Long-range Temporal Correlations Research Articles

Environment-mediated long-ranged correlations in many-body system

Quantum states in complex aggregates are unavoidably affected by environmental effects, which typically cannot be accurately modeled by simple Markovian processes. As system sizes scale up, nonperturbative simulation becomes thus unavoidable, but they are extremely challenging due to the intimate interplay of intrinsic many-body interaction and time-retarded feedback from environmental degrees of freedom. In this work, we utilize the recently developed quantum dissipation with minimally extended state space approach to address reservoir induced long-ranged temporal correlations in finite size Ising-type spin chains. For thermal reservoirs with ohmic and subohmic spectral density, we simulate the quantum time evolution from finite to zero temperature. The competition between thermal fluctuations, quantum fluctuations, and anti-/ferromagnetic interactions reveals a rich pattern of dynamical phases, including dissipative induced phase transitions and spatiotemporal correlations.

Multifractal properties of Covid-19 data

Multifractal detrended moving average analysis (MFDFA) has been performed on time series of three different epidemiological indices, namely daily number of new cases per million population, reproduction rate and positive rate, recorded during the Covid-19 pandemic. We consider India, Japan, USA and UK for this study. For all the series the scaling behavior of MFDMA fluctuation functions has been examined, and the multifractal variables like the generalised Hurst exponent spectra and singularity spectra have been calculated. It is found that the time series of the Covid-19 indices are of multifractal nature. The degree of multifractality of the reproduction rate series is significantly weaker than the other two series for all the countries. To find out the source(s) of multifractality, we generate a set of one hundred shuffled series and Amplitude-Adjusted Fourier Transform surrogate series for each of the original series. Comparing the results obtained from the original series with those from the shuffled and surrogate series we understand that the main source of multifractality in Covid-19 data is long-range temporal correlation among the series values.

Deep video compression based on Long-range Temporal Context Learning

Video compression allows for efficient storage and transmission of data, benefiting imaging and vision applications, e.g. computational imaging, photography, and displays by delivering high-quality videos. To exploit more informative contexts of video, we propose DVCL, a novel Deep Video Compression based on Long-range Temporal Context Learning. Aiming at high coding performance, this new compression paradigm makes full use of long-range temporal correlations derived from multiple reference frames to learn richer contexts. Motion vectors (MVs) are estimated to represent the motion relations of videos. By employing MVs, a long-range temporal context learning (LTCL) module is presented to extract context information from multiple reference frames, such that a more accurate and informative temporal contexts can be learned and constructed. The long-range temporal contexts serve as conditions and generate the predicted frames by contextual encoder and decoder. To address the challenge of imbalanced training, we develop a multi-stage training strategy to ensure the whole DVCL framework is trained progressively and stably. Extensive experiments demonstrate the proposed DVCL achieves the highest objective and subjective quality, while maintaining relatively low complexity. Specifically, 25.30% and 45.75% bitrate savings on average can be obtained than x265 codec at the same PSNR and MS-SSIM, respectively.

Hebbian plasticity induced by temporally coincident BCI enhances post-stroke motor recovery

Functional electrical stimulation (FES) can support functional restoration of a paretic limb post-stroke. Hebbian plasticity depends on temporally coinciding pre- and post-synaptic activity. A tight temporal relationship between motor cortical (MC) activity associated with attempted movement and FES-generated visuo-proprioceptive feedback is hypothesized to enhance motor recovery. Using a brain–computer interface (BCI) to classify MC spectral power in electroencephalographic (EEG) signals to trigger FES-delivery with detection of movement attempts improved motor outcomes in chronic stroke patients. We hypothesized that heightened neural plasticity earlier post-stroke would further enhance corticomuscular functional connectivity and motor recovery. We compared subcortical non-dominant hemisphere stroke patients in BCI-FES and Random-FES (FES temporally independent of MC movement attempt detection) groups. The primary outcome measure was the Fugl-Meyer Assessment, Upper Extremity (FMA-UE). We recorded high-density EEG and transcranial magnetic stimulation-induced motor evoked potentials before and after treatment. The BCI group showed greater: FMA-UE improvement; motor evoked potential amplitude; beta oscillatory power and long-range temporal correlation reduction over contralateral MC; and corticomuscular coherence with contralateral MC. These changes are consistent with enhanced post-stroke motor improvement when movement is synchronized with MC activity reflecting attempted movement.

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.

Associations of movement behaviours and dietary intake with arterial stiffness: results from the ORISCAV-LUX 2 cross-sectional study

ObjectiveAdopting a physically active lifestyle and maintaining a diet rich in antioxidants can reduce the risk of vascular diseases. Arterial stiffness is an early marker for cardiovascular diseases, indicating vascular...

Role of the Locus Coeruleus Arousal Promoting Neurons in Maintaining Brain Criticality across the Sleep-Wake Cycle.

Sleep control depends on a delicate interplay among brain regions. This generates a complex temporal architecture with numerous sleep-stage transitions and intermittent fluctuations to micro-states and brief arousals. These temporal dynamics exhibit hallmarks of criticality, suggesting that tuning to criticality is essential for spontaneous sleep-stage and arousal transitions. However, how the brain maintains criticality remains not understood. Here, we investigate θ- and δ-burst dynamics during the sleep-wake cycle of rats (Sprague-Dawley, adult male) with lesion in the wake-promoting locus coeruleus (LC). We show that, in control rats, θ- and δ-bursts exhibit power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, as well as power-law long-range temporal correlations (LRTCs)-typical of non-equilibrium systems self-organizing at criticality. Furthermore, consecutive θ- and δ-bursts durations are characterized by anti-correlated coupling, indicating a new class of self-organized criticality that emerges from underlying feedback between neuronal populations and brain areas involved in generating arousals and sleep states. In contrast, we uncover that LC lesion leads to alteration of θ- and δ-burst critical features, with change in duration distributions and correlation properties, and increase in θ-δ coupling. Notably, these LC-lesion effects are opposite to those observed for lesions in the sleep-promoting ventrolateral preoptic (VLPO) nucleus. Our findings indicate that critical dynamics of θ- and δ-bursts arise from a balanced interplay of LC and VLPO, which maintains brain tuning to criticality across the sleep-wake cycle-a non-equilibrium behavior in sleep micro-architecture at short timescales that coexists with large-scale sleep-wake homeostasis.

Application of HFO and scaling analysis of neuronal oscillations in the presurgical evaluation of focal epilepsy

PurposeTo explore the utility of high frequency oscillations (HFO) and long-range temporal correlations (LRTCs) in preoperative assessment of epilepsy. MethodsMEG ripples were detected in 59 drug-resistant epilepsy patients, comprising 5 with parietal lobe epilepsy (PLE), 21 with frontal lobe epilepsy (FLE), 14 with lateral temporal lobe epilepsy (LTLE), and 19 with mesial temporal lobe epilepsy (MTLE) to identify the epileptogenic zone (EZ). The results were compared with clinical MEG reports and resection area. Subsequently, LRTCs were quantified at the source-level by detrended fluctuation analysis (DFA) and life/waiting -time at 5 bands for 90 cerebral cortex regions. The brain regions with larger DFA exponents and standardized life-waiting biomarkers were compared with the resection results. ResultsCompared to MEG sensor-level data, ripple sources were more frequently localized within the resection area. Moreover, source-level analysis revealed a higher proportion of DFA exponents and life-waiting biomarkers with relatively higher rankings, primarily distributed within the resection area (p<0.01). Moreover, these two LRCT indices across five distinct frequency bands correlated with EZ. ConclusionHFO and source-level LRTCs are correlated with EZ. Integrating HFO and LRTCs may be an effective approach for presurgical evaluation of epilepsy.

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.

Adaptive Graph Convolutional Recurrent Network with Transformer and Whale Optimization Algorithm for Traffic Flow Prediction

Accurate traffic flow prediction plays a crucial role in the development of intelligent traffic management. Despite numerous investigations into spatio-temporal methods, achieving high accuracy in traffic flow prediction remains challenging. This challenge arises from the complex dynamic spatio-temporal correlations within the traffic road network and the limitations imposed by the selection of hyperparameters based on experiments and manual experience, which can affect the performance of the network architecture. This paper introduces a novel transformer-based adaptive graph convolutional recurrent network. The proposed network automatically infers the interdependencies among different traffic sequences and incorporates the capability to capture global spatio-temporal correlations. This enables the dynamic capture of long-range temporal correlations. Furthermore, the whale optimization algorithm is employed to efficiently design an optimal network structure that aligns with the requirements of the traffic domain and maximizes the utilization of limited computational resources. This design approach significantly enhances the model’s performance and improves the accuracy of traffic flow prediction. The experimental results on four real datasets demonstrate the efficacy of our approach. In PEMS03, it improves MAE by 2.6% and RMSE by 1.4%. In PEMS04, improvements are 1.6% in MAE and 1.4% in RMSE, with a similar MAPE score to the best baseline. For PEMS07, our approach shows a 4.1% improvement in MAE and 2.2% in RMSE. On PEMS08, it surpasses the current best baseline with a 3.4% improvement in MAE and 1.6% in RMSE. These results confirm the good performance of our model in traffic flow prediction across multiple datasets.

Assessment of the excitation-inhibition ratio in the Fmr1 KO2 mouse using neuronal oscillation dynamics.

In vitro and ex vivo studies have shown consistent indications of hyperexcitability in the Fragile X Messenger Ribonucleoprotein 1 (Fmr1) knockout mouse model of autism spectrum disorder. We recently introduced a method to quantify network-level functional excitation-inhibition ratio from the neuronal oscillations. Here, we used this measure to study whether the implicated synaptic excitation-inhibition disturbances translate to disturbances in network physiology in the Fragile X Messenger Ribonucleoprotein 1 (Fmr1) gene knockout model. Vigilance-state scoring was used to extract segments of inactive wakefulness as an equivalent behavioral condition to the human resting-state and, subsequently, we performed high-frequency resolution analysis of the functional excitation-inhibition biomarker, long-range temporal correlations, and spectral power. We corroborated earlier studies showing increased high-frequency power in Fragile X Messenger Ribonucleoprotein 1 (Fmr1) knockout mice. Long-range temporal correlations were higher in the gamma frequency ranges. Contrary to expectations, functional excitation-inhibition was lower in the knockout mice in high frequency ranges, suggesting more inhibition-dominated networks. Exposure to the Gamma-aminobutyric acid (GABA)-agonist clonazepam decreased the functional excitation-inhibition in both genotypes, confirming that increasing inhibitory tone results in a reduction of functional excitation-inhibition. In addition, clonazepam decreased electroencephalogram power and increased long-range temporal correlations in both genotypes. These findings show applicability of these new resting-state electroencephalogram biomarkers to animal for translational studies and allow investigation of the effects of lower-level disturbances in excitation-inhibition balance.

Computational EEG attributes predict response to therapy for epileptic spasms

ObjectiveWe set out to evaluate whether response to treatment for epileptic spasms is associated with specific candidate computational EEG biomarkers, independent of clinical attributes. MethodsWe identified 50 children with epileptic spasms, with pre- and post-treatment overnight video-EEG. After EEG samples were preprocessed in an automated fashion to remove artifacts, we calculated amplitude, power spectrum, functional connectivity, entropy, and long-range temporal correlations (LRTCs). To evaluate the extent to which each feature is independently associated with response and relapse, we conducted logistic and proportional hazards regression, respectively. ResultsAfter statistical adjustment for the duration of epileptic spasms prior to treatment, we observed an association between response and stronger baseline and post-treatment LRTCs (P = 0.042 and P = 0.004, respectively), and higher post-treatment entropy (P = 0.003). On an exploratory basis, freedom from relapse was associated with stronger post-treatment LRTCs (P = 0.006) and higher post-treatment entropy (P = 0.044). ConclusionThis study suggests that multiple EEG features—especially LRTCs and entropy—may predict response and relapse. SignificanceThis study represents a step toward a more precise approach to measure and predict response to treatment for epileptic spasms.

Dynamics of neuronal firing modulated by high-frequency electrical pulse stimulations at axons in rat hippocampus

Objective. The development of electrical pulse stimulations in brain, including deep brain stimulation, is promising for treating various brain diseases. However, the mechanisms of brain stimulations are not yet fully understood. Previous studies have shown that the commonly used high-frequency stimulation (HFS) can increase the firing of neurons and modulate the pattern of neuronal firing. Because the generation of neuronal firing in brain is a nonlinear process, investigating the characteristics of nonlinear dynamics induced by HFS could be helpful to reveal more mechanisms of brain stimulations. The aim of present study is to investigate the fractal properties in the neuronal firing generated by HFS. Approach. HFS pulse sequences with a constant frequency 100 Hz were applied in the afferent fiber tracts of rat hippocampal CA1 region. Unit spikes of both the pyramidal cells and the interneurons in the downstream area of stimulations were recorded. Two fractal indexes—the Fano factor and Hurst exponent were calculated to evaluate the changes of long-range temporal correlations (LRTCs), a typical characteristic of fractal process, in spike sequences of neuronal firing. Main results. Neuronal firing at both baseline and during HFS exhibited LRTCs over multiple time scales. In addition, the LRTCs significantly increased during HFS, which was confirmed by simulation data of both randomly shuffled sequences and surrogate sequences. Conclusion. The purely periodic stimulation of HFS pulses, a non-fractal process without LRTCs, can increase rather than decrease the LRTCs in neuronal firing. Significance. The finding provides new nonlinear mechanisms of brain stimulation and suggests that LRTCs could be a new biomarker to evaluate the nonlinear effects of HFS.

Behavioral state-dependent associations between EEG temporal correlations and depressive symptoms

Previous studies have shown abnormal long-range temporal correlations in neuronal oscillations among individuals with Major Depressive Disorders, occurring during both resting states and transitions between resting and task states. However, the understanding of this effect in preclinical individuals with depression remains limited. This study investigated the association between temporal correlations of neuronal oscillations and depressive symptoms during resting and task states in preclinical individuals, specifically focusing on male action video gaming experts. Detrended fluctuation analysis (DFA), Lifetimes, and Waitingtimes were employed to explore temporal correlations across long-range and short-range scales. The results indicated widespread changes from the resting state to the task state across all frequency bands and temporal scales. Rest-task DFA changes in the alpha band exhibited a negative correlation with depressive scores at most electrodes. Significant positive correlations between DFA values and depressive scores were observed in the alpha band during the resting state but not in the task state. Similar patterns of results emerged concerning maladaptive negative emotion regulation strategies. Additionally, short-range temporal correlations in the alpha band echoed the DFA results. These findings underscore the state-dependent relationships between temporal correlations of neuronal oscillations and depressive symptoms, as well as maladaptive emotion regulation strategies, in preclinical individuals.

Long-range temporal correlations in resting state alpha oscillations in major depressive disorder and obsessive-compulsive disorder.

Mental disorders are a significant concern in contemporary society, with a pressing need to identify biological markers. Long-range temporal correlations (LRTC) of brain rhythms have been widespread in clinical cohort studies, especially in major depressive disorder (MDD). However, research on LRTC in obsessive-compulsive disorder (OCD) is severely limited. Given the high co-occurrence of OCD and MDD, we conducted a comparative LRTC investigation. We assumed that the LRTC patterns will allow us to compare measures of brain cortical balance of excitation and inhibition in OCD and MDD, which will be useful in the area of differential diagnosis. In this study, we used the 64-channel resting state EEG of 29 MDD participants, 26 OCD participants, and a control group of 37 volunteers. Detrended fluctuation analyzes was used to assess LRTC. Our results indicate that all scaling exponents of the three subject groups exhibited persistent LRTC of EEG oscillations. There was a tendency for LRTC to be higher in disorders than in controls, but statistically significant differences were found between the OCD and control groups in the entire frontal and left parietal occipital areas, and between the MDD and OCD groups in the middle and right frontal areas. We believe that these results indicate abnormalities in the inhibitory and excitatory neurotransmitter systems, predominantly affecting areas related to executive functions.

A deep learning-based Monte Carlo simulation scheme for stochastic differential equations driven by fractional Brownian motion

Stochastic differential equations (SDEs) are widely used models to describe the evolution of stochastic processes. Among them, SDEs driven by fractional Brownian motion (fBm) have been shown to be capable of describing systems with temporal dependencies. In this paper, we develop a neural network based Monte Carlo methodology in which we can efficiently simulate SDEs that are governed by fBm. Particularly, we focus on large time step simulations. A property of fBm that complicates the development of such Monte Carlo schemes is the long-range temporal correlation. To this end, we build the network based on the encoder–decoder framework and employ the attention mechanism to learn the temporal relationships in the historical paths of such SDEs. In addition, a loss function based on the quantile loss is used, where the quantile levels to be predicted are determined by means of the stochastic collocation method. Experimental results show that this kind of loss function is superior to conventional loss functions in terms of solution accuracy, and the resulting scheme can learn and simulate SDEs driven by fBm accurately and highly efficiently.

Dynamical Attention Hypergraph Convolutional Network for Group Activity Recognition.

Recently, group activity recognition (GAR) has drawn growing interests in video analysis and computer vision communities. The current models of GAR tasks are often impractical in that they suppose that all interactions between actors are pairwise, which only models and leverages part of the information in real entire interactions. Motivated by this, we design a distinct dynamical attention hypergraph convolutional network framework, referred to as DAHGCN, for precise GAR, modeling the entire interactions and capturing the high-order relationships among involved actors in a real-life scenario. Specifically, to learn complementary feature representations for fine-grained GAR, a multilevel feature descriptor (MLFD) module is proposed. Furthermore, for learning higher order interaction relationships, we construct a DAHGCN to accommodate complex group interactions, which can dynamically change the topology of the hypergraph and learn these key representations by virtue of the "similarity-based shared nearest-neighbor (SSNN) clustering" and "attention mechanisms" on hypergraph. Finally, a multiscale temporal convolution (MSTC) module is utilized to explore various long-range temporal dynamic correlations across different frames. In addition, comprehensive experiments on three commonly used GAR datasets clearly demonstrate that, when compared with the state-of-the-art methods, our proposed method can achieve the most optimal performance.

Decreased long-range temporal correlations in the resting-state functional magnetic resonance imaging blood-oxygen-level-dependent signal reflect motor sequence learning up to 2 weeks following training.

Decreased long-range temporal correlations (LRTC) in brain signals can be used to measure cognitive effort during task execution. Here, we examined how learning a motor sequence affects long-range temporal memory within resting-state functional magnetic resonance imaging signal. Using the Hurst exponent (HE), we estimated voxel-wise LRTC and assessed changes over 5 consecutive days of training, followed by a retention scan 12 days later. The experimental group learned a complex visuomotor sequence while a complementary control group performed tightly matched movements. An interaction analysis revealed that HE decreases were specific to the complex sequence and occurred in well-known motor sequence learning associated regions including left supplementary motor area, left premotor cortex, left M1, left pars opercularis, bilateral thalamus, and right striatum. Five regions exhibited moderate to strong negative correlations with overall behavioral performance improvements. Following learning, HE values returned to pretraining levels in some regions, whereas in others, they remained decreased even 2 weeks after training. Our study presents new evidence of HE's possible relevance for functional plasticity during the resting-state and suggests that a cortical subset of sequence-specific regions may continue to represent a functional signature of learning reflected in decreased long-range temporal dependence after a period of inactivity.

Prenatal experience with language shapes the brain.

Human infants acquire language with notable ease compared to adults, but the neural basis of their remarkable brain plasticity for language remains little understood. Applying a scaling analysis of neural oscillations to address this question, we show that newborns' electrophysiological activity exhibits increased long-range temporal correlations after stimulation with speech, particularly in the prenatally heard language, indicating the early emergence of brain specialization for the native language.

Trend analysis in the presence of short- and long-range correlations with application to regional warming.

Many real-world time series exhibit both significant short- and long-range temporal correlations. Such correlations enhance the errors of linear trend analysis. In this paper, we provide a general framework for trend analysis under the consideration of such correlations. We propose a parsimonious model containing both a single short-range autoregressive parameter and long-range fractional parameter. We derive analytical closed-form results for the error bars of the least-squares estimate of the trend for such time series, highlighting the different effects of short- and of long-range correlations. We employ an ensemble method for the automated extraction of scaling regions to estimate the fractional parameter of the data model together with its error bar, and the Grünwald-Letnikov derivative for the identification of the autoregressive parameter. We apply this framework to the study of warming trends on gridded temperature data in central Europe. We make use of the redundancy of the trend signal in adjacent grid points using methods of spatial averaging and the first principal component of empirical orthogonal function analysis. We find good agreement between the results of these two methods. We find a statistically significant decadal warming trend in central Europe over the past 70 years, which shows a particularly dramatic increase over the past 20 years.