Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.

Structural Characteristics and Influencing Factors of Carbon Emission Spatial Association Network:A Case Study of Yangtze River Delta City Cluster,China

City cluster is an effective platform for encouraging regionally coordinated development.Coordinated reduction of carbon emissions within city cluster via the spatial association network between cities can help coordinate the regional carbon emission management,realize sustainable development,and assist China in achieving the carbon peaking and carbon neutrality goals.This paper applies the improved gravity model and social network analysis(SNA)to the study of spatial correlation of carbon emissions in city clusters and analyzes the structural characteristics of the spatial correlation network of carbon emissions in the Yangtze River Delta(YRD)city cluster in China and its influencing factors.The results demonstrate that:1)the spatial association of carbon emissions in the YRD city cluster exhibits a typical and complex multi-threaded network structure.The network association number and density show an upward trend,indicating closer spatial association between cities,but their values remain generally low.Meanwhile,the network hierarchy and network efficiency show a downward trend but remain high.2)The spatial association network of carbon emissions in the YRD city cluster shows an obvious‘core-edge’distribution pattern.The network is centered around Shanghai,Suzhou and Wuxi,all of which play the role of‘bridges’,while cities such as Zhoushan,Ma'anshan,Tongling and other cities characterized by the remote location,single transportation mode or lower economic level are positioned at the edge of the network.3)Geographic proximity,varying levels of economic development,different industrial structures,degrees of urbanization,levels of technological innovation,energy intensities and environmental regulation are important influencing factors on the spatial association of within the YRD city cluster.Finally,policy implications are provided from four aspects:government macro-control and market mechanism guidance,structural characteristics of the‘core-edge’network,reconfiguration and optimization of the spatial layout of the YRD city cluster,and the application of advanced technologies.

Identification of key recovering node for spatial networks

Many networks in the real world have spatial attributes, such as location of nodes and length of edges, called spatial networks. When these networks are subject to some random or deliberate attacks, some nodes in the network fail, which causes a decline in the network performance. In order to make the network run normally, some of the failed nodes must be recovered. In the case of limited recovery resources, an effective key node identification method can find the key recovering node in the failed nodes, by which the network performance can be recovered most of the failed nodes. We propose two key recovering node identification methods for spatial networks, which are the Euclidean-distance recovery method and the route-length recovery method. Simulations on homogeneous and heterogeneous spatial networks show that the proposed methods can significantly recover the network performance.

Using BlazePose on Spatial Temporal Graph Convolutional Networks for Action Recognition

The ever-growing available visual data(i.e.,uploaded videos and pictures by internet users)has attracted the research community’s attention in the computer vision field.Therefore,finding efficient solutions to extract knowledge from these sources is imperative.Recently,the BlazePose system has been released for skeleton extraction from images oriented to mobile devices.With this skeleton graph representation in place,a Spatial-Temporal Graph Convolutional Network can be implemented to predict the action.We hypothesize that just by changing the skeleton input data for a different set of joints that offers more information about the action of interest,it is possible to increase the performance of the Spatial-Temporal Graph Convolutional Network for HAR tasks.Hence,in this study,we present the first implementation of the BlazePose skeleton topology upon this architecture for action recognition.Moreover,we propose the Enhanced-BlazePose topology that can achieve better results than its predecessor.Additionally,we propose different skeleton detection thresholds that can improve the accuracy performance even further.We reached a top-1 accuracy performance of 40.1%on the Kinetics dataset.For the NTU-RGB+D dataset,we achieved 87.59%and 92.1%accuracy for Cross-Subject and Cross-View evaluation criteria,respectively.

Spatial prediction of soil organic carbon in coal mining subsidence areas based on RBF neural network

A quantitative research on the effect of coal mining on the soil organic carbon(SOC)pool at regional scale is beneficial to the scientific management of SOC pools in coal mining areas and the realization of coal low-carbon mining.Moreover,the spatial prediction model of SOC content suitable for coal mining subsidence area is a scientific problem that must be solved.Tak-ing the Changhe River Basin of Jincheng City,Shanxi Province,China,as the study area,this paper proposed a radial basis function neural network model combined with the ordinary kriging method.The model includes topography and vegetation factors,which have large influence on soil properties in mining areas,as input parameters to predict the spatial distribution of SOC in the 0-20 and 2040 cm soil layers of the study area.And comparing the prediction effect with the direct kriging method,the results show that the mean error,the mean absolute error and the root mean square error between the predicted and measured values of SOC content predicted by the radial basis function neural network are lower than those obtained by the direct kriging method.Based on the fitting effect of the predicted and measured values,the R^(2) obtained by the radial basis artificial neural network are 0.81,0.70,respectively,higher than the value of 0.44 and 0.36 obtained by the direct kriging method.Therefore,the model combining the artificial neural network and kriging,and considering environmental factors can improve the prediction accuracy of the SOC content in mining areas.

Structural characteristics and influencing factors of spatial correlation network for regional high-quality development in China

On the basis of measuring the regional high-quality development in China from 2011 to 2020,this study uses gravity model to build spatial correlation network,and uses social network analysis method to analyze the structural characteristics and influencing factors of correlation network.The results are shown as follows.First,from 2011 to 2020,the level of regional high-quality development in China is rising gradually,and the discrete characteristics between regions are gradually obvious,showing a step-like distribution structure decreasing from east to west.Second,the network density of regional high-quality development is generally low and tends to decline,but it has strong stability and correlation strength.Third,the spatial correlation network has an obvious core-edge structure.Shanghai is always at the center of the network and plays a significant intermediary role,while Qinghai and Xinjiang are always at the edge of the network.Fourth,the regional high-quality development association network can be divided into four major sectors:main benefit,net benefit,net spillover,and broker,showing the spatial correlation characteristics of inter-plate contact and intra-plate agglomeration.Fifth,the level of economic development,the level of urbanization and geographical proximity have a significant impact on the formation of regional high-quality development correlation network.

Migration Networks Pattern of China’s Floating Population from the Perspective of Complex Network

Since China’s reform and opening-up,the growing disparity between urban and rural areas and regions has led to massive migration.With China’s Rural Revitalization Strategy and the industrial transfer from the eastern coastal areas to the inland,the migration direction and pattern of the floating population have undergone certain changes.Using the 2017 China Migrants Dynamic Survey(CMDS),excluding Hong Kong,Macao,and Taiwan regions of China,organized by China’s National Health Commission,the relationship matrix of the floating population is constructed according to the inflow place of the interviewees and their outflow place(the location of the registered residence)in the questionnaire survey.We then apply the complex network model to analyze the migration direction and network pattern of China’s floating population from the city scale.The migration network shows an obvious hierarchical agglomeration.The first-,second-,third-and fourth-tier distribution cities are municipalities directly under the central government,provincial capital cities,major cities in the central and western regions and ordinary cities in all provinces,respectively.The migration trend is from the central and western regions to the eastern coastal areas.The migration network has‘small world’characteristics,forming nine communities.It shows that most node cities in the same community are closely linked and geographically close,indicating that the migration network of floating population is still affected by geographical proximity.Narrowing the urban-rural and regional differences will promote the rational distribution this population.It is necessary to strengthen the reform of the registered residence system,so that the floating population can enjoy urban public services comparable to other populations,and allow migrants to live and work in peace.

Analysis of spatial distribution characteristics and driving factors of ethnicminority villages in China using geospatial technology and statistical models

This study aims to reveal the spatial structural characteristics of 1,652 Ethnic-Minority Villages(EMV)in China and to analyze the mechanisms driving their spatial heterogeneity.EMV are a special type of settlement space that preserve a large number of historical traces of the ethnic culture of ancient China.They are important carriers of China’s excellent traditional culture and are key to the implementation of rural revitalization strategies.In this study,1652 EMV in China were selected as the research subjects.The Nearest Neighbor Index,kernel density,and spatial autocorrelation index were employed to reveal the spatial structural characteristics of minority villages.Neural network models,spatial lag models,and geographical detectors were used to analyze the formation mechanism of spatial heterogeneity in EMV.The results indicate that:(1)EMV exhibit significant spatial differentiation characterized by“single-core with multiple surrounding sub-centers,”“polarization between east and west,”“decreasing quantity from southwest to east coast to northeast to northwest,”and“large dispersion with small agglomeration.”(2)EMV are mainly distributed in areas rich in intangible cultural heritage,with high vegetation coverage and low altitude,far from central cities,and having limited arable land and an underdeveloped economy and transportation,particularly in shaded or riverbank areas.(3)Distance from the nearest river(X3),distance from central cities(X8),national intangible cultural heritage(X9),and NDVI(X10)were the main driving factors affecting the spatial distribution of EMV,whereas elevation(X1)and GDP(X5)had the weakest influence.As EMV are a relatively unique territorial spatial unit,the identification of their spatial heterogeneity characteristics not only deepens the research content of settlement geography,but also involves the assessment,protection,and development of Minority Villages,which is of great significance for the inheritance and utilization of excellent ethnic cultures in the era.

Drivers for Inter-city Innovation Networks Across Chinese Cities:Modelling Physical Versus Intangible Effects

Cross-region innovation is widely recognized as an important source of the long-term regional innovation capacity.In the recent past,a growing number of studies has investigated the network structure and mechanisms of cross-region innovation collaboration in various contexts.However,existing research mainly focuses on physical effects,such as geographical distance and high-speed railway connections.These studies ignore the intangible drivers in a changing environment,the more digitalized economy and the increasingly solidified innovation network structure.Thus,the focus of this study is on estimating determinants of innovation networks,especially on intangible drivers,which have been largely neglected so far.Using city-level data of Chinese patents(excluding Hong Kong,Macao,and Taiwan Province of China),we trace innovation networks across Chinese cities over a long period of time.By integrating a measure on Information and Communications Technology(ICT)development gap and network structural effects into the general proximity framework,this paper explores the changing mechanisms of Chinese innovation networks from a new perspective.The results show that the structure of cross-region innovation networks has changed in China.As mechanisms behind this development,the results confirm the increasingly important role of intangible drivers in Chinese inter-city innovation collaboration when controlling for effects of physical proximity,such as geographical distance.Since digitalization and coordinated development are the mainstream trends in China and other developing countries,these countries'inter-city innovation collaboration patterns will witness dramatic changes under the influence of intangible drivers.

NFHP-RN:AMethod of Few-Shot Network Attack Detection Based on the Network Flow Holographic Picture-ResNet

Due to the rapid evolution of Advanced Persistent Threats(APTs)attacks,the emergence of new and rare attack samples,and even those never seen before,make it challenging for traditional rule-based detection methods to extract universal rules for effective detection.With the progress in techniques such as transfer learning and meta-learning,few-shot network attack detection has progressed.However,challenges in few-shot network attack detection arise from the inability of time sequence flow features to adapt to the fixed length input requirement of deep learning,difficulties in capturing rich information from original flow in the case of insufficient samples,and the challenge of high-level abstract representation.To address these challenges,a few-shot network attack detection based on NFHP(Network Flow Holographic Picture)-RN(ResNet)is proposed.Specifically,leveraging inherent properties of images such as translation invariance,rotation invariance,scale invariance,and illumination invariance,network attack traffic features and contextual relationships are intuitively represented in NFHP.In addition,an improved RN network model is employed for high-level abstract feature extraction,ensuring that the extracted high-level abstract features maintain the detailed characteristics of the original traffic behavior,regardless of changes in background traffic.Finally,a meta-learning model based on the self-attention mechanism is constructed,achieving the detection of novel APT few-shot network attacks through the empirical generalization of high-level abstract feature representations of known-class network attack behaviors.Experimental results demonstrate that the proposed method can learn high-level abstract features of network attacks across different traffic detail granularities.Comparedwith state-of-the-artmethods,it achieves favorable accuracy,precision,recall,and F1 scores for the identification of unknown-class network attacks through cross-validation onmultiple datasets.

Lightweight Cross-Modal Multispectral Pedestrian Detection Based on Spatial Reweighted Attention Mechanism

Multispectral pedestrian detection technology leverages infrared images to provide reliable information for visible light images, demonstrating significant advantages in low-light conditions and background occlusion scenarios. However, while continuously improving cross-modal feature extraction and fusion, ensuring the model’s detection speed is also a challenging issue. We have devised a deep learning network model for cross-modal pedestrian detection based on Resnet50, aiming to focus on more reliable features and enhance the model’s detection efficiency. This model employs a spatial attention mechanism to reweight the input visible light and infrared image data, enhancing the model’s focus on different spatial positions and sharing the weighted feature data across different modalities, thereby reducing the interference of multi-modal features. Subsequently, lightweight modules with depthwise separable convolution are incorporated to reduce the model’s parameter count and computational load through channel-wise and point-wise convolutions. The network model algorithm proposed in this paper was experimentally validated on the publicly available KAIST dataset and compared with other existing methods. The experimental results demonstrate that our approach achieves favorable performance in various complex environments, affirming the effectiveness of the multispectral pedestrian detection technology proposed in this paper.

Real-Time Prediction of Urban Traffic Problems Based on Artificial Intelligence-Enhanced Mobile Ad Hoc Networks(MANETS)

Traffic in today’s cities is a serious problem that increases travel times,negatively affects the environment,and drains financial resources.This study presents an Artificial Intelligence(AI)augmentedMobile Ad Hoc Networks(MANETs)based real-time prediction paradigm for urban traffic challenges.MANETs are wireless networks that are based on mobile devices and may self-organize.The distributed nature of MANETs and the power of AI approaches are leveraged in this framework to provide reliable and timely traffic congestion forecasts.This study suggests a unique Chaotic Spatial Fuzzy Polynomial Neural Network(CSFPNN)technique to assess real-time data acquired from various sources within theMANETs.The framework uses the proposed approach to learn from the data and create predictionmodels to detect possible traffic problems and their severity in real time.Real-time traffic prediction allows for proactive actions like resource allocation,dynamic route advice,and traffic signal optimization to reduce congestion.The framework supports effective decision-making,decreases travel time,lowers fuel use,and enhances overall urban mobility by giving timely information to pedestrians,drivers,and urban planners.Extensive simulations and real-world datasets are used to test the proposed framework’s prediction accuracy,responsiveness,and scalability.Experimental results show that the suggested framework successfully anticipates urban traffic issues in real-time,enables proactive traffic management,and aids in creating smarter,more sustainable cities.

Unknown DDoS Attack Detection with Fuzzy C-Means Clustering and Spatial Location Constraint Prototype Loss

Since its inception,the Internet has been rapidly evolving.With the advancement of science and technology and the explosive growth of the population,the demand for the Internet has been on the rise.Many applications in education,healthcare,entertainment,science,and more are being increasingly deployed based on the internet.Concurrently,malicious threats on the internet are on the rise as well.Distributed Denial of Service(DDoS)attacks are among the most common and dangerous threats on the internet today.The scale and complexity of DDoS attacks are constantly growing.Intrusion Detection Systems(IDS)have been deployed and have demonstrated their effectiveness in defense against those threats.In addition,the research of Machine Learning(ML)and Deep Learning(DL)in IDS has gained effective results and significant attention.However,one of the challenges when applying ML and DL techniques in intrusion detection is the identification of unknown attacks.These attacks,which are not encountered during the system’s training,can lead to misclassification with significant errors.In this research,we focused on addressing the issue of Unknown Attack Detection,combining two methods:Spatial Location Constraint Prototype Loss(SLCPL)and Fuzzy C-Means(FCM).With the proposed method,we achieved promising results compared to traditional methods.The proposed method demonstrates a very high accuracy of up to 99.8%with a low false positive rate for known attacks on the Intrusion Detection Evaluation Dataset(CICIDS2017)dataset.Particularly,the accuracy is also very high,reaching 99.7%,and the precision goes up to 99.9%for unknown DDoS attacks on the DDoS Evaluation Dataset(CICDDoS2019)dataset.The success of the proposed method is due to the combination of SLCPL,an advanced Open-Set Recognition(OSR)technique,and FCM,a traditional yet highly applicable clustering technique.This has yielded a novel method in the field of unknown attack detection.This further expands the trend of applying DL and ML techniques in the development of intrusion detection systems and cybersecurity.Finally,implementing the proposed method in real-world systems can enhance the security capabilities against increasingly complex threats on computer networks.

The Study on the Evolution of Urban Spatial Structure in Zhuhai City Based on Spatial Syntax

With the deepening of the Guangdong-Hong Kong-Macao Greater Bay Area strategy and the accelerated integration and development of the east and west sides of the Pearl River Estuary,Zhuhai’s hub position is becoming more and more prominent.The city of Zhuhai has a dense water network and is divided into two urban areas,the east and the west,under the influence of the Mordor Gate waterway.Based on the theory of spatial syntax,this paper carries out an analytical study on the urban spatial structure of Zhuhai,identifies the distribution characteristics of urban POIs,and provides theoretical support for the urban development of Zhuhai.

AN OPTIMUM VEHICULAR PATH ALGORITHM FOR TRAFFIC NETWORK BASED ON HIERARCHICAL SPATIAL REASONING

Human beings’ intellection is the characteristic of a distinct hierarchy and can be taken to construct a heuristic in the shortest path algorithms.It is detailed in this paper how to utilize the hierarchical reasoning on the basis of greedy and directional strategy to establish a spatial heuristic,so as to improve running efficiency and suitability of shortest path algorithm for traffic network.The authors divide urban traffic network into three hierarchies and set forward a new node hierarchy division rule to avoid the unreliable solution of shortest path.It is argued that the shortest path,no matter distance shortest or time shortest,is usually not the favorite of drivers in practice.Some factors difficult to expect or quantify influence the drivers’ choice greatly.It makes the drivers prefer choosing a less shortest,but more reliable or flexible path to travel on.The presented optimum path algorithm,in addition to the improvement of the running efficiency of shortest path algorithms up to several times,reduces the emergence of those factors,conforms to the intellection characteristic of human beings,and is more easily accepted by drivers.Moreover,it does not require the completeness of networks in the lowest hierarchy and the applicability and fault tolerance of the algorithm have improved.The experiment result shows the advantages of the presented algorithm.The authors argued that the algorithm has great potential application for navigation systems of large_scale traffic networks.

Deep learning neural networks for spatially explicit prediction of flash flood probability

Flood probability maps are essential for a range of applications,including land use planning and developing mitigation strategies and early warning systems.This study describes the potential application of two architectures of deep learning neural networks,namely convolutional neural networks(CNN)and recurrent neural networks(RNN),for spatially explicit prediction and mapping of flash flood probability.To develop and validate the predictive models,a geospatial database that contained records for the historical flood events and geo-environmental characteristics of the Golestan Province in northern Iran was constructed.The step-wise weight assessment ratio analysis(SWARA)was employed to investigate the spatial interplay between floods and different influencing factors.The CNN and RNN models were trained using the SWARA weights and validated using the receiver operating characteristics technique.The results showed that the CNN model(AUC=0.832,RMSE=0.144)performed slightly better than the RNN model(AUC=0.814,RMSE=0.181)in predicting future floods.Further,these models demonstrated an improved prediction of floods compared to previous studies that used different models in the same study area.This study showed that the spatially explicit deep learning neural network models are successful in capturing the heterogeneity of spatial patterns of flood probability in the Golestan Province,and the resulting probability maps can be used for the development of mitigation plans in response to the future floods.The general policy implication of our study suggests that design,implementation,and verification of flood early warning systems should be directed to approximately 40%of the land area characterized by high and very susceptibility to flooding.

Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency （wave number） of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.

Spatial Structure,Hierarchy and Formation Mechanisms of Scientific Collaboration Networks:Evidence of the Belt and Road Regions

Scientific collaboration has become an important part of the people-to-people exchanges in the Belt and Road initiative,and remarkable progress has been made since 2013.Taking the 65 countries along the Belt and Road(BRI countries)as the research areas and using collaborated Web of Science(WOS)core collection papers to construct an international scientific collaboration matrix,the paper explores the spatial structure,hierarchy and formation mechanisms of scientific collaboration networks of 65 countries along the Belt and Road.The results show that:1)Beyond the Belt and Road regions(BRI regions),Central&Eastern Europe,China and West Asia&North Africa have formed a situation in which they all have the most external links with other countries beyond BRI regions.China has the dominant role over other BRI countries in generating scientific links.The overall spatial structure has changed to a skeleton structure consisting of many dense regions,such as Europe,North America,East Asia and Oceania.2)Within the Belt and Road regions,Central&Eastern Europe has become the largest collaboration partner with other sub-regions in BRI countries.The spatial structure of scientific collaboration networks has transformed from the‘dual core’composed of China and the Central&Eastern Europe region,to the‘multi-polarization’composed of‘one zone and multi-points’.3)The hierarchical structure of scientific collaboration networks presents a typical‘core-periphery’structure,and changes from‘single core’to‘double cores’.4)Among the formation mechanisms of scientific collaboration networks,scientific research strength and social proximity play the most important roles,while geographical distance gradually weakens the hindrance to scientific collaboration.

A Spatial-Temporal Network Perspective for the Propagation Dynamics of Air Traffic Delays

Intractable delays occur in air traffic due to the imbalance between ever-increasing air traffic demand and limited airspace capacity.As air traffic is associated with complex air transport systems,delays can be magnified and propagated throughout these systems,resulting in the emergent behavior known as delay propagation.An understanding of delay propagation dynamics is pertinent to modern air traffic management.In this work,we present a complex network perspective of delay propagation dynamics.Specifically,we model air traffic scenarios using spatial–temporal networks with airports as the nodes.To establish the dynamic edges between the nodes,we develop a delay propagation method and apply it to a given set of air traffic schedules.Based on the constructed spatial-temporal networks,we suggest three metrics-magnitude,severity,and speed-to gauge delay propagation dynamics.To validate the effectiveness of the proposed method,we carry out case studies on domestic flights in the Southeastern Asia region(SAR)and the United States.Experiments demonstrate that the propagation magnitude in terms of the number of flights affected by delay propagation and the amount of propagated delays for the US traffic are respectively five and ten times those of the SAR.Experiments further reveal that the propagation speed for US traffic is eight times faster than that of the SAR.The delay propagation dynamics reveal that about six hub airports in the SAR have significant propagated delays,while the situation in the United States is considerably worse,with a corresponding number of around 16.This work provides a potent tool for tracing the evolution of air traffic delays.

Improved control for distributed parameter systems with time-dependent spatial domains utilizing mobile sensor-actuator networks

A guidance policy for controller performance enhancement utilizing mobile sensor-actuator networks （MSANs） is proposed for a class of distributed parameter systems （DPSs）, which are governed by diffusion partial differential equations （PDEs） with time-dependent spatial domains. Several sufficient conditions for controller performance enhancement are presented. First, the infinite dimensional operator theory is used to derive an abstract evolution equation of the systems under some rational assumptions on the operators, and a static output feedback controller is designed to control the spatial process. Then, based on Lyapunov stability arguments, guidance policies for collocated and non-collocated MSANs are provided to enhance the performance of the proposed controller, which show that the time-dependent characteristic of the spatial domains can significantly affect the design of the mobile scheme. Finally, a simulation example illustrates the effectiveness of the proposed policy.