The cross-frequency mediation mechanism of intracortical information transactions

In a seminal paper by von Stein and Sarnthein (2000), it was hypothesized that "bottom-up" information processing of "content" elicits local, high frequency (beta-gamma) oscillations, whereas "top-down" processing is "contextual", characterized by large scale integration spanning distant cortical regions, and implemented by slower frequency (theta-alpha) oscillations. This corresponds to a mechanism of cortical information transactions, where synchronization of beta-gamma oscillations between distant cortical regions is mediated by widespread theta-alpha oscillations. It is the aim of this paper to express this hypothesis quantitatively, in terms of a model that will allow testing this type of information transaction mechanism. The basic methodology used here corresponds to statistical mediation analysis, originally developed by (Baron and Kenny 1986). We generalize the classical mediator model to the case of multivariate complex-valued data, consisting of the discrete Fourier transform coefficients of signals of electric neuronal activity, at different frequencies, and at different cortical locations. The "mediation effect" is quantified here in a novel way, as the product of "dual frequency RV-coupling coefficients", that were introduced in (Pascual-Marqui et al 2016, http://arxiv.org/abs/1603.05343). Relevant statistical procedures are presented for testing the cross-frequency mediation mechanism in general, and in particular for testing the von Stein & Sarnthein hypothesis.Comment: https://doi.org/10.1101/119362 licensed as CC-BY-NC-ND 4.0 International license: http://creativecommons.org/licenses/by-nc-nd/4.0

The Scale Invariant Wigner Spectrum Estimation of Gaussian Locally Self-Similar Processes

We study locally self-similar processes (LSSPs) in Silverman's sense. By deriving the minimum mean-square optimal kernel within Cohen's class counterpart of time-frequency representations, we obtain an optimal estimation for the scale invariant Wigner spectrum (SIWS) of Gaussian LSSPs. The class of estimators is completely characterized in terms of kernels, so the optimal kernel minimizes the mean-square error of the estimation. We obtain the SIWS estimation for two cases: global and local, where in the local case, the kernel is allowed to vary with time and frequency. We also introduce two generalizations of LSSPs: the locally self-similar chrip process and the multicomponent locally self-similar process, and obtain their optimal kernels. Finally, the performance and accuracy of the estimation is studied via simulation.Comment: 28 page

Multi-taper S-transform method for estimating Wigner-Ville and Loève spectra of quasi-stationary harmonizable processes

Current non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to overestimation and ambiguity of structural responses. The quasi-stationary harmonizable process with its Wigner-Ville spectrum (WVS) and Loève spectrum, which do not suffer from the deficiencies of EPSD, is suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, the multi-taper S-transform (MTST) method for estimating WVS and Loève spectrum of multi-variate quasi-stationary harmonizable processes is presented. The analytical biases and variances of the WVS, Loève spectrum, and time-invariant and time-varying coherence estimators from the MTST method are provided under the assumption that the target multi-variate harmonizable process is Gaussian. Using a numerical case of a bivariate harmonizable wind speed process, the superiority and reliability of the MTST method are demonstrated through comparisons with several existing methods for the WVS and Loève spectrum estimations. Finally, the MTST method is applied to two pieces of ground motion acceleration records measured during the Turkey earthquake in 2023

A Statistical Study of Wavelet Coherence for Stationary and Nonstationary Processes

The coherence function measures the correlation between a pair of random processes in the frequency domain. It is a well studied and understood concept, and the distributional properties of conventional coherence estimators for stationary processes have been derived and applied in a number of physical settings. In recent years the wavelet coherence measure has been used to analyse correlations between a pair of processes in the time-scale domain, typically in hypothesis testing scenarios, but it has proven resistant to analytic study with resort to simulations for statistical properties. As part of the null hypothesis being tested, such simulations invariably assume joint stationarity of the series. In this thesis two methods of calculating wavelet coherence have been developed and distributional properties of the wavelet coherence estimators have been fully derived. With the first method, in an analogous framework to multitapering, wavelet coherence is estimated using multiple orthogonal Morse wavelets. The second coherence estimator proposed uses time-domain smoothing and a single Morlet wavelet. Since both sets of wavelets are complex-valued, we consider the case of wavelet coherence calculated from discrete-time complex-valued and stationary time series. Under Gaussianity, the Goodman distribution is shown, for large samples, to be appropriate for wavelet coherence. The true wavelet coherence value is identified in terms of its frequency domain equivalent and degrees of freedom can be readily derived. The theoretical results are verified via simulations. The notion of a spectral function is considered for the nonstationary case. Particular focus is given to Priestley’s evolutionary process and a Wold-Cramér nonstationary representation where time-varying spectral functions can be clearly defined. Methods of estimating these spectra are discussed, including the continuous wavelet transform, which when performed with a Morlet wavelet and temporal smoothing is shown to bear close resemblance to Priestley’s own estimation procedure. The concept of coherence for bivariate evolutionary nonstationary processes is discussed in detail. In such situations it can be shown that the coherence function, as in the stationary case, is invariant of time. It is shown that for spectra that vary slowly in time the derived statistics of the temporally smoothed wavelet coherence estimator are appropriate. Further to this the similarities with Priestleys spectral estimator are exploited to derive distributional properties of the corresponding Priestley coherence estimator. A well known class of the evolutionary and Wold-Cramér nonstationary processes are the modulated stationary processes. Using these it is shown that bivariate processes can be constructed that exhibit coherence variation with time, frequency, and time-and-frequency. The temporally smoothed Morlet wavelet coherence estimator is applied to these processes. It is shown that accurate coherence estimates can be achieved for each type of coherence, and that the distributional properties derived under stationarity are applicable

The dual frequency RV-coupling coefficient: a novel measure for quantifying cross-frequency information transactions in the brain

Identifying dynamic transactions between brain regions has become increasingly important. Measurements within and across brain structures, demonstrating the occurrence of bursts of beta/gamma oscillations only during one specific phase of each theta/alpha cycle, have motivated the need to advance beyond linear and stationary time series models. Here we offer a novel measure, namely, the "dual frequency RV-coupling coefficient", for assessing different types of frequency-frequency interactions that subserve information flow in the brain. This is a measure of coherence between two complex-valued vectors, consisting of the set of Fourier coefficients for two different frequency bands, within or across two brain regions. RV-coupling is expressed in terms of instantaneous and lagged components. Furthermore, by using normalized Fourier coefficients (unit modulus), phase-type couplings can also be measured. The dual frequency RV-coupling coefficient is based on previous work: the second order bispectrum, i.e. the dual-frequency coherence (Thomson 1982; Haykin & Thomson 1998); the RV-coefficient (Escoufier 1973); Gorrostieta et al (2012); and Pascual-Marqui et al (2011). This paper presents the new measure, and outlines relevant statistical tests. The novel aspects of the "dual frequency RV-coupling coefficient" are: (1) it can be applied to two multivariate time series; (2) the method is not limited to single discrete frequencies, and in addition, the frequency bands are treated by means of appropriate multivariate statistical methodology; (3) the method makes use of a novel generalization of the RV-coefficient for complex-valued multivariate data; (4) real and imaginary covariance contributions to the RV-coherence are obtained, allowing the definition of a "lagged-coupling" measure that is minimally affected by the low spatial resolution of estimated cortical electric neuronal activity.Comment: technical report, pre-print, 2016-03-1

Spectral analysis of stationary random bivariate signals

A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as complex-valued sequences. This makes possible the definition of a scalar quaternion-valued spectral density for bivariate signals. This spectral density can be meaningfully interpreted in terms of frequency-dependent polarization attributes. A natural decomposition of any random bivariate signal in terms of unpolarized and polarized components is introduced. Nonparametric spectral density estimation is investigated, and we introduce the polarization periodogram of a random bivariate signal. Numerical experiments support our theoretical analysis, illustrating the relevance of the approach on synthetic data.Comment: 11 pages, 3 figure

High-Q spectral peaks and nonstationarity in the deep ocean infragravity wave band: Tidal harmonics and solar normal modes

Author Posting. © American Geophysical Union, 2019. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research-Oceans 124(3), (2019):2072-2087, doi:10.1029/2018JC014586.Infragravity waves have received the least study of any class of waves in the deep ocean. This paper analyzes a 389‐day‐long deep ocean pressure record from the Hawaii Ocean Mixing Experiment for the presence of narrowband (≲2 μHz) components and nonstationarity over 400–4,000 μHz using a combination of fitting a mixture noncentral/central χ2 model to spectral estimates, high‐resolution multitaper spectral estimation, and computation of the offset coherence between distinct frequencies for a given data segment. In the frequency band 400–1,000 μHz there is a noncentral fraction of 0.67 ± 0.07 that decreases with increasing frequency. Evidence is presented for the presence of tidal harmonics in the data over the 400‐ to 1,400‐μHz bands. Above ~2,000 μHz the noncentral fraction rises with frequency, comprising about one third of the spectral estimates over 3,000–4,000 μHz. The power spectrum exhibits frequent narrowband peaks at 6–11 standard deviations above the noise level. The widths of the peaks correspond to a Q of at least 1,000, vastly exceeding that of any oceanic or atmospheric process. The offset coherence shows that the spectral peaks have substantial (p = 0.99–0.9999) interfrequency correlation, both locally and between distinct peaks within a given analysis band. Many of the peak frequencies correspond to the known values for solar pressure modes that have previously been observed in solar wind and terrestrial data, while others are the result of nonstationarity that distributes power across frequency. Overall, this paper documents the existence of two previously unrecognized sources of infragravity wave variability in the deep ocean.This work was supported at WHOI by an Independent Research and Development award and the Walter A. and Hope Noyes Smith Chair for Excellence in Oceanography. At the University of Hawaii, Martin Guiles provided a number of consequential data analyses, and work was supported by NSF‐OCE1460022. D. J. T. acknowledges support from Queen's University and NSERC. The data used in this study are available from the supporting information.2019-08-2