Distributed Optimal Formation Control for Unmanned Surface Vessels by a Regularized Game-Based Approach

Dear Editor,This letter explores optimal formation control for a network of unmanned surface vessels(USVs).By designing an individual objective function for each USV,the optimal formation problem is transformed into a noncooperative game.Under this game theoretic framework,the optimal formation is achieved by seeking the Nash equilibrium of the regularized game.A modular structure consisting of a distributed Nash equilibrium seeker and a regulator is proposed.

Multivariate Time Series Anomaly Detection Based on Spatial-Temporal Network and Transformer in Industrial Internet of Things

In the Industrial Internet of Things(IIoT),sensors generate time series data to reflect the working state.When the systems are attacked,timely identification of outliers in time series is critical to ensure security.Although many anomaly detection methods have been proposed,the temporal correlation of the time series over the same sensor and the state(spatial)correlation between different sensors are rarely considered simultaneously in these methods.Owing to the superior capability of Transformer in learning time series features.This paper proposes a time series anomaly detection method based on a spatial-temporal network and an improved Transformer.Additionally,the methods based on graph neural networks typically include a graph structure learning module and an anomaly detection module,which are interdependent.However,in the initial phase of training,since neither of the modules has reached an optimal state,their performance may influence each other.This scenario makes the end-to-end training approach hard to effectively direct the learning trajectory of each module.This interdependence between the modules,coupled with the initial instability,may cause the model to find it hard to find the optimal solution during the training process,resulting in unsatisfactory results.We introduce an adaptive graph structure learning method to obtain the optimal model parameters and graph structure.Experiments on two publicly available datasets demonstrate that the proposed method attains higher anomaly detection results than other methods.

Comprehensive evaluation and spatial-temporal evolution characteristics of urban resilience in Chengdu-Chongqing Economic Circle

To clarify the connotations and extensions of urban resilience,this study focuses on the Chengdu-Chongqing Economic Circle with 16 cities as research subjects.A comprehensive evaluation index system was constructed to measure the resilience of each city from 2003 to 2020.The spatial-temporal evolution characteristics were analyzed using Kernel density estimation,standard deviation ellipse,and spatial Markov chain analysis,and the spatial Tobit model was introduced to discover the influencing factors.The results indicate the following:①Urban resilience in the Chengdu-Chongqing Economic Circle displays an upward trend,with the center of gravity moving to the southwest,and the polarization phenomenon intensifying.②The urban resilience level in a region has certain spatial and geographical dependence,while the probability of urban resilience transfer differs in adjacent cities with different resilience levels.③Urban centrality,economic scale,openness level,and financial development promote urban resilience,whereas government scale significantly inhibits it.Finally,this paper proposes countermeasures and suggestions to improve the urban resilience of the Chengdu-Chongqing Economic Circle.

AFSTGCN:Prediction for multivariate time series using an adaptive fused spatial-temporal graph convolutional network

The prediction for Multivariate Time Series(MTS)explores the interrelationships among variables at historical moments,extracts their relevant characteristics,and is widely used in finance,weather,complex industries and other fields.Furthermore,it is important to construct a digital twin system.However,existing methods do not take full advantage of the potential properties of variables,which results in poor predicted accuracy.In this paper,we propose the Adaptive Fused Spatial-Temporal Graph Convolutional Network(AFSTGCN).First,to address the problem of the unknown spatial-temporal structure,we construct the Adaptive Fused Spatial-Temporal Graph(AFSTG)layer.Specifically,we fuse the spatial-temporal graph based on the interrelationship of spatial graphs.Simultaneously,we construct the adaptive adjacency matrix of the spatial-temporal graph using node embedding methods.Subsequently,to overcome the insufficient extraction of disordered correlation features,we construct the Adaptive Fused Spatial-Temporal Graph Convolutional(AFSTGC)module.The module forces the reordering of disordered temporal,spatial and spatial-temporal dependencies into rule-like data.AFSTGCN dynamically and synchronously acquires potential temporal,spatial and spatial-temporal correlations,thereby fully extracting rich hierarchical feature information to enhance the predicted accuracy.Experiments on different types of MTS datasets demonstrate that the model achieves state-of-the-art single-step and multi-step performance compared with eight other deep learning models.

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

Spatial-temporal distribution and geochemistry of highly evolved Mesozoic granites in Great Xing’an Range,NE China:Discriminant criteria and geological significance

Highly evolved granite is an important sign of the mature continent crust and closely associated with deposits of rare metals.In this work,the authors undertake systematically zircon U-Pb ages and whole rock elemental data for highly evolved granitic intrusions from the Great Xing’an Range(GXR),NE China,to elucidate their discriminant criteria,spatial-temporal distribution,differentiation and geodynamic mecha-nism.Geochemical data of these highly evolved granites suggest that high w(SiO_(2))(>70%)and differentiation index(DI>88)could be quantified indicators,while strong Eu depletion,high TE_(1,3),lowΣREE and low Zr/Hf,Nb/Ta,K/Rb could only be qualitative indicators.Zircon U-Pb ages suggest that the highly evolved gran-ites in the GXR were mainly formed in Late Mesozoic,which can be divided into two major stages:Late Ju-rassic-early Early Cretaceous(162-136 Ma,peak at 138 Ma),and late Early Cretaceous(136-106 Ma,peak at 126 Ma).The highly evolved granites are mainly distributed in the central-southern GXR,and display a weakly trend of getting younger from northwest to southeast,meanwhile indicating the metallogenic potential of rare metals within the central GXR.The spatial-temporal distribution,combined with regional geological data,indicates the highly evolved Mesozoic granites in the GXR were emplaced in an extensional environ-ment,of which the Late Jurassic-early Early Cretaceous extension was related to the closure of the Mongol-Okhotsk Ocean and roll-back of the Paleo-Pacific Plate,while the late Early Cretaceous extension was mainly related to the roll-back of the Paleo-Pacific Plate.

Spatial-temporal Divergence Characteristics and Driving Factors of Green Economic Efficiency in the Yangtze River Economic Belt of China

The spatial and temporal variation of green economic efficiency and its driving factors are of great significance for the con-struction of high-efficiency and low-consumption green development model and sustainable socio-economic development.The research focused on the Yangtze River Economic Belt(YREB)and employed the miniumum distance to strong efficient frontier DEA(MinDs)model to measure the green economic efficiency of the municipalities in the region between 2008 and 2020.Then,the spatial autocorrel-ation model was used to analyze the evolution characteristics of its spatial pattern.Finally,Geodetector was applied to reveal the drivers and their interactions on green economic efficiency.It is found that:1)the overall green economic efficiency of the YREB from 2008 to 2020 shows a W-shaped fluctuating upward trend,green economic efficiency is greater in the downstream and smallest in the upstream;2)the spatial distribution of green economic efficiency shows clustering characteristics,with multi-core clustering based on‘city clusters-central cities'becoming more obvious over time;the High-High agglomeration type is mainly clustered in Jiangsu and Zheji-ang,while the Low-Low agglomeration type is clustered in the western Sichuan Plateau area and southwestern Yunnan;3)from input-output factors,whether it is the YREB as a whole or the upper,middle and lower reaches regions,the economic development level,labor input,and capital investment are the leading factors in the spatial-temporal evolution of green economic efficiency,with the com-prehensive influence of economic development level and pollution index being the most important interactive driving factor;4)from so-cio-economic factors,information technology drivers such as government intervention,transportation accessibility,information infra-structure,and Internet penetration are always high impact influencers and dominant interaction factors for green economic efficiency in the YREB and the three major regions in the upper,middle and lower reaches.Accordingly,the article puts forward relevant policy re-commendations in terms of formulating differentiated green transformation strategies,strengthening network leadership and informa-tion technology construction and coordinating multi-factor integrated development,which could provide useful reference for promoting synergistic green economic efficiency in the YREB.

Adaptive spatial-temporal graph attention network for traffic speed prediction

Considering the nonlinear structure and spatial-temporal correlation of traffic network,and the influence of potential correlation between nodes of traffic network on the spatial features,this paper proposes a traffic speed prediction model based on the combination of graph attention network with self-adaptive adjacency matrix(SAdpGAT)and bidirectional gated recurrent unit(BiGRU).First-ly,the model introduces graph attention network(GAT)to extract the spatial features of real road network and potential road network respectively in spatial dimension.Secondly,the spatial features are input into BiGRU to extract the time series features.Finally,the prediction results of the real road network and the potential road network are connected to generate the final prediction results of the model.The experimental results show that the prediction accuracy of the proposed model is im-proved obviously on METR-LA and PEMS-BAY datasets,which proves the advantages of the pro-posed spatial-temporal model in traffic speed prediction.

Spatial-temporal Variation Characteristics of Water Quality in the Lower Reaches of the Nenjiang River

As an important river in the western part of Jilin Province,the lower reach of the Nenjiang River is an important wetland water source conservation area in Jilin Province.Within the watershed,it governs the Momoge Wetland,the Xianghai Wetland,and the Danjiang Wetland in Jilin Province.The main problem in the lower reaches of the Nenjiang River is the uneven distribution of water resources in time and space,and the intensification of land salinization.Zhenlai County and Da an City in the Nenjiang River Basin have sufficient surface water resources,with surface water as the drinking water source.Baicheng City and Tongyu County have scarce surface water resources,and both use groundwater as their domestic water source.The main polluted section in the basin is the Xianghai Reservoir,and the annual water quality evaluation is Class V.However,the water quality of the Tao er River,the main stream of the Nenjiang River,is significantly better than that of the Xianghai Reservoir.In order to better study the water environmental pollution situation in the Nenjiang River basin,monitoring data from five sections of non seasonal rivers in the basin from 2012 to 2021 were selected for studying water quality.This in-depth exploration of the water pollution status and river water quality change trends in the Nenjiang River basin is of great significance for future rural development,agricultural pattern transformation,and the promotion of water ecological civilization construction.

Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.

Spatial-temporal difference between nitrate in groundwater and nitrogen in soil based on geostatistical analysis

The study of temporal and spatial variations of nitrate in groundwater under different soil nitrogen environments is helpful to the security of groundwater resources in agricultural areas.In this paper,based on 320 groups of soil and groundwater samples collected at the same time,geostatistical analysis and multiple regression analysis were comprehensively used to conduct the evaluation of nitrogen contents in both groundwater and soil.From May to August,as the nitrification of groundwater is dominant,the average concentration of nitrate nitrogen is 34.80 mg/L;The variation of soil ammonia nitrogen and nitrate nitrogen is moderate from May to July,and the variation coefficient decreased sharply and then increased in August.There is a high correlation between the nitrate nitrogen in groundwater and soil in July,and there is a high correlation between the nitrate nitrogen in groundwater and ammonium nitrogen in soil in August and nitrate nitrogen in soil in July.From May to August,the area of low groundwater nitrate nitrogen in 0-5 mg/L and 5-10 mg/L decreased from 10.97%to 0,and the proportion of high-value area(greater than 70 mg/L)increased from 21.19%to 27.29%.Nitrate nitrogen is the main factor affecting the quality of groundwater.The correlation analysis of nitrate nitrogen in groundwater,nitrate nitrogen in soil and ammonium nitrogen shows that they have a certain period of delay.The areas with high concentration of nitrate in groundwater are mainly concentrated in the western part of the study area,which has a high consistency with the high value areas of soil nitrate distribution from July to August,and a high difference with the spatial position of soil ammonia nitrogen distribution in August.

STGSA:A Novel Spatial-Temporal Graph Synchronous Aggregation Model for Traffic Prediction

The success of intelligent transportation systems relies heavily on accurate traffic prediction,in which how to model the underlying spatial-temporal information from traffic data has come under the spotlight.Most existing frameworks typically utilize separate modules for spatial and temporal correlations modeling.However,this stepwise pattern may limit the effectiveness and efficiency in spatial-temporal feature extraction and cause the overlook of important information in some steps.Furthermore,it is lacking sufficient guidance from prior information while modeling based on a given spatial adjacency graph(e.g.,deriving from the geodesic distance or approximate connectivity),and may not reflect the actual interaction between nodes.To overcome those limitations,our paper proposes a spatial-temporal graph synchronous aggregation(STGSA)model to extract the localized and long-term spatial-temporal dependencies simultaneously.Specifically,a tailored graph aggregation method in the vertex domain is designed to extract spatial and temporal features in one graph convolution process.In each STGSA block,we devise a directed temporal correlation graph to represent the localized and long-term dependencies between nodes,and the potential temporal dependence is further fine-tuned by an adaptive weighting operation.Meanwhile,we construct an elaborated spatial adjacency matrix to represent the road sensor graph by considering both physical distance and node similarity in a datadriven manner.Then,inspired by the multi-head attention mechanism which can jointly emphasize information from different r epresentation subspaces,we construct a multi-stream module based on the STGSA blocks to capture global information.It projects the embedding input repeatedly with multiple different channels.Finally,the predicted values are generated by stacking several multi-stream modules.Extensive experiments are constructed on six real-world datasets,and numerical results show that the proposed STGSA model significantly outperforms the benchmarks.

Spatial-temporal variations and driving factors of soil organic carbon in forest ecosystems of Northeast China

Forest soil carbon is a major carbon pool of terrestrial ecosystems,and accurate estimation of soil organic carbon(SOC)stocks in forest ecosystems is rather challenging.This study compared the prediction performance of three empirical model approaches namely,regression kriging(RK),multiple stepwise regression(MSR),random forest(RF),and boosted regression trees(BRT)to predict SOC stocks in Northeast China for 1990 and 2015.Furthermore,the spatial variation of SOC stocks and the main controlling environmental factors during the past 25 years were identified.A total of 82(in 1990)and 157(in 2015)topsoil(0–20 cm)samples with 12 environmental factors(soil property,climate,topography and biology)were selected for model construction.Randomly selected80%of the soil sample data were used to train the models and the other 20%data for model verification using mean absolute error,root mean square error,coefficient of determination and Lin's consistency correlation coefficient indices.We found BRT model as the best prediction model and it could explain 67%and 60%spatial variation of SOC stocks,in 1990,and 2015,respectively.Predicted maps of all models in both periods showed similar spatial distribution characteristics,with the lower SOC in northeast and higher SOC in southwest.Mean annual temperature and elevation were the key environmental factors influencing the spatial variation of SOC stock in both periods.SOC stocks were mainly stored under Cambosols,Gleyosols and Isohumosols,accounting for 95.6%(1990)and 95.9%(2015).Overall,SOC stocks increased by 471 Tg C during the past 25 years.Our study found that the BRT model employing common environmental factors was the most robust method for forest topsoil SOC stocks inventories.The spatial resolution of BRT model enabled us to pinpoint in which areas of Northeast China that new forest tree planting would be most effective for enhancing forest C stocks.Overall,our approach is likely to be useful in forestry management and ecological restoration at and beyond the regional scale.

Air combat target maneuver trajectory prediction based on robust regularized Volterra series and adaptive ensemble online transfer learning

Target maneuver trajectory prediction is an important prerequisite for air combat situation awareness and maneuver decision-making.However,how to use a large amount of trajectory data generated by air combat confrontation training to achieve real-time and accurate prediction of target maneuver trajectory is an urgent problem to be solved.To solve this problem,in this paper,a hybrid algorithm based on transfer learning,online learning,ensemble learning,regularization technology,target maneuvering segmentation point recognition algorithm,and Volterra series,abbreviated as AERTrOS-Volterra is proposed.Firstly,the model makes full use of a large number of trajectory sample data generated by air combat confrontation training,and constructs a Tr-Volterra algorithm framework suitable for air combat target maneuver trajectory prediction,which realizes the extraction of effective information from the historical trajectory data.Secondly,in order to improve the real-time online prediction accuracy and robustness of the prediction model in complex electromagnetic environments,on the basis of the TrVolterra algorithm framework,a robust regularized online Sequential Volterra prediction model is proposed by integrating online learning method,regularization technology and inverse weighting calculation method based on the priori error.Finally,inspired by the preferable performance of models ensemble,ensemble learning scheme is also incorporated into our proposed algorithm,which adaptively updates the ensemble prediction model according to the performance of the model on real-time samples and the recognition results of target maneuvering segmentation points,including the adaptation of model weights;adaptation of parameters;and dynamic inclusion and removal of models.Compared with many existing time series prediction methods,the newly proposed target maneuver trajectory prediction algorithm can fully mine the prior knowledge contained in the historical data to assist the current prediction.The rationality and effectiveness of the proposed algorithm are verified by simulation on three sets of chaotic time series data sets and a set of real target maneuver trajectory data sets.

Dense Spatial-Temporal Graph Convolutional Network Based on Lightweight OpenPose for Detecting Falls

Fall behavior is closely related to high mortality in the elderly,so fall detection becomes an important and urgent research area.However,the existing fall detection methods are difficult to be applied in daily life due to a large amount of calculation and poor detection accuracy.To solve the above problems,this paper proposes a dense spatial-temporal graph convolutional network based on lightweight OpenPose.Lightweight OpenPose uses MobileNet as a feature extraction network,and the prediction layer uses bottleneck-asymmetric structure,thus reducing the amount of the network.The bottleneck-asymmetrical structure compresses the number of input channels of feature maps by 1×1 convolution and replaces the 7×7 convolution structure with the asymmetric structure of 1×7 convolution,7×1 convolution,and 7×7 convolution in parallel.The spatial-temporal graph convolutional network divides the multi-layer convolution into dense blocks,and the convolutional layers in each dense block are connected,thus improving the feature transitivity,enhancing the network’s ability to extract features,thus improving the detection accuracy.Two representative datasets,Multiple Cameras Fall dataset(MCF),and Nanyang Technological University Red Green Blue+Depth Action Recognition dataset(NTU RGB+D),are selected for our experiments,among which NTU RGB+D has two evaluation benchmarks.The results show that the proposed model is superior to the current fall detection models.The accuracy of this network on the MCF dataset is 96.3%,and the accuracies on the two evaluation benchmarks of the NTU RGB+D dataset are 85.6%and 93.5%,respectively.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results

We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0.

Alternative Methods of Regular and Singular Perturbation Problems

Making exact approximations to solve equations distinguishes applied mathematicians from pure mathematicians, physicists, and engineers. Perturbation problems, both regular and singular, are pervasive in diverse fields of applied mathematics and engineering. This research paper provides a comprehensive overview of algebraic methods for solving perturbation problems, featuring a comparative analysis of their strengths and limitations. Serving as a valuable resource for researchers and practitioners, it offers insights and guidance for tackling perturbation problems in various disciplines, facilitating the advancement of applied mathematics and engineering.

Composition Analysis and Identification of Ancient Glass Products Based on L1 Regularization Logistic Regression

In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.