the dynamic condition of underwater environment. To overcome this, a novel IDS for UIoTWSN is proposed by combining the features of advanced deep learning techniques in an optimized manner. The proposed hybrid model comprises convolutional LSTM network with NADAM optimizer to analyze the spatial and temporal features to detect the intrusions. To handle the dynamic nature of underwater sensor network and to improve the convergence speed of the proposed IDS, NADAM optimizer is integrated in this research work. Experimentations of the proposed model validates the higher accuracy of 96.7%, precision of 94.5% and recall of 95.2% which is better than the conventional techniques.

GTR: GAN-Based Trusted Routing Algorithm for Underwater Wireless Sensor Networks.

The transmission environment of underwater wireless sensor networks is open, and important transmission data can be easily intercepted, interfered with, and tampered with by malicious nodes. Malicious nodes can be mixed in the network and are difficult to distinguish, especially in time-varying underwater environments. To address this issue, this article proposes a GAN-based trusted routing algorithm (GTR). GTR defines the trust feature attributes and trust evaluation matrix of underwater network nodes, constructs the trust evaluation model based on a generative adversarial network (GAN), and achieves malicious node detection by establishing a trust feature profile of a trusted node, which improves the detection performance for malicious nodes in underwater networks under unlabeled and imbalanced training data conditions. GTR combines the trust evaluation algorithm with the adaptive routing algorithm based on Q-Learning to provide an optimal trusted data forwarding route for underwater network applications, improving the security, reliability, and efficiency of data forwarding in underwater networks. GTR relies on the trust feature profile of trusted nodes to distinguish malicious nodes and can adaptively select the forwarding route based on the status of trusted candidate next-hop nodes, which enables GTR to better cope with the changing underwater transmission environment and more accurately detect malicious nodes, especially unknown malicious node intrusions, compared to baseline algorithms. Simulation experiments showed that, compared to baseline algorithms, GTR can provide a better malicious node detection performance and data forwarding performance. Under the condition of 15% malicious nodes and 10% unknown malicious nodes mixed in, the detection rate of malicious nodes by the underwater network configured with GTR increased by 5.4%, the error detection rate decreased by 36.4%, the packet delivery rate increased by 11.0%, the energy tax decreased by 11.4%, and the network throughput increased by 20.4%.

Cooperative Communication Based Protocols for Underwater Wireless Sensors Networks: A Review.

Underwater wireless sensor networks are gaining popularity since supporting a broad range of applications, both military and civilian. Wireless acoustics is the most widespread technology adopted in underwater networks, the realization of which must face several challenges induced by channel propagation like signal attenuation, multipath and latency. In order to address such issues, the attention of researchers has recently focused on the concept of cooperative communication and networking, borrowed from terrestrial systems and to be conveniently recast in the underwater scenario. In this paper, we present a comprehensive literature review about cooperative underwater wireless sensor networks, investigating how nodes cooperation can be exploited at the different levels of the network protocol stack. Specifically, we review the diversity techniques employable at the physical layer, error and medium access control link layer protocols, and routing strategies defined at the network layer. We also provide numerical results and performance comparisons among the most widespread approaches. Finally, we present the current and future trends in cooperative underwater networks, considering the use of machine learning algorithms to efficiently manage the different aspects of nodes cooperation.

RL-ANC: Reinforcement Learning-Based Adaptive Network Coding in the Ocean Mobile Internet of Things

As the demand for sensing and monitoring the marine environment increases, the Ocean Mobile Internet of Things (OM-IoT) has gradually attracted the interest of researchers. However, the unreliability of communication links represents a significant challenge to data transmission in the OM-IoT, given the complex and dynamic nature of the marine environment, the mobility of nodes, and other factors. Consequently, it is necessary to enhance the reliability of underwater data transmission. To address this issue, this paper proposes a reinforcement learning-based adaptive network coding (RL-ANC) approach. Firstly, the channel conditions are estimated based on the reception acknowledgment, and a feedback-independent decoding state estimation method is proposed. Secondly, the sliding coding window is dynamically adjusted based on the estimates of the channel erasure probability and decoding probability, and the sliding rule is adaptively determined using a reinforcement learning algorithm and an enhanced greedy strategy. Subsequently, an adaptive optimization method for coding coefficients based on reinforcement learning is proposed to enhance the reliability of the underwater data transmission and underwater network coding while reducing the redundancy in the coding. Finally, the sampling period and time slot table are updated using the enhanced simulated annealing algorithm to optimize the accuracy and timeliness of the channel estimation. Simulation experiments demonstrate that the proposed method effectively enhances the data transmission reliability in unreliable communication links, improves the performance of underwater network coding in terms of the packet delivery rate, retransmission, and redundancy transmission ratios, and accelerates the convergence speed of the decoding probability.

Design and performance evaluation of SEANet, a software-defined networking platform for the Internet of Underwater Things

This paper presents the design and performance evaluation of the SEANet platform, a software-defined acoustic modem designed for enhancing underwater networking and Internet of Underwater Things (IoUT) applications. Addressing the limitations of traditional acoustic modems, which suffer from low data rates and rigid architectures, SEANet introduces a versatile, adaptive framework capable of reconfiguring all layers of the protocol stack in real-time to accommodate diverse marine applications. The platform integrates high-performance, wideband data converters with modular hardware and software components, enabling real-time adaptation to changing environmental and operational conditions. Experimental evaluations conducted in oceanic settings demonstrate the SEANet capability to significantly exceed the performance of existing commercial underwater modems, supporting data rates up to 150 kbit/s and effectively doubling the performance metrics of conventional systems. Our robust testing also highlights the SEANet proficiency in channel estimation, Orthogonal Frequency-Division Multiplexing (OFDM) link establishment, and interoperability through the JANUS communication standard. Our results underscore the SEANet potential to transform underwater communication technologies, providing a scalable and efficient solution that supports high data rate applications and fosters the expansion of IoUT deployments.

Improved Grey Wolf Optimization Based Node Localization Approach in Underwater Wireless Sensor Networks

Abstract Underwater Wireless Sensor Networks (UWSNs) are established by Autonomous Underwater Vehicles (AUVs) or static Sensor Nodes (SN) that collect and transmit information over the underwater environment. Localization plays a vital role in the effective deployment, navigation and coordination of these nodes for many applications, namely underwater surveillance, underwater exploration, oceanographic data collection and environmental monitoring. Due to the unique characteristics of underwater transmission and acquisition, this is a fundamental challenge in underwater networks. However, localization in UWSNs is problematic due to the unique features of underwater transmission and the harsh underwater environment. To address these challenges, this paper presents an Improved Grey Wolf Optimization Based Node Localization Approach in UWSN (IGWONL-UWSN) technique. The presented IGWONL-UWSN technique is inspired by the hunting behavior of grey wolves with the Dimension Learning-based Hunting (DLH) search process. The proposed IGWONL-UWSN technique uses the Improved Grey Wolf Optimization Based (IGWO) algorithm to calculate the optimal location of the nodes in the UWSN. Moreover, the IGWONL-UWSN technique incorporates the DLH search process to improve the convergence and accuracy. The simulation results of the IGWONL-UWSN technique are validated using a set of performance measures. The simulation results show the improvements of the IGWONL-UWSN method over other approaches with respect to various metrics.

Split Learning with Differential Privacy for Integrated Terrestrial and Non-Terrestrial Networks

Integrated terrestrial and non-terrestrial networks (TNTNs) have become promising architecture for enabling ubiquitous connectivity. Smart remote sensing is one of the typical applications of TNTNs that collects and analyzes various dimensions of remote sensing data by deploying Internet of Things (IoT) sensors and edge computing in terrestrial, space, aerial, and underwater networks. To improve the analysis accuracy of remote sensing data, the owners of different networks should conduct collaborative learning on different dimensions of data, while data and label privacy should be jointly considered. However, the existing collaborative learning paradigms are difficult to meet this demand. In this article, we propose a paradigm of split learning (SL), where the data owner and the label owner train different parts of the deep learning model and only exchange the intermediate data (i.e., smashed data and cut layer gradients). We explore the potential privacy attacks that recover the raw data and label information based on the intermediate data and propose the differential privacy (DP) based defense mechanisms that inject randomly generated Laplace noise into the intermediate data to disturb the attack performance. We also conduct a simulation study based on a real-world satellite remote sensing dataset to validate that the SL paradigm with defense mechanisms can effectively balance the performance of the collaborative model training and the protection of the data and label privacy. Finally, we discuss the main challenges and potential research directions of the privacy-preserving SL paradigm for smart remote sensing over TNTNs.

An adaptive MAC-agnostic ranging scheme for underwater acoustic mobile networks

In the last ten years several simulation studies on Autonomous Underwater Vehicle (AUV) swarm fleet formation have been performed, and some preliminary sea demonstrations of proof-of-concept prototypes were carried out. However, their actual realization is hindered by the challenges imposed by the underwater acoustic channel and the difficulties of keeping track of the vehicles’ positions due to the long latency required by traditional Two-Way Travel-Time (TWTT) ranging measurements, that require a specific signaling, hence limiting the throughput of the underwater network. Although One-Way Travel-Time (OWTT) halves the latency, it requires a high precision oscillator, such as an atomic clock or an oven controlled crystal oscillator (OCXO), to be installed in each modem processing unit: while atomic clocks are still very expensive, OCXO are very power demanding, making their application to underwater acoustic networks not always possible, especially in the case of low cost vehicle swarms.In this paper we present a network protocol stack able to perform ranging and localization within the communication task in underwater acoustic networks, limiting the network overhead. Specifically, new layers have been added to the preexisting DESERT Underwater protocol stack to perform the ranging tasks without compromising the correct operation of the communication network. A ranging layer is placed on top of the Medium Access Control (MAC) scheme, allowing the latter to be changed according to the network topology and requirements. This MAC-agnostic ranging layer is further optimized by adapting the amount of data transmitted according to the channel state, and the ranging entries inserted in the data packets according to the least recent information transmitted, hence minimizing the Age of Information. Simulation results obtained with the DESERT Underwater Framework show how this layer allows all AUVs in the swarm to know their distance from every other node in the network, thus limiting the probability of vehicle collisions and allowing better mission coordination.

Internet of Underwater Things: A Survey on Simulation Tools and 5G-Based Underwater Networks

The term “Internet of Underwater Things (IoUT)” refers to a network of intelligent interconnected underwater devices designed to monitor various underwater activities. The IoUT allows for a network of autonomous underwater vehicles (AUVs) to communicate with each other, sense their surroundings, collect data, and transmit them to control centers on the surface at typical Internet speeds. These data serve as a valuable resource for various tasks, including conducting crash surveys, discovering shipwrecks, detecting early signs of tsunamis, monitoring animal health, obtaining real-time aquatic information, and conducting archaeological expeditions. This paper introduces an additional set of alternative simulation tools for underwater networks. We categorize these tools into open-source and licensed simulator options and recommend that students consider using open-source simulators for monitoring underwater networks. There has not been widespread deployment or extensive research on underwater 5G-based networks. However, simulation tools provide some general insights into the challenges and potential issues associated with evaluating such networks, based on the characteristics of underwater communication and 5G, by surveying 5G-based underwater networks and 5G key aspects addressed by the research community in underwater network systems. Through an extensive review of the literature, we discuss the architecture of both Internet of Underwater application-assisted AUVs and Internet of Underwater Things communications in the 5G-based system.

Energy-Efficient Routing Optimization for Underwater Internet of Things using Hybrid Q-Learning and Predictive Learning Approach

The Underwater Internet of Things (U-IoT) connects devices used in underwater exploration, collection and transmission of data for exploration, monitoring, and management purposes. However, power supply unpredictability, harsh climates, and bandwidth limitations present significant challenges for these devices. The traditional methods used for routing include shortest path algorithms, fat routing, static routing, clustering-based routing, and geographic routing to name a few. These approaches provide a foundation for routing in underwater networks but may not be explicitly used to optimize energy conservation with robustness. The proposed solution combines a predictive learning algorithm with a reinforcement learning method to design a robust solution. Furthermore, the predictive learning algorithm that involves the use of MLP uses real-time and historical data simultaneously to forecast future network states. Simulations are carried out on NS3 and Matlab to evaluate the viability of the proposed method. On the basis of the result analysis, it is proved that the proposed method enhances energy conservation in U-IoT systems by 3.78%.

A Primer on Underwater Quantum Key Distribution

The growing importance of underwater networks (UNs) in mission-critical activities at sea enforces the need for secure underwater communications (UCs). Classical encryption techniques can be used to achieve secure data exchange in UNs. However, the advent of quantum computing will pose threats to classical cryptography, thus challenging UCs. Currently, underwater cryptosystems mostly adopt symmetric ciphers, which are considered computationally quantum robust but pose the challenge of distributing the secret key upfront. Post-quantum public-key (PQPK) protocols promise to overcome the key distribution problem. The security of PQPK protocols, however, only relies on the assumed computational complexity of some underlying mathematical problems. Moreover, the use of resource-hungry PQPK algorithms in resource-constrained environments such as UNs can require nontrivial hardware/software optimization efforts. An alternative approach is underwater quantum key distribution (QKD), which promises unconditional security built upon the physical principles of quantum mechanics (QM). This tutorial provides a basic introduction to free-space underwater QKD (UQKD). At first, the basic concepts of QKD are presented, based on a fully worked out QKD example. A thorough state-of-the-art analysis of UQKD is carried out. The paper subsequently provides a theoretical analysis of the QKD performance through free-space underwater channels and its dependence on the key optical parameters of the system and seawater. Finally, open challenges, points of strength, and perspectives of UQKD are identified and discussed.

A cross-layer approach for load balancing and energy-efficient QoS-based routing reliability for UWSN

Considering several fundamental needs of network performance, the Routing and Media Access Control (MAC) layers are crucially checked out for their operations. Sometimes, MAC protocol faces difficulties in modifying the situations over underwater communication which are specifically considered to be dynamic. The nodes in water tend to remain unstable and network fluctuations are made depending upon the number of competitors. The existing hybrid MAC protocol does not possess dynamic network loads. It also involves a lack of modification in access control approaches which provide variations in network loads. Finally, it leads to delayed network performance. The routing layer focus on some difficult parameters like increased packet loss, restricted bandwidth with substantial energy incursion, reduced network lifetime, increased propagation delay, less remaining energy, consistent data transfer, and energy organization which are considered to be the most important research issues in Underwater Acoustic Sensor Networks (UWASNs). In MAC and routing layers, a Cross-layer approach involves some techniques which are discussed and implemented using Ns3 simulation to obtain the performance report. It is also proposed to compare the algorithm with existing techniques to provide accurate results. Reinforcement Learning (RL) in the MAC layer for SINR-based time slot allocation and Integrated Artificial Fish Swarm with Bacterial Foraging Algorithm (IAFSBFA) for energy-aware QoS reliable routing in the network layer are used in this system. In this cross-layer approach, load balancing in the MAC layer and efficient routing using a hybrid algorithm gives out better performance in the underwater network.

Node deployment optimization of underwater wireless sensor networks using intelligent optimization algorithm and robot collaboration

This study aims to optimize the node deployment of underwater wireless sensor networks (UWSNs) using intelligent optimization algorithms and robot collaboration technology to enhance network performance and coverage. The study employs the chemical reaction optimization (CRO) algorithm, which combines the advantages of genetic algorithms, simulated annealing algorithms, and ant colony algorithms. The CRO algorithm is enhanced through a structure correction function to determine the optimal node deployment scheme to achieve effective and optimal coverage control of the UWSN. Additionally, the flexibility and autonomy of robots are leveraged to improve the efficiency of node deployment and address the unique challenges posed by the underwater environment. Furthermore, the study conducts a comparative analysis of different intelligent optimization algorithms and demonstrates the effectiveness and advantages of the enhanced CRO algorithm in optimizing node deployment for UWSNs. The study findings reveal that the improved algorithm achieves an average coverage rate of 95.66%, significantly outperforming traditional intelligent optimization algorithms. The coverage of UWSNs can be significantly improved by utilizing the enhanced CRO algorithm and robot collaboration technology for node deployment optimization, which offers an effective approach for achieving optimal node deployment. Moreover, the rational deployment of nodes enhances the monitoring capability, resource utilization efficiency, and accuracy of environmental monitoring in underwater networks. The results of this study hold great practical significance for underwater environment monitoring, marine resource exploration, and marine scientific research.

Trajectory Optimization for Target Localization Using Time Delays and Doppler Shifts in Bistatic Sonar-Based Internet of Underwater Things

Efficient target localization is critical to many marine applications in the Internet of Underwater Things (IoUT). Doppler effect becomes more predominant in the underwater environment when the relative speed of the moving object, i.e., the observer, to the signal propagation speed in water is much larger than that in the air. This along with the observer-target geometry will bring in a notable impact on the localization performance. In this paper, we derive the Cram´er–Rao lower bound (CRLB) and formulate the A-optimality criterion-based observer trajectory optimization problem to improve the localization performance based on time delay and Doppler shift measurements. We show that in the worst-case scenario, there will be a conflict between the non-accessible zone constraint and the observer dynamics constraint, which will lead to an erroneous result. To address this problem, we propose a warning zone-based augmented Lagrange multiplier method (ALMM) where the non-accessible zone constraint is relaxed to resolve the conflict and ensure the non-accessible requirement of the targeted zone is maintained. Performance evaluations are conducted through extensive simulations for different scenarios, and the results are compared to other methods with or without trajectory optimization. We demonstrate that trajectory optimization using time delays and Doppler shifts can greatly improve the target localization accuracy in underwater networks.

Adaptive Power-Controlled Depth-Based Routing Protocol for Underwater Wireless Sensor Networks

Low energy consumption has always been one of the core issues in the routing design of underwater sensor networks. Due to the high cost and difficulty of deployment and replacement of current underwater nodes, many underwater applications require the routing protocol design to consider the network lifetime extension problem. Based on this, we designed a new routing protocol that takes into account both low energy consumption and balanced energy consumption, and achieves effective extension of the network lifetime, called adaptive power-controlled depth-based routing protocol for underwater wireless sensor networks (APCDBRP). The protocol consists of two phases: (1) the route establishment phase and (2) the data transmission phase. In the route establishment phase, the initial path is established by the sink node broadcasting beacon packets at the maximum transmission power. The receiving nodes update their routing tables based on the beacon information and forward the beacon packets. In the data transmission phase, APCDBRP introduces a novel forwarding factor that considers both energy efficiency and energy balance. It selects the optimal next hop based on high energy efficiency and relatively abundant energy, thus extending the network’s lifetime. Additionally, APCDBRP proposes a new data protection and route reconstruction mechanism to address issues such as network topology changes due to node mobility and data transmission failures. Our simulation is based on AquaSim–Next Generation, which is a specialized tool built on the NS3 platform for researching underwater networks. Simulation results demonstrate that, compared to other typical routing protocols, APCDBRP exhibits superior performance in reducing network energy consumption and extending the network’s lifetime. It also achieves a high packet delivery rate with lower energy consumption.

A time-varying acoustic channel-aware topology control mechanism for cooperative underwater sonar detection network

Topology control plays a vital role in cooperative underwater sonar detection networks (USDNs) to ensure detection applications. By incorporating spatio-temporal uncertainties in acoustic channel and limited resources in underwater networks, a large number of node deployment schemes have been proposed to overcome these difficulties through topology control. However, the channel uncertainty has not been solved fundamentally. In order to effectively deal with the time-space-frequency uncertainty of the acoustic channel, this paper proposes a time-varying acoustic channel-aware (TVAC) topology control mechanism to deploy sonar nodes in USDNs. Initially, a time-varying acoustic channel state information (CSI) estimation algorithm and a prediction algorithm are proposed by applying three sub-modules: a feature stitching deep neural network-based temperature prediction model that we designed, a deep neural network-based sound velocity estimation model, and a BELLHOP-based propagation loss calculation model. After that, a TVAC topology control mechanism is adopted to adaptively deploy nodes based on the CSI estimation and prediction results. Using the improved weighted set covering algorithm, the current CSI is adopted to determine the working modes of sonar nodes, and the predicted CSI is adopted to obtain the cycle of topology update. What is more, we develop an offline–online CSI prediction model to improve the accuracy and stability of node working modes management. Simulation results show that compared with other topology control schemes, TVAC can obtain superior coverage performance, full connectivity, and prolong the network lifetime with guaranteed coverage and connectivity.

Data collection optimization of ocean observation network based on AUV path planning and communication

The Ocean Observation Network (OON) is an ocean science and engineering observation platform which integrates underwater wireless sensors, acoustic buoys, submersible buoys, and sonars. The complex underwater environment makes it challenging to place the observation nodes flexibly. In this research, firstly, a novel OON data collection optimization scheme is proposed, which is based on Autonomous Underwater Vehicle (AUV) path planning and communication. By combining the Voronoi diagram and K-means algorithm, an optimized clustering algorithm (VorK-means) is proposed to optimize the location of junction boxes and reduce the losses in the transmission energy of submarine cables in the OON simultaneously. Subsequently, a computational algorithm for AUV data collection position is proposed based on Voronoi vertices and communication circles. Moreover, an improved Grey Wolf Optimization (GWO) algorithm, based on the Levy flight and dimension (LD) search strategy, is proposed and applied for the AUV path planning, which is named LD-GWO. The accuracy and efficiency are validated by applying the proposed algorithms to the Canadian North-East Pacific Time-series Underwater Networked Experiment (NEPTUNE). Compared with the K-means algorithm, the VorK-means algorithm can reduce the total length of submarine cables by nearly 14%, and compared with the GWO algorithm, LD-GWO can obtain shorter data collection paths under identical parameter settings.

Network intelligence vs. jamming in underwater networks: how learning can cope with misbehavior

In this paper, we present a machine-learning technique to counteract jamming attacks in underwater networks. Indeed, this is relevant in security applications where sensor devices are located in critical regions, for example, in the case of national border surveillance or for identifying any unauthorized intrusion. To this aim, a multi-hop routing protocol that relies on the exploitation of a Q-learning methodology is presented with a focus on increasing reliability in data communication and network lifetime. Performance results assess the effectiveness of the proposed solution as compared to other efficient state-of-the-art approaches.