Long-range Spatiotemporal 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.

Thermodynamic analog of integrate-and-fire neuronal networks by maximum entropy modelling

Recent results have evidenced that spontaneous brain activity signals are organized in bursts with scale free features and long-range spatio-temporal correlations. These observations have stimulated a theoretical interpretation of results inspired in critical phenomena. In particular, relying on maximum entropy arguments, certain aspects of time-averaged experimental neuronal data have been recently described using Ising-like models, allowing the study of neuronal networks under an analogous thermodynamical framework. This method has been so far applied to a variety of experimental datasets, but never to a biologically inspired neuronal network with short and long-term plasticity. Here, we apply for the first time the Maximum Entropy method to an Integrate-and-fire (IF) model that can be tuned at criticality, offering a controlled setting for a systematic study of criticality and finite-size effects in spontaneous neuronal activity, as opposed to experiments. We consider generalized Ising Hamiltonians whose local magnetic fields and interaction parameters are assigned according to the average activity of single neurons and correlation functions between neurons of the IF networks in the critical state. We show that these Hamiltonians exhibit a spin glass phase for low temperatures, having mostly negative intrinsic fields and a bimodal distribution of interaction constants that tends to become unimodal for larger networks. Results evidence that the magnetization and the response functions exhibit the expected singular behavior near the critical point. Furthermore, we also found that networks with higher percentage of inhibitory neurons lead to Ising-like systems with reduced thermal fluctuations. Finally, considering only neuronal pairs associated with the largest correlation functions allows the study of larger system sizes.

Spatiotemporal analysis of earthquake occurrence in synthetic and worldwide data

The present work presents spatiotemporal analyses of distributions between successive earthquakes. This study comprehends data produced by a modified version of the Olami–Feder–Christensen model with a small-world topology and actual worldwide earthquakes from 2000 to 2019. The distributions were studied from the nonextensive statistical mechanic’s viewpoint, which was shown to be a suitable approach since q-exponential functions produced better fittings to data than pure power laws. Our results show that, by applying scaling relationships, the probability distributions have data collapses in all cases. It reinforces the conception of a critical behavior in the seismological phenomenon and that there is no differentiation between the spatiotemporal statistical features of earthquakes, whether small or large in size or magnitude. In addition, the presence of q-exponential distributions and the ability of a small-world-like OFC model to reproduce spatiotemporal features of real worldwide earthquakes indicate self-organized criticality and long-range spatiotemporal correlations between earthquakes.

STSGAN: Spatial-Temporal Global Semantic Graph Attention Convolution Networks for Urban Flow Prediction

Accurate urban traffic flow prediction plays a vital role in Intelligent Transportation System (ITS). The complex long-term and long-range spatiotemporal correlations of traffic flow pose a significant challenge to the prediction task. Most current research methods focus only on spatial correlations in local areas, ignoring global geographic contextual information. It is challenging to capture spatial information from distant nodes using shallow graph neural networks (GNNs) to model long-range spatial correlations. To handle this problem, we design a novel spatiotemporal global semantic graph-attentive convolutional network model (STSGAN), which is a deep-level network to achieve the simultaneous modelling of spatiotemporal correlations. First, we propose a graph-attentive convolutional network (GACN) to extract the importance of different spatial features and learn the spatial correlation of local regions and the global spatial semantic information. The temporal causal convolution structure (TCN) is utilized to capture the causal relationships between long-short times, thus enabling an integrated consideration of local and overall spatiotemporal correlations. Several experiments are conducted on two real-world traffic flow datasets, and the results show that our approach outperforms several state-of-the-art baselines.

Kinetic roughening and nontrivial scaling in the Kardar–Parisi–Zhang growth with long-range temporal correlations

Long-range spatiotemporal correlations may play important roles in non-equilibrium surface growth processes. In order to explore the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we carry out extensive numerical simulations of the (1 + 1)- and (2 + 1)-dimensional Kardar–Parisi–Zhang (KPZ) growth system in the presence of temporally correlated noise, and compare our results with previous theoretical predictions and numerical simulations. We find that surface morphologies are obviously affected with long-range temporal correlations, and as the temporal correlation exponent increases, the KPZ surfaces develop gradually faceted patterns in the saturated growth regimes. Our results show that the temporal correlated KPZ system displays evidently nontrivial dynamic properties when 0 < θ < 0.5, the characteristic roughness exponents satisfy α < α s, and α loc exhibits non-universal scaling within local window sizes, which differs with the existing dynamic scaling hypotheses, both in the (1 + 1)- and (2 + 1)-dimensions.

A Progressive Fusion Generative Adversarial Network for Realistic and Consistent Video Super-Resolution.

How to effectively fuse temporal information from consecutive frames remains to be a non-trivial problem in video super-resolution (SR), since most existing fusion strategies (direct fusion, slow fusion, or 3D convolution) either fail to make full use of temporal information or cost too much calculation. To this end, we propose a novel progressive fusion network for video SR, in which frames are processed in a way of progressive separation and fusion for the thorough utilization of spatio-temporal information. We particularly incorporate multi-scale structure and hybrid convolutions into the network to capture a wide range of dependencies. We further propose a non-local operation to extract long-range spatio-temporal correlations directly, taking place of traditional motion estimation and motion compensation (ME&MC). This design relieves the complicated ME&MC algorithms, but enjoys better performance than various ME&MC schemes. Finally, we improve generative adversarial training for video SR to avoid temporal artifacts such as flickering and ghosting. In particular, we propose a frame variation loss with a single-sequence training method to generate more realistic and temporally consistent videos. Extensive experiments on public datasets show the superiority of our method over state-of-the-art methods in terms of performance and complexity. Our code is available at https://github.com/psychopa4/MSHPFNL.

Complex Dynamics of Propagating Waves in a Two-Dimensional Neural Field.

Propagating waves with complex dynamics have been widely observed in neural population activity. To understand their formation mechanisms, we investigate a type of two-dimensional neural field model by systematically varying its recurrent excitatory and inhibitory inputs. We show that the neural field model exhibits a rich repertoire of dynamical activity states when the relevant strength of excitation and inhibition is increased, ranging from localized rotating and traveling waves to global waves. Particularly, near the transition between stable states of rotating and traveling waves, the model exhibits a bistable state; that is, both the rotating and the traveling waves can exist, and the inclusion of noise can induce spontaneous transitions between them. Furthermore, we demonstrate that when there are multiple propagating waves, they exhibit rich collective propagation dynamics with variable propagating speeds and trajectories. We use techniques from time series analysis such detrended fluctuation analysis to characterize the effect of the strength of excitation and inhibition on these collective dynamics, which range from purely random motion to motion with long-range spatiotemporal correlations. These results provide insights into the possible contribution of excitation and inhibition toward a range of previously observed spatiotemporal wave phenomena.

Anomalous diffusion for inertial particles under gravity in parallel flows.

We investigate the bounds between normal or anomalous effective diffusion for inertial particles transported by parallel flows. The infrared behavior of the fluid kinetic-energy spectrum, i.e., the possible presence of long-range spatiotemporal correlations, is modeled as a power law by means of two parameters, and the problem is studied as a function of these latter. Our results, obtained in the limit of weak relative inertia, extend well-known results for tracers and apply to particles of any mass density, subject to gravity and Brownian diffusion. We consider both steady and time-dependent flows, and cases of both vanishing and finite particle sedimentation.

Extreme synergy: Spatiotemporal correlations enable rapid image reconstruction from computer-generated spike trains

Over the brief time intervals available for processing retinal output, the number of spikes generated by individual ganglion cells can be quite variable. Here, two examples of extreme synergy are used to illustrate how realistic long-range spatiotemporal correlations can greatly improve the quality of retinal images reconstructed from computer-generated spike trains that are 25-400 ms in duration, approximately the time between saccadic eye movements. Firing probabilities were specified both explicitly: using time-varying waveforms consistent with stimulus-evoked oscillations measured experimentally, and implicitly: by superimposing realistic fixational eye movements on a biophysical model of primate outer retina. Synergistic encoding was investigated across arrays of model neurons up to 32 x 32 in extent, containing over 1 million pairwise correlations. The difficulty of estimating pairwise, spatiotemporal correlations on single trials from only a few events was overcome by using oscillatory, local multiunit activity to weight contributions from all spike pairs. Stimuli were reconstructed using either an independent rate code or the first principal component of the single-trial, pairwise correlation matrix. Spatiotemporal correlations mediated dramatic improvements in signal/noise without eliminating fine spatial detail, demonstrating how extreme synergy can support rapid image reconstruction using far fewer spikes than required by an independent rate code.

IDENTIFICATION OF SELF-ORGANIZED CRITICALITY IN ATMOSPHERIC LOW FREQUENCY VARIABILITY

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as self-similar fractal geometry to the global cloud cover pattern concomitant with inverse power law form fB. Such non-local connections are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. Standard models in meteorological theory cannot explain satisfactorily the observed self-organized criticality in atmospheric flows. A recently developed cell dynamical model for atmospheric flows predicts the observed self-organized criticality as a direct consequence of quantumlike mechanics governing flow dynamics. The model predictions are in agreement with continuous periodogram power spectral analyses of two-day mean TOGA temperature time-series. The application of model concepts for prediction of atmospheric low frequency variability is discussed.

Cantorian Fractal Spacetime, Quantum-like Chaos and Scale Relativity in Atmospheric Flows

Cantorian fractal spacetime fluctuations characterize quantum-like chaos in atmospheric flows. The macroscale atmospheric flow structure behaves as a unified whole quantum system, where the superimposition of a continuum of eddies results in the observed global weather patterns with long-range spatiotemporal correlations, such as that of the widely investigated El Nino phenomenon. Large eddies are visualised as envelopes enclosing smaller eddies, thereby generating a hierarchy of eddy circulations, originating initially from a fixed primary small scale energising perturbation, e.g., the frictional upward momentum flux at the boundary layer of the Earths surface. In this paper, it is shown that the relative motion concepts of Einsteins Special and General Theories of Relativity are applicable to eddy circulations originating from a constant primary perturbation.

Superstrings, Cantorian-fractal Spacetime and Quantum-like Chaos in Atmospheric Flows

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with the inverse power law form for spectra of temporal fluctuations. Such non-local connections are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. A recently developed cell dynamical system model for atmospheric flows predicts the observed self-organized criticality as a natural consequence of quantum-like mechanics governing flow dynamics. The model is based on the concept that spatial integration of enclosed small scale fluctuations results in the formation of large eddy circulations. The model predicts the following: (a) The flow structure consists of an overall logarithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal structure. (b) Conventional power spectrum analysis will resolve such spiral trajectories as a continuum of eddies with progressive increase in phase. (c) Increments in phase are concomitant with increases in period length and also represent the variance, a characteristic of quantum systems identified as Berrys phase. (d) The universal algorithm for self-organized criticality is expressed in terms of the universal Feigenbaum constants, a and d, as 2 a 2= πd, where the fractional volume intermittency of occurrence πd contributes to the total variance 2 a 2 of fractal structures. (e) The Feigenbaum constants are expressed as functions of the golden mean. ( f) The quantum mechanical constants fine structure constant and ratio of proton mass to electron mass, which are pure numbers and are obtained by experimental observations only, are now derived in terms of the Feigenbaum constant, a. (g) Atmospheric flow structure follows Keplers third law of planetary motion. Therefore, Newtons inverse square law for gravitation also applies to eddy masses. The centripetal acceleration representing the inertial masses (of eddies) are equivalent to gravitational masses. The fractal-Cantorian structure of spacetime can also be visualized as a nested continuum of vortex (eddy) circulations, whose inertial masses obey Newtons inverse square law of gravitation. The model concept resembles a superstring model for subatomic dynamics which incorporates gravitational forces.

Cantorian Fractal Spacetime and Information in Neural Network of the Human Brain

The neural networks of the human brain act as very efficient parallel processing computers co-ordinating memory related responses to a multitude of input signals from sensory organs. Information storage, update and appropriate retrieval are controlled at the molecular level by the neuronal cytoskeleton which serves as the internal communication network within neurons. Information flow in the highly ordered parallel networks of the filamentous protein polymers which make up the cytoskeleton may be compared to atmospheric flows which exhibit long-range spatiotemporal correlations, i.e. long-term memory. Such long-range spatiotemporal correlations are ubiquitous to real world dynamical systems and is recently identified as signature of self-organized criticality or chaos. The signatures of self-organized criticality i.e. long-range temporal correlations have recently been identified in the electrical activity of the brain. The physics of self-organized criticality or chaos is not yet identified. A recently developed non-deterministic cell dynamical system model for atmospheric flows predicts the observed long-range spatiotemporal correlations as intrinsic to quantum-like mechanics governing flow dynamics. The model visualises large scale circulations to form as the result of spatial integration of enclosed small scale perturbations with intrinsic two-way ordered energy flow between the scales. Such a concept maybe applied for the collection and integration of a multitude of signals at the cytoskeletal level and manifested in activation of neurons in the macroscale. The cytoskeleton networks inside neurons may be the elementary units of a unified dynamic memory circulation network with intrinsic global response to local stimuli. A cell dynamical system model for human memory circulation network analogous to atmospheric circulations network is presented in this paper. The model like the analysis of Koruga et al. make use of certain connections to the concept of Cantorian-Fractal spacetime.

Signatures of a universal spectrum for atmospheric interannual variability in some disparate climatic regimes

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-tie scales ranging from turbulence (centimetersseconds) to climate (kilometers-years). Long-range spatiotemporal correlations are ubiquitous to dynamical systems in nature and are identified as signatures ofself-organized criticality. Standard models in meteorological theory cannot explain satisfactorily the observed self-organized criticality in atmospheric flows. Mathematical models for simulation and prediction of atmospheric flows are nonlinear and do not possess analytical solutions. Finite precision computer realizations of nonlinear models give unrealistic solutions because ofdeterministic chaos, a direct consequence of round-off error growth in iterative numerical computations. Recent studies show that roundoff error doubles on an average for each iteration of iterative computations. Round-off error propagates to the main stream computation and gives unrealistic solutions in numerical weather prediction (NWP) and climate models which incorporate thousands of iterative computations in long-term numerical integration schemes. An alternative non-deterministic cell dynamical system model for atmospheric flows described in this paper predicts the observed self-organized criticality as intrinsic to quantumlike mechanics governing flow dynamics. The model provides universal quantification for self-organized criticality in terms of the statistical normal distribution. Model predictions are in agreement with a majority of observed spectra of time series of several standard climatological data sets representative of disparate climatic regimes. Universal spectrum for natural climate variability rules out linear trends. Man-made greenhouse gas related atmospheric warming will result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference to possible prediction of climate change.

Universal spectrum for short period (days) variability in atmospheric total ozone

Long-range spatio-temporal correlations manifested as the self-similar fractal geometry to the spatial pattern concomitant with inverse power law form for the power spectrum of temporal fluctuations are ubiquitous to real world dynamical systems and are recently identified as signatures of self-organized criticality Self-organised criticality in atmospheric flows is exhibited as the fractal geometry 10 the global cloud cover pattern and the inverse power law form for the atmospheric eddy energy spectrum, In this paper, a recently developed cell dynamical system model for atmospheric flows is summarized. The model predicts inverse power law form of the statistical normal distribution for atmospheric eddy energy spectrum as a natural consequence of quantum-like mechanics governing atmospheric flows extending up to stratospheric levels and above, Model Predictions are in agreement with continuous periodogram analyses of atmospheric total ozone. Atmospheric total ozone variability (in days) exhibits the temporal signature of self-organized criticality, namely, inverse power law form for the power spectrum. Further, the long-range temporal correlations implicit to self-organized criticality can be quantified in terms of the universal characteristics of the normal distribution. Therefore the total pattern of fluctuations of total ozone over a period of time is predictable.&#x0D;

Random shearing direction models for isotropic turbulent diffusion

Recently, a rigorous renormalization theory for various scalar statistics has been developed for special modes of random advection diffusion involving random shear layer velocity fields with long-range spatiotemporal correlations. New random shearing direction models for isotropic turbulent diffusion are introduced here. In these models the velocity field has the spatial second-order statistics of an arbitrary prescribed stationary incompressible isotropic random field including long-range spatial correlations with infrared divergence, but the temporal correlations have finite range. The explicit theory of renormalization for the mean and second-order statistics is developed here. With e the spectral parameter, for −∞<e<4 and measuring the strength of the infrared divergence of the spatial spectrum, the scalar mean statistics rigorously exhibit a phase transition from mean-field behavior for e<2 to anomalous behavior for e with 2<e<4 as conjectured earlier by Avellaneda and the author. The universal inertial range renormalization for the second-order scalar statistics exhibits a phase transition from a covariance with a Gaussian functional form for e with e<2 to an explicit family with a non-Gaussian covariance for e with 2<e<4. These non-Gaussian distributions have tails that are broader than Gaussian as e varies with 2<e<4 and behave for large values like exp(−C c |x|4−e), withC c an explicit constant. Also, here the attractive general principle is formulated and proved that every steady, stationary, zero-mean, isotropic, incompressible Gaussian random velocity field is well approximated by a suitable superposition of random shear layers.

Deterministic chaos, fractals, and quantumlike mechanics in atmospheric flows

The complex spatiotemporal patterns of atmospheric flows that result from the cooperative existence of fluctuations ranging in size from millimetres to thousands of kilometres are found to exhibit long-range spatial and temporal correlations. These correlations are manifested as the self-similar fractal geometry of the global cloud cover pattern and the inverse power-law form for the atmospheric eddy energy spectrum. Such long-range spatiotemporal correlations are ubiquitous in extended natural dynamical systems and are signatures of deterministic chaos or self-organized criticality. In this paper, a cell dynamical system model for atmospheric flows is developed by consideration of microscopic domain eddy dynamical processes. This nondeterministic model enables formulation of a simple closed set of governing equations for the prediction and description of observed atmospheric flow structure characteristics as follows. The strange-attractor design of the field of deterministic chaos in atmospheric flows consists of a nested continuum of logarithmic spiral circulations that trace out the quasi-periodic Penrose tiling pattern, identified as the quasi-crystalline structure in condensed matter physics. The atmospheric eddy energy structure follows laws similar to quantum mechanical laws. The apparent waveparticle duality that characterizes quantum mechanical laws is attributed to the bimodal phenomenological form of energy display in the bidirectional energy flow that is intrinsic to eddy circulations, e.g., formation of clouds in updrafts and dissipation of clouds in downdrafts that result in the observed discrete cellular geometry of cloud structure.