Spatiotemporal Matrix Research Articles

The chain reaction of carbon emission trading policy in efficiency and rebound: evidence from spatial perspective in China

Evaluating and improving environmental policies are significantly impacted by the question of whether increased energy efficiency results in an energy rebound effect. Utilizing carbon emission trading policies (CETP) as a quasi-natural experiment, this study created a spatial difference-in-differences (SDID) model with an endogenous spatio-temporal weight matrix. The analysis applied Chinese provincial panel data from 2008 to 2018 to assess the direct and spatial spillover effects of CETP on total factor carbon emissions efficiency (TCEE). On this premise, it is further explored to see if CETP causes the energy rebound (ER) effect via TCEE. It revealed that CETP exhibited positive spatial spillover effects on TCEE. Specifically, CETP was observed to enhance TCEE in pilot areas through green innovation (GI) but impede TCEE in neighboring regions due to siphoning and pollution haven effects. Further research, however, revealed that the CETP increased the ER in the pilot areas by improving the TCEE, causing the policy to fall into the trap of ineffective emission reduction, but it had a warning effect on the nearby areas. This study is of great significance for improving the emission reduction policy system and promoting the “dual carbon” goals.

Spatio-temporal quasi-experimental methods for rare disease outcomes: the impact of reformulated gasoline on childhood haematologic cancer

Abstract Although some pollutants emitted in vehicle exhaust, such as benzene, are known to cause leukaemia in adults with high exposure levels, less is known about the relationship between traffic-related air pollution (TRAP) and childhood haematologic cancer. In the 1990s, the US EPA enacted the reformulated gasoline program in select areas of the U.S., which drastically reduced ambient TRAP in affected areas. This created an ideal quasi-experiment to study the effects of TRAP on childhood haematologic cancers. However, existing methods for quasi-experimental analyses can perform poorly when outcomes are rare and unstable, as with childhood cancer incidence. We develop Bayesian spatio-temporal matrix completion methods to conduct causal inference in quasi-experimental settings with rare outcomes. Selective information sharing across space and time enables stable estimation, and the Bayesian approach facilitates uncertainty quantification. We evaluate the methods through simulations and apply them to estimate the causal effects of TRAP on childhood leukaemia and lymphoma.

Wavelet-based spatiotemporal sparse quaternion dictionary learning for reconstruction of multi-channel vibration data

Accurate reconstruction of multi-source data information plays an essential role in remote intelligent operation, and prognostic and health maintenance (RIO-PHM) of industrial systems. However, traditional signal reconstruction methods such as compressed sensing fail to capture the spatio-temporal characteristics and coupling nature of the multi-source or multi-channel data. To alleviate this bottleneck, in this paper, a new wavelet-based spatiotemporal sparse quaternion dictionary learning (WSTS-QDL) algorithm is formulated for the reconstruction of multi-channel vibration data for the first time. Specifically, the wavelet-based spatiotemporal sparse low-rank matrix (SLRM) algorithm is elaborated and the sparse coefficient matrix of the multi-channel signals can be estimated using the split Bregman iteration (SBI) technique. Then, quaternion-based dictionary learning is introduced for multi-channel data reconstruction according to the updated sparse coefficient matrix during quaternion dictionary learning. Eventually, two equipmental scenarios including run-to-failure data of rolling bearing in bearing test bench and vibration signal of the failured bearing in corn thresher, are utilized for verification. The experimental results demonstrate that the highest recovery accuracy performance with scoring function and the lowest errors are achieved by the proposed method in contrast with the state-of-the-art benchmarks such as orthogonal matching pursuit (OMP) method and spatiotemporal sparse Bayesian learning (SSBL), and the waveform of phase space trajectory and points cloud distribution of the Poincare section in the original signal are similar/same to that obtained by the proposed method.

Learning Constrained Dynamic Correlations in Spatiotemporal Graphs for Motion Prediction.

Human motion prediction is challenging due to the complex spatiotemporal feature modeling. Among all methods, graph convolution networks (GCNs) are extensively utilized because of their superiority in explicit connection modeling. Within a GCN, the graph correlation adjacency matrix drives feature aggregation, and thus, is the key to extracting predictive motion features. State-of-the-art methods decompose the spatiotemporal correlation into spatial correlations for each frame and temporal correlations for each joint. Directly parameterizing these correlations introduces redundant parameters to represent common relations shared by all frames and all joints. Besides, the spatiotemporal graph adjacency matrix is the same for different motion samples, and thus, cannot reflect samplewise correspondence variances. To overcome these two bottlenecks, we propose dynamic spatiotemporal decompose GC (DSTD-GC), which only takes 28.6% parameters of the state-of-the-art GC. The key of DSTD-GC is constrained dynamic correlation modeling, which explicitly parameterizes the common static constraints as a spatial/temporal vanilla adjacency matrix shared by all frames/joints and dynamically extracts correspondence variances for each frame/joint with an adjustment modeling function. For each sample, the common constrained adjacency matrices are fixed to represent generic motion patterns, while the extracted variances complete the matrices with specific pattern adjustments. Meanwhile, we mathematically reformulate GCs on spatiotemporal graphs into a unified form and find that DSTD-GC relaxes certain constraints of other GC, which contributes to a better representation capability. Moreover, by combining DSTD-GC with prior knowledge like body connection and temporal context, we propose a powerful spatiotemporal GCN called DSTD-GCN. On the Human3.6M, Carnegie Mellon University (CMU) Mocap, and 3D Poses in the Wild (3DPW) datasets, DSTD-GCN outperforms state-of-the-art methods by 3.9%-8.7% in prediction accuracy with 55.0%-96.9% fewer parameters. Codes are available at https://github.com/Jaakk0F/DSTD-GCN.

A spatiotemporal data mining method for advanced prediction and assessment of large combined excavation-induced wall deformations and risks

A holistic and precise assessment of retaining wall deformations is critical for on-site risk management of large combined deep excavation projects, where the risk-related points are highly dispersed, evolving, and interacting. Despite extensive exploration of this topic in previous studies, the omission of intricate spatiotemporal characteristics of wall deformations has resulted in diminished prediction accuracy and stability. To mitigate this deficiency, a spatiotemporal characteristics matrix for all data points and time series was first generated for a deep excavation scenario and used as input for a new hybrid model that combines convolutional neural network (CNN) and long short-term memory (LSTM) with incorporated attention mechanism (CNN-LSTM-Att), which enables the cross-learning mechanism and improves interpretability. In addition, by leveraging the attention weight, a new risk assessment index for retaining wall deformations across various scenarios was formulated. Then the proposed method was applied in a large combined deep excavation in Shanghai, China. The results show that: (1) The incorporation of fed-in characteristic data and the attention mechanism enables the proposed method to produce satisfactory prediction results for the holistic spatiotemporal distribution of a large combined excavation; (2) Compared with other published models, the proposed model shows much better prediction accuracy, interpretability, and stability, especially in medium- and long-term predictions; and (3) The new risk assessment index serves as a reliable decision-making tool for assessing the risk evolution of retaining wall deformations and provides valuable guidance for effective risk management in multi-scenario excavation projects.

Turning peril into opportunity: Construction and validation of a resilience assessment system for China's coastal megacities

Enhancing urban resilience and strengthening risk resistance capacities have emerged as pivotal concerns in the construction and governance of contemporary urban landscapes globally. Given the uniqueness of coastal megacities in terms of geography and population, a more targeted and effective resilience assessment is urgently needed. This investigation develops a comprehensive, multidimensional index system to assess the resilience life cycle of China's coastal megacities. First, we creatively introduce the process perspective of the 4R model of crisis management into urban resilience assessment, revealing the preventive, defensive, recovery, and transformative resilience of China's coastal megacities. Second, we propose a spatio-temporal assessment matrix that integrates four processes of urban resilience and six representative subsystems in coastal megacities: social, economic, ecological, infrastructural, technological, and institutional. Third, we select 59 indicators to construct a three-level assessment index system for China's coastal megacities. This index system is strictly screened and optimized through qualitative and quantitative methods. Fourth, we validate the assessment system using Qingdao's data by calculating an urban resilience index and analyzing trends. We find the most important improvement goals and resilience enhancement suggestions for Qingdao by analyzing the indicator sensitivity. This study contributes to the development of urban resilience theories and identifies weaknesses in different dimensions to strengthen and improve the resilience of coastal megacities.

Development of explainable recognition models for ADMFB flow regimes based on ensemble learning

The spatiotemporal characteristics of fluidization within an Air Dense Medium Fluidized Bed (ADMFB) are critical for its heat and mass transfer, as well as for mixing and separation processes. Yet, detailed analyses of the dynamic behavior of flow regimes during progressive transformations are scarce. This study captured synchronous pressure drop signals at multiple points along the sidewall of the bed using a non-intrusive measurement technique. Statistical analyses were utilized to extract the pressure drop's characteristic parameters and examine the statistical features' spatiotemporal fluctuations during fluidization state transitions. We proposed a method to quantitatively characterize the bed's real-time fluidization state through the combined use of multiple-point pressure characteristics. Following this approach, a multidimensional spatio-temporal matrix was constructed to depict the flow regime transitions quantitatively. Concurrently, ensemble learning techniques were applied to classify flow regimes based on various feature parameters and sample lengths. In the final phase, comprehensive interpretations and detailed visual analyses were deployed on the inputs to the optimized ensemble learning model, XGBoost, utilizing the Shapley Additive Explanations (SHAP) framework. This study provides additional insights and methodologies for managing the transition and intelligent control of flow regimes within an ADMFB.

Spatiotemporal characteristics of residents' intercity travel in China under the impact of COVID-19 pandemic

Investigating the spatiotemporal characteristics of residents' intercity travel affected by the coronavirus disease (COVID-19) pandemic is of great significance to understanding and extending the impact of major public health affairs on intercity travelers, urban management policies, and intercity cooperative interactions. Taking 366 cities in China as an example, this study proposed a novel research framework for analyzing the spatiotemporal characteristics of intercity population flows. Using AutoNavi population migration big data sets from web crawling, the spatiotemporal structure patterns of intercity travel in China from January 1st to June 30th, 2020 were extracted by using the singular value decomposition (SVD) method. Then the spatial organization patterns of intercity travel networks in China and its five major urban agglomerations were identified by the weighted stochastic block model (WSBM). The results showed that the total volume of intercity travel in China and its five major urban agglomerations experienced a process of rapid decline followed by a slow recovery, presenting a “V-shaped” distribution since the outbreak of the COVID-19 pandemic. Three distinctive intercity travel patterns, namely the stable, holiday, and weekday-weekend intercity trip patterns, were extracted from the spatiotemporal OD matrix of intercity travel. Strong intercity travels were mainly distributed in eastern and central China, forming an intercity travel pattern in which core cities pushed and pulled each other within the national urban agglomerations. However, intercity migration flows were dominated by weak-intensity flows. Intercity trips during the holidays had a phenomenon of “escaping from the metropolis”. Meanwhile, it had significant spatial proximity and directionality. The daily intercity trips were characterized by a remarkable periodicity with seven days as a repeat. A more interesting finding is that when weekends overlap with holidays, intercity travel on the 1–2 days before the vacations has presented an effect of “suppression travel”. Furthermore, at the national scale, the stable intercity travel network has formed a polycentric core-periphery structure of “Three Cores-Six Semi-peripheries-Five Peripheries”. At the urban agglomeration scale, they formed respectively distinguished monocentric, bicentric, and polycentric core-periphery structures.

An accurate and low-cost vehicle-induced deflection prediction framework for long-span bridges using deep learning and monitoring data

Accurate vehicle-induced deflection prediction is critical to bridge structural management and maintenance. However, most existing studies use finite element models and weigh-in-motion (WIM) system to predict the deflection of bridges, the cost of building finite element models is expensive. An accurate and low-cost vehicle-induced deflection prediction framework is developed in this study. In this framework, the calculation method of the spatio-temporal distribution matrix of the vehicle loads is proposed. A fusion attention mechanism bidirectional long short-term memory (ATT-BiLSTM) model is used to predict vehicle-induced deflection. Taking a suspension bridge in China as an example, the accuracy of short- and long-term vehicle-induced deflection prediction is tested, and different deep learning models are used for comparison. The results show that the proposed framework can predict short-term vehicle-induced deflection with a mean absolute error (MAE) of less than 2 mm, which can also accurately predict the extrema of vehicle-induced deflection within a certain time window. The proposed framework is independent of finite element models and lowers the cost of bridge deflection prediction.

Simulating a turbulent video affected by spatiotemporally varying blur and tilt using temporal cross correlation of intermodal Zernike coefficients

Videos captured in long-distance horizontal imaging through the atmosphere suffer from dynamic spatiotemporal movements and blur caused by the air turbulence. Simulations of atmospheric turbulence in such videos, which have been conducted in the past, are difficult to compute. Our goal in this research is to develop an effective simulation algorithm of videos affected by atmospheric turbulence characterized by spatiotemporally varying blur and tilt, when supplied with a given image. We accomplish this via extending an already established method that simulates atmospheric turbulence in a single image, by incorporating turbulence properties in the time domain that include both the tilts and blurring effects. This study also extends our previous work that simulated turbulence, but did not consider the space-varying property of the blur. This is done by employing the relationship between turbulence image distortions and the intermodal correlations of the Zernike coefficients in time and space, and also via analyzing the spatiotemporal matrix that represents the spatial correlation of movements between different frames. The proposed method can facilitate the production of simulations, given turbulence properties that include turbulence strength, object distance, and height. The simulation is applied to videos with low and high frame rates, and the differences between them are analyzed. The proposed method can prove useful when generating machine-learning algorithms that apply to videos affected by atmospheric turbulence, which require large labeled video datasets (with controlled turbulence and imaging parameters) for training.

Urban green and blue infrastructure: unveiling the spatiotemporal impact on carbon emissions in China's Yangtze River Delta.

Blue-green infrastructure (BGI) plays a crucial role in regulating urban carbon cycles. Nonetheless, the spatiotemporal effect of BGI on carbon emissions has not received extensive attention. This study used the Yangtze River Delta (YRD) region as the study area and quantified the landscape patterns of BGI. Using a spatiotemporal geographically weighted regression model, we analyzed the impact of evolving spatiotemporal characteristics of BGI on carbon emissions. Additionally, we constructed a spatiotemporal weight matrix using the Moran index ratio to examine the spillover effects of BGI among different regions. Our results show that the aggregation effect of carbon emissions in the YRD region is gradually increasing while BGI has a dynamic impact on carbon emissions. In terms of spatial and temporal spillovers, under the influence of economic connections between regions, patch fragmentation and distance exert a persistent positive influence on carbon emissions, while shape complexity has a negative impact, with area and layout characteristics showing no significant effects. However, area and patch distance have a persistent positive influence on carbon emissions in adjacent areas, while shape complexity exhibits a negative impact. Therefore, optimizing urban BGI through a regional synergistic governance system is important to promote low-carbon urban development.

Risk factors for tick attachment in companion animals in Great Britain: a spatiotemporal analysis covering 2014-2021.

Ticks are an important driver of veterinary health care, causing irritation and sometimes infection to their hosts. We explored epidemiological and geo-referenced data from > 7 million electronic health records (EHRs) from cats and dogs collected by the Small Animal Veterinary Surveillance Network (SAVSNET) in Great Britain (GB) between 2014 and 2021 to assess the factors affecting tick attachment in an individual and at a spatiotemporal level. EHRs in which ticks were mentioned were identified by text mining; domain experts confirmed those with ticks on the animal. Tick presence/absence records were overlaid with a spatiotemporal series of climate, environment, anthropogenic and host distribution factors to produce a spatiotemporal regression matrix. An ensemble machine learning spatiotemporal model was used to fine-tune hyperparameters for Random Forest, Gradient-boosted Trees and Generalized Linear Model regression algorithms, which were then used to produce a final ensemble meta-learner to predict the probability of tick attachment across GB at a monthly interval and averaged long-term through 2014-2021 at a spatial resolution of 1km. Individual host factors associated with tick attachment were also assessed by conditional logistic regression on a matched case-control dataset. In total, 11,741 consultations were identified in which a tick was recorded. The frequency of tick records was low (0.16% EHRs), suggesting an underestimation of risk. That said, increased odds for tick attachment in cats and dogs were associated with younger adult ages, longer coat length, crossbreeds and unclassified breeds. In cats, males and entire animals had significantly increased odds of recorded tick attachment. The key variables controlling the spatiotemporal risk for tick attachment were climatic (precipitation and temperature) and vegetation type (Enhanced Vegetation Index). Suitable areas for tick attachment were predicted across GB, especially in forests and grassland areas, mainly during summer, particularly in June. Our results can inform targeted health messages to owners and veterinary practitioners, identifying those animals, seasons and areas of higher risk for tick attachment and allowing for more tailored prophylaxis to reduce tick burden, inappropriate parasiticide treatment and potentially TBDs in companion animals and humans. Sentinel networks like SAVSNET represent a novel complementary data source to improve our understanding of tick attachment risk for companion animals and as a proxy of risk to humans.

Temperature response spatiotemporal correlation model and non-destructive reconstruction of temperature field in laser irradiated biological tissues

The biological tissue temperature field monitoring is essential for laser-induced tumor thermotherapy (LITT). Through observable temperature information to reconstruct the temperature field is an important means of obtaining transient temperature fields within tissues. In this work, a new method is proposed to reconstruct the biological tissue temperature field during LITT by means of a temperature response spatiotemporal correlation model. Firstly, based on the bioheat transfer equation, the external description of the spatiotemporal mapping relationship for the heat transfer process in laser irradiated biological tissues is established. Further, through the external description of the spatiotemporal mapping relationship, the temperature response spatiotemporal correlation model in laser irradiated biological tissues is constructed. Afterwards, for the pathological problem of temperature response spatiotemporal correlation model, a construction scheme of temperature response spatiotemporal correlation matrix based on regular optimization technique is established to turn the temperature response spatiotemporal correlation problem into a well-pose problem. Finally, the temperature response spatiotemporal correlation model is used to achieve non-destructive reconstruction of biological tissue temperature field based on rolling optimization. The reliability of the above temperature response spatiotemporal correlation model is indirectly demonstrated by the existing experimental data of laser irradiated biological tissues. Numerical experiment is performed to investigated the effects of laser irradiation form and measurement error on the reconstruction results.

A Latent-Factor-Model-Based Approach for Traffic Data Imputation with Road Network Information

With the rapid development of the economy, car ownership has grown rapidly, which causes many traffic problems. In recent years, intelligent transportation systems have been used to solve various traffic problems. To achieve effective and efficient traffic management, intelligent transportation systems need a large amount of complete traffic data. However, the current traffic data collection methods result in different forms of missing data. In the last twenty years, although many approaches have been proposed to impute missing data based on different mechanisms, these all have their limitations, which leads to low imputation accuracy, especially when the collected traffic data have a large amount of missing values. To this end, this paper proposes a latent-factor-model-based approach to impute the missing traffic data. In the proposed approach, the spatial information of the road network is first combined with the spatiotemporal matrix of the original traffic data. Then, the latent-factor-model-based algorithm is employed to impute the missing data in the combined matrix of the traffic data. Based on the real traffic data from METR-LA, we found that the imputation accuracy of the proposed approach was better than that of most of the current traffic-data-imputation approaches, especially when the original traffic data are limited.

Full-Field Vibration Response Estimation from Sparse Multi-Agent Automatic Mobile Sensors Using Formation Control Algorithm.

In structural vibration response sensing, mobile sensors offer outstanding benefits as they are not dedicated to a certain structure; they also possess the ability to acquire dense spatial information. Currently, most of the existing literature concerning mobile sensing involves human drivers manually driving through the bridges multiple times. While self-driving automated vehicles could serve for such studies, they might entail substantial costs when applied to structural health monitoring tasks. Therefore, in order to tackle this challenge, we introduce a formation control framework that facilitates automatic multi-agent mobile sensing. Notably, our findings demonstrate that the proposed formation control algorithm can effectively control the behavior of the multi-agent systems for structural response sensing purposes based on user choice. We leverage vibration data collected by these mobile sensors to estimate the full-field vibration response of the structure, utilizing a compressive sensing algorithm in the spatial domain. The task of estimating the full-field response can be represented as a spatiotemporal response matrix completion task, wherein the suite of multi-agent mobile sensors sparsely populates some of the matrix's elements. Subsequently, we deploy the compressive sensing technique to obtain the dense full-field vibration complete response of the structure and estimate the reconstruction accuracy. Results obtained from two different formations on a simply supported bridge are presented in this paper, and the high level of accuracy in reconstruction underscores the efficacy of our proposed framework. This multi-agent mobile sensing approach showcases the significant potential for automated structural response measurement, directly applicable to health monitoring and resilience assessment objectives.

Differential working memory function between phonological and visuospatial strategies: a magnetoencephalography study using a same visual task.

Previous studies have reported that, in working memory, the processing of visuospatial information and phonological information have different neural bases. However, in these studies, memory items were presented via different modalities. Therefore, the modality in which the memory items were presented and the strategy for memorizing them were not rigorously distinguished. In the present study, we explored the neural basis of two working memory strategies. Nineteen right-handed young adults memorized seven sequential directions presented visually in a task in which the memory strategy was either visuospatial or phonological (visuospatial/phonological condition). Source amplitudes of theta-band (5-7 Hz) rhythm were estimated from magnetoencephalography during the maintenance period and further analyzed using cluster-based permutation tests. Behavioral results revealed that the accuracy rates showed no significant differences between conditions, while the reaction time in the phonological condition was significantly longer than that in the visuospatial condition. Theta activity in the phonological condition was significantly greater than that in the visuospatial condition, and the cluster in spatio-temporal matrix with p < 5% difference extended to right prefrontal regions in the early maintenance period and right occipito-parietal regions in the late maintenance period. The theta activity results did not indicate strategy-specific neural bases but did reveal the dynamics of executive function required for phonological processing. The functions seemed to move from attention control and inhibition control in the prefrontal region to inhibition of irrelevant information in the occipito-parietal region.

Spatio-temporal bidirectional redundancy removal for quality prediction of dynamic processes: A novel dynamic feature extraction strategy

Data-driven modeling has been widely recognized as an effective and essential approach for predicting key quality variables in industrial processes. However, due to the long production process and the dynamic fluctuation of operating conditions, it is necessary to integrate data from various spatial and temporal points to comprehensively describe the production process. Furthermore, data is characterized by massive redundancies and high dimensionalities, which pose challenges for modeling dynamic processes. To address these issues, this paper proposes a strategy of spatio-temporal bidirectional redundancy removal to extract dynamic features and applies it to quality prediction. Firstly, it constructs input samples with the spatio-temporal two-dimensional structure. Then, information redundancy is removed by implementing feature extraction in both the spatial and temporal directions, respectively. Additionally, a spatio-temporal weight matrix is used in this process to capture dynamic information which is more related to the output quality variable. Its effectiveness was verified by applying it to the debutanizer column process and the leaching process in zinc smelting. Results show that the proposed strategy generates efficient dynamic features with no information redundancy and low dimensionalities. Moreover, it outperforms other common types of dynamic process modeling methods in terms of quality prediction performance.

Multi-dimensional spatial–temporal graph convolution for urban sensors imputation and enhancement

Spatio-temporal data are critical for intelligent systems, such as smart transportation and smart cities. However, due to sensor failure or power failure, the spatiotemporal data missing tends to have a big impact on downstream tasks. Meanwhile, if sensors are scarce, some spatial positions without sensors need data enhancement through intelligent methods. Existing workarounds focus on modeling temporal information (such as time series), often ignoring spatial dependency, or modeling the spatial and temporal domain separately for imputation. In this paper, we propose a Long-term Multi-dimensional Spatial–Temporal Graph Convolution Network (LMSTGCN), which not only inductively estimates some missing data, but also achieves data augmentation of target locations. It contains a periodic temporal encoding mechanism, a gated temporal capture module, and a multi-dimensional spatial–temporal GCN module. The long-term temporal dependencies are captured by the periodic temporal encoding mechanism. The spatial and extra-short-term temporal dependencies are simultaneously modeled by the multi-dimensional GCN module, which can achieve exponential growth in the range of receptive fields. Corresponding to this module, we designed a spatiotemporal adjacency matrix construction method. It generates spatiotemporal adjacency matrices of corresponding time length as needed. The short-term dependencies in sequences are captured by the gated temporal capture module. In experimental analysis, results demonstrate that the proposed model outperforms the state-of-the-art baselines on real-world data sets.

The impacts of industrial collaborative agglomeration on industrial sulfur dioxide emissions in China: from the novel perspective of spatiotemporal matrix.

This paper explores the impacts of industrial collaborative agglomeration on industrial sulfur dioxide intensity from a spatiotemporal perspective based on panel data on the 284 prefecture-level cities from 2003 to 2019, with systematic consideration of the underlying mechanism of channels and actions. The empirical results show that industrial co-agglomeration significantly intensifies industrial SO2 intensity, especially with increasing agglomeration. In addition, its positive spatial spillover effects are established in geographical proximity to the city. Furthermore, the channel analysis shows that the industrial structure path, industrial efficiency path, and industrial scale path account for a sharp increase in industrial SO2 intensity. The market forces reverse and moderate this exacerbating process more significantly than the government does, which provides evidence for the importance of pursuing a dynamic equilibrium between them. Finally, there exist heterogeneous effects across cities with different administrative levels, innovation capacities, and macropolicies of special emission limits for air pollutant policy. While arguing for the environmental pollution effects of industrial co-agglomeration, this paper also provides solid support and a new perspective for promoting sustainable economic development and achieving win-win economic and environmental benefits.

Temperature response spatiotemporal correlation model of heat transfer system

For a linear heat transfer system, the unit step response of the temperature field to any system inputs, such as internal and external heat sources, is specific. This means that there is a definite temperature response correlation between any spatial points in the system spatiotemporally, which is independent of the system inputs. It is significant to achieve a quantitative description of the temperature response spatiotemporal correlation between the spatial points for solving the temperature field reconstruction problem of the heat transfer system with unknown inputs. In this paper, a temperature response spatiotemporal correlation model (RSTCM) of the heat transfer system is established originally to reveal the inherent quantitative relationship between the responses of any system spatial points theoretically. Firstly, an external description of the spatiotemporal mapping relationship of the heat transfer process is established according to the heat transfer equations. Furthermore, a basic RSTCM form is proposed and a response spatiotemporal correlation matrix is determined with the help of the external description. Finally, considering the ill-posed characteristic of the response spatiotemporal correlation problem, the regularization technology is employed to transform the original problem into a well-pose problem and to provide a response spatiotemporal correlation matrix with regularization. Effectiveness of the RSTCM is verified by the existing heat transfer experimental data. Besides, adaptability of the proposed model is demonstrated by the achieved numerical experiment results on a two-dimensional heat transfer system.