Long-range temporal correlations of broadband EEG oscillations for depressed subjects following different hemispheric cerebral infarction

Abnormal long-range temporal correlation (LRTC) in EEG oscillation has been observed in several brain pathologies and mental disorders. This study examined the relationship between the LRTC of broadband EEG oscillation and depression following cerebral infarction with different hemispheric lesions to provide a novel insight into such depressive disorders. Resting EEGs of 16 channels in 18 depressed (9 left and 9 right lesions) and 21 non-depressed (11 left and 10 right lesions) subjects following cerebral infarction and 19 healthy control subjects were analysed by means of detrended fluctuation analysis, a quantitative measurement of LRTC. The difference among groups and the correlation between the severity of depression and LRTC in EEG oscillation were investigated by statistical analysis. The results showed that LRTC of broadband EEG oscillations in depressive subjects was still preserved but attenuated in right hemispheric lesion subjects especially in left pre-frontal and right inferior frontal and posterior temporal regions. Moreover, an association between the severity of psychiatric symptoms and the attenuation of the LRTC was found in frontal, central and temporal regions for stroke subjects with right lesions. A high discriminating ability of the LRTC in the frontal and central regions to distinguish depressive from non-depressive subjects suggested potential feasibility for LRTC as an assessment indicator for depression following right hemispheric cerebral infarction. Different performance of temporal correlation in depressed subjects following the two hemispheric lesions implied complex association between depression and stroke lesion location.     

Long-range correlations in prokaryotic chromosomes

One of the fascinating properties of the DNA sequences of prokaryotic and eukaryotic chromosomes is that they possess long-range order. Computational methods like spectral analysis, mutual information and DNA random walks have been used to probe long-range order via-long range correlations. This work attempts to show the advantage of using the Information Theoretic measure of mutual information for this purpose. A number Mu is found which indicates the existence of long-range order. Mu is the ratio between the value of mutual information function between two nucleotides of a DNA sequence separated by a large distance of 100 kilobases to the value expected from a randomized sequence of the same DNA. It is found that in spite of the constant shuffling of nucleotides due to insertion, deletion, inversion and recombination that occur during evolution, the chromosomal structure of prokaryotes is not always mosaic. While all archaeal chromosomes show mosaic structure and lack long-range order, a sizable fraction of the bacterial chromosomes do possess long-range order. A statistical multivariate analysis has been done to find which of the physical variables like genome size or GC% affects the organization of the chromosome or correlates with the long-range order. The existence of long-range order in bacterial chromosomes could be directly correlated to the degree of gene strand bias shown by it. Firmicutes which have low GC content also have pronounced strand bias and show long-range correlations. It is observed that the occurrence of long-range order in bacteria is independent of genome size, but depends on its GC content and gene strand bias.     

Long-range correlations in the helix free energy distribution in DNA

In this paper we explore the free energy distribution in the helical form of DNA using the genome of the virus Rickettsia prowazekii Madrid E as an example. The genome of this organism has been determined by Andersson et al. (Nature 396 (1998) 133) and is available on the World Wide Web (www.tigr.org). Using the helix statistical weights based on nearest-neighbor base pairs of SantaLucia (Proc. Natl. Acad. Sci. USA 95 (1998) 1460), we calculate the free energy in consecutive blocks of m base pairs in the DNA sequence and then construct the free energy distribution for these values. Using the maximum-entropy method we can fit the distribution curves with a function based on the moments of the distribution. For blocks containing 10-20 base pairs the distribution is slightly skewed and we require four moments to accurately fit the function. For blocks containing 100 base pairs or more, the distribution is well approximated by a Gaussian function based on the first two moments of the distribution. We find that the free energy distribution for m=20 can be reproduced using random sequences that have the local (singlet, doublet or triplet) statistics of Rickettsia. However, for much larger blocks, for example m=500, the width of the free energy distribution based on the actual Rickettsia genome is broader by almost a factor of 3 than the distributions based on random local statistics. We find that the distribution functions for the C or G content in blocks of m base pairs have almost the same behavior as a function of block size as do the free energy distributions. In order to duplicate the width of the distribution functions based on the actual Rickettsia sequence, we need to introduce tables (matrices) that correlate the states of consecutive blocks hundreds of base pairs long. This indicates that correlations on the order of the number of base pairs contained in the average gene are required to give the actual widths for either the C or G content or the helix free energy distributions. Above a certain m value, the distributions for larger m can be accurately expressed in terms of the distribution functions for smaller m. Thus, for example, the distribution for m=5000 can be expressed in terms of the generating function for m=1000.     

Long-range doublet correlations in DNA and the coding regions.

Long-range two-body correlations in a DNA sequence should in theory approach a constant value very rapidly with increasing value of the correlation length. It is shown that for most DNA sequences, the long-range correlations exhibit oscillations superimposed on the constant background. These oscillations persist for very large correlation lengths. The oscillations are shown to be three-point cycles and are related to the coding regions in the DNA. A method for discovering the coding regions in DNA sequences is presented. The limitations of the method are discussed.     

Long range temporal correlations in EEG oscillations of subclinically depressed individuals: their association with brooding and suppression

Long-range temporal correlations (LRTC) in brain oscillations have been found to be associated with depression severity in clinically depressed patients. Less is known, however, about the relationships between LRTC and proneness to engage in depression-related cognitive emotion regulation (ER) strategies which characterize both clinically and subclinically depressed (SBD) people. In this study we applied detrended fluctuation analysis to the amplitude envelope of broad band, theta band, and alpha band spontaneous EEG oscillations of a group of SBD individuals and a group of non-depressed individuals (both groups from a sample of healthy adults, N = 120), to whom brooding and thought suppression questionnaires were administered. Between-groups differences were not found for any band scaling exponents at any brain location, but linear correlations pointed out several associations between exponents at frontal, central, parietal, temporal, and occipital sites and maladaptive ER strategies. These results suggest that alterations in brain dynamics are related with the proneness that depressive individuals show to engage in brooding and thought suppression in order to cognitively regulate their emotions.     

Long-range spatial correlations in the turbulent edge plasma of the L-2M stellarator

Long-range spatial correlations in the turbulent plasma of the L-2M stellarator were revealed experimentally, and their relation to the geometry of magnetic surfaces was analyzed (Plasma Phys. Control. Fusion 50, 045001 (2008)). The operation modes of the facility in which fast transport transitions in plasma are possible were studied. Upon these transitions, the turbulence level is found to decrease substantially. It is shown that long-range spatial correlations are typical of relatively narrow frequency ranges. In particular, before a transport transition, such frequency ranges are f ～ 30–40 kHz and f ～ 1–3 kHz. After the transition, long-range spatial correlations in the frequency range of f ～ 30–40 kHz disappear due to a significant decrease in the turbulence level in this frequency range. At the same time, correlations in the low frequency range are retained and new correlations at frequencies of f ～ 6-12 kHz occur. It is found that global electromagnetic oscillations in the frequency range of f ～ 1–3 kHz are related to the m/n = 0/0 perturbation and its toroidal satellites (here, m and n are the poloidal and toroidal mode numbers, respectively). It is also shown that, after the transport transition, a three-dimensional localized electromagnetic mode at the frequency of the geodesic acoustic mode governed by the average magnetic field curvature is excited. At higher frequencies typical of a geodesic acoustic mode related to the three-dimensional curvature of the magnetic field, no long-range spatial correlations were observed both before and after the transport transition.     

The dynamic characteristics of the interhemispheric correlations of the EEG during the recovery of human neuropsychic activities

In patients (34 right-handed) in remote terms of cerebral trauma (CT) characteristics were studied of interhemispheric EEG correlations depending on lateralization of lesion in comparison with healthy subjects (20 right-handed). Disturbance of neuropsychic activity in patients with CT before treatment was accompanied by changes of interhemispheric asymmetry of conjunction in the form of a decrease of coherence values in the injured hemisphere; the decrease of conjunction values of symmetric cortical zones was determined by laterality of the lesion. After treatment the most effective restoration of neuropsychic activity and of interhemispheric EEG correlations was in patients in whose dynamics of the restoration process the stage of the right hemisphere activation was observed. This stage came earlier and restoration period was shorter in patients with the left hemisphere lesion.     

Long-range correlations improve understanding of the influence of network structure on contact dynamics

Models of infectious diseases are characterized by a phase transition between extinction and persistence. A challenge in contemporary epidemiology is to understand how the geometry of a host’s interaction network influences disease dynamics close to the critical point of such a transition. Here we address this challenge with the help of moment closures. Traditional moment closures, however, do not provide satisfactory predictions close to such critical points. We therefore introduce a new method for incorporating longer-range correlations into existing closures. Our method is technically simple, remains computationally tractable and significantly improves the approximation’s performance. Our extended closures thus provide an innovative tool for quantifying the influence of interaction networks on spatially or socially structured disease dynamics. In particular, we examine the effects of a network’s clustering coefficient, as well as of new geometrical measures, such as a network’s square clustering coefficients. We compare the relative performance of different closures from the literature, with or without our long-range extension. In this way, we demonstrate that the normalized version of the Bethe approximation-extended to incorporate long-range correlations according to our method-is an especially good candidate for studying influences of network structure. Our numerical results highlight the importance of the clustering coefficient and the square clustering coefficient for predicting disease dynamics at low and intermediate values of transmission rate, and demonstrate the significance of path redundancy for disease persistence.     

Long-range autocorrelations of CpG islands in the human genome

In this paper, we use a statistical estimator developed in astrophysics to study the distribution and organization of features of the human genome. Using the human reference sequence we quantify the global distribution of CpG islands (CGI) in each chromosome and demonstrate that the organization of the CGI across a chromosome is non-random, exhibits surprisingly long range correlations (10 Mb) and varies significantly among chromosomes. These correlations of CGI summarize functional properties of the genome that are not captured when considering variation in any particular separate (and local) feature. The demonstration of the proposed methods to quantify the organization of CGI in the human genome forms the basis of future studies. The most illuminating of these will assess the potential impact on phenotypic variation of inter-individual variation in the organization of the functional features of the genome within and among chromosomes, and among individuals for particular chromosomes.     

Long-range correlations between DNA bending sites: relation to the structure and dynamics of nucleosomes

It has been established that the precise positioning of nucleosomes on genomic DNA can be achieved, at least for a minority of them, through sequence-dependent processes. However, to what extent DNA sequences play a role in the positioning of the major part of nucleosomes is still debated. The aim of the present study is to examine to what extent long-range correlations (LRC) are related to the presence of nucleosomes. Using the wavelet transform technique, we perform a comparative analysis of the DNA text and of the corresponding bending profiles generated with curvature tables based on nucleosome positioning data. The exploration of a number of eukaryotic and bacterial genomes through the optics of the so-called "wavelet transform microscope" reveals a characteristic scale of 100-200 bp that separates two regimes of different LRC. Here, we focus on the existence of LRC in the small-scale regime (10-200 bp) which are actually observed in eukaryotic genomes, in contrast to their absence in eubacterial genomes. Analysis of viral DNA genomes shows that, like their host's genomes, eukaryotic viruses present LRC but eubacterial viruses do not. There is one exception for genomes of poxviruses (Vaccinia and Melamoplus sanguinipes) which do not replicate in the cell nucleus and do not exhibit LRC. No small-scale LRC are detected in the genomes of all examined RNA viruses, with the exception of retroviruses. These results together with the observation of LRC between particular sequence motifs known to participate in the formation of nucleosomes (e.g. AA dinucleotides) strongly suggest that the 10-200 bp LRC are a signature of the sequence-dependence of nucleosome positioning. Finally, we discuss possible interpretations of these LRC in terms of the physical mechanisms that might govern the positioning and the dynamics of the nucleosomes along the DNA chain through cooperative processes.     

Developmental changes of BOLD signal correlations with global human EEG power and synchronization during working memory

In humans, theta band (5-7 Hz) power typically increases when performing cognitively demanding working memory (WM) tasks, and simultaneous EEG-fMRI recordings have revealed an inverse relationship between theta power and the BOLD (blood oxygen level dependent) signal in the default mode network during WM. However, synchronization also plays a fundamental role in cognitive processing, and the level of theta and higher frequency band synchronization is modulated during WM. Yet, little is known about the link between BOLD, EEG power, and EEG synchronization during WM, and how these measures develop with human brain maturation or relate to behavioral changes. We examined EEG-BOLD signal correlations from 18 young adults and 15 school-aged children for age-dependent effects during a load-modulated Sternberg WM task. Frontal load (in-)dependent EEG theta power was significantly enhanced in children compared to adults, while adults showed stronger fMRI load effects. Children demonstrated a stronger negative correlation between global theta power and the BOLD signal in the default mode network relative to adults. Therefore, we conclude that theta power mediates the suppression of a task-irrelevant network. We further conclude that children suppress this network even more than adults, probably from an increased level of task-preparedness to compensate for not fully mature cognitive functions, reflected in lower response accuracy and increased reaction time. In contrast to power, correlations between instantaneous theta global field synchronization and the BOLD signal were exclusively positive in both age groups but only significant in adults in the frontal-parietal and posterior cingulate cortices. Furthermore, theta synchronization was weaker in children and was--in contrast to EEG power--positively correlated with response accuracy in both age groups. In summary we conclude that theta EEG-BOLD signal correlations differ between spectral power and synchronization and that these opposite correlations with different distributions undergo similar and significant neuronal developments with brain maturation.     

Dynamic processes in the human EEG

The possible mechanisms which determine the temporal dynamics of discrete narrow-band spectral components of human EEG recorded by a single electrode in the state of rest were analyzed. The dynamics of short-segment spectra was observed by application of Fast Fourier Transform (FFT) to 5-s EEG epochs successively shifted by 0.32 s. For each subject the matrices were formed and presented in a graphic mode. Matrix rows represented the number of points in each short-segment spectrum, and the columns represented the number of short-segment spectra. The columns reflect the amplitude dynamics of a given frequency, and power transition between the columns reflects the frequency dynamics. The most common type of the amplitude dynamics consisted in short (2-8 s) periods of stable activity of the discrete spectral components replaced by symmetrical bifurcation or confluence of spectral peaks. The obtained results suggest by the presence of both additive and multiplicative mechanisms of oscillatory interactions in the EEG. More detailed analysis of the amplitude-modulated EEG processes is provided by application of some additive features of the FFT to both EEG and computer-simulated signals.     

The spectral correlations of human brain electrical activity (the EEG) in the alpha-rhythm range occurring while performing latent inhibition]

Changes in perception of a stimulus and impairment of retrieval of memory trace resulted from the stimulus loss of novelty are called the latent inhibition (LI). The present study was undertaken to investigate the human LI using the analysis of changes in frequency power and coherence of the alpha rhythm. The results indicate that the loss of novelty of a stimulus is accompanied by a significant increase in the power of the upper alpha in the frontal regions of the right hemisphere and temporal regions of both hemispheres resulting in an impairment of memory retrieval in the frontal regions. Analysis of coherence changes revealed the reduction of interaction between the right temporal region and anteriofrontal, temporo-occipital, and right parietooccipital regions in response to administration of the conditioned words in comparison with the control ones. The findings suggest that the LI is a manifestation of the more general physiological process--the hidden inhibition.     

Extraction of reproducible seizure patterns based on EEG scalp correlations

The objective of this work is to identify similarities in the spatio-temporal dynamics of epileptic seizures, record with scalp EEG. A comprehensive method is proposed and applied in EEG of the patients who suffer from temporal lobe epilepsy. The method is based on the computation of the time-varying degree of non linear correlation between scalp electrodes at seizure onset and during seizure spread, determined by a nonlinear regression analysis. The quantification and coding of these similarity relations allow the comparison between two epileptic networks. Results show that reproducible patterns may be extracted from different seizures of the same patient and confirm the existence of different subtypes of temporal lobe epilepsy.     

Long-range physical mapping around the human steroid sulfatase locus

The region of the human X chromosome containing the steroid sulfatase locus was analyzed by pulsed-field gel electrophoresis. Restriction site maps were generated for the X chromosome in the blood of a normal male individual and that in the mouse-human hybrid cell line ThyB-X; these maps extend over approximately 4.3 Mb of DNA of the former, and 3.2 Mb of the latter. Physical linkage was defined between the STS locus and sequences detected by the probes GMGX9 (DXS237), GMGXY19 (DYS74), CRI-S232 (DXS278), and dic56 (DXS143), and the order telomere--(STS, DYS74)--DXS237--DXS278--DXS143--centromere was deduced. The pulsed-field maps were used to demonstrate a deletion of 180 kb of DNA from the X chromosome of an individual with X-linked ichthyosis. Also, possible locations for the Kallmann syndrome gene were revealed, and the distance between the steroid sulfatase locus and the pseudoautosomal region was estimated to be at least 4 Mb.