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Deep learning has achieved great success in hyperspectral image classification. However, its success relies on the availability of sufficient training samples. Unfortunately, the collection of training samples is expensive, time-consuming, and even impossible in some cases. Natural image data sets that are different from HSI, such as Image Net and mini-ImageNet, have abundant texture and structure information. Effective knowledge transfer between two heterogeneous data sets can significantly improve the accuracy of HSI classification. In this letter, heterogeneous few-shot learning (HFSL) for HSI classification is proposed with only a few labeled samples per class. Firstly, few-shot learning is performed on the mini-ImageNet data sets to learn the transferable knowledge. Then, to make full use of the spatial and spectral information, a spectral-spatial fusion network is devised. Spectral information is obtained by the residual network with pure one-dimensional operators. Spatial information is extracted by a convolution network with pure two-dimensional operators, and the weights of the spatial network are initialized by the weights of the model trained on the mini-ImageNet data sets. Finally, few-shot learning is fine-tuned on HSI to extract discriminative spectral-spatial features and individual knowledge, which can improve the classification performance of the new classification task. Experiments conducted on two public HSI data sets demonstrate that the HFSL outperforms the existing few-shot learning methods and supervised learning methods for HSI classification with only a few labeled samples. Our source code is available at https://github.com/Li-ZK/HFSL.

This paper presents an effective dissimilarity measure for geometric graphs representing shapes. The proposed dissimilarity measure is a distance that combines a sparsification of the geometric graph based on the maximum diversity problem and a new node embedding that captures the topological neighborhood of nodes. The sparsification step aims to reduce the size of the graph and to correct the misdistribution of nodes on the geometric graph induced by the noise of image handling. Experimental evaluation shows that the sparsification algorithm retains the form of the shapes while decreasing the number of processed nodes which reduces the overall matching time. Furthermore, the proposed node embedding and similarity measure give better performance in comparison with existing graph matching approaches.

We prove concentration inequality results for geometric graph properties of an instance of the Cooper–Frieze [5] preferential attachment model withedge-steps. More precisely, we investigate a random graph model that at each time$t\in \mathbb{N}$, with probabilitypadds a new vertex to the graph (avertex-stepoccurs) or with probability$1-p$an edge connecting two existent vertices is added (anedge-stepoccurs). We prove concentration results for theglobal clustering coefficientas well as theclique number. More formally, we prove that the global clustering, with high probability, decays as$t^{-\gamma(p)}$for a positive function$\gamma$ofp, whereas the clique number of these graphs is, up to subpolynomially small factors, of order$t^{(1-p)/(2-p)}$.

Existing researches on cascading failures mainly focus on static spatial networks, but rarely consider network scenarios where mobile nodes and static nodes coexist. Therefore, in this work, we explore the impact of node mobility on cascading failures in spatial networks. We first develop a cascading model for static-mobile spatial network systems. In this model, we use the general betweenness to characterize the load of static nodes in the network, and adopt the Gauss–Markov mobility model to generate the movement trajectory of mobile nodes. On this basis, we develop three node interaction modes ( i.e., all-connection mode, high-load priority mode and low-load priority mode) to characterize the interaction between static nodes and mobile nodes. Experimental results have shown that 1) unlike the traditional cascading process that is a continuous process, the cascading process of static-mobile spatial networks consists of multiple cascading processes that occur at different times; 2) expanding the network size and reducing the number of mobile nodes can help the network resist cascading failures; 3) there is a tolerance space for network configuration parameters . When the configuration parameters fall into this space, the network can avoid cascading failures; 4) among the three interaction modes, the network robustness in all-connection mode is the worst, followed by low-load priority mode, and finally high-load priority mode. The obtained results can provide theoretical guidance for users to establish a more robust static-mobile spatial network.

Wireless sensor network (WSNs) technology and Internet technology penetrate and extend each other. It is a good way for physical changes of objects, state recognition and data collection, and becomes an important source of network data in big data. Compared with traditional wireless networks, WSNs have the characteristics of integrating sensing, processing, and transmission, limited hardware resources, limited power supply capacity, no center, self-organization, multi-hop routing, dynamic topology, large number of nodes, and dense distribution. In order to improve the energy utilization rate of a single node to a greater extent, reduce the energy consumption of the entire WSNs, and extend the life cycle of WSNs, high-efficiency networking is essential in the application of WSNs. Networking is one of the foundations to the large-scale WSNs. The network model and node location deployment are important technologies for WSNs networking. Based on the network characteristics of large-scale WSNs and the transmission capacity of big data, a new type of network model suitable is presented which combined the advantages of Star model and Mesh model. More importantly, the deployment environment of sensor nodes is a spatial network. The data collected and transmitted by large-scale WSNs is very large. The deployment of sensor nodes in space can ensure that the big data collected and transmitted are true and effective. This research proposes the space density first (SDF) algorithm, which improves the neighbor density first algorithm with the space node deployment and the density-optimized SDF algorithm. The SDF algorithm saves network energy and extends the life of the network. Experimental results show that large-scale WSNs built with a new networking model and SDF algorithm can collect and transmit big data stably and reliably, which saves network energy and improves the accuracy of big data.

We introduce the concept of local spanners for planar point sets with respect to a family of regions, and prove the existence of local spanners of small size for some families. For a geometric graph G on a point set $$P$$ and a region R belonging to a family $${\mathcal {R}}$$ , we define $$G \cap R$$ to be the part of the graph G that is inside R (or is induced by R). A local t-spanner w.r.t $${\mathcal {R}}$$ is a geometric graph G on $$P$$ such that for any region $$R \in {\mathcal {R}}$$ , the graph $$G\cap R$$ is a t-spanner for $$K(P) \cap R$$ , where $$K(P)$$ is the complete geometric graph on P. For any set $$P$$ of n points and any constant $$\varepsilon > 0$$ , we prove that $$P$$ admits local $$(1 + \varepsilon )$$ -spanners of sizes $$O(n \log ^{6} n)$$ and $$O(n \log n)$$ w.r.t axis-parallel squares and vertical slabs, respectively. If adding Steiner points is allowed, then local $$(1 + \varepsilon )$$ -spanners with O(n) edges and $$O(n \log ^2 n)$$ edges can be obtained for axis-parallel squares and disks using O(n) Steiner points, respectively.

In order to improve the intelligent effect of English performance rating, this paper analyzes the English performance rating process and builds the corresponding algorithm model based on the wisdom of teaching ideas, and it combines BP spatial network technology with spatial sampling and spatial statistical algorithms to construct the system kernel algorithm. Moreover, this paper extracts students’ English answers through text recognition and compares them with the standard library. Among them, objective questions are mainly scored directly through standard answer comparison, and subjective questions compare student scores with standard answers. In addition, this paper uses a needs analysis to construct the framework of the entire English performance rating system and evaluates the practical effect of the system constructed in the paper through experimental research. According to statistical research data, the English performance rating system in this paper is known to have certain effects.

The interaction of regional ecological efficiency is important for promoting ecological efficiency. Using a gravity model and social network analysis, this study investigated the spatial network characteristics of the sustainable total-factor ecology efficiency (STFEcE) in 30 provinces of China from 2005 to 2016 for the first time. The quadratic assignment procedure (QAP) was also used to analyze the factors affecting the network. The results are as follows. (1) The STFEcE between regions exhibited a spatial network relationship. (2) Jiangsu, Guangdong, Shandong, Ningxia, and other provinces were in the center of the network, whereas Guangxi, Anhui, and other provinces were on the edge. (3) The 30 provinces were divided into four plates, and the connections in the network were primarily based on the relationship between plates. (4) The difference between urban population, energy structure, and technical advancement negatively impacted the network relationship. The provinces should fully understand the value of the STFEcE network and implement appropriate measures to achieve collaborative improvement of regional ecological efficiency according to their roles in the network.

In the study of human action recognition, two-stream networks have made excellent progress recently. However, there remain challenges in distinguishing similar human actions in videos. This paper proposes a novel local-aware spatio-temporal attention network with multi-stage feature fusion based on compact bilinear pooling for human action recognition. To elaborate, taking two-stream networks as our essential backbones, the spatial network first employs multiple spatial transformer networks in a parallel manner to locate the discriminative regions related to human actions. Then, we perform feature fusion between the local and global features to enhance the human action representation. Furthermore, the output of the spatial network and the temporal information are fused at a particular layer to learn the pixel-wise correspondences. After that, we bring together three outputs to generate the global descriptors of human actions. To verify the efficacy of the proposed approach, comparison experiments are conducted with the traditional hand-engineered IDT algorithms, the classical machine learning methods (i.e., SVM) and the state-of-the-art deep learning methods (i.e., spatio-temporal multiplier networks). According to the results, our approach is reported to obtain the best performance among existing works, with the accuracy of 95.3% and 72.9% on UCF101 and HMDB51, respectively. The experimental results thus demonstrate the superiority and significance of the proposed architecture in solving the task of human action recognition.

Public space is characterised by visible spaces and featured by observable activities, forming the atmosphere that humans can perceive, interpret, and experience. This article conceptualises urban space as a set of viewsheds connecting functions visually which can be represented as functional visibility graphs – the graphs with mutual-visibility edges between space and function nodes. It begins with an introduction of three basic measures: visual function size, entropy, and mean angular depth step, then proposes advanced measures: namely visual function connectivity, function visibility, and visible function closeness, showing spatial narratives along paths, visual centrality in place, and functional regions for continuous areas, respectively. This framework is enabled by social media check-in data that records people’s engagements across function nodes tagged by them. An application in a real example in Tianjin City is shown. The novelty of using social media check-ins as a delegation of actual function usage is demonstrated for modelling urban movement with improved precision. By tracing the shifting performance of the functional visibility graphs for the same spatial layout, this study outlines how such analysis can be conducted for uncovering short-term transformation of the visual landscape, contributing to the fine-scale, high-resolution implementations of land use policies from a real human-focused perspective, with the socially sensed data.

In many applications of graph processing, the input data is often generated from an underlying geometric point data set. However, existing high-performance graph processing frameworks assume that the input data is given as a graph. Therefore, to use these frameworks, the user must write or use external programs based on computational geometry algorithms to convert their point data set to a graph, which requires more programming effort and can also lead to performance degradation. In this paper, we present our ongoing work on the Geo- Graph framework for shared-memory multicore machines, which seamlessly supports routines for parallel geometric graph construction and parallel graph processing within the same environment. GeoGraph supports graph construction based on k-nearest neighbors, Delaunay triangulation, and b-skeleton graphs. It can then pass these generated graphs to over 25 graph algorithms. GeoGraph contains highperformance parallel primitives and algorithms implemented in C++, and includes a Python interface. We present four examples of using GeoGraph, and some experimental results showing good parallel speedups and improvements over the Higra library. We conclude with a vision of future directions for research in bridging graph and geometric data processing.

We give a statement of a multipoint boundary value problem on a geometric graph. The characteristics of the graph admitting such a statement are described. The form of the boundary value problem adjoint to the problem posed is found. An analog of the Keldysh residue theorem is obtained for the Green’s function of the spectral multipoint boundary value problem on the graph.

In this paper, the province construction and demolition waste (CDW) generation in China from 2005 to 2018 is calculated by using the area estimation method. Together with the use of the gravity model and the social network analysis method (SNA), the characteristics and effects of the spatial correlation structure network of China's province construction and demolition waste generation are studied. It has been found that from 2005 to 2018, the construction and demolition waste in China had seen a significant rise, and the spatial difference in province generation is significant. During that time, China's inter-provincial construction and demolition waste generation demonstrated significant characteristics of a spatial correlation network with a complex network hierarchy and showed a trend of year-by-year increase in its overall network density and number of correlation. In this spatial connection network, nine provinces, including Beijing, Tianjin, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Hubei and Guangdong, played a core role as "bridges", Beijing, Shanghai, Jiangsu, Guangdong, Shandong, Fujian and Zhejiang provinces are "beneficiaries", Chongqing, Tianjin, Hubei, Anhui, Sichuan, Henan, Jiangxi, Hunan and Hebei are "brokers" while other provinces are "the damaged". Indexes such as network density, network hierarchy and network efficiency all have a significant impact on the national construction and demolition waste generation intensity. The reduction of network density, the improvement of network hierarchy and network efficiency can significantly reduce the difference in construction and demolition waste generation intensity. The structure of spatial correlation network has significant influence on the difference of construction and demolition waste generation intensity.

Despite extensive and active research on network structures in tourist destinations, literature on the spatial network structure of the tourism economy in urban agglomeration is limited. Taking Urban Agglomeration in the middle reaches of the Yangtze River (UAMRYR) as the case study, this study aims to examine the characteristics associated with the spatial network structure of the tourism economy by adopting the tourism economic gravity model and social network analysis (SNA). The main conclusions are as follows. The spatial network structure of the tourism economy in UAMRYR was loose, with limited adequate tourism economic connections and collaboration among various plates. As the three core cities, Wuhan, Changsha, and Nanchang not only had more tourism economic connections among other cities but also acted as an intermediary and a bridge between the spatial network structure of the tourism economy. To sum up, the findings of this study could be applied to formulate scientific policies to promote spatial integration and tourism economic cooperation in urban agglomerations.

Parochialism occurs when an individual mentally codes the population into in-group and out-group members and cooperates only with in-group members. Conditional cooperation of this kind is distinct from strategies such as tit-for-tat where the decision to cooperate is conditioned on others’ previous actions. Parochialists practice in-group favoritism by cooperating with others, conditional on their spatial proximity or cultural similarity. We consider an evolutionary model of local interaction with three types of strategies: altruists “always cooperate”; egoists “always defect”; and parochialists cooperate only with neighbors within a certain radius on a spatial network. In the model, we provide a new explanation for why parochialism is durable and can stably remain prevalent in human populations. The main driving force is the homophily effect. Interestingly, the homophily effect leads to the prevalence of parochialists but not altruists who benefit more from homophilic association, because altruists are invaded by parochialists. The two groups can coexist only if egoists buffer their direct interaction. Accordingly, the proportion of egoists can be greater than that of altruists in our model, contrary to the result of Eshel et al. (1998). Simulations show, for most parameter values, that the socially optimal cooperation radius (achieving the greatest mean fitness across the entire population) is two and that narrow in-group parochialism is prevalent regardless of frequency of interaction within a society.

We classify $n$-dimensional geometric graph manifolds with nonnegative scalar curvature, and first show that if $n>3$, the universal cover splits off a codimension 3 Euclidean factor. We then proceed with the classification of the 3-dimensional case by showing that such a manifold is either a lens space or a prism manifold with a very rigid metric. This allows us to also classify the moduli space of such metrics: it has infinitely many connected components for lens spaces, while it is connected for prism manifolds., 19 pages, 3 figures. Second version with an additional corollary and improved exposition. arXiv admin note: substantial text overlap with arXiv:1611.06572

Mixed networks of hydrogen bonds in a water–monoethanolamine (MEA) liquid system formed from solvents with a spatial network of hydrogen bonds are described topologically. This allows the comparison of networks of different systems and selection of the best one (particularly for cryobiological problems). The coordinates of atoms in the Н2О–MEA system are obtained via molecular dynamics (MD). The mixed network is described by means of graph theory and Delaunay simplices at 300 K throughout the range of concentration of monoethanolamine in water, based on MD results. Earlier works and published data on structure and interaction in the system are used to explain the observations. The amine group of a MEA molecule plays a key role in the formation of the MEA⋅H2O stable complex in the mixed network of H-bonds of the system in the entire concentration range. The graph theory results are compared to ones obtained with Delaunay simplices. The results are compared to similar studies of the mixed network of a H2O–EG system.

We propose a novel phase based analysis with the purpose of quantifying the periodic bursts of activity observed in various neuronal systems. The way bursts are intiated and propagate in a spatial network is still insufficiently characterized. In particular, we investigate here how these spatiotemporal dynamics depend on the mean connection length. We use a simplified description of a neuron’s state as a time varying phase between firings. This leads to a definition of network bursts, that does not depend on the practitioner’s individual judgment as the usage of subjective thresholds and time scales. This allows both an easy and objective characterization of the bursting dynamics, only depending on system’s proper scales. Our approach thus ensures more reliable and reproducible measurements. We here use it to describe the spatiotemporal processes in networks of intrinsically oscillating neurons. The analysis rigorously reveals the role of the mean connectivity length in spatially embedded networks in determining the existence of “leader” neurons during burst initiation, a feature incompletely understood observed in several neuronal cultures experiments. The precise definition of a burst with our method allowed us to rigorously characterize the initiation dynamics of bursts and show how it depends on the mean connectivity length. Although presented with simulations, the methodology can be applied to other forms of neuronal spatiotemporal data. As shown in a preliminary study with MEA recordings, it is not limited to in silico modeling.

Amyotrophic lateral sclerosis (ALS) is a neurological disease that starts at a focal point and gradually spreads to other parts of the nervous system. One of the main clinical symptoms of ALS is muscle weakness. To study spreading patterns of muscle weakness, we analyze spatiotemporal binary muscle strength data, which indicates whether observed muscle strengths are impaired or healthy. We propose a hidden Markov model-based approach that assumes the observed disease status depends on two latent disease states. The model enables us to estimate the incidence rate of ALS disease and the probability of disease state transition. Specifically, the latter is modeled by a logistic autoregression in that the spatial network of susceptible muscles follows a Markov process. The proposed model is flexible to allow both historical muscle conditions and their spatial relationships to be included in the analysis. To estimate the model parameters, we provide an iterative algorithm to maximize sparse-penalized likelihood with bias correction, and use the Viterbi algorithm to label hidden disease states. We apply the proposed approach to analyze the ALS patients' data from EMPOWER Study.

Toxicity analysis is a major challenge in drug design and discovery. Recently significant progress has been made through machine learning due to its accuracy, efficiency, and lower cost. US Toxicology in the 21st Century (Tox21) screened a large library of compounds, including approximately 12 000 environmental chemicals and drugs, for different mechanisms responsible for eliciting toxic effects. The Tox21 Data Challenge offered a platform to evaluate different computational methods for toxicity predictions. Inspired by the success of multiscale weighted colored graph (MWCG) theory in protein—ligand binding affinity predictions, we consider MWCG theory for toxicity analysis. In the present work, we develop a geometric graph learning toxicity (GGL-Tox) model by integrating MWCG features and the gradient boosting decision tree (GBDT) algorithm. The benchmark tests of the Tox21 Data Challenge are employed to demonstrate the utility and usefulness of the proposed GGL-Tox model. An extensive comparison with other state-of-the-art models indicates that GGL-Tox is an accurate and efficient model for toxicity analysis and prediction.

Research on urban agglomerations from the perspective of network spatial structure is important to promote their sustainable development. Based on online and traditional data, this paper first improves three aspects of the traditional spatial gravity model—city quality, the gravitation coefficient, and city distance—considering urban center functional intensity and population mobility tendencies. The resulting improved directional gravity model is applied to analyze the structure of the city network for two urban agglomerations in China, the Beijing-Tianjin-Hebei urban agglomeration (BTHUA) and the Yangtze River Delta urban agglomeration (YRDUA). The results of the study are as follows: (1) the existing urban connections have obvious hierarchies and imbalances, with the YRDUA urban hierarchical connections being of larger scale. (2) Cities are closely connected, but city networks are unbalanced, though the YRDUA has more balanced urban development. (3) Each node city has a clear radiation range limit, and spatial distance remains an important constraint on urban connections. The backbone network of the BTHUA has a triangular shape and trends toward a “sparse north and dense south,” while the YRDUA is characterized by multiple axes and an overall distribution that trends toward a “dense north and sparse south.” (4) Cities with poor comprehensive strength are more likely to be captured, forming an attract and be attracted relationship. (5) The BTHUA and the YRDUA each form three communities.

Local assemblages are embedded in networks of communities connected by dispersal, and understanding the processes that mediate this local-regional interaction is central to understanding biodiversity patterns. In this network (i.e. metacommunity), the strength of dispersal relative to the intensity of environmental selection typically determines whether local communities are comprised of species well-adapted to the local environment (i.e. species sorting) or are dominated by regionally successful species that may not be locally adapted (i.e. mass effects), which by extension determines the capacity of the landscape to sustain diversity. Despite the fundamentally spatial nature of these dispersal-mediated processes, much of our theoretical understanding comes from spatially implicit systems, a special case of spatial structure in which patches are all connected to each other equally. In many real systems, both the connections among patches (i.e. network topology) and the distributions of environments across patches (i.e. spatial autocorrelation) are not arranged uniformly. Here, we use a metacommunity model to investigate how spatial heterogeneities may change the balance between species sorting versus mass effects and diversity outcomes. Our simulations show that, in general, the spatially implicit model generates an outlier in biodiversity patterns compared to other networks, and most likely amplifies mass effects relative to species sorting. Network topology has a strong effect on metacommunity outcome, with topologies of sparse connections and few loops promoting sorting of species into suitable patches. Spatial autocorrelation is another key factor; by interacting with spatial topology, intermediate-scale clusters of similar patches can emerge, leading to a reduction of regional competition, and hence maintenance of gamma diversity. These results provide a better understanding of the role that complex spatial landscape structure plays in metacommunity processes, a necessary step to understanding how metacommunity processes relate to biodiversity conservation.

At the global level, international migration can be considered as a network of migration exchanges between different countries. Employing an exploratory network analysis of the international migration structure, the present paper examines the structural characteristics of this network and the status of the countries. The analysis is done using the socio-spatial approach. Results show that as the severity of network ties grow, the number of ties reduce significantly and ties are asymmetric. Most of the migrations in the international migration structure have also taken place outside the near and neighboring countries. The network analysis showed two migration patterns of "International Migratory Highways" and "Migratory Clusters". In the first migration pattern, migrations are largely asymmetric and towards the major centers of immigration, while in the second one, migrations are mostly symmetric and within specific geographical areas.

We present a framework for solving simultaneously the problems of facility location and path optimization in static and dynamic spatial networks. In the static setting, the objective is to determine facility locations and transportation paths from each node to the destination via the network of facilities such that the total cost of commodity transportation is minimized. This is an NP-hard problem. We propose a novel stage-wise viewpoint of the paths which is instrumental in designing the decision variable space in our framework. We use the maximum entropy principle to solve the resulting optimization problem. In the dynamic setting, nodes and destinations are dynamic. We design an appropriate control Lyapunov function to determine the time evolution of facilities and paths such that the transportation cost at each time instant is minimized. Our framework enables quantifying attributes of the facilities and transportation links in terms of the decision variables. Consequently, it becomes possible to incorporate application specific constraints on individual facilities, links, and network topology. We demonstrate the efficacy of our proposed framework through extensive simulations.

Geometric graph model is suggested for the dynamical Casimir effect. The wave equation is considered at the graph edges and the Kirchhoff condition at the internal vertex. It is assumed that the edge lengths depend on time. Photon generation is considered in the framework of the Dodonov–Klimov model.

Transport network planning in Egypt suffers from insufficient planning that should be done prior to execution. This research presses on the fact that personal experience and cognition alone cannot be the main factors of design that it should go hand in hand with scientific measurable analysis and evidence. Hence, it focuses on having a deeper understanding of the influence of spatial network configuration on urban activity and centrality. It proposes that Space Syntax, as a syntactic model, has potential to be utilized in optimizing transportation networks, based on Space Syntax ability to model and predict streets with most urban activity and areas that act as central gathering points, and therefore, giving a scientific basis to evident decisions to choose optimum routes and stations for transit networks. The study hypothesizes that adding Space Syntax spatial configuration analysis as a layer to the whole process can give a better understanding of the network. This research applies Space Syntax configurational analysis with the aim to present an evidence approach to optimize its transportation network. The proposed approach is applied on Mansoura City, an intermediate city in Dakahlia governorate in Egypt. The methodology includes field observations using gate counting technique to identify movement flows in different parts of the city, running a segment map analysis of the city’s street network and validating the results of the analysis through comparing computed values with observations. Results identify streets with major urban movement which represent potential transit routes and areas that are considered urban centers which represent potential transit stations. These results verify the important role of accessibility analysis in transportation planning, and therefore presents an applicable approach to identify optimum transit routes and stations that have higher potential to act as active movement corridors at a city scale.

The naïve algorithm for generating nearest-neighbour models determines the distance between every pair of nodes, resulting in quadratic running time. Such time complexity is common among spatial problems and impedes the generation of larger spatial models. In this article, an improved algorithm for the Mocnik model, an example of nearest-neighbour models, is introduced. Instead of solving k nearest-neighbour problems for each node (k dynamic in the sense that it varies among the nodes), the improved algorithm presented exploits the notion of locality through introducing a corresponding spatial index, resulting in a linear average-case time complexity. This makes possible to generate very large prototypical spatial networks, which can serve as testbeds to evaluate and improve spatial algorithms, in particular, with respect to the optimization of algorithms towards big geospatial data.

In this paper, we introduce a dynamic spatial interaction econometric model. There are n forward-looking agents of whom each has a parametric linear-quadratic payoff, and they interact with their neighbors through a spatial network. Considering a Markov perfect equilibrium (MPE), we derive a unique Nash equilibrium equation and construct a new spatial dynamic panel data (SDPD) model. For estimation, we suggest mainly the quasi-maximum likelihood (QML) method. Asymptotic properties of the QML estimator are investigated. In a Monte Carlo study, we estimate the model’s parameters and compare the results with those from traditional SDPD models. The model is applied to an empirical study on counties’ public safety spending in North Carolina.

Ultra-dense network (UDN) is a promising solution to meet the huge data requirements of future 5G wireless communication systems. With many irregularly deployed small cell base stations (SBSs), it is very difficult to accurately measure network energy efficiency (EE) in UDN. Considering the necessity of saving energy in modern-day networks, in this paper, I present the EE evaluation of UDN based on the random spatial network model. In this considered system, the SBSs and the macro cell users (MUEs) are modeled as a homogeneous Poisson point process (PPP). Unlike the existing literature, I derive the simple closed-form expressions for the successful transmission probabilities of MUEs and small cells by Laplace transformation. Then, based on the obtained successful transmission probabilities, I derive the closed form expression for EE of the small cells in both uplink and downlink under some practical constraints. Further, to obtain the optimal SBS density in UDN, I propose a joint uplink and downlink power allocation (JUDPA) algorithm. The JUDPA algorithm obtains the maximum EE in small cells by iteratively optimizing the uplink and downlink powers. Our theoretical analysis and simulated results demonstrate the accuracy of the proposed model with better power allocation and less complexity than conventional solutions.

We present a novel approach for traffic forecasting in urban traffic scenarios using a combination of spectral graph analysis and deep learning. We predict both the low-level information (future trajectories) as well as the high-level information (road-agent behavior) from the extracted trajectory of each road-agent. Our formulation represents the proximity between the road agents using a weighted dynamic geometric graph (DGG). We use a two-stream graph-LSTM network to perform traffic forecasting using these weighted DGGs. The first stream predicts the spatial coordinates of road-agents, while the second stream predicts whether a road-agent is going to exhibit overspeeding, underspeeding, or neutral behavior by modeling spatial interactions between road-agents. Additionally, we propose a new regularization algorithm based on spectral clustering to reduce the error margin in long-term prediction (3-5 seconds) and improve the accuracy of the predicted trajectories. Moreover, we prove a theoretical upper bound on the regularized prediction error. We evaluate our approach on the Argoverse, Lyft, Apolloscape, and NGSIM datasets and highlight the benefits over prior trajectory prediction methods. In practice, our approach reduces the average prediction error by approximately 75% over prior algorithms and achieves a weighted average accuracy of 91.2% for behavior prediction. Additionally, our spectral regularization improves long-term prediction by up to 70%., Accepted to RAL/IROS 2020 as a dual journal and conference submission

Industrial Internet of Things (IIoT) requires reliable, low-latency, and secure wireless links to support rate/delay/security-intensive applications. In this letter, we model the IIoT network as a geometric graph with a virtual coordinate system (VCS). One major problem with VCS is that it is sensitive to the placement of reference nodes. This letter first proposes a general formulation for selecting a specific set of reference nodes that minimizes the network error. Then, we derive the upper bound for the optimization problem and present a novel iterative method that selects additional reference nodes based on the network inference. Simulation results compare the proposed method with the random selection of reference nodes and show that the proposed method performs better regarding packet delivery rate, network connectivity, and total energy consumption.

We study boundary conditions for the diffusion operator defined on a star-shaped geometric graph consisting of three edges with a common vertex. We show that if the edge lengths are pairwise distinct, then there do not exist degenerate boundary conditions for the diffusion operator. If the edge lengths coincide and the potentials are symmetric, then the characteristic determinant of a boundary value problem for the diffusion operator cannot be a constant other than zero, and the set of boundary value problems for which the characteristic determinant is identically zero is infinite (a continuum). We show that, for the diffusion operator on the star-shaped graph, the set of boundary value problems whose spectrum fills the entire plane consists of eighteen classes, each of which contains eight to nine arbitrary constants. Recall that for the diffusion operator defined on an interval this set consists of two problems.

Promoted by both the “going out” policy and the “One Belt and One Road” (OBOR) Initiative, China's outward foreign direct investment (OFDI) has grown rapidly in the past two decades. A spatial network has gradually formed that facilitates global production, sales, and innovation. This paper studies the spatial correlation of China's OFDI network along the OBOR and its determinants. The block model analysis suggests that China's OFDI spatial network comprises four gradient sections. In addition, the analyses of quadratic assignment procedure and exponential random graph models demonstrate a tendency of agglomeration of China's OFDI, which may hinder the further development of its spatial correlation networks. Finally, we present some policy suggestions stemming from the study in the hope of helping both the government and firms to optimize their OFDI spatial layout strategy along the OBOR.

Recent geometric deep learning works define convolution operations in local regions and have enjoyed remarkable success on non-Euclidean data, including graph and point clouds. However, the high-level geometric correlations between the input and its neighboring coordinates or features are not fully exploited, resulting in suboptimal segmentation performance. In this article, we propose a novel graph convolution architecture, which we term as Taylor Gaussian mixture model (GMM) network (TGNet), to efficiently learn expressive and compositional local geometric features from point clouds. The TGNet is composed of basic geometric units, TGConv, that conduct local convolution on irregular point sets and are parametrized by a family of filters. Specifically, these filters are defined as the products of the local point features and the neighboring geometric features extracted from local coordinates. These geometric features are expressed by Gaussian weighted Taylor kernels. Then, a parametric pooling layer aggregates TGConv features to generate new feature vectors for each point. TGNet employs TGConv on multiscale neighborhoods to extract coarse-to-fine semantic deep features while improving its scale invariance. Additionally, a conditional random field (CRF) is adopted within the output layer to further improve the segmentation results. Using three point cloud data sets, qualitative and quantitative experimental results demonstrate that the proposed method achieves 62.2% average accuracy on ScanNet, 57.8% and 68.17% mean intersection over union (mIoU) on Stanford Large-Scale 3D Indoor Spaces (S3DIS) and Paris-Lille-3D data sets, respectively.

The complete twisted graph of order n, denoted by $$T_n$$ , is a complete simple topological graph with vertices $$u_1, u_2, \ldots , u_n$$ such that two edges $$u_iu_j$$ and $$u_{i'}u_{j'}$$ cross if and only if $$ i

In various wireless networking settings, node locations determine a network’s topology, allowing the network to be modelled by a geometric graph drawn in the plane. Without any additional information, local geometric routing algorithms can guarantee delivery to the target node only in restricted classes of geometric graphs, such as triangulations. In order to guarantee delivery on more general classes of geometric graphs (e.g., convex subdivisions or planar subdivisions), previous local geometric routing algorithms required [Formula: see text] state bits to be stored and passed with the message. We present the first local geometric routing algorithm using only one state bit to guarantee delivery on convex subdivisions and, when the algorithm has knowledge of the incoming port (the preceding node on the route), the first stateless local geometric routing algorithm that guarantees delivery on edge-augmented monotone subdivisions (including all convex subdivisions). We also show that [Formula: see text] state bits are necessary in planar subdivisions in which faces may have three or more reflex vertices.

A comprehensive understanding of the relationship between public transportation supply and demand is crucial for the construction and sustainable development of urban transportation. Due to the spatial and networked nature of public transportation, revealing the spatial configuration and structural disparities between public transportation supply and demand networks (TSN and TDN) can provide significant insights into complex urban systems. In this study, we explored the spatial configuration and structural disparities between TSN and TDN in the complex urban environment of Beijing. By constructing subdistrict-scale TSN and TDN using urban public transportation operation data and mobile phone data, we analyzed the spatial characteristics and structural disparities of these networks from various dimensions, including global indicators, three centralities, and community structure, and measured the current public transportation supply and demand matching pattern in Beijing. Our findings revealed strong structural and geographic heterogeneities of TSN and TDN, with significant traffic supply–demand mismatch being observed in urban areas within the Sixth Ring Road. Moreover, based on the percentage results of supply–demand matching patterns, we identified that the current public transportation supply–demand balance in Beijing is approximately 64%, with around 18% of both excess and shortage of traffic supply. These results provide valuable insights into the structure and functioning of public transportation supply–demand networks for policymakers and urban planners; these can be used to facilitate the development of a sustainable urban transportation system.

To understand and model public health emergencies, epidemiologists need data that describes how humans are moving and interacting across physical space. Such data has traditionally been difficult for researchers to obtain with the temporal resolution and geographic breadth that is needed to study, for example, a global pandemic. This paper describes Colocation Maps, which are spatial network datasets that have been developed within Facebook’s Data For Good program. These Maps estimate how often people from different regions are colocated: in particular, for a pair of geographic regions x and y, these Maps estimate the probability that a randomly chosen person from x and a randomly chosen person from y are simultaneously located in the same place during a randomly chosen minute in a given week. These datasets are well suited to parametrize metapopulation models of disease spread or to measure temporal changes in interactions between people from different regions; indeed, they have already been used for both of these purposes during the COVID-19 pandemic. In this paper, we show how Colocation Maps differ from existing data sources, describe how the datasets are built, provide examples of their use in compartmental modeling, and summarize ideas for further development of these and related datasets. We also conduct the first large-scale analysis of human colocation patterns across the world. Among the findings of this study, we observe that a pair of regions can exhibit high colocation despite few people moving between them. We also find that although few pairs of people are colocated for many days over the course of a week, these pairs can contribute significant fractions of the total colocation time within a region or between pairs of regions.

The most important model of a random graph where nodes are connected at random was proposed by Erdos and Renyi [242] and constitutes an archetype—or at least a benchmark—for constructing more complex random graphs. It is then natural to ask if we can extend this model to the case where nodes are located in space. In this chapter, we will discuss some of the possible extensions that were proposed in the literature. In particular, we will discuss the Waxman graph which was proposed as a model for intra-domain Internet network. Another important model is the Watts–Strogatz graph [7] which interpolates between a lattice and the Erdos–Renyi random graph and is able to produce graphs with simultaneously a large clustering coefficient and a small diameter (varying as \(\log N\)). In this model, there is an underlying lattice and it can thus be considered as a spatial network. We will discuss some of the properties of this network and end this chapter with a presentation of navigability problems and the demonstration of Kleinberg’s result [243].

BackgroundDescribing and understanding the process of diffusion can allow local managers better plan emergence scenarios. Thus, the main aim of this study was to describe and unveil the spatiotemporal patterns of diffusion of the COVID-19 in Brazil from February 2020 until April 2021.MethodsThis is a retrospective purely observational ecologic study including all notified cases and deaths. We used satellite-derived night light imagery and spatiotemporal Empirical Orthogonal Function analysis to quantify the spatial network structure of lighted development and the spatiotemporal transmission of the pathogen through the network.ResultsThe more populous state capitals within the largest network components presented higher frequency of deaths and earlier onset compared to the increasing numbers of smaller, less populous municipalities trending toward lower frequency of deaths and later onset. By week 48 2020, the full network was almost completely affected. Cases and deaths showed a distinct second wave of wider geographic expansion beginning in early November 2020.ConclusionsThe spatiotemporal diffusion in Brazil was characterized by an intertwined process of overseas relocation, hierarchical network transmission and contagious effects. A rapid response as the immediate control of all ports, airports and borders combined with mandatory quarantine are critical to retard disease diffusion.

The spatial directionality of Millennials’ migration has been underexplored. This study utilizes local spatial network autocorrelation to identify migration clusters of Millennials in a metropolitan area. The result found that Millennials migrate within an urban core and move to newer districts in surrounding areas. We found spatially distinct migration clusters by age group, possibly reflecting different motives through life stages. The analysis demonstrated that this method is effective for detecting migration clusters and for comparing subsets.

Micro-anatomical reentry has been identified as a potential driver of atrial fibrillation (AF). In this paper, we introduce a novel computational method which aims to identify which atrial regions are most susceptible to micro-reentry. The approach, which considers the structural basis for micro-reentry only, is based on the premise that the accumulation of electrically insulating interstitial fibrosis can be modelled by simulating percolation-like phenomena on spatial networks. Our results suggest that at high coupling, where micro-reentry is rare, the micro-reentrant substrate is highly clustered in areas where the atrial walls are thin and have convex wall morphology. However, as transverse connections between fibres are removed, mimicking the accumulation of interstitial fibrosis, the substrate becomes less spatially clustered, and the bias to forming in thin, convex regions of the atria is reduced. Comparing our algorithm on image-based models with and without atrial fibre structure, we find that strong longitudinal fibre coupling can suppress the micro-reentrant substrate, whereas regions with disordered fibre orientations have an enhanced risk of micro-reentry. We suggest that with further development, these methods may have future potential for patient-specific risk stratification, taking a longitudinal view of the development of the micro-reentrant substrate.Author summaryAtrial fibrillation (AF) is the most common abnormal heart rhythm, yet, despite extensive research, treatment success rates remain poor. In part, this is because there is an incomplete understanding of the mechanistic origin of AF. In this paper, we investigate one proposed mechanism of AF, the formation of “micro-reentrant circuits”, which can be thought of as a “short circuit”, forming when electrically insulating fibrosis (structural repair tissue) infiltrates the space between heart muscle cells. Previously, such circuits have been found in experimental hearts, but identifying these circuits clinically is difficult. Here, we aim to take a small step towards developing computational methods for identifying where in the atria these circuits are most likely to form, drawing on techniques from network science. Our approach indicates that a number of factors are key to determining where circuits form, most notably the thickness of the heart muscle, and the alignment of muscle fibres.

Este documento expresa como la representación escrita en forma analítica de un teorema del conjunto de los números reales, acompañada de un gráfico geométrico, confirma la veracidad y validez de la demostración además de mostrarla de una manera visual.

Multisource aggregation (MSA) is an important function in the remote sensing data processing. In this letter, we propose and study a novel MSA search and scheduling problem to improve the performance of remote sensing data cluster. Given a static spatial network, a set of query points $Q$ , and a set of data locations $O$ (candidates for cluster centers), the MSA function retrieves the data location with the minimum aggregation distance (the sum of the distances to all query points). We believe that such function plays an important role in remote sensing data cluster and classification. The MSA problem faces two challenges: 1) how to prune the search space effectively and retrieve the results of MSA in real time and 2) how to schedule multiple query sources during search processing. To overcome these challenges, we make the following contributions. First, upper and lower bounds on aggregation distance are defined to prune the search space effectively. Second, each query source is given a priority label, and a best-first scheduling strategy is developed to further enhance the query performance. Finally, we conduct extensive experiments on real and synthetic data sets to verify the high performance of the developed algorithms.

Colocation mining is useful for understanding the interactions or dependencies that occur among geographic phenomena. Most colocation mining methods are based on planar space. However, in urban spaces, many human-related activities are constrained by a road network. Planar colocation mining methods are not suitable for studying the concerning geographic phenomena in an urban space. In this paper, we propose a visualization method to discover colocation patterns constrained by a road network. The method consists of two major components: network kernel density estimation and network colocation rule map construction. In the colocation rule map construction component, spatial interactions among spatial network geographic phenomena are modeled based on the idea of color mixing. We use simulated datasets with different spatial patterns, different sample sizes, and different maximum distances between road network events to test our method. The results show that our method is effective for mining colocation patterns in different situations. We also change the resolution of the network colocation rule maps, and the results show that the resolution has little influence on the results. In the case study, we apply our method to explore the spatial association between crimes and city facilities in the Loop and the Near North Side districts of Chicago.

In recent years, correlation filtering and deep learning have achieved good performance in object tracking. Correlation filtering is an efficient and real-time method because its formula provides a fast solution in the Fourier domain, but it does not benefit from end-to-end training. Although deep learning is an effective method for learning object representations, training deep networks online with one or a few examples is challenging. To address these problems, we propose a deep ensemble object tracking algorithm that fuses temporal and spatial information to improve algorithm precision and robustness. The framework of our algorithm includes four aspects: feature extraction, a baseline network, a branch network and adaptive ensemble learning. Feature extraction extracts the general object representation. The baseline network integrates feature extraction and a correlation filtering algorithm into a convolutional neural network for end-to-end training. The branch network is composed of a temporal network and a spatial network. The temporal and spatial networks capture the object temporal and spatial information and further refine the object position. Our algorithm only needs an initial frame to train all networks. Adaptive ensemble learning compensates for the object information deficiency and improves tracking accuracy. Many experiments on tracking benchmark datasets demonstrate that our algorithm performs favourably compared with state-of-the-art tracking algorithms.