Spatial Network Research Articles

Clear cell renal cell carcinoma (ccRCC) is the most common histological subtype of renal cancer and remains a clinical challenge due to its frequent resistance to therapy and poor prognosis in advanced stages. Apoptosis, a fundamental tumor-suppressive mechanism, exhibits paradoxical roles in cancer, wherein apoptotic tumor cells can also contribute to immunosuppression and tumor progression. However, the spatial dynamics, transcriptional heterogeneity, and prognostic relevance of apoptosis-related gene programs in ccRCC remain poorly defined. We performed an integrative analysis combining single-cell RNA sequencing (scRNA-seq), spatial transcriptomics, and summary-based Mendelian randomization (SMR) to dissect apoptosis-related malignant cell states in ccRCC. Cancer cells were stratified based on apoptosis gene signatures and CASP9 expression. Cell-cell communication was assessed using CellChat and spatial interaction networks were constructed using RCTD and mistyR. SMR was employed to link genetically regulated CASP9 expression with renal cancer risk. A CASP9-associated prognostic model was developed using LASSO Cox regression and DeepSurv on TCGA and E-MTAB-1980 cohorts. We identified transcriptionally and spatially distinct apoptosis-high and apoptosis-low malignant cell subpopulations. Apoptosis-high tumor cells, characterized by elevated CASP9 expression, preferentially localized near macrophage-enriched stromal regions and exhibited stronger spatial clustering. Ligand-receptor modeling revealed directional signaling via the SPP1-CD44 axis between CASP9-high cancer cells and macrophages. SMR analysis provided genetic evidence supporting CASP9 as a causal gene for renal cancer. CASP9-high cells demonstrated distinct developmental trajectories and formed multicellular spatial modules with macrophages and cycling cells. A five-gene apoptosis-related signature derived from CASP9-stratified tumor cells robustly predicted patient survival across both training and validation cohorts. Low-risk patients exhibited enriched immune infiltration, increased immune checkpoint expression, and enhanced immune pathway activity. Our study reveals that apoptosis, particularly CASP9-driven programs, defines a spatially organized, immunosuppressive malignant cell state in ccRCC. CASP9 acts as both a genetic driver and spatial regulator of tumor-macrophage interactions, contributing to disease progression. The CASP9-associated risk model demonstrates strong prognostic utility and highlights apoptosis as a promising therapeutic axis in ccRCC.

In the big data era, spatial network data has become increasingly important and popular in many real-world objects, ranging from microscale (e.g., molecule structures), to middle-scale (e.g., biological neural networks), to macro-scale (e.g., mobility networks). Spatial networks consists of nodes and edges that are embedded in a geometric space. Although, it is critical to model and understand the generative process of spatial networks, this task remains largely under-explored due to the significant difficulty in automatically modeling and distinguishing the dependency and relevance among various spatial and network semantic factors. In addition, containing both spatial and network information makes the modeling of spatial networks bear large time and memory cost, especially for large graphs. To address the aforementioned challenges, we first propose a novel objective for joint spatial-network disentangled representation learning from the perspective of information bottleneck as well as a novel progressive optimization algorithm to optimize the intractable objective. Based on this, a spatial-network variational autoencoder (SND-VAE) is proposed to discover the independent and dependent latent factors of spatial and networks. To reduce the timec complexity, an efficient version SND-VAE-light is proposed, which is based on a novel efficient spatial-network message passing neural network (ES-MPNN). Qualitative and quantitative experiments on both synthetic and real-world datasets with various scales of graph size demonstrate the superiority of the proposed model over the state-of-the-arts by up to 66.9% for graph generation and 37.3% for interpretability. In addition, the ES-MPNN is also proved to reduced the time complexity of the encoder in the generative model from cubic to linear growth.

This paper investigates novel topological structures on graphs through the lens of $j$-neighbourhoods, specifically out, in, intersection, and union-based neighbourhoods. We develop a systematic framework for constructing subbases and topologies on directed graphs using these neighbourhoods and analyze their topological properties. Our work provides a rigorous comparative study of neighbourhood types, their interrelations, and their role in generating induced topologies. In addition, we explore potential applications in digital topology, spatial networks, and data structure. The theoretical results are supported by aircraft paths on an airline as an illustrative example and comparison tables that highlight structural differences and practical implications.

The real estate market requires effective and precise house price prediction, as conventional models often face difficulties in generalization, computational efficiency, and interpretability. The research problem is addressed by introducing the House Price Evaluation Model (HPEM), which utilizes a hybrid deep learning network for analyzing multi-source geographic data. The network integrates the attention mechanism with spatial feature extraction, and a bat optimization algorithm is used to improve explainability and accuracy. The gathered properties are processed using normalized techniques to convert unstructured data into structured data, which directly improves the overall prediction accuracy. The bat-optimized attention mechanism with spatial networks dynamically arranges high-impact features to effectively address unstable feature importances, computation inefficiency, and poor generalization issues. In addition, the echolocation-inspired approach explores optimal solutions by balancing exploration and exploitation, thereby minimizing the deviation between the outputs and reducing training time by 30% compared to existing methods. The efficiency of the system is then evaluated using the Housing Price Dataset information, where HPEM achieves 98.5% feature stability, 1.2 hours of human-in-loop updates, and a 4.2% mean absolute error (MAE) under distribution shifts. The effective exploration of dynamic features through bat optimization integration yields 15% closer convergences, enhancing regulatory compliance and accuracy. Therefore, the developed model is effectively utilized in real estate valuation schemes.

Understanding community disaster resilience is critical to mitigating the disproportionate impacts of climate change and natural disasters on socially vulnerable populations. However, despite extensive discussion on disaster resilience, a systematic analysis of the extent of social inequity across climate scenarios, geographic locations, spatial scales, and sociodemographic groups remains underexplored. Our study introduces a human-centric framework to investigate social inequities in community disaster resilience related to human well-being. We combined flood hazard maps under both historical and future SSP scenarios with a compound multilayer urban spatial network model consisting of roads, communities, and essential services to evaluate the residents' service resilience during flood events. Then, we utilized the Gini coefficient and Lorenz curve to quantify the degree of inequities in resilience among different sub-populations. With Central Chongqing as a case study, our analysis reveals a significant increase in both the number of affected communities and their vulnerability under future climate conditions. We further observed a striking spatial polarization in community resilience due to the islanding effect, whereby communities are increasingly divided into those with severely limited service availability and those with sufficient resources. In addition, we found that the extent of social inequity in resilience is highly spatial and scale-specific, with moderate levels of inequity at the city level, but the degree of inequity varies greatly across sociodemographic groups at a localized level. This widening socio-spatial differentiation may trigger widespread dissatisfaction in disadvantaged communities, hindering the collective disaster response actions and engagements to enhance community resilience. Our research highlights the importance of embedding future climate variabilities, human well-being, and social equity in inclusive disaster response policies, processes, and practices.

Joint prediction and understanding of multimodal traffic flow with a bidirectional temporal dynamic spatial hypergraph neural network model

Spatial Transformer Correlation Network for natural image classification

Delay-feedback reservoirs are a subset of reservoir computers characterized by a hardware-efficient architecture that trades spatial complexity for temporal processing. It employs a single non-linear node, a delay line, and a time-multiplexed input signal to generate a network of "virtual nodes," effectively emulating a larger spatial neural network. One of the most powerful aspects of delay-feedback reservoirs is their versatility. Our previous work found that the non-linear node performs two mathematical functions, a non-linear transform and integration. The non-linear transform can be represented by any number of non-linear functions, making it difficult to optimize a delay-feedback reservoir to solve a specific computational task. This work explores different non-linear functions in order to determine their effect on the dynamics of the reservoir, in order to provide insight into this optimization problem. Five different non-linear functions are compared in terms of performance, metrics, and utilization: Mackey-Glass, sine squared, double sinusoids, Tan, and Tanh. Our results find that the Mackey-Glass non-linear function shows limited system dynamics, performing well on non-linear tasks but performing poorly on memory intensive tasks. We then demonstrate the distinct system dynamics within the other four non-linear functions. We found that sine squared shows limited overall performance, double sinusoid performs well in non-linear tasks, Tan resembles an odd valued exponent Mackey-Glass reservoir but with greater parameter sensitivity, and tanh offers balanced performance across both task types. We find that modifying the system dynamics of a reservoir is an important step toward optimizing a delay-feedback reservoir for specific computational tasks.

A dual spatial temporal neural network for bottleneck prediction in manufacturing systems

ISFE-Net: An important spatial feature extraction network for UAV-Based hyperspectral water quality monitoring in rivers

Decoding muscle activity via CNN-LSTM from 3D spatiotemporal EEG.

Coronary artery disease poses a significant global health challenge, often necessitating percutaneous coronary intervention (PCI) with stent implantation. Assessing stent apposition is crucial for preventing and identifying PCI complications leading to in-stent restenosis. Here we propose a novel three-dimensional (3D) distancecolor-coded assessment (DccA) for PCI stent apposition via deep-learning-based 3D multi-object segmentation in intravascular optical coherence tomography (IV-OCT). Our proposed 3D DccA accurately segments 3D vessel lumens and stents in IV-OCT images, using a hybrid-dimensional spatial matching network and dual-layer training with style transfer. It quantifies and maps stent-lumen distances into a 3D color space, achieving a 3D visual assessment of PCI stent apposition. Achieving over 95% segmentation precision for both stent struts and the lumen and having 3D color visualization, our proposed 3D DccA improves the clinical evaluation of PCI stent deployment and facilitates personalized treatment planning.

TEANet: Automated tooth extraction and arrangement with tooth-level graph spatial transformation network.

Localized seeding for triggering the global social contagion in higher-order spatial networks

As tourism increasingly drives the revitalization of traditional villages, rural spaces are undergoing a transformation from functional living areas to spaces for cultural display and leisure. This shift has amplified the spatial usage discrepancies between multiple stakeholders, such as tourists and villagers, highlighting conflicts in spatial resource allocation and behavior path organization. Using Wulin Village, a typical example of a Minnan overseas Chinese village, as a case study, this paper introduces social network analysis to construct a “spatial–behavioral” dual network model. The model integrates both architectural and public spaces, alongside behavior path data from villagers and tourists, to analyze the spatial structure at three scales: village-level network completeness, district-level structural balance, and point-level node vulnerability. The study integrates two dimensions—architectural space and public space—along with behavioral path data from both villagers and tourists. It reveals the characteristics of spatial structure under the intervention of multiple behavioral agents from three scales: village-level network completeness, district-level structural balance, and point-level node vulnerability. The core research focus of the spatial network includes the network structure of architectural and public spaces, while the behavioral network concerns the activity paths and behavior patterns of tourists and villagers. The study finds that, at the village scale, Wulin Village’s spatial network demonstrates good connectivity and structural integrity, but the behavior paths of both tourists and villagers are highly concentrated in core areas, leading to underutilization of peripheral spaces. This creates an asymmetry characterized by “structural integrity—concentrated behavioral usage.” At the district scale, the spatial node distribution appears balanced, but tourist behavior paths are concentrated around cultural nodes, such as the ancestral hall, visitor center, and theater, while other areas remain inactive. At the point scale, both tourist and villager activities are highly dependent on a few high-degree, high-cluster nodes, improving local efficiency but exacerbating systemic vulnerability. Comparison with domestic and international studies on cultural settlements shows that tourism often leads to over-concentration of spatial paths and node overload, revealing significant discrepancies between spatial integration and behavioral usage. In response, this study proposes multi-scale spatial optimization strategies: enhancing accessibility and path redundancy in non-core areas at the village scale; guiding behavior distribution towards multifunctional nodes at the district scale; and strengthening the capacity and resilience of core nodes at the point scale. The results not only extend the application of behavioral network methods in spatial structure research but also provide theoretical insights and practical strategies for spatial governance and cultural continuity in tourism-driven cultural villages.

The early postnatal period is crucial for brain development and understanding neurodevelopmental disorders. This study examines spatial brain network development in early infancy, a less-explored area. Using independent component analysis on longitudinal resting-state functional magnetic resonance imaging data from 74 neurotypical infants, we examined how the spatial organization of brain networks evolves from birth to 6 months. Our findings show significant age-related changes in spatial characteristics. Network-averaged spatial similarity, reflecting alignment between individual and group-level network maps, increased with age. Concurrently, network engagement range, representing voxel intensity fluctuation within networks, decreased, suggesting a consolidation process where voxel contributions became more uniform. Network strength, calculated as the average of all the significant voxel intensities in the network, indicating the degree of involvement in the specific functional network, increased across age in networks such as the frontal-medial prefrontal cortex and visual networks. We found that network size and network center of mass (illustrating spatial distribution alterations of brain networks) increased in the temporal network. These findings fill a gap in infant neuroimaging by spatially characterizing early functional network development. Quantifying changes in topology, size, and similarity offers a framework for understanding early brain maturation and identifying atypical trajectories.

How are systems supporting high-level cognition organized in the human brain? We hypothesize that cognitive processes involved in understanding people and places are implemented by distinct neural systems with parallel anatomical organization. We test this hypothesis using precision neuroimaging of individual human brains on diverse tasks involving perception and cognition in the domains of familiar people, places, and objects. We find that thinking about people and places elicits responses in distinct areas of high-level association cortex within the default mode network, spanning the frontal, parietal, and temporal lobes. Person- and place-preferring brain regions are systematically spatially adjacent across cortical zones. These areas have strongly domain-specific response profiles across visual, semantic, and episodic tasks and are specifically functionally connected to other parts of association cortex with like domain preference. Social and spatial networks remain anatomically separated at the apex of a unimodal-to-transmodal gradient across cortex and include regions with anatomical connections to the hippocampal formation. These results demonstrate the existence of parallel, domain-specific networks reaching the cortical apex.

Future pandemics could arise from several sources, notably, emerging infectious diseases (EID); and lab leaks from high containment biological laboratories (HCBL). Recent advances in infectious disease, information technology, and biotechnology provide building blocks to reduce pandemic risk if deployed intelligently. However, the global nature of infectious diseases, distribution of HCBLs, and increasing complexity of transmission dynamics due to travel networks make it difficult to determine how to best deploy mitigation efforts. Increasing understanding of the risk landscape posed by EID and HCBL lab leaks could improve risk reduction efforts. The presented paper develops a country-level spatial network susceptible-infected-removed model based on global travel network data and relative risk measures of potential origin sources, EID, and lab leaks from biological safety level 3+ and 4 labs, to explore expected infections over the first 30 days of a pandemic. Model outputs indicate that EID and lab leaks in India, the USA, and China are most impacted at day 30. For EID, expected infections shift from high EID origin potential countries at day 10 to the USA, India, and China, while for lab leaks, the USA and India start with high lab leak potential. With respect to model uncertainties and limitations, results indicate several large, wealthy countries are influential to pandemic risk from both EID and lab leaks, indicating high leverage points for mitigation efforts.

The rational utilization of cultivated land resources is central to ensuring both ecological and food security in the Yangtze River Economic Belt (YREB), holding strategic significance for regional sustainable development. Using panel data from 2010 to 2023 for 130 cities in the YREB, this study examines a spatial correlation network (SCN) for non-grain land use (NGLU) and its driving forces via a modified gravity model, social network analysis (SNA), and quadratic assignment procedure regression. The results show the following: (1) The risk of NGLU continues to increase, with the spatial pattern evolving from a “single-peak right deviation” pattern to a “multi-peak coexistence” pattern featuring three-level polarization and gradient transmission, primarily driven by economic potential disparities. (2) The SCN has increased in density, but its pathways are relatively singular. Node functions exhibit significant differentiation, with high-degree nodes forming “control poles”, high-intermediate nodes dominating cross-regional risk transmission, and low-proximity nodes experiencing “protective marginalization”. Node centrality distribution is highly connected with the regional development gradient. (3) The formation of the spatial network is jointly driven by multiple factors. Geographical proximity, economic potential differences, comparative benefit differences, non-agricultural employment differences, and factor mobility all positively contribute to the spillover effect. Conversely, implementing cultivated land protection policies and the regional imbalance in local industrial development path dependence significantly inhibit the non-grain trend. This study further reveals that a synergistic governance system characterized by “axial management, node classification, and edge support” should be recommended to prevent the gradient risk transmission induced by economic disparities, providing a scientific basis for achieving sustainable use of regional cultivated land resources and coordinated governance of food security.

Abstract. Tensor fields, as spatial derivatives of scalar or vector potentials, offer powerful insight into subsurface structures in geophysics. However, accurately interpolating these measurements–such as those from full-tensor potential field gradiometry–remains difficult, especially when data are sparse or irregularly sampled. We present a physics-informed spatial neural network that treats tensors according to their nature as derivatives of an underlying scalar field, enabling consistent, high-fidelity interpolation across the entire domain. By leveraging the differentiable nature of neural networks, our method not only honours the physical constraints inherent to potential fields but also reconstructs the scalar and vector fields that generate the observed tensors. We demonstrate the approach on synthetic gravity gradiometry data and real full-tensor magnetic data from Geyer, Germany. Results show significant improvements in interpolation accuracy, structural continuity, and uncertainty quantification compared to conventional methods.