Spatial Topology Research Articles

MSMGE-CNN: A multi-scale multi-graph embedding convolutional neural network for motor related EEG decoding

Abstract Deep learning (DL) technique has been widely used for decoding motor related electroencephalography (EEG) signals, which has considerably driven the development of motor related brain-computer interfaces (BCIs). However, traditional convolutional neural networks (CNNs) cannot fully represent spatial topology information and dynamic temporal characteristics of multi-channel EEG signals, resulting in limited decoding accuracy. To address such challenges, a novel multi-scale multi-graph embedding convolutional neural network (MSMGE-CNN) is proposed in this study. The proposed MSMGE-CNN contains two crucial components: multi-scale time convolution and multi-graph embedding. Specifically, we design a multi-branch CNN architecture with mixed-scale time convolutions based on EEGNet to sufficiently extract robust time domain features. Afterward, we embed multi-graph information obtained based on physical distance proximity and functional connectivity of multi-channel EEG signals into the time-domain features to capture rich spatial topological dependencies via multi-graph convolution operation. We extensively evaluated the proposed method on three benchmark EEG datasets commonly used for motor imagery/execution (MI/ME) classification and obtained accuracies of 79.59 % (BCICIV-2a Dataset), 69.77 % (OpenBMI Dataset) and 96.34 % (High Gamma Dataset), respectively. These results powerfully demonstrate that MSMGE-CNN outperforms several state-of-the-art algorithms. In addition, we further conducted a series of ablation experiments to validate the rationality of our network architecture. Overall, the proposed MSMGE-CNN method dramatically improves the accuracy and robustness of MI/ME-EEG decoding, which can effectively enhance the performance of motor related BCI system.

Advancing complex urban traffic forecasting: A fully attentional spatial-temporal network enhanced by graph representation

Accurate urban traffic forecasting is essential for intelligent transportation systems (ITS). However, the majority of existing forecasting methodologies predominantly concentrate on point-based forecasts (e.g., traffic detector forecasts). A limited number of them pay attention to the urban bidirectional road segments and the complex road network topology. To advance accurate traffic forecasting in complex urban scenarios, this paper proposes a Graph Representation enhanced Fully Attentional Spatial-Temporal network (GR-FAST). First, we construct a refined bidirectional road network graph (BRG) to depict the urban road network topology more accurately, particularly focusing on the turning patterns at intersections. Then, we adopt the graph representation methodology and introduce spatial information encoding (SIE) to explicitly characterize the significance of roads and network structure from multiple perspectives. Enhanced by SIE, spatial attention can capture spatial dependencies from both road network topologies and traffic pattern similarities, thereby forming a unified urban spatial cognition. Finally, a multi-scale residual perception (MRP) module is designed to balance the interplay of short-term temporal variability and long-term periodicity. Experiments on a real-world urban dataset from Wuhan, China, demonstrate that GR-FAST outperforms the state-of-the-art deep learning methods, achieving an improvement of 9.19%. Furthermore, ablation studies suggest that the explicit incorporation of complex road spatial topologies can significantly enhance forecasting accuracy.

Smooth Gowdy-symmetric generalised Taub–NUT solutions with polynomial initial data

Abstract We consider smooth Gowdy-symmetric generalised Taub–NUT solutions, a class of inhomogeneous cosmological models with spatial three-sphere topology. They are characterised by existence of a smooth past Cauchy horizon and, with the exception of certain singular cases, they also develop a regular future Cauchy horizon. Several examples of exact solutions were previously constructed, where the initial data (in form of the initial Ernst potentials) are polynomials of low degree. Here, we generalise to polynomial initial data of arbitrary degree. Utilising methods from soliton theory, we obtain a simple algorithm that allows us to construct the resulting Ernst potential with purely algebraic calculations. We also derive an explicit formula in terms of determinants, and we illustrate the method with two examples.

Cross-scale study of heat transfer performance in metal rubber with complex topological structures

Metal Rubber (MR), characterized by its porous topology and metal-based entangled structure, is commonly utilized in high-temperature environments. The intricate nature of MR's structure complicates the accurate experimental investigation of its thermophysical properties, thereby restricting its broader applications. Therefore, based on numerical simulation, the three-dimensional reconstruction of the spatial topology of MR is achieved. Additionally, MATLAB-LS/DYNA-ABAQUS is coupled to replicate the heat transfer process of MR at macro-microscopic scales. Our findings elucidate the relationship between MR's density, number of contact points, and thermal conductivity, revealing a stepwise decrease in thermal conductivity along the forming direction and a spatially varying anisotropic heat transfer mechanism that involves energy feedback on non-forming surfaces. Specifically, at the material level of investigation, a molecular dynamics model for heat transfer in microscopic metal wire contacts was generated. This model enables the simulation and dynamic tracking of atomic group thermal behavior under temperature effects. Finally, equivalent thermal conductivity (ETC) tests were conducted concurrently. By integrating the thermoelectric analogy method, we introduced for the first time a hybrid series-parallel mode and the tortuosity of discontinuous materials. This approach comprehensively considers critical factors such as porosity, temperature, and interlayer thermal resistance, culminating in the development of a predictive numerical model for thermal conductivity in porous metal-based materials. In this study, a bottom-up multiscale research approach is proposed to deeply explore the spatially multidirectional heat transfer mechanisms of microporous metal-based tangled materials, from the material level to the complex topological structural level. Simultaneously, new dimensions are opened for the study of such materials with unique discontinuous structural characteristics.

Vacuum currents in curved tubes

We investigate the combined effects of spatial curvature and topology on the properties of the vacuum state for a charged scalar field localized on rotationally symmetric 2D curved tubes. For a general spatial geometry and for quasiperiodicity condition with a general phase, the representation of the Hadamard function is provided where the topological contribution is explicitly extracted. As an important local characteristic of the vacuum state the expectation value of the current density is studied. The vacuum current is a periodic function of the magnetic flux enclosed by the tube with the period of flux quantum. The general formula is specified for constant radius and conical tubes. As another application, we consider the Hadamard function and the vacuum current density for a scalar field on the Beltrami pseudosphere. Several representations are provided for the corresponding expectation value. For small values of the proper radius of the tube, compared with the curvature radius, the effect of spatial curvature on the vacuum current is weak and the leading term in the corresponding expansion coincides with the current density on a constant radius tube. The effect of curvature is essential for proper radii of the tube larger than the radius of spatial curvature. In this limit the falloff of the current density, as a function of the proper radius, follows a power law for both massless and massive fields. This behavior is in clear contrast to the one for a constant radius tube with exponential decay for massive fields. We also compare the vacuum currents on the Beltrami pseudosphere and on locally de Sitter and anti–de Sitter 2D tubes. Published by the American Physical Society 2024

A photovoltaic cell defect detection model capable of topological knowledge extraction

As the global transition towards clean energy accelerates, the demand for the widespread adoption of solar energy continues to rise. However, traditional object detection models prove inadequate for handling photovoltaic cell electroluminescence (EL) images, which are characterized by high levels of noise. To address this challenge, we developed an advanced defect detection model specifically designed for photovoltaic cells, which integrates topological knowledge extraction. Our approach begins with the introduction of a multi-scale dynamic context-based feature extraction method, capable of generating static context by thoroughly capturing the local texture and structural information of multi-scale defects. This static context is then combined with dynamic context to produce fine-grained local features. Subsequently, we developed a centralized feature pyramid structure, enhanced by spatial semantics, which models the explicit visual center. This structure effectively elucidates the relationship between local and global features in defect images, thereby improving the representation of defect characteristics. Finally, we implemented a feature enhancement strategy grounded in spatial semantic knowledge extraction. This strategy uncovers potential correlations among defect targets by constructing a spatial semantic topology of features, mapping these features to a higher-order representation, and ultimately delivering precise defect detection results.

Spectral-Spatial Global Graph Reasoning for Hyperspectral Image Classification.

Convolutional neural networks (CNNs) have been widely applied to hyperspectral image classification (HSIC). However, traditional convolutions can not effectively extract features for objects with irregular distributions. Recent methods attempt to address this issue by performing graph convolutions on spatial topologies, but fixed graph structures and local perceptions limit their performances. To tackle these problems, in this article, different from previous approaches, we perform the superpixel generation on intermediate features during network training to adaptively produce homogeneous regions, obtain graph structures, and further generate spatial descriptors, which are served as graph nodes. Besides spatial objects, we also explore the graph relationships between channels by reasonably aggregating channels to generate spectral descriptors. The adjacent matrices in these graph convolutions are obtained by considering the relationships among all descriptors to realize global perceptions. By combining the extracted spatial and spectral graph features, we finally obtain a spectral-spatial graph reasoning network (SSGRN). The spatial and spectral parts of SSGRN are separately called spatial and spectral graph reasoning subnetworks. Comprehensive experiments on four public datasets demonstrate the competitiveness of the proposed methods compared with other state-of-the-art graph convolution-based approaches.

Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave background in the test case of Euclidean E 1 topology (the 3-torus) with a cubic fundamental domain of a size scale significantly smaller than the diameter of the last scattering surface. This is the first step toward developing a machine learning approach to classification of cosmic topology and likelihood-free inference of topological parameters. Different machine learning approaches are capable of classifying the harmonic-space realizations with accuracy greater than 99% if the topology scale is half of the diameter of the last-scattering surface and orientation of the topology is known. For distinguishing random rotations of these sky realizations from realizations of the covering space, the extreme gradient boosting classifier algorithm performs best with an accuracy of 88%. Slightly lower accuracies of 83% to 87% are obtained with the random forest classifier along with one- and two-dimensional convolutional neural networks. The techniques presented here can also accurately classify non-rotated cubic E 1 topology realizations with a topology scale slightly larger than the diameter of the last-scattering surface, if enough training data are provided. While information compressing methods like most machine learning approaches cannot exceed the statistical power of a likelihood-based approach that captures all available information, they potentially offer a computationally cheaper alternative. A principle challenge appears to be accounting for arbitrary orientations of a given topology, although this is also a significant hurdle for likelihood-based approaches.

Multi-Scale Spatial-Temporal Attention Networks for Functional Connectome Classification.

Many neuropsychiatric disorders are considered to be associated with abnormalities in the functional connectivity networks of the brain. The research on the classification of functional connectivity can therefore provide new perspectives for understanding the pathology of disorders and contribute to early diagnosis and treatment. Functional connectivity exhibits a nature of dynamically changing over time, however, the majority of existing methods are unable to collectively reveal the spatial topology and time-varying characteristics. Furthermore, despite the efforts of limited spatial-temporal studies to capture rich information across different spatial scales, they have not delved into the temporal characteristics among different scales. To address above issues, we propose a novel Multi-Scale Spatial-Temporal Attention Networks (MSSTAN) to exploit the multi-scale spatial-temporal information provided by functional connectome for classification. To fully extract spatial features of brain regions, we propose a Topology Enhanced Graph Transformer module to guide the attention calculations in the learning of spatial features by incorporating topology priors. A Multi-Scale Pooling Strategy is introduced to obtain representations of brain connectome at various scales. Considering the temporal dynamic characteristics between dynamic functional connectome, we employ Locality Sensitive Hashing attention to further capture long-term dependencies in time dynamics across multiple scales and reduce the computational complexity of the original attention mechanism. Experiments on three brain fMRI datasets of MDD and ASD demonstrate the superiority of our proposed approach. In addition, benefiting from the attention mechanism in Transformer, our results are interpretable, which can contribute to the discovery of biomarkers. The code is available at https://github.com/LIST-KONG/MSSTAN.

Effective Emotion Recognition by Learning Discriminative Graph Topologies in EEG Brain Networks.

Multichannel electroencephalogram (EEG) is an array signal that represents brain neural networks and can be applied to characterize information propagation patterns for different emotional states. To reveal these inherent spatial graph features and increase the stability of emotion recognition, we propose an effective emotion recognition model that performs multicategory emotion recognition with multiple emotion-related spatial network topology patterns (MESNPs) by learning discriminative graph topologies in EEG brain networks. To evaluate the performance of our proposed MESNP model, we conducted single-subject and multisubject four-class classification experiments on two public datasets, MAHNOB-HCI and DEAP. Compared with existing feature extraction methods, the MESNP model significantly enhances the multiclass emotional classification performance in the single-subject and multisubject conditions. To evaluate the online version of the proposed MESNP model, we designed an online emotion monitoring system. We recruited 14 participants to conduct the online emotion decoding experiments. The average online experimental accuracy of the 14 participants was 84.56%, indicating that our model can be applied in affective brain-computer interface (aBCI) systems. The offline and online experimental results demonstrate that the proposed MESNP model effectively captures discriminative graph topology patterns and significantly improves emotion classification performance. Moreover, the proposed MESNP model provides a new scheme for extracting features from strongly coupled array signals.

Short-Term Origin-Destination Demand Prediction Based on Spatiotemporal Encoder-Decoder Network with a Residual Feature Extractor

Online ride-hailing services play a crucial role in daily transportation, However, challenges persist in certain regions with limited access, and drivers encounter difficulties in receiving orders. Accurate prediction of short-term origin-destination (OD) demand is crucial for addressing these issues. This study leverages recent advancements in artificial intelligence and big data to introduce a spatiotemporal encoder-decoder network with a residual feature extractor (RF-STED) for short-term OD demand prediction in online ride-hailing services. The RF-STED model, built on deep learning models such as graph convolutional networks and convolutional long short-term memory (Conv-LSTM), includes spatiotemporal networks, encoding layers, and a residual feature extractor. The spatiotemporal network has two branches: branch one processes multi-pattern OD data using a multi-pattern temporal feature extraction module, utilizing a multi-channel Conv-LSTM to capture temporal correlations. Branch two utilizes a multi-spatial feature extraction module to convert OD pair associations into a spatial topology, extracting multi-spatial correlations. The encoding layer captures spatiotemporal dependencies, while the residual feature extractor decodes compressed vectors back into an OD graph for forecasting future demand. Experiments with a Manhattan taxi dataset in the U.S. show the RF-STED model outperforms 10 baseline models and four ablation models. The results emphasize the model’s strength and robustness in short-term OD flow prediction.

Optimizing Maintenance Resource Scheduling and Site Selection for Urban Metro Systems: A Multi-Objective Approach to Enhance System Resilience

This study developed an optimization model for the strategic location of maintenance resource supply sites and the scheduling of multiple resources following failures in urban metro systems, with the objective of enhancing system resilience. The model employs a multi-objective optimization framework, focusing primarily on minimizing resource scheduling time and reducing costs. It incorporates critical factors such as spatial location, network topology, station size, and passenger flow. A hybrid method, combining the non-dominated sorting genetic algorithm III and the technique for order of preference by similarity to ideal solution, is used to solve the model, with its effectiveness confirmed through a case study of the Nanjing Metro system. The simulation results yielded an optimal number of 21 maintenance resource supply stations and provided their placement. In the event of large-scale failures, the optimal resource scheduling strategy ensures demand satisfaction rates exceed 90% at critical stations, maintaining an overall rate of 87.09%, therefore significantly improving resource scheduling efficiency and the system’s emergency response capabilities and enhancing the physical resilience and recovery capabilities of the urban metro system. Moreover, the model accounts for economic factors, striving to balance emergency response capabilities with production continuity and cost efficiency through effective maintenance strategies and resource utilization. This approach provides a systematic framework for urban metro systems to manage sudden failures, ensuring rapid recovery to normal operations and minimizing operational disruptions in scenarios of limited resources.

Examples of cosmological spacetimes without CMC Cauchy surfaces

CMC (constant mean curvature) Cauchy surfaces play an important role in mathematical relativity as finding solutions to the vacuum Einstein constraint equations is made much simpler by assuming CMC initial data. However, Bartnik (Commun Math Phys 117(4):615–624, 1988) constructed a cosmological spacetime without a CMC Cauchy surface whose spatial topology is the connected sum of two three-dimensional tori. Similarly, Chruściel et al. (Commun Math Phys 257(1):29–42, 2005) constructed a vacuum cosmological spacetime without CMC Cauchy surfaces whose spatial topology is also the connected sum of two tori. In this article, we enlarge the known number of spatial topologies for cosmological spacetimes without CMC Cauchy surfaces by generalizing Bartnik’s construction. Specifically, we show that there are cosmological spacetimes without CMC Cauchy surfaces whose spatial topologies are the connected sum of any compact Euclidean or hyperbolic three-manifold with any another compact Euclidean or hyperbolic three-manifold. Analogous examples in higher spacetime dimensions are also possible. We work with the Tolman–Bondi class of metrics and prove gluing results for variable marginal conditions, which allows for smooth gluing of Schwarzschild to FLRW models.

Control effect on the divergent and convergent riblets in particle-laden turbulent boundary layer

Particle image velocimetry was employed to investigate the impact of convergent–divergent riblets on turbulent boundary layers in both clear water and liquid–solid two-phase flow fields containing 155 μm polystyrene particles. The turbulence statistics such as turbulence intensity and Reynolds stress were investigated. The spatial topology of spanwise vortex head and the development and evolution process of hairpin vortices were explored from Euler and Lagrange perspectives, respectively. Additionally, the particle distribution, concentration, and dispersion within the turbulent boundary layer were statistically analyzed. The results indicated that the boundary layer thickness, friction resistance, integrated turbulence intensity, and Reynolds stress were significantly lower on divergent riblet walls compared to convergent riblet walls. Notably, divergent riblets with a yaw angle of 30° exhibited the best drag reduction effect in both single-phase and two-phase flow fields. The addition of particles resulted in an increase in boundary layer thickness but effectively reduced turbulent fluctuations in the logarithmic region, enhancing drag reduction. This extended the drag reduction range of divergent riblets to a yaw angle of 45°, increasing the maximum drag reduction rate to 26.18%. Through spatial multi-scale local average structure function and finite-time Lyapunov exponent field analysis, it was found that the 30° divergent riblet wall significantly inhibited the development of vortex structures and reduced momentum exchange within the boundary layer. Conversely, the 30° convergent riblet wall had the opposite effect, while the particle phase inhibited the development of all wall turbulent structures. Analysis of particle concentration variations within different regions of the turbulent boundary layer revealed that as the normal height of the boundary layer increased, particle concentration gradually increased, and particle dispersion decreased accordingly. The analysis further showed that particle dispersion was mainly influenced by flow structures, whereas concentration was significantly affected by turbulence intensity. These findings elucidate the effect of the flow field on the particle phase and provide insights into the interaction mechanism between the flow field and particles.

Analysis of coherent structures over interacting barchan dunes based on tomographic particle image velocimetry

The influence of barchan dune interaction upon unsteady flow separation and wake dynamics around the fixed-bed downstream barchan dune (DBD) model are experimentally investigated at a Reynolds number of 2640 based on the tomographic particle image velocimetry (PIV) system. The time-averaged statistics including the mean velocities, recirculation area, vortex spatial topology, Reynolds stress, and turbulent kinetic energy were used to characterize the flow field and large-scale anisotropy. It was found that arch-shaped vortex “chains” with strong spanwise coherence shedding from isolated barchan crestline populate the whole wake region, while elongated rod-shaped vortex structures with strong streamwise coherence induced by the up-downwash flow around the DBD were found to fill the whole measurement range, which is closely related to “sheltering” effect on the incoming flow acting at DBD due to the presence of upstream barchan dune (UBD). Additionally, in order to study the complex dynamic features of these predominated vortex structure transformations, time-resolved planar particle image velocimetry was applied. This technique allows for providing complementary insights into the temporal behavior of the unsteady coherent flow structures populating the wake field in different experimental configurations. It was found that the basic unsteady flapping motion, vortex roll-up, and complex vortex interactions including vortex pairing, merging, and breaking up can all be analyzed by dividing into certain scales with ease in a combination wavelet and Lagrangian framework.

Brain-computer interfaces inspired spiking neural network model for depression stage identification

BackgroundDepression is a global mental disorder, and traditional diagnostic methods mainly rely on scales and subjective evaluations by doctors, which cannot effectively identify symptoms and even carry the risk of misdiagnosis. Brain-Computer Interfaces inspired deep learning-assisted diagnosis based on physiological signals holds promise for improving traditional methods lacking physiological basis and leads next generation neuro-technologies. However, traditional deep learning methods rely on immense computational power and mostly involve end-to-end network learning. These learning methods also lack physiological interpretability, limiting their clinical application in assisted diagnosis. MethodologyA brain-like learning model for diagnosing depression using electroencephalogram (EEG) is proposed. The study collects EEG data using 128-channel electrodes, producing a 128×128 brain adjacency matrix. Given the assumption of undirected connectivity, the upper half of the 128×128 matrix is chosen in order to minimise the input parameter size, producing 8,128-dimensional data. After eliminating 28 components derived from irrelevant or reference electrodes, a 90×90 matrix is produced, which can be used as an input for a single-channel brain-computer interface image. ResultAt the functional level, a spiking neural network is constructed to classify individuals with depression and healthy individuals, achieving an accuracy exceeding 97.5 %. Comparison with existing methodsCompared to deep convolutional methods, the spiking method reduces energy consumption. ConclusionAt the structural level, complex networks are utilized to establish spatial topology of brain connections and analyse their graph features, identifying potential abnormal brain functional connections in individuals with depression.

Spatio-Temporal Graph Hubness Propagation Model for Dynamic Brain Network Classification.

Dynamic brain network has the advantage over static brain network in characterizing the variation pattern of functional brain connectivity, and it has attracted increasing attention in brain disease diagnosis. However, most of the existing dynamic brain networks analysis methods rely on extracting features from independent brain networks divided by sliding windows, making them hard to reveal the high-order dynamic evolution laws of functional brain networks. Additionally, they cannot effectively extract the spatio-temporal topology features in dynamic brain networks. In this paper, we propose to use optimal transport (OT) theory to capture the topology evolution of the dynamic brain networks, and develop a multi-channel spatio-temporal graph convolutional network that collaboratively extracts the temporal and spatial features from the evolution networks. Specifically, we first adaptively evaluate the graph hubness of brain regions in the brain network of each time window, which comprehensively models information transmission among multiple brain regions. Second, the hubness propagation information across adjacent time windows is captured by optimal transport, describing high-order topology evolution of dynamic brain networks. Moreover, we develop a spatio-temporal graph convolutional network with attention mechanism to collaboratively extract the intrinsic temporal and spatial topology information from the above networks. Finally, the multi-layer perceptron is adopted for classifying the dynamic brain network. The extensive experiment on the collected epilepsy dataset and the public ADNI dataset show that our proposed method not only outperforms several state-of-the-art methods in brain disease diagnosis, but also reveals the key dynamic alterations of brain connectivities between patients and healthy controls.

Topo: Towards a fine-grained topological data processing framework on Tianhe-3 supercomputer

Big data frameworks are widely deployed in supercomputers for analyzing large-scale datasets. Topological data processing is an emerging approach that focuses on analyzing the topological structures in high-dimensional scientific data. However, incorporating topological data processing into current big data frameworks presents three main challenges: (1) The frequent data exchange poses challenges to the traditional coarse-grained parallelism. (2) The spatial topology makes parallel programming harder using oversimplified MapReduce APIs. (3) The massive intermediate data and NUMA architecture hinder resource utilization and scalability on novel supercomputers and many-core processors.In this paper, we present Topo, a generic distributed framework that enhances topological data processing on many-core supercomputers. Topo relies on three concepts. (1) It employs fine-grained parallelism, with awareness of topological structures in datasets, to support interactions among collaborative workers before each shuffle phase. (2) It provides intuitive APIs for topological data operations. (3) It implements efficient collective I/O and NUMA-aware dynamic task scheduling to improve multi-threading and load balancing. We evaluate Topo's performance on the Tianhe-3 supercomputer, which utilizes state-of-the-art ARM many-core processors. Experimental results of execution time show that compared to popular frameworks, Topo achieves an average speedup of 5.3× and 6.3×, with a maximum speedup of 8.4× and 20×, on HPC workloads and big data benchmarks, respectively. Topo further reduces total execution time on processing skewed datasets by 41%.

A dynamic topology analysis method for multi-ship encounters based on multi time-space network trees

This paper innovatively proposes a novel approach of topological analysis in the dynamic time-space domain of ship encounters under the joint action of multi-space network structural elements, based on the GIS spatial information platform and spatial topology analysis theory. The proposed method based on the ship's navigational motion information, encounter dynamic mode, relative time-space position distribution, etc., the method divides and intersects the time-space domain of the ship's encounter dynamics, and establishes an encountering dynamic time-space network tree in which space and attribute elements are collaboratively associated during the navigation. From the perspective of network topology analysis, the high-precision analysis of the spatial coupling characteristics and time-space trends of potential encountered dangers during ships dynamic navigation is achieved. To verify the effectiveness of the method, real encounter scenarios of M/T SANCHI and M/V CF Crystal were used as analysis cases. The results showed that the proposed method can precisely extract spatial relationships and spatio-temporal coupling feature information of potential hazards encountered between ships, with an average error of about 2.54% and an overall error between 1.94% and 3.53%.Simultaneously, the method's time efficiency results are thoroughly studied and compared, and it is discovered that the proposed method has good stability.

Spacetime magnetic hopfions from internal excitations and braiding of skyrmions

Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime magnetic hopfions: magnetic textures in two spatial dimensions that when excited by a time-periodic drive develop spacetime topology. We uncover two complementary construction routes using skyrmions by braiding their center of mass position and by controlling their internal low-energy excitations. Spacetime magnetic hopfions can be realized in nanopatterned grids to braid skyrmions and in frustrated magnets under an applied AC electric field. Their topological invariant, the spacetime Hopf index, can be tuned by the applied electric field as demonstrated by our collective coordinate modeling and micromagnetic simulations. The principles we have introduced to actively control spacetime topology are not limited to magnetic solitons, opening avenues to explore spacetime topology of general order parameters and fields.