Complex Spatiotemporal Dynamics Research Articles

Spatio-Temporal Dual Kriging with Adaptive Coefficient Drift Function

Research on spatio-temporal geostatistical modeling remains a critical challenge in numerous scientific and engineering disciplines. This paper introduces a novel extension of dual kriging, called spatio-temporal dual kriging (ST-DK), in which drift functions with fixed and adaptive coefficients are established. The approach appears to be effective in modeling complex spatio-temporal dynamics, particularly when relevant auxiliary variables exert substantial influence on the target variable. To illustrate its performance, we compare the ST-DK model with the classical spatio-temporal regression kriging (ST-RK) and geographically and temporally weighted regression (GTWR) models for estimating temperature and air pressure data from Thailand in 2018. Our findings demonstrate that both the ST-DK and ST-RK models when utilizing adaptive coefficients outperform their fixed coefficient counterparts. Furthermore, the ST-DK method consistently exhibits superior performance compared to the ST-RK and GTWR methods.

A multiscale spatial modeling framework for the germinal center response.

The germinal center response or reaction (GCR) is a hallmark event of adaptive humoral immunity. Unfolding in the B cell follicles of the secondary lymphoid organs, a GC culminates in the production of high-affinity antibody-secreting plasma cells along with memory B cells. By interacting with follicular dendritic cells (FDC) and T follicular helper (Tfh) cells, GC B cells exhibit complex spatiotemporal dynamics. Driving the B cell dynamics are the intracellular signal transduction and gene regulatory network that responds to cell surface signaling molecules, cytokines, and chemokines. As our knowledge of the GC continues to expand in depth and in scope, mathematical modeling has become an important tool to help disentangle the intricacy of the GCR and inform novel mechanistic and clinical insights. While the GC has been modeled at different granularities, a multiscale spatial simulation framework - integrating molecular, cellular, and tissue-level responses - is still rare. Here, we report our recent progress toward this end with a hybrid stochastic GC framework developed on the Cellular Potts Model-based CompuCell3D platform. Tellurium is used to simulate the B cell intracellular molecular network comprising NF-κB, FOXO1, MYC, AP4, CXCR4, and BLIMP1 that responds to B cell receptor (BCR) and CD40-mediated signaling. The molecular outputs of the network drive the spatiotemporal behaviors of B cells, including cyclic migration between the dark zone (DZ) and light zone (LZ) via chemotaxis; clonal proliferative bursts, somatic hypermutation, and DNA damage-induced apoptosis in the DZ; and positive selection, apoptosis via a death timer, and emergence of plasma cells in the LZ. Our simulations are able to recapitulate key molecular, cellular, and morphological GC events, including B cell population growth, affinity maturation, and clonal dominance. This novel modeling framework provides an open-source, customizable, and multiscale virtual GC simulation platform that enables qualitative and quantitative in silico investigations of a range of mechanistic and applied research questions on the adaptive humoral immune response in the future.

Evolution of clusters of turbulent reattachment due to shear layer instability in flow past a circular cylinder

We perform large eddy simulations of flow past a circular cylinder for the Reynolds number (Re) range, 2×103≤Re≤4×105, spanning subcritical, critical, and supercritical regimes. We investigate the spanwise coherence of the flow in the critical and supercritical regimes using complex networks. In these regimes, the separated flow reattaches to the surface in a turbulent state due to the turbulence generated by the shear layer instability. In the early critical regime, the turbulent reattachment does not occur simultaneously at all span locations. It occurs incoherently along the span in clusters. We treat strong surface pressure fluctuations due to the shear layer instability as extreme events and construct time-varying spatial proximity networks where links are based on synchronization between events. This analysis unravels the underlying complex spatiotemporal dynamics by enabling the estimation of characteristics of clusters of turbulent reattachment via the concept of connected components. In the critical regime, the number and size of the clusters increase with the increase in Re. At higher Re in the supercritical regime, they coalesce to form bigger clusters, resulting in increase in spanwise coherence of turbulent reattachment. We find that the size and number of clusters govern the variation of the time-averaged coefficient of drag (C¯D) in the critical and supercritical regimes. C¯D exhibits power-law distribution with the largest cluster size (C¯D∝S¯CL−25) and the most probable cluster size [C¯D∝E(SC)−25].

Data driven reduced modeling for fluidized bed with immersed tubes based on PCA and Bi-LSTM neural networks

The fast and accurate reduced-order modeling of fluidized beds is a challenging task in the field of fluid dynamics, owing to their high dimensionality and nonlinear dynamic behavior. In this study, a nonintrusive reduced order modeling method, the reduced order model based on principal component analysis and bidirectional long short-term memory networks (PBLSTM ROM), was developed to capture complex spatio-temporal dynamics of fluidized beds. By combining principal component analysis and Bidirectional long- short-term memory networks, the PBLSTM ROM effectively extracted dynamic evolution information without any prior knowledge of governing equations, enabling reduced-order modeling of unsteady flow fields. The PBLSTM ROM was validated using the solid volume fraction and gas velocity flow fields of a fluidized bed with immersed tubes, showing superior performance over both the PLSTM and PANN ROMs in accurately capturing temporal changes in the fluidization fields, especially in the region near immersed tubes where severe fluctuations appear. Moreover, the PBLSTM ROM improved the simulation speed by five orders of magnitude compared to traditional computational fluid dynamics simulations. These findings suggest that the PBLSTM ROM presents a promising approach for analyzing the complex fluid flows in engineering practice.

Propagating population activity patterns during spontaneous slow waves in the thalamus of rodents

Slow waves (SWs) represent the most prominent electrophysiological events in the thalamocortical system under anesthesia and during deep sleep. Recent studies have revealed that SWs have complex spatiotemporal dynamics and propagate across neocortical regions. However, it is still unclear whether neuronal activity in the thalamus exhibits similar propagation properties during SWs. Here, we report propagating population activity in the thalamus of ketamine/xylazine-anesthetized rats and mice visualized by high-density silicon probe recordings. In both rodent species, propagation of spontaneous thalamic activity during up-states was most frequently observed in dorsal thalamic nuclei such as the higher order posterior (Po), lateral posterior (LP) or laterodorsal (LD) nuclei. The preferred direction of thalamic activity spreading was along the dorsoventral axis, with over half of the up-states exhibiting a gradual propagation in the ventral-to-dorsal direction. Furthermore, simultaneous neocortical and thalamic recordings collected under anesthesia demonstrated that there is a weak but noticeable interrelation between propagation patterns observed during cortical up-states and those displayed by thalamic population activity. In addition, using chronically implanted silicon probes, we detected propagating activity patterns in the thalamus of naturally sleeping rats during slow-wave sleep. However, in comparison to propagating up-states observed under anesthesia, these propagating patterns were characterized by a reduced rate of occurrence and a faster propagation speed. Our findings suggest that the propagation of spontaneous population activity is an intrinsic property of the thalamocortical network during synchronized brain states such as deep sleep or anesthesia. Additionally, our data implies that the neocortex may have partial control over the formation of propagation patterns within the dorsal thalamus under anesthesia.

A way to determine groundwater contributions to large river systems: The Elbe River during drought conditions

Study regionOur study region extends over 450 stream km of the German part of the Elbe River, an ecologically and economically important first order river, between Schöna and Wittenberge. Study focusDiffuse groundwater born nutrients are major contributors to increased algae growth in rivers, leading to eutrophication with serious consequences for water quality and ecosystem health. Therefore, knowledge of the spatial and temporal dynamics of diffuse groundwater discharge are required since groundwater often remains as a ‘black box’ for the identification of nutrient sources by managers. The multi-method approach, based on the inverse geochemical and tritium modelling, a flux balance, a darcy approach and hydraulic gradients, showed complex spatiotemporal dynamics along the studied reach of the Elbe River. Groundwater inflow was variable but occurred along the entire river. Areas of high groundwater fluxes were located in the upstream mountainous catchment areas and decreasing downstream. New hydrological insights for the regionThe multi-method approach provides a blueprint for the assessment of other large river systems. No single method was able to create conclusive results and most other approaches are only applicable in smaller stream systems. First time an estimation of groundwater flux rates, that can be used to quantify matter inputs, was made. In addition, we showed a way to detect and assess the impact of drainage channels in a heterogenous river system.

Deep online recommendations for connected E-taxis by coupling trajectory mining and reinforcement learning

There is a growing interest in the optimization of vehicle fleets management in urban environments. However, limited attention has been paid to the integrated optimization of electric taxi fleets accounting for different operations as well as complex spatiotemporal demand dynamics. To this end, this study develops a real-time recommendation framework based on deep reinforcement learning (DRL) for electric taxis (E-taxis) to improve their system performance with explicit modeling of multiple vehicle actions and varying travel demand across space and over time. Spatiotemporal patterns of urban taxi travels are extracted from large-scale taxi trajectories. Spatiotemporal strategies are proposed to coordinate E-taxis’ repositioning and recharging with optimized recommendation for next destinations and charging stations. A spatiotemporal double deep Q-network (ST-DDQN) is embedded in the DRL framework to maximize the daily profit. A prototype real-time recommendation system for E-taxis is implemented for the decision-making of E-taxi drivers and sensitivity analyses are carried out. The experimental results in Shenzhen, China suggest that the proposed framework could improve the overall performance. This study will benefit the promotion of connected E-taxis and the development of clean and smart transportation.

Multivariate spatio-temporal modeling of drought prediction using graph neural network

Abstract Drought is a serious natural disaster that causes huge losses to various regions of the world. To effectively cope with this disaster, we need to use drought indices to classify and compare the drought conditions of different regions. We can take appropriate measures according to the category of drought to mitigate the impact of drought. Recently, deep learning models have shown promising results in this domain. However, few of these models consider the relationships between different areas, which limits their ability to capture the complex spatio-temporal dynamics of droughts. In this study, we propose a novel multivariate spatio-temporal sensitive network (MSTSN) for drought prediction, which incorporates both geographical and temporal knowledge in the network and improves its predictive power. We obtained the standardized precipitation evapotranspiration index and meteorological data from the climatic research unit dataset, covering the period from 1961 to 2018. This is the first deep learning method that embeds geographical knowledge in drought prediction. We also provide a solid foundation for comparing our method with other deep learning baselines and evaluating their performance. Experiments show that our method consistently outperforms the existing state-of-the-art methods on various metrics, validating the effectiveness of geospatial and temporal information.

Comparative Analysis of BALSSA and Conventional NWP Methods: A Case Study in Extreme Storm Surge Prediction in Macao

In coastal regions, accurate storm surge prediction is crucial for effective disaster management and risk mitigation. This study presents a comparative analysis between BALSSA (Bidirectional Attention-based LSTM for Storm Surge Architecture) and the Japan Meteorological Agency (JMA) numerical storm surge model, focusing on the Saola-induced storm surge in Macao, September 2023. To train and assess the model, we leverage an extensive dataset comprising meteorological and tide level information from more than 80 typhoon occurrences in Macao spanning the period from 2017 to 2023. The results provide evidence of BALSSA’s effectiveness in capturing the complex spatio-temporal dynamics of storm surges, with a lead time of up to 72 h, as reflected by its MAE of 0.019 and RMSE of 0.024. It demonstrates reliable accuracy in predicting storm surge magnitude, timing, and spatial extent, potentially contributing to more precise and timely warnings for coastal communities. Furthermore, the real-time data assimilation feature of BALSSA ensures up-to-date information, aligned with the latest observations, which is essential for effective emergency preparedness and response. The high-resolution grids enhance risk assessment, highlighting BALSSA’s potential for early warnings, emergency planning, and coastal risk management. This study contributes valuable insights to the broader field of storm surge prediction, guiding decision-making processes and supporting the development of effective strategies to enhance coastal resilience.

Temporal and spatial properties of vestibular signals for perception of self-motion.

It is well recognized that the vestibular system is involved in numerous important cognitive functions, including self-motion perception, spatial orientation, locomotion, and vector-based navigation, in addition to basic reflexes, such as oculomotor or body postural control. Consistent with this rationale, vestibular signals exist broadly in the brain, including several regions of the cerebral cortex, potentially allowing tight coordination with other sensory systems to improve the accuracy and precision of perception or action during self-motion. Recent neurophysiological studies in animal models based on single-cell resolution indicate that vestibular signals exhibit complex spatiotemporal dynamics, producing challenges in identifying their exact functions and how they are integrated with other modality signals. For example, vestibular and optic flow could provide congruent and incongruent signals regarding spatial tuning functions, reference frames, and temporal dynamics. Comprehensive studies, including behavioral tasks, neural recording across sensory and sensory-motor association areas, and causal link manipulations, have provided some insights into the neural mechanisms underlying multisensory self-motion perception.

A two-phase fluid model for epidemic flow.

We propose a new mathematical and computational modeling framework that incorporates fluid dynamics to study the spatial spread of infectious diseases. We model the susceptible and infected populations as two inviscid fluids which interact with each other. Their motion at the macroscopic level characterizes the progression and spread of the epidemic. To implement the two-phase flow model, we employ high-order numerical methods from computational fluid dynamics. We apply this model to simulate the COVID-19 outbreaks in the city of Wuhan in China and the state of Tennessee in the US. Our modeling and simulation framework allows us to conduct a detailed investigation into the complex spatiotemporal dynamics related to the transmission and spread of COVID-19.

Long Short-Term Memory and Attention Models for Simulating Urban Densification

This paper introduces a novel cellular automata model that combines Long Short-Term Memory, Attention, and Neural Network models to capture spatio-temporal Land Use Change (LUC) behaviors while addressing the challenge of imbalanced datasets. The proposed method is developed and validated using data from Belgium, defined as three (100x100) m raster-based built-up maps for 2000, 2010, and 2020. The model is trained and validated using data from 2000 to 2010, and its effectiveness is tested using data from 2010 to 2020. The key contribution of our approach lies in its ability to tackle long-term temporal dependency and class imbalance problems in LUC science. Our proposed method significantly enhances the performance of spatio-temporal LUC simulation. Additionally, we adopt a data splitting strategy that takes into account the different transitions between classes, improving the accuracy of the model predictions of minority class. The obtained results demonstrate the efficiency of the proposed model in capturing complex spatio-temporal dynamics and reducing the impact of imbalanced datasets surpassing existing methods. The implications of our study extend beyond LUC modeling, as the proposed approach can be applied to a wide range of applications where machine learning is used to model complex environmental and geographical phenomena.

Dynamics of three-dimensional spatiotemporal solitons in multimode waveguides

In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in these structures can be described by using a Gross–Pitaevskii equation with a two-dimensional parabolic spatial potential. Our investigations compare variational approaches, based on the Ritz optimization method, with extensive numerical simulations. We found that, with a Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low pulse energies, where our analytical results find a perfect agreement with the numerical simulations. However, with progressively increasing energies, solitons eventually undergo wave collapse: this occurs below the theoretical limit, which is predicted within the variational approach. In a self-defocusing scenario, a similar trend is found, where the good agreement persists for low energies. For large soliton energies, however, complex spatiotemporal dynamics emerge.

Machine learning simulation of one-dimensional deterministic water wave propagation

Deterministic phase-resolved prediction of the evolution of surface gravity waves in water is challenging due to their complex spatio-temporal dynamics. Physics-based methods of varying complexity are available, but the conflicting objectives of numerical efficiency and accuracy impede real-time wave prediction. Data-driven methods may be able to overcome this challenge by using training data generated by complex numerical methods. This work explores the potential of a machine learning (ML) approach based on a fully convolutional encoder–decoder architecture for the efficient and accurate prediction of water waves. The high-order spectral (HOS) method forms the foundation for the generation of the training data. The HOS method is applied for different, consecutive orders of nonlinearity starting from first order up to fourth order. The JONSWAP wave energy spectrum serves as the basis for modeling the one-dimensional irregular sea states. The overall objective of this work is to evaluate whether the complex non-linear physical processes can be identified and learned by the ML approach. The trained ML flow mapper is used to perform time integration of an initial sea state. The results indicate that the proposed ML approach is able to reproduce the distinctive physical processes of the different orders of nonlinearities. It is shown that the ML approach enables fast and accurate predictions of one-dimensional waves over a time horizon that spans multiple peak periods.

Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing.

The large-scale activity of the human brain exhibits rich and complex patterns, but the spatiotemporal dynamics of these patterns and their functional roles in cognition remain unclear. Here by characterizing moment-by-moment fluctuations of human cortical functional magnetic resonance imaging signals, we show that spiral-like, rotational wave patterns (brain spirals) are widespread during both resting and cognitive task states. These brain spirals propagate across the cortex while rotating around their phase singularity centres, giving rise to spatiotemporal activity dynamics with non-stationary features. The properties of these brain spirals, such as their rotational directions and locations, are task relevant and can be used to classify different cognitive tasks. We also demonstrate that multiple, interacting brain spirals are involved in coordinating the correlated activations and de-activations of distributed functional regions; this mechanism enables flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing. Our findings suggest that brain spirals organize complex spatiotemporal dynamics of the human brain and have functional correlates to cognitive processing.

Techniques for in vivo serotonin detection in the brain: State of the art.

Neuronal circuits in the brain that utilize the neurotransmitter serotonin are essential to the regulation of mood and emotional expression. Disruptions in serotonin signaling underlie neuropsychiatric conditions such as depression and anxiety. However, the cellular mechanisms that regulate serotonergic signaling in the brain in healthy and diseased states remain to be better understood. In particular, as more is learned about serotonin in the brain, we recognize an urgent need to develop techniques capable of mapping its complex spatiotemporal dynamics in awake, behaving animals. Notably, analytical methods to detect serotonin in situ, including tomography, are widely used but still recognized as limited in terms of their spatiotemporal resolution, their methodological caveats, and their technical limitations when cross-referenced with behavioral studies. To overcome such limitations, genetically encoded serotonin indicators were developed, leading to the introduction of novel imaging modalities that enable researchers to achieve remarkable spatiotemporal resolution in the study of serotonergic circuits in preclinical models of neuropsychiatric disorders. These novel approaches, while remarkably powerful, are also not without limitations. Here, we review the current techniques for detecting and quantifying serotonin in vivo within the brain and discuss how novel approaches such as genetically encoded serotonin indicators will lead to new insights into the roles of serotonergic circuits in health and disease.

Optimal restoration for pollination services increases forest cover while doubling agricultural profits.

Pollinators are currently facing dramatic declines in abundance and richness across the globe. This can have profound impacts on agriculture, as 75% of globally common food crops benefit from pollination services. As many native bee species require natural areas for nesting, restoration efforts within croplands may be beneficial to support pollinators and enhance agricultural yields. Yet, restoration can be challenging to implement due to large upfront costs and the removal of land from production. Designing sustainable landscapes will require planning approaches that include the complex spatiotemporal dynamics of pollination services flowing from (restored) vegetation into crops. We present a novel planning framework to determine the best spatial arrangement for restoration in agricultural landscapes while accounting for yield improvements over 40 years following restoration. We explored a range of production and conservation goals using a coffee production landscape in Costa Rica as a case study. Our results show that strategic restoration can increase forest cover by approximately 20% while doubling collective landholder profits over 40 years, even when accounting for land taken out of production. We show that restoration can provide immense economic benefits in the long run, which may be pivotal to motivating local landholders to undertake conservation endeavours in pollinator-dependent croplands.

Spatially coordinated collective phosphorylation filters spatiotemporal noises for precise circadian timekeeping

The circadian (∼24h) clock is based on a negative-feedback loop centered around the PERIOD protein (PER), translated in the cytoplasm and then enters the nucleus to repress its own transcription at the right time of day. Such precise nucleus entry is mysterious because thousands of PER molecules transit through crowded cytoplasm and arrive at the perinucleus across several hours. To understand this, we developed a mathematical model describing the complex spatiotemporal dynamics of PER as a single random time delay. We find that the spatially coordinated bistable phosphoswitch of PER, which triggers the phosphorylation of accumulated PER at the perinucleus, leads to the synchronous and precise nuclear entry of PER. This leads to robust circadian rhythms even when PER arrival times are heterogeneous and perturbed due to changes in cell crowdedness, cell size, and transcriptional activator levels. This shows how the circadian clock compensates for spatiotemporal noise.

Adaptive Gaussian Markov random field spatiotemporal models for infectious disease mapping and forecasting

Recent disease mapping literature presents adaptively parameterized spatiotemporal (ST) autoregressive (AR) or conditional autoregressive (CAR) models for Bayesian prediction of COVID-19 infection risks. These models were motivated to capture complex spatiotemporal dynamics and heterogeneities of infection risks. In the present paper, we synthesize, generalize, and unify the ST AR and CAR model constructions for models augmented by adaptive Gaussian Markov random fields, with an emphasis on disease forecasting. A general convolution construction is presented, with illustrative models motivated to (i) characterize local risk dependencies and influences over both spatial and temporal dimensions, (ii) model risk heterogeneities and discontinuities, and (iii) predict and forecast areal-level disease risks and occurrences. The broadened constructions allow rich options of intuitive parameterization for disease mapping and spatial regression. Illustrative parameterizations are presented for Bayesian hierarchical models of Poisson, zero-inflated Poisson, and Bernoulli data models, respectively. They are also discussed in the context of quantifying time-varying or time-invariant effects of (omitted) covariates, with application to prediction and forecasting areal-level COVID-19 infection occurrences and probabilities of zero-infection. The model constructions presented herein have much wider scope in offering a flexible framework for modelling complex spatiotemporal data and for estimation, learning, and forecasting purposes.

Mapping nonlinear brain dynamics by phase space embedding with fMRI data

The human brain is a complex neurobiological system exhibiting complex nonlinear spatiotemporal dynamics. While functional magnetic resonance imaging (fMRI) has been widely used to study brain activity, whole-brain nonlinear dynamics in fMRI data have not been extensively examined. The present study applied phase space embedding on resting-state fMRI data and characterized their phase space dynamics with the sum of lengths of portrait edges (SE) in the reconstructed phase portrait. The effects of repetition time (TR), bandpass filtering and the added noise power of BOLD signals on the optimal embedding parameters (embedding time delay τ and embedding dimension m) were examined with experimental or simulated fMRI data. Our results show that τ and m vary with the three acquisition parameters. The present method was applied to the autism spectrum disorder dataset from Autism Imaging Data Exchange I to demonstrate its capability in the characterization of abnormal brain dynamics. The resultant SE maps were statistically compared between patients and controls, and the significant differences in SE were fed into a support vector machine (SVM) for classification. A significant increase in SE in the default mode network (DMN) and salience network (SN), as well as the visual network, was found in autistic patients. With the SE features of these regions, our SVM classifier achieved superior accuracy (74.55% with 10-folds cross validation) compared with prior studies, indicating that phase space embedding and SE mapping are promising in characterizing the nonlinear dynamics of the BOLD signal and might be useful for brain biomarker discovery in clinical psychiatry.