Long-range Temporal Correlations Research Articles

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.

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.

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.

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.

Abnormal spectral and scale-free properties of resting-state EEG in girls with Rett syndrome

Spontaneous EEG contains important information about neuronal network properties that is valuable for understanding different neurological and psychiatric conditions. Rett syndrome (RTT) is a rare neurodevelopmental disorder, caused by mutation in the MECP2 gene. RTT is characterized by severe motor impairments that prevent adequate assessment of cognitive functions. Here we probe EEG parameters obtained in no visual input condition from a 28-channels system in 23 patients with Rett Syndrome and 38 their typically developing peers aged 3–17 years old. Confirming previous results, RTT showed a fronto-central theta power (4–6.25 Hz) increase that correlates with a progression of the disease. Alpha power (6.75–11.75 Hz) across multiple regions was, on the contrary, decreased in RTT, also corresponding to general background slowing reported previously. Among novel results we found an increase in gamma power (31–39.5 Hz) across frontal, central and temporal electrodes, suggesting elevated excitation/inhibition ratio. Long-range temporal correlation measured by detrended fluctuation analysis within 6–13 Hz was also increased, pointing to a more predictable oscillation pattern in RTT. Overall measured EEG parameters allow to differentiate groups with high accuracy, ROC AUC value of 0.92 ± 0.08, indicating clinical relevance.

Brain criticality predicts individual levels of inter-areal synchronization in human electrophysiological data

Neuronal oscillations and their synchronization between brain areas are fundamental for healthy brain function. Yet, synchronization levels exhibit large inter-individual variability that is associated with behavioral variability. We test whether individual synchronization levels are predicted by individual brain states along an extended regime of critical-like dynamics – the Griffiths phase (GP). We use computational modelling to assess how synchronization is dependent on brain criticality indexed by long-range temporal correlations (LRTCs). We analyze LRTCs and synchronization of oscillations from resting-state magnetoencephalography and stereo-electroencephalography data. Synchronization and LRTCs are both positively linearly and quadratically correlated among healthy subjects, while in epileptogenic areas they are negatively linearly correlated. These results show that variability in synchronization levels is explained by the individual position along the GP with healthy brain areas operating in its subcritical and epileptogenic areas in its supercritical side. We suggest that the GP is fundamental for brain function allowing individual variability while retaining functional advantages of criticality.

Improved finite-difference and pseudospectral schemes for the Kardar–Parisi–Zhang equation with long-range temporal correlations

Improved finite-difference and pseudospectral schemes for the Kardar–Parisi–Zhang equation with long-range temporal correlations

Multiscale approaches to music and the embodied brain

A wide body of research is currently being devoted to investigating the multiscale processes across the brain and body, and the nature of their interactions. The purpose of this paper is to supplement these analyses of brain and body dynamics by providing a comprehensive account of the multiscale organisations also found in music, and ways in which these systems interact. We proceed in identifying scaling laws as a signature for multiscale features of a system and make the methodological choice of distinguishing 1) scale free structure from 2) scale free dynamics. We follow these distinctions in demonstrating how specifically i.) hierarchical temporal structures, ii.) long-range temporal correlations, and iii.) musical information as scale free structures relate to activity in the brain and body at various temporal or spatial scales during music perception and performance. Further, this is paralleled by fixing our focus to a limited choice of scale free dynamics, namely, iv.) resonance and entrainment, v.) power law distributions, and vi.) 1/f scaling. Though the ubiquitous scaling relations across musical activities, performance and music itself touch on the theme of universality, we outline how differing theoretical proposals concerning the relation between brain, body and musical environment arise in such contexts. Using these examples, we identify their overlap and divergence, and propose future directions for inquiry along these lines.

Temporary disruption in language processing reflected as multiscale temporal discoordination in a recurrent network

By juxtaposing time series analyses of activity measured from a fully recurrent network undergoing disrupted processing and of activity measured from a continuous meta-cognitive report of disruption in real-time language comprehension, we present an opportunity to compare the temporal statistics of the state-space trajectories inherent to both systems. Both the recurrent network and the human language comprehension process appear to exhibit long-range temporal correlations and low entropy when processing is undisrupted and coordinated. However, when processing is disrupted and discoordinated, they both exhibit more short-range temporal correlations and higher entropy. We conclude that by measuring human language comprehension in a dense-sampling manner similar to how we analyze the networks, and analyzing the resulting data stream with nonlinear time series analysis techniques, we can obtain more insight into the temporal character of these discoordination phases than by simply marking the points in time at which they peak.

Temporary disruption in language processing reflected as multiscale temporal discoordination in a recurrent network

By juxtaposing time series analyses of activity measured from a fully recurrent network undergoing disrupted processing and of activity measured from a continuous meta-cognitive report of disruption in real-time language comprehension, we present an opportunity to compare the temporal statistics of the state-space trajectories inherent to both systems. Both the recurrent network and the human language comprehension process appear to exhibit long-range temporal correlations and low entropy when processing is undisrupted and coordinated. However, when processing is disrupted and discoordinated, they both exhibit more short-range temporal correlations and higher entropy. We conclude that by measuring human language comprehension in a dense-sampling manner similar to how we analyze the networks, and analyzing the resulting data stream with nonlinear time series analysis techniques, we can obtain more insight into the temporal character of these discoordination phases than by simply marking the points in time at which they peak.

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).

Diagnosing the benign paroxysmal positional vertigo via 1D and deep-learning composite model.

Benign Paroxysmal Positional Vertigo (BPPV) is the leading cause of vertigo, and its characteristic nystagmus induced by positional maneuvers makes it a good model for Artificial Intelligence (AI) diagnosis. However, during the testing procedure, up to 10min of indivisible long-range temporal correlation data are produced, making the AI-informed real-time diagnosing unlikely in clinical practice. A combined 1D and Deep-Learning (DL) composite model was proposed. Two separate cohorts were recruited, with one for model generation and the other for evaluation of model's real-world generalizability. Eight features, including two head traces and three eye traces and their corresponding slow phase velocity (SPV) value, were served as the inputs. Three candidate models were tested, and a sensitivity study was conducted to determine the saliently important features. The study included 2671 patients in the training cohort and 703 in the test cohort. A hybrid DL model achieved a micro-area under the receiver operating curve (AUROC) of 0.982 (95% CI 0.965, 0.994) and macro-AUROC of 0.965 (95% CI 0.898, 0.999) for overall classification. The highest accuracy was observed for right posterior BPPV, with an AUROC of 0.991 (95% CI 0.972, 1.000), followed by left posterior BPPV, with an AUROC of 0.979 (95% CI 0.940, 0.998), the lowest AUROC was 0.928 (95% CI 0.878, 0.966) for lateral BPPV. The SPV was consistently identified as the most predictive feature in the models. If the model process is carried out 100 times for a 10-min data, one single running takes 0.79 ± 0.06s. This study designed DL models which can accurately detect and categorize the subtype of BPPV, enabling a quick and straightforward diagnosis of BPPV in clinical setting. The critical feature identified in the model helps expand our understanding of this disorder.

Genuine multifractality in time series is due to temporal correlations.

Based on the mathematical arguments formulated within the multifractal detrended fluctuation analysis (MFDFA) approach it is shown that, in the uncorrelated time series from the Gaussian basin of attraction, the effects resembling multifractality asymptotically disappear for positive moments when the length of time series increases. A hint is given that this applies to the negative moments as well and extends to the Lévy stable regime of fluctuations. The related effects are also illustrated and confirmed by numerical simulations. This documents that the genuine multifractality in time series may only result from the long-range temporal correlations, and the fatter distribution tails of fluctuations may broaden the width of the singularity spectrum only when such correlations are present. The frequently asked question of what makes multifractality in time series-temporal correlations or broad distribution tails-is thus ill posed. In the absence of correlations only the bifractal or monofractal cases are possible. The former corresponds to the Lévy stable regime of fluctuations while the latter to the ones belonging to the Gaussian basin of attraction in the sense of the central limit theorem.

Transformer-Based Self-Supervised Monocular Depth and Visual Odometry

Self-supervised monocular depth and visual odometry (VO) are often cast as coupled tasks. Accurate depth contributes to precise pose estimation and vice versa. Existing architectures typically exploit stacking convolution layers and long short-term memory (LSTM) units to capture long-range dependencies. However, their intrinsic locality hinders the model from getting the expected performance gain. In this article, we propose a Transformer-based architecture, named Transformer-based self-supervised monocular depth and VO (TSSM-VO), to tackle these problems. It comprises two main components: 1) a depth generator that leverages the powerful capability of multihead self-attention (MHSA) on modeling long-range spatial dependencies and 2) a pose estimator built upon a Transformer to learn long-range temporal correlations of image sequences. Moreover, a new data augmentation loss based on structural similarity (SSIM) is introduced to constrain further the structural similarity between the augmented depth and the augmented predicted depth. Rigorous ablation studies and exhaustive performance comparison on the KITTI and Make3D datasets demonstrate the superiority of TSSM-VO over other self-supervised methods. We expect that TSSM-VO would enhance the ability of intelligent agents to understand the surrounding environments.

Scale-Free Dynamics in Instantaneous Alpha Frequency Fluctuations: Validation, Test-Retest Reliability and Its Relationship with Task Manipulations.

Previous studies showed that scale-free structures and long-range temporal correlations are ubiquitous in physiological signals (e.g., electroencephalography). This is supposed to be associated with optimized information processing in human brain. The instantaneous alpha frequency (IAF) (i.e., the instantaneous frequency of alpha band of human EEG signals) may dictate the resolution at which information is sampled and/or processed by cortical neurons. To the best of our knowledge, no research has examined the scale-free dynamics and potential functional significance of IAF. Here, through three studies (Study 1: 25 participants; Study 2: 82 participants; Study 3: 26 participants), we investigated the possibility that time series of IAF exhibit scale-free property through maximum likelihood based detrended fluctuation analysis (ML-DFA). This technique could provide the scaling exponent (i.e., DFA exponent) on the basis of presence of scale-freeness being validated. Then the test-retest reliability (Study 1) and potential influencing factors (Study 2 and Study 3) of DFA exponent of IAF fluctuations were investigated. Firstly, the scale-free property was found to be inherent in IAF fluctuations with fairly high test-retest reliability over the parietal-occipital region. Moreover, the task manipulations could potentially modulate the DFA exponent of IAF fluctuations. Specifically, in Study 2, we found that the DFA exponent of IAF fluctuations in eye-closed resting-state condition was significantly larger than that in eye-open resting-state condition. In Study 3, we found that the DFA exponent of IAF fluctuations in eye-open resting-state condition was significantly larger than that in visual n-back tasks. The DFA exponent of IAF fluctuations in the 0-back task was significantly larger than in the 2-back and 3-back tasks. The results in studies 2 and 3 indicated that: (1) a smaller DFA exponent of IAF fluctuations should signify more efficient online visual information processing; (2) the scaling property of IAF fluctuations could reflect the physiological arousal level of participants.

Realizing avalanche criticality in neuromorphic networks on a 2D hBN platform.

Networks and systems which exhibit brain-like behavior can analyze information from intrinsically noisy and unstructured data with very low power consumption. Such characteristics arise due to the critical nature and complex interconnectivity of the brain and its neuronal network. We demonstrate a system comprising of multilayer hexagonal boron nitride (hBN) films contacted with silver (Ag), which can uniquely host two different self-assembled networks, which are self-organized at criticality (SOC). This system shows bipolar resistive switching between the high resistance state (HRS) and the low resistance state (LRS). In the HRS, Ag clusters (nodes) intercalate in the van der Waals gaps of hBN forming a network of tunnel junctions, whereas the LRS contains a network of Ag filaments. The temporal avalanche dynamics in both these states exhibit power-law scaling, long-range temporal correlation, and SOC. These networks can be tuned from one to another with voltage as a control parameter. For the first time, two different neural networks are realized in a single CMOS compatible, 2D material platform.