Long-range Spatial Correlations Research Articles

Capturing and interpreting wildfire spread dynamics: attention-based spatiotemporal models using ConvLSTM networks

Predicting the trajectory of geographical events, such as wildfire spread, presents a formidable task due to the dynamic associations among influential biophysical factors. Geo-events like wildfires frequently display short and long-range spatial and temporal correlations. Short-range effects are the direct contact and near-contact spread of the fire front. Long-range effects are represented by processes such as spotting, where firebrands carried by the wind ignite fires distant from the flaming front, altering the shape and speed of an advancing fire front. This study addresses these modeling challenges by clearly defining and analyzing the scale-dependent spatiotemporal dynamics that influence wildfire spread, focusing on the interplay between biophysical factors and fire behavior. We propose two unique attention-based spatiotemporal models using Convolutional Long Short-Term Memory (ConvLSTM) networks. These models are designed to learn and capture a range of local to global and short and long-range spatiotemporal correlations. The proposed models were tested on two datasets: a high-resolution wildfire spread dataset produced with a semi-empirical percolation model and a satellite observed wildfire spread data in California 2012–2021. Results indicate that attention-based models accurately predict fire front movements that are consistent with known wildfire spread-biophysical dynamics. Our research suggests there is considerable potential for attention mechanisms to capture the spatiotemporal behavior of wildfire spread, with model transferability, that can guide rapid deployment of wildfire management operations. We also highlight directions for future studies that focus on how the self-attention mechanism could enhance model performance for a range of geospatial applications.

Continuum percolation of two-dimensional adaptive dynamics systems.

The percolation phase transition of a continuum adaptive neuron system with homeostasis is investigated. In order to maintain their average activity at a particular level, each neuron (represented by a disk) varies its connection radius until the sum of overlapping areas with neighboring neurons (representing the overall connection strength in the network) has reached a fixed target area for each neuron. Tuning the two key parameters in the model, i.e., the density defined as the number of neurons (disks) per unit area and the sum of the overlapping area of each disk with its adjacent disks, can drive the system into the critical percolating state. These two parameters are inversely proportional to each other at the critical state, and the critical filling factors are fixed about 0.7157, which is much less than the case of the continuum percolation with uniform disks. It is also confirmed that the critical exponents in this model are the same as the two-dimensional standard lattice percolation. Although the critical state is relatively more sensitive and exhibits long-range spatial correlation, local fluctuations do not propagate in a long-range manner through the system by the adaptive dynamics, which renders the system overall robust against perturbations.

Beehive scale-free emergent dynamics

It has been repeatedly reported that the collective dynamics of social insects exhibit universal emergent properties similar to other complex systems. In this note, we study a previously published data set in which the positions of thousands of honeybees in a hive are individually tracked over multiple days. The results show that the hive dynamics exhibit long-range spatial and temporal correlations in the occupancy density fluctuations, despite the characteristic short-range bees’ mutual interactions. The variations in the occupancy unveil a non-monotonic function between density and bees’ flow, reminiscent of the car traffic dynamic near a jamming transition at which the system performance is optimized to achieve the highest possible throughput. Overall, these results suggest that the beehive collective dynamics are self-adjusted towards a point near its optimal density.

STFEformer: Spatial–Temporal Fusion Embedding Transformer for Traffic Flow Prediction

In the realm of Intelligent Transportation Systems (ITSs), traffic flow prediction is crucial for multiple applications. The primary challenge in traffic flow prediction lies in the handling and modeling of the intricate spatial–temporal correlations inherent in transport data. In recent years, many studies have focused on developing various Spatial–Temporal Graph Neural Networks (STGNNs), and researchers have also begun to explore the application of transformers to capture spatial–temporal correlations in traffic data. However, GNN-based methods mainly focus on modeling spatial correlations statically, which significantly limits their capacity to discover dynamic and long-range spatial patterns. Transformer-based methods have not sufficiently extracted the comprehensive representation of traffic data features. To explore dynamic spatial dependencies and comprehensively characterize traffic data, the Spatial–Temporal Fusion Embedding Transformer (STFEformer) is proposed for traffic flow prediction. Specifically, we propose a fusion embedding layer to capture and fuse both native information and spatial–temporal features, aiming to achieve a comprehensive representation of traffic data characteristics. Then, we introduce a spatial self-attention module designed to enhance detection of dynamic and long-range spatial correlations by focusing on interactions between similar nodes. Extensive experiments conducted on three real-world datasets demonstrate that STFEformer significantly outperforms various baseline models, notably achieving up to a 5.6% reduction in Mean Absolute Error (MAE) on the PeMS08 dataset compared to the next-best model. Furthermore, the results of ablation experiments and visualizations are employed to clarify and highlight our model’s performance. STFEformer represents a meaningful advancement in traffic flow prediction, potentially influencing future research and applications in ITSs by providing a more robust framework for managing and analyzing traffic data.

GLIMS: Attention-guided lightweight multi-scale hybrid network for volumetric semantic segmentation

Convolutional Neural Networks (CNNs) have become widely adopted for medical image segmentation tasks, demonstrating promising performance. However, the inherent inductive biases in convolutional architectures limit their ability to model long-range dependencies and spatial correlations. While recent transformer-based architectures address these limitations by leveraging self-attention mechanisms to encode long-range dependencies and learn expressive representations, they often struggle to extract low-level features and are highly dependent on data availability. This motivated us for the development of GLIMS, a data-efficient attention-guided hybrid volumetric segmentation network. GLIMS utilizes Dilated Feature Aggregator Convolutional Blocks (DACB) to capture local–global feature correlations efficiently. Furthermore, the incorporated Swin Transformer-based bottleneck bridges the local and global features to improve the robustness of the model. Additionally, GLIMS employs an attention-guided segmentation approach through Channel and Spatial-Wise Attention Blocks (CSAB) to localize expressive features for fine-grained border segmentation. Quantitative and qualitative results on glioblastoma and multi-organ CT segmentation tasks demonstrate GLIMS’ effectiveness in terms of complexity and accuracy. GLIMS demonstrated outstanding performance on BraTS2021 and BTCV datasets, surpassing the performance of Swin UNETR. Notably, GLIMS achieved this high performance with a significantly reduced number of trainable parameters. Specifically, GLIMS has 47.16 M trainable parameters and 72.30G FLOPs, while Swin UNETR has 61.98 M trainable parameters and 394.84G FLOPs. The code is publicly available at https://github.com/yaziciz/GLIMS.

Stochastic thermodynamics of a probe in a fluctuating correlated field

We develop a framework for the stochastic thermodynamics of a probe coupled to a fluctuating medium with spatio-temporal correlations, described by a scalar field. For a Brownian particle dragged by a harmonic trap through a fluctuating Gaussian field, we show that near criticality (where the field displays long-range spatial correlations) the spatially-resolved average heat flux develops a dipolar structure, where heat is absorbed in front and dissipated behind the dragged particle. Moreover, a perturbative calculation reveals that the dissipated power displays three distinct dynamical regimes depending on the drag velocity.

LCDFormer: Long-term correlations dual-graph transformer for traffic forecasting

Traffic forecasting has always been a critical component of intelligent transportation systems. Due to the complexity of traffic prediction models, most research just only consider short-term historical data in the temporal dimension. However, learning temporal patterns necessitates the involvement of long-term historical data. Additionally, many models are limited in capturing spatial features by only considering short-distance spatial information connected to the target node. To solve these problems, we propose a dual-graph transformer, namely Long-term Correlations Dual-graph transFormer (LCDFormer), designed to capture long-term correlations and long-distance spatial correlations. It is entirely based on attention mechanisms, and as far as we know, there is limited research adopting this approach. Our work addresses this gap in the literature. In particular, we have devised a time aggregation method capable of consolidating long-term historical time series, concurrently addressing the impact of long-term temporal correlations while minimizing the influence of redundant data. Subsequently, we have introduced a novel spatio-temporal attention module that compresses spatial information to generate short-term input sequences while modeling dynamic long-range spatial correlations. We conducted extensive experiments with LCDFormer on five real-world traffic datasets. The results indicate that LCDFormer, considering long-term spatio-temporal correlations, is better able to learn the spatio-temporal patterns of traffic data. Compared to the current state-of-the-art baseline, our model has demonstrated outstanding predictive performance with a maximum improvement of 5.02% in mean absolute error, 4.33% in root mean square error and 7.32% in mean absolute percentage error. The source codes are available at: https://github.com/NanakiC/LCDFormer.

An Adaptive Region-Based Transformer for Nonrigid Medical Image Registration With a Self-Constructing Latent Graph.

Nonrigid registration of medical images is formulated usually as an optimization problem with the aim of seeking out the deformation field between a referential-moving image pair. During the past several years, advances have been achieved in the convolutional neural network (CNN)-based registration of images, whose performance was superior to most conventional methods. More lately, the long-range spatial correlations in images have been learned by incorporating an attention-based model into the transformer network. However, medical images often contain plural regions with structures that vary in size. The majority of the CNN-and transformer-based approaches adopt embedding of patches that are identical in size, disallowing representation of the inter-regional structural disparities within an image. Besides, it probably leads to the structural and semantical inconsistencies of objects as well. To address this issue, we put forward an innovative module called region-based structural relevance embedding (RSRE), which allows adaptive embedding of an image into unequally-sized structural regions based on the similarity of self-constructing latent graph instead of utilizing patches that are identical in size. Additionally, a transformer is integrated with the proposed module to serve as an adaptive region-based transformer (ART) for registering medical images nonrigidly. As demonstrated by the experimental outcomes, our ART is superior to the advanced nonrigid registration approaches in performance, whose Dice score is 0.734 on the LPBA40 dataset with 0.318% foldings for deformation field, and is 0.873 on the ADNI dataset with 0.331% foldings.

CSRL-Net: contextual self-rasterization learning network with joint weight loss for remote sensing image semantic segmentation

ABSTRACTSemantic segmentation plays a vital role in the intelligent comprehension of remote sensing images (RSIs). However, research on semantic segmentation of RSIs still faces the following challenges: 1) The complexity of ground object structures, including variations in scale and shading environments, poses difficulties for current methods in capturing global context. 2) In long-tail distributed remote sensing data, the scarcity of tail classes makes it difficult for their features to be effectively learned, as features of head classes often overshadow them. To address these issues, we propose a contextual self-rasterization learning network (CSRL-Net) for the semantic segmentation of RSIs. Our approach comprises the following two key components. Firstly, a grid context perception mechanism is developed to collaboratively establish context dependencies within and among multi-scale grids, capturing long-range spatial correlations. Secondly, a joint weight loss function is designed to convert the prior knowledge into weight factors. This loss function combines re-weighting and logit adjustment, giving more attention to tail classes and integrally balancing learning bias. To evaluate the effectiveness of our proposed method, we apply it to the Potsdam, Vaihingen, and GID datasets and compare its performance with current advanced models. Experimental results demonstrate that our method achieves excellent performance in terms of MIoU, mean F1 and OA, with improvements ranging from 0.364% to 1.764% compared to the 17 comparison models. Notably, the proposed joint weight loss significantly improves IoU and F1 for tail classes, resulting in increases of 2.909% (IoU) and 2.085% (F1) on the Vaihingen dataset and 4.697% (IoU) and 4.043% (F1) on the GID dataset.

Blue-Noise-Based Disordered Photonic Structures Show Isotropic and Ultrawide Band Gaps

Spatially disordered but uniformly distributed point patterns characterized by so-called blue-noise long-range spatial correlations are of great benefit in computer graphics, especially in spatial dithering thanks to the spatial isotropy. Herein, the potential photonic properties of blue-noise disordered, homogeneous point processes based on farthest-point optimization are numerically investigated for silicon photonics. The photonic properties of blue-noise two-dimensional patterns are studied as a function of the filling fraction and benchmarked with photonic crystals with a triangular lattice. Ultrawide and omnidirectional photonic band gaps spanning most of the visible spectrum are found with estimates of gap–midgap ratios of up to 55.4% for transverse magnetic polarization, 59.4% for transverse electric polarization, and 32.7% for complete band gaps. The waveguiding effect in azimuthal defect lines is also numerically evaluated. These results corroborate the idea that long-range correlated disordered structures are helpful for engineering novel devices with the additional degree of freedom of spatial isotropy, and capable of bandgap opening even without total suppression of infinite-wavelength density fluctuations.

Spatial biology of Ising-like synthetic genetic networks

BackgroundUnderstanding how spatial patterns of gene expression emerge from the interaction of individual gene networks is a fundamental challenge in biology. Developing a synthetic experimental system with a common theoretical framework that captures the emergence of short- and long-range spatial correlations (and anti-correlations) from interacting gene networks could serve to uncover generic scaling properties of these ubiquitous phenomena.ResultsHere, we combine synthetic biology, statistical mechanics models, and computational simulations to study the spatial behavior of synthetic gene networks (SGNs) in Escherichia coli quasi-2D colonies growing on hard agar surfaces. Guided by the combined mechanisms of the contact process lattice simulation and two-dimensional Ising model (CPIM), we describe the spatial behavior of bi-stable and chemically coupled SGNs that self-organize into patterns of long-range correlations with power-law scaling or short-range anti-correlations. These patterns, resembling ferromagnetic and anti-ferromagnetic configurations of the Ising model near critical points, maintain their scaling properties upon changes in growth rate and cell shape.ConclusionsOur findings shed light on the spatial biology of coupled and bistable gene networks in growing cell populations. This emergent spatial behavior could provide insights into the study and engineering of self-organizing gene patterns in eukaryotic tissues and bacterial consortia.

Robust intra-model teleconnection patterns for extreme heatwaves

Introduction: The goal of this study is to provide analysis of statistics and dynamics of extreme heatwaves over two areas of Europe, France and Scandinavia, while comparing and contrasting the representation in climate models and reanalysis.Methods: The 1000 year long datasets are generated using respectively two climate models of different complexity. The composite maps of the heatwaves found in these datasets are compared to the ones observed in reanalysis by estimating significance of such patterns. We also employ time series analysis, in particular compare return time plots and use Gaussian stochastic processes to model the temporal correlations for rare events.Results: Our investigation reveals that recurrent wavenumber three teleconnection patterns distinctly underpin heatwaves in France and Scandinavia. These patterns manifest in both surface temperature and mid-tropospheric geopotential height. For heatwaves of return times of 4 years such patterns are robustly represented across diverse models of complexity and reanalysis data. For longer return times, reanalysis records are too short to give statistically significant results, while models confirm the relevance of these large scale patterns for the most extreme heatwaves. Moreover, A time series analysis shows that heatwave indices defined at synoptic scale are fairly well described by Gaussian stochastic processes, and that these Gaussian processes reproduce well return time plots even for very rare events.Discussion: These results suggest that extreme heatwaves over different areas of Europe show recurrent typical behaviours in terms of long-range spatial correlations and subseasonal-scale temporal correlations. These properties are consistently represented among models of different complexity and observations, thus suggesting their relevance for a better understanding of the drivers and causes of the occurrence of extreme midlatitude heatwaves and their predictability.

Breaking Rayleigh's Law with Spatially Correlated Disorder to Control Phonon Transport.

Controlling thermal transport in insulators and semiconductors is crucial for many technological fields such as thermoelectrics and thermal insulation, for which a low thermal conductivity (κ) is desirable. A major obstacle for realizing low κ materials is Rayleigh's law, which implies that acoustic phonons, which carry most of the heat, are insensitive to scattering by point defects at low energy. We demonstrate, with large scale simulations on tens of millions of atoms, that isotropic long-range spatial correlations in the defect distribution can dramatically reduce phonon lifetimes of important low-frequency heat-carrying modes, leading to a large reduction of κ-potentially an order of magnitude at room temperature. We propose a general and quantitative framework for controlling thermal transport in complex functional materials through structural spatial correlations, and we establish the optimal functional form of spatial correlations that minimize κ. We end by briefly discussing experimental realizations of various correlated structures.

Local and global measures of the shear moduli of jammed disk packings.

Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as 〈G〉=(1-F_{-})〈G_{+}〉+F_{-}〈G_{-}〉, where F_{-} is the fraction of jammed packings with negative shear moduli and 〈G_{+}〉 and 〈G_{-}〉 are the average values from packings with positive and negative moduli, respectively. We show that 〈G_{+}〉 and 〈|G_{-}|〉 obey different power-law scaling relations above and below pN^{2}∼1. For pN^{2}>1, both 〈G_{+}〉N and 〈|G_{-}|〉N∼(pN^{2})^{β}, where β∼0.5 for repulsive linear spring interactions. Despite this, 〈G〉N∼(pN^{2})^{β^{'}} with β^{'}≳0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN^{2} and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN^{2}≪1 limit. As pN^{2} increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN^{2}≫1 limit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when G>0. The spatial correlation function of local shear moduli C(r[over ⃗]) displays weak correlations for pn_{sub}^{2}<10^{-2}, where n_{sub} is the number of particles within each subsystem. However, C(r[over ⃗]) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pn_{sub}^{2}≳10^{-2}.

Breakdown of long-range spatial correlations of infraslow amplitude fluctuations of EEG oscillations in patients with current and past major depressive disorder.

Identifying biomarkers for depression from brain activity is important for the diagnosis and treatment of depression disorders. We investigated spatial correlations of the amplitude fluctuations of electroencephalography (EEG) oscillations as a potential biomarker of depression. The amplitude fluctuations of EEG oscillations intrinsically reveal both temporal and spatial correlations, indicating rapid and functional organization of the brain networks. Amid these correlations, long-range temporal correlations are reportedly impaired in patients with depression, exhibiting amplitude fluctuations closer to a random process. Based on this occurrence, we hypothesized that the spatial correlations of amplitude fluctuations would also be altered by depression. In the present study, we extracted the amplitude fluctuations of EEG oscillations by filtering them through infraslow frequency band (0.05-0.1 Hz). We found that the amplitude fluctuations of theta oscillations during eye-closed rest depicted lower levels of spatial correlation in patients with major depressive disorder (MDD) compared to control individuals. This breakdown of spatial correlations was most prominent in the left fronto - temporal network, specifically in patients with current MDD rather than in those with past MDD. We also found that the amplitude fluctuations of alpha oscillations during eye-open rest exhibited lower levels of spatial correlation in patients with past MDD compared to control individuals or patients with current MDD. Our results suggest that breakdown of long-range spatial correlations may offer a biomarker for the diagnosis of depression (current MDD), as well as the tracking of the recovery from depression (past MDD).

Delivering Ultra-Reliable Low-Latency Communications via Statistical Radio Maps

High reliability guarantees for Ultra-Reliable Low-Latency Communications (URLLC) require accurate knowledge of channel statistics used as an input for rate selection. Exploiting the spatial consistency of channel statistics arises as a promising solution, allowing a base station to predict the propagation conditions and select the communication parameters for a new user from samples collected from previous users of the network. Based on this idea, this article provides a timely framework to exploit long-range channel spatial correlation through so-called statistical radio maps, enabling URLLC communications with given statistical guarantees. The framework is exemplified by predicting the channel capacity distribution both in a location-based radio map and in a latent space rendered by a channel chart, the latter being a localization-free approach based on channel state information. It is also shown how to use the maps to select the transmission rate in a new location that achieves a target level of reliability. Lastly, several future directions and research challenges are also discussed.

Unveiling Phase Transitions in 1D Systems with Short-Range Interactions

The statement that any phase transition is related to the appearance or disappearance of long-range spatial correlations and precludes a finite transition temperature in one-dimensional (1D) systems is rooted in condensed matter theory. In this paper, we demonstrate that the 1D Ising model with short-range exchange interactions exhibits a second-order phase transition at a finite temperature relying on the proper choice of the order parameter. We combined analytical calculations and high-precision entropic sampling simulations and chose a slightly different order parameter, namely, the modulus of the magnetization. Notably, we detected a phase transition with a corresponding critical temperature around 15 K, which is in excellent agreement with experimental results. Our study indicates that the incorrect choice of the order parameter may mask phase transitions in 1D systems.

Two-dimensional dynamic perylene ordering on Ag(110)

We present a room temperature STM study of dynamics of the quasi-liquid perylene monolayer formed on Ag(110) under thermal equilibrium. We observe that the thermodynamic balance of the molecule–molecule and molecule–substrate interactions generates a compact two-dimensional (2D) quasi-liquid state established by mobile perylene molecules dynamically distributed into three distinct motion modes. Monitoring of the quasi-liquid monolayer indicates that each motion mode is triggered by spontaneous recognition of specific locations of the substrate lattice into which transient locking occurs. Analysis of the STM topographies shows that the substrate lattice guides the whole molecule ensemble and provides each of the modes with a distinct register. In each mode, the substrate registry forces the transiently immobile molecules to alternate with the transiently mobile ones. The dynamic interminglement of the modes prevents segregation of the dynamically active and inactive molecules. The substrate provides memory to the intermingled molecules and eliminates ergodicity of the quasi-liquid state. Fourier transform of the topographies unravels the long-range spatial correlations and epitaxial character of the quasi-liquid state. Analysis of the short-range mode coupling allows us to understand the mechanism of the long-range mode coupling. The substrate force field induces the dynamical ergodic–non-ergodic phase transition giving rise to the stationary long-range ordered −12.532 quasi-liquid state.

For the aged: A novel PM2.5 concentration forecasting method based on spatial-temporal graph ordinary differential equation networks in home-based care parks

The immune ability of the elderly is not strong, and the functions of the body are in a stage of degeneration, the ability to clear PM2.5 is reduced, and the cardiopulmonary system is easily affected. Accurate prediction of PM2.5 can provide guidance for the travel of the elderly, thereby reducing the harm of PM2.5 to the elderly. In PM2.5 prediction, existing works usually used shallow graph neural network (GNN) and temporal extraction module to model spatial and temporal dependencies, respectively, and do not uniformly model temporal and spatial dependencies. In addition, shallow GNN cannot capture long-range spatial correlations. External characteristics such as air humidity are also not considered. We propose a spatial-temporal graph ordinary differential equation network (STGODE-M) to tackle these problems. We capture spatial-temporal dynamics through tensor-based ordinary differential equation, so we can build deeper networks and exploit spatial-temporal features simultaneously. In addition, in the construction of the adjacency matrix, we not only used the Euclidean distance between the stations, but also used the wind direction data. Besides, we propose an external feature fusion strategy that uses air humidity as an auxiliary feature for feature fusion, since air humidity is also an important factor affecting PM2.5 concentration. Finally, our model is evaluated on the home-based care parks atmospheric dataset, and the experimental results show that our STGODE-M can more fully capture the spatial-temporal characteristics of PM2.5, achieving superior performance compared to the baseline. Therefore, it can provide better guarantee for the healthy travel of the elderly.

LS-NTP: Unifying long- and short-range spatial correlations for near-surface temperature prediction

The near-surface temperature prediction (NTP) is an important spatial–temporal forecast problem, which can be used to prevent temperature crises. Most of the previous approaches fail to explicitly model the long- and short-range spatial correlations simultaneously, which is critical to making an accurate temperature prediction. In this study, both long- and short-range spatial correlations are captured to fill this gap by a novel convolution operator named Long- and Short-range Convolution (LS-Conv). The proposed LS-Conv operator includes three key components, namely, Node-based Spatial Attention (NSA), Long-range Adaptive Graph Constructor (LAGC), and Long- and Short-range Integrator (LSI). To capture long-range spatial correlations, NSA and LAGC are proposed to evaluate node importance aiming at auto-constructing long-range spatial correlations, which is named as Long-range aware Graph Convolution Network (LR-GCN). After that, the Short-range aware Convolution Neural Network (SR-CNN) accounts for the short-range spatial correlations. Finally, LSI is proposed to capture both long- and short-range spatial correlations by intra-unifying LR-GCN and SR-CNN. Upon the proposed LS-Conv operator, a new model called Long- and Short-range for NPT (LS-NTP) is developed. Extensive experiments are conducted on two real-world datasets and the results demonstrate that the proposed method outperforms state-of-the-art techniques. The source code is available on GitHub:https://github.com/xuguangning1218/LS_NTP.