Wavelet Cross-coherence Research Articles

Pan-cortical electrophysiologic changes underlying attention

We previously reported that pan-cortical effects occur when cognitive tasks end afterdischarges. For this report, we analyzed wavelet cross-coherence changes during cognitive tasks used to terminate afterdischarges studying multiple time segments and multiple groups of inter-electrode-con distances. We studied 12 patients with intractable epilepsy, with 970 implanted electrode contacts, and 39,871 electrode contact combinations. When cognitive tasks ended afterdischarges, coherence varied similarly across the cortex throughout the tasks, but there were gradations with time, distance, and frequency: (1) They tended to progressively decrease relative to baseline with time and then to increase toward baseline when afterdischarges ended. (2) During most time segments, decreases from baseline were largest for the closest inter-contact distances, moderate for intermediate inter-contact distances, and smallest for the greatest inter-contact distances. With respect to our patients’ intractable epilepsy, the changes found suggest that future therapies might treat regions beyond those closest to regions of seizure onset and treat later in a seizure’s evolution. Similar considerations might apply to other disorders. Our findings also suggest that cognitive tasks can result in pan-cortical coherence changes that participate in underlying attention, perhaps complementing the better-known regional mechanisms.

Timing of cognitive effects on afterdischarge termination

ObjectiveWe previously studied efficacy of cognitive tasks on afterdischarge termination in patients undergoing cortical stimulation and found that diffuse wavelet cross-coherence changes on electrocorticography were associated with termination efficacy. We now report wavelet cross-coherence findings during different time segments of trials during which afterdischarges ended. MethodsFor 12 patients with implanted subdural electrodes, we compared wavelet cross-coherence findings among several 1-second portions of cognitive tasks, reflecting task presentation, patient replies, and afterdischarge termination. ResultsCoherence decreased significantly and progressively over time for 16.89, 22.53, and 30.03 Hz frequency ranges, but increased with afterdischarge termination. Coherence first increased, and then decreased for the 7.13 Hz frequency range. ConclusionsThe findings suggest that cumulative but non-specific factors, likely related primarily to attention, influence the coherence results throughout the task, with a separate effect due to resolution of the afterdischarges at the end. SignificanceTask performance is well known to localize to specific brain regions and to be restricted in timing. In contrast, attention and overall mental activation might be due to emergent properties of brain as a whole and that are less circumscribed in space or time. Cognitive tasks might modify seizures and other neurological disorders.

Epileptic-seizure onset detection using PARAFAC model with cross-wavelet transformation on multi-channel EEG.

Finding components from multi-channel EEG signal for localizing and detection of onset of seizure, is a new approach in biomedical signal analysis. Tensor-based approaches are utilized to fit the components into multi-dimensional arrays in recent works. We initially decompose EEG signals into Beta band using discrete wavelet transform (DWT). We compare patient templates with normal template for cross-wavelet analysis to obtain Wavelet cross spectrum (WCS) and Wavelet cross coherence coefficients. Next we apply parallel factorization (PARAFAC) modeling, a three-way tensor-based representation in channel, frequency and time-points dimensions on features. Finally, we utilize the ensemble classifier for detecting seizure-free, onset and seizure classes. The clinical dataset for this work comprises of 5 normal subjects and 6 epileptiform patients. The classification performances of WCS features on PARAFAC model for Seizure detection using Ensemble Bagged-Trees classifier obtains 82.21% accuracy, while for Wavelet Coherence features, it provides higher 84.76% accuracy. The results have been compared with well-known Fine Gaussian SVM, Weighted KNN and Ensemble Subspace KNN classifiers. The aim is to analyze data over three dimensions namely, time, frequency and space (channels). This EEG based analysis is significant and effective as an automatic method for detection of seizure before its actual manifestation.

Pan-cortical coordination underlying mental effort

ObjectiveIt is well known that activity in, or coordination among, brain regions, can underlie movement, sensation, language, and cognition but there are observations that tasks unrelated to specific brain regions can nonetheless alter activity in those regions. These tasks might invoke activity in multiregional networks, but it also is possible that they are associated with changes beyond these networks. We therefore evaluated the possibility that more widespread, or even whole-cortical, mechanisms might complement or alter focal or multifocal cortical activity. MethodsWe assessed the extent of electroencephalographic changes occurring outside areas with epileptiform activity, but that were associated with termination of the epileptiform activity. To do this, we measured the distribution of wavelet cross-coherence changes based on electrocorticography from 15 patients who showed regional afterdischarges in response to electrical brain stimulation prior to epilepsy surgery and in whom cognitive tasks were used in attempts to end the afterdischarges. There were 1276 electrodes implanted in these patients, and we analyzed a total of 55,494 electrode combinations. We compared recordings when cognitive effort was versus when it was not successful in ending afterdischarges. ResultsWe found that when afterdischarges were suppressed there were changes in electrocorticographic coherence that were similar throughout cortex, regardless of the distance between sites. ConclusionsThe similarity implies coordination of the changes, and the similarity regardless of distance or location implies a pan-cortical effect. SignificanceOur results provide physical support for hypotheses that pan-cortical processes complement the well-known regional and multiregional networks. These processes may participate in, be recruited by, modify, or underlie the conative experiences of waking life.

Temperature and pressure variability in mid-latitude low atmosphere and stratosphere-ionosphere coupling

This study presents the continuation of our previous analysis of variations of atmospheric and space weather parameters above Iberian Peninsula along two years near the 24th solar cycle maximum. In the previous paper (Morozova et al., 2017) we mainly discussed the first mode of principal component analysis of tropospheric and lower stratospheric temperature and pressure fields, which was shown to be correlated with lower stratospheric ozone and anti-correlated with cosmic ray flux. Now we extend the investigation to the second mode, which suggests a coupling between the stratosphere and the ionosphere.This second mode, located in the low and middle stratosphere (and explaining ~7% of temperature and ~3% of geopotential height variations), showed to be statistically significantly correlated with variations of the middle stratosphere ozone content and anti-correlated with variations of ionospheric total electron content. Similar co-variability of these stratospheric and ionospheric parameters was also obtained with the wavelet cross-coherence analysis.To investigate the role of atmospheric circulation dynamics and the causal nature of the found correlations, we applied the convergent cross mapping (CCM) analysis to our series. Strong evidence for the stratosphere-ionosphere coupling were obtained for the winter 2012–2013 that is characterized by the easterly QBO phase (quasi-biennial oscillations of the direction of the stratospheric zonal winds) and a strong SSW (sudden stratospheric warming event). Further analysis (for the three-year time interval 2012–2015) hint that SSWs events play main role in emphasizing the stratosphere-ionosphere coupling.

Cognitive effort decreases beta, alpha, and theta coherence and ends afterdischarges in human brain

ObjectiveMental activation has been reported to modify the occurrence of epileptiform activity. We studied its effect on afterdischarges. MethodIn 15 patients with implanted electrodes we presented cognitive tasks when afterdischarges occurred. We developed a wavelet cross-coherence function to analyze the electrocorticography before and after the tasks and compared findings when cognitive tasks did or did not result in afterdischarge termination. Six patients returned for functional MRI (fMRI) testing, using similar tasks. ResultsCognitive tasks often could terminate afterdischarges when direct abortive stimulation could not. Wavelet cross-coherence analysis showed that, when afterdischarges stopped, there was decreased coherence throughout the brain in the 7.13–22.53 Hz frequency ranges (p values 0.008–0.034). This occurred a) regardless of whether an area activated on fMRI and b) regardless of whether there were afterdischarges in the area. ConclusionsIt is known that cognitive tasks can alter localized or network synchronization. Our results show that they can change activity throughout the brain. These changes in turn can terminate localized epileptiform activity. SignificanceCognitive tasks result in diffuse brain changes that can modify focal brain activity. Combined with a seizure detection device, cognitive activation might provide a non-invasive method of terminating or modifying seizures.

Multiscale Pressure-Balanced Structures in Three-dimensional Magnetohydrodynamic Turbulence

Abstract Observations of solar wind turbulence indicate the existence of multiscale pressure-balanced structures (PBSs) in the solar wind. In this work, we conduct a numerical simulation to investigate multiscale PBSs and in particular their formation in compressive magnetohydrodynamic turbulence. By the use of the higher-order Godunov code Athena, a driven compressible turbulence with an imposed uniform guide field is simulated. The simulation results show that both the magnetic pressure and the thermal pressure exhibit a turbulent spectrum with a Kolmogorov-like power law, and that in many regions of the simulation domain they are anticorrelated. The computed wavelet cross-coherence spectra of the magnetic pressure and the thermal pressure, as well as their space series, indicate the existence of multiscale PBSs, with the small PBSs being embedded in the large ones. These multiscale PBSs are likely to be related to the highly oblique-propagating slow-mode waves, as the traced multiscale PBS is found to be traveling in a certain direction at a speed consistent with that predicted theoretically for a slow-mode wave propagating in the same direction.

Link of volcanic activity and climate change in Altai studied in the ice core from Belukha Mountain

In the present research we discuss a role of volcanic activity in Altai thermal regime. Here we analyses the sulfate and temperature data reconstructed from the natural paleoarchive – ice core from the Belukha Mountain saddle. Sulfate ice-core reconstructions can serve as volcanic markers. The both – sulfate and temperature reconstructions – are for the last 750 years. As the characteristic of volcanic activity we consider Volcanic Explosivity Index (VEI), Dust Veil Index (DVI) and Ice core volcanic index (IVI). The analysis was done using wavelet analysis and analysis of wavelet cross coherence and phase. As the result, we conclude that observed increases in the values of the indexes VEI, DVI, IVI basically correspond to decreases of temperature and increases of sulfate concentrations. This confirms the dependence of changes in the thermal regime of the Altai from volcanic activity. But in the 1750–1850 years period there is a delay of the changes in temperature with respect to the changes in volcanic activity. We suggest that it can be due to the superposition of the influence of solar and volcanic activity on changes in the thermal regime of Altai.

SMALL-SCALE PRESSURE-BALANCED STRUCTURES DRIVEN BY OBLIQUE SLOW MODE WAVES MEASURED IN THE SOLAR WIND

Recently, small-scale pressure-balanced structures (PBSs) were identified in the solar wind, but their formation mechanism remains unclear. This work aims to reveal the dependence of the properties of small-scale PBSs on the background magnetic field (B 0) direction and thus to corroborate the in situ mechanism that forms them. We analyze the plasma and magnetic field data obtained by WIND in the quiet solar wind at 1 AU. First, we use a developed moving-average method to obtain B 0(s, t) for every temporal scale (s) at each time moment (t). By wavelet cross-coherence analysis, we obtain the correlation coefficients between the thermal pressure P th and the magnetic pressure P B, distributing against the temporal scale and the angle θxB between B 0(s, t) and Geocentric Solar Ecliptic coordinates (GSE)-x. We note that the angle coverage of a PBS decreases with shorter temporal scale, but the occurrence of the PBSs is independent of θxB. Suspecting that the isolated small PBSs are formed by compressive waves in situ, we continue this study by testing the wave modes forming a small-scale PBS with B 0(s, t) quasi-parallel to GSE-x. As a result, we identify that the cross-helicity and the compressibility attain values for a slow mode from theoretical calculations. The wave vector is derived from minimum variance analysis. Besides, the proton temperatures obey T ⊥ < T ∥ derived from the velocity distribution functions, excluding a mirror mode, which is the other candidate for the formation of PBSs in situ. Thus, a small-scale PBS is shown to be driven by oblique, slow-mode waves in the solar wind.

External forcing on air–surface temperature: Geographical distribution of sensitive climate zones

In this paper we analyze the geographical distribution of the climate response to external forcing (solar, volcanic and geomagnetic) on the periods of 11 and 22 years. As a climate characteristic we use the data of the air–surface temperature (regional data sets). The analysis is performed by the wavelet phase/coherence technique which is applied to the solar (sunspot numbers), volcanic (Dust Veil Index), geomagnetic (C9-index) activities and the temperature data on interannual timescales for the common time interval covering most of the 20th century. Besides, we analyze the statistics of the temperature response to the solar and geomagnetic factors on the periods of 11 and 22 years for different geographical sectors. In particular, we find the existence of a combined forcing of solar and volcanic activity on the Earth temperature on the 11-year period in the second half of the 20th century over the globe, whereas a set of stations (mostly in North Atlantic) shows a coherence between solar activity and the Earth temperature on the 11-year periodicity even in absence of the combined effect; it was found that the maximal number of stations demonstrating statistically significant amplitudes of wavelet spectra corresponds to the wavelet cross-coherence between geomagnetic activity and the Earth air–surface temperature on the periods about 22 years during the time interval without intensive volcanic eruptions capable to change significantly the level of DVIGlobal.

Multi-scale pressure-balanced structures in the solar wind observed by WIND

This work detects multi-scale, from hour to seconds, pressure-balanced structures (PBSs) in the solar wind based on the anti-correlation between the plasma thermal pressure and the magnetic pressure measured by WIND at 1 AU on April 5th, 2001. In our former research based on Cluster measurements, we showed the anti-correlation between the electron density and the magnetic field strength in multi-scales, and we supposed these structures may be pressure-balanced structures. Thus, in this work we aim to prove our speculation by the direct evidence on pressure measurements. Different from our previous work, we apply the WIND measurements this time, for they have both the magnetic pressure and the plasma pressure which Cluster could not offer. We use the wavelet cross-coherence method to analyze the correlation between the plasma pressure (Pth) and the magnetic pressure (PB), and also the electron density (Ne) and the magnetic field strength (B) on various scales. We observe the anti-correlation between Pth and PB distributed at different temporal scales ranging from 1000 s down to 10 s. This result directly indicates the existence of pressure-balanced structures (PBSs) with different sizes in the solar wind. Further, We compare the wavelet cross correlation spectrum of Pth-PB and Ne-B. We notice that the two spectra are similar in general. Thus this result confirms that the relation between Pth-PB and Ne-B are consistent with each other in the PBSs we study. Moreover, we compare the power spectrum density (PSD) of relative Ne fluctuation with our previous work based on Cluster measurements. The two spectra show similar trend with Komolgorov’s −5/3 as their slopes. This may imply the similarity of the structures observed by both WIND and Cluster spacecrafts. Finally, we discuss the possible formation mechanisms for these multi-scale pressure-balanced structures. Our result is important to support the existence of multi-scale PBSs from one-hour scale down to one-minute, and is helpful to understand the role of compressive fluctuation in the solar wind turbulence dominated by Alfveenic cascading.

MULTI-SCALE ANTI-CORRELATION BETWEEN ELECTRON DENSITY AND MAGNETIC FIELD STRENGTH IN THE SOLAR WIND

This work focuses on the relation between the electron density and the magnetic field strength in the solar wind, and aims to reveal its compressive nature and to determine the level of compressibility. For this purpose, we choose a period of quiet solar wind data obtained at 1 AU by the Cluster C1 satellite. The electron density is derived with a sampling time as high as 0.2 s from the spacecraft-potential measurements made by the Electric Field and Waves instrument. We use the wavelet cross-coherence method to analyze the correlation between the electron density and the magnetic field strength on various scales. We find a dominant anti-correlation between them at different timescales ranging from 1000 s down to 10 s, a result which has never been reported before. This may indicate the existence of pressure-balanced structures (PBSs) with different sizes in the solar wind. The small (mini) PBSs appear to be embedded in the large PBSs, without affecting the pressure balance between the large structures. Thus, a nesting of these possible multi-scale PBSs is found. Moreover, we find for the first time that the relative fluctuation spectra of both the electron number density and the magnetic field strength look almost the same in the range from 0.01 Hz to 2.5 Hz, implying a similar cascading for these two types of fluctuations. Probable formation mechanisms for the multi-scale possible PBSs are discussed. The results of our work are believed to be helpful for understanding the compressive nature of solar wind turbulence as well as the connections between the solar wind streams and their coronal sources.

Wavelet cross-correlation analysis of wind speed series generated by ANN based models

To obtain, over medium term periods, wind speed time series on a site, located in the southern part of the Paris region (France), where long recording are not available, but where nearby meteorological stations provide large series of data, use was made of ANN based models. The performance of these models have been evaluated by using several commonly used statistics such as average absolute error, root mean square error, normalized mean square error, and correlation coefficient. Such global criteria are good indicators of the “robustness” of the models but are unable to provide useful information about their “effectiveness” in accurately generating wind speed fluctuations over a wide range of scales. Therefore a complementary wavelet cross coherence analysis has been performed. Wavelet cross coherence, wavelet cross-correlation and spectral wavelet cross-correlation coefficients, have been calculated and displayed as functions of the equivalent Fourier period. These coefficients provide quantitative measures of the scale-dependence of the model performance. In particular the spectral wavelet cross coherence coefficient can be used to have a rapid and efficient identification of the validity range of the models. The results show that the ANN models employed in this study are only effective in computing large-scale fluctuations of large amplitude. To obtain a more representative time series, with much higher resolution, small-scale fluctuations have to be simulated by a superimposed statistical model. By combining ANN and statistical models, both the high and the low-frequency segments of the wind velocity spectra can be simulated, over a range of several hours, at the target site.