Perspectives of Non-Gaussianity in Atmospheric Synoptic and Low-Frequency Variability

Abstract Understanding non-Gaussian statistics of atmospheric synoptic and low-frequency variability has important consequences in the atmospheric sciences, not least because weather and climate risk assessment depends on knowing and understanding the exact shape of the system’s probability density function. While there is no doubt that many atmospheric variables exhibit non-Gaussian statistics on many time (and spatial) scales, a full and complete understanding of this phenomenon remains a challenge. Various mechanisms behind the observed atmospheric non-Gaussian statistics have been proposed but remain, however, multifaceted and scattered in the literature: nonlinear dynamics, multiplicative noise, cross-frequency coupling, nonlinear boundary layer drag, and others. Given the importance of this subject for weather and climate research, and in an attempt to contribute to this topic, a thorough review and discussion of the different mechanisms that lead to non-Gaussian weather and climate variability are presented in this paper and an outlook is given.

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Signature patterns for top-down and bottom-up information processing via cross-frequency coupling in macaque auditory cortex

10.1101/403980 ◽

2018 ◽

Author(s):

Christian D. Márton ◽

Makoto Fukushima ◽

Corrie R. Camalier ◽

Simon R. Schultz ◽

Bruno B. Averbeck

Keyword(s):

Information Processing ◽

Auditory Cortex ◽

Predictive Coding ◽

Low Frequency ◽

Information Need ◽

Top Down ◽

Bottom Up ◽

Low Frequencies ◽

Frequency Coupling ◽

Cross Frequency Coupling

AbstractPredictive coding is a theoretical framework that provides a functional interpretation of top-down and bottom up interactions in sensory processing. The theory has suggested that specific frequency bands relay bottom-up and top-down information (e.g. “γ up, β down”). But it remains unclear whether this notion generalizes to cross-frequency interactions. Furthermore, most of the evidence so far comes from visual pathways. Here we examined cross-frequency coupling across four sectors of the auditory hierarchy in the macaque. We computed two measures of cross-frequency coupling, phase-amplitude coupling (PAC) and amplitude-amplitude coupling (AAC). Our findings revealed distinct patterns for bottom-up and top-down information processing among cross-frequency interactions. Both top-down and bottom-up made prominent use of low frequencies: low-to-low frequency (θ, α, β) and low frequency-to-high γ couplings were predominant top-down, while low frequency-to-low γ couplings were predominant bottom-up. These patterns were largely preserved across coupling types (PAC and AAC) and across stimulus types (natural and synthetic auditory stimuli), suggesting they are a general feature of information processing in auditory cortex. Moreover, our findings showed that low-frequency PAC alternated between predominantly top-down or bottom-up over time. Altogether, this suggests sensory information need not be propagated along separate frequencies upwards and downwards. Rather, information can be unmixed by having low frequencies couple to distinct frequency ranges in the target region, and by alternating top-down and bottom-up processing over time.1SignificanceThe brain consists of highly interconnected cortical areas, yet the patterns in directional cortical communication are not fully understood, in particular with regards to interactions between different signal components across frequencies. We employed a a unified, computationally advantageous Granger-causal framework to examine bi-directional cross-frequency interactions across four sectors of the auditory cortical hierarchy in macaques. Our findings extend the view of cross-frequency interactions in auditory cortex, suggesting they also play a prominent role in top-down processing. Our findings also suggest information need not be propagated along separate channels up and down the cortical hierarchy, with important implications for theories of information processing in the brain such as predictive coding.

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Toward a Midlatitude Ocean Frequency–Wavenumber Spectral Density and Trend Determination

Journal of Physical Oceanography ◽

10.1175/2010jpo4376.1 ◽

2010 ◽

Vol 40 (10) ◽

pp. 2264-2281 ◽

Cited By ~ 28

Author(s):

Carl Wunsch

Keyword(s):

Sea Level ◽

Spatial Scales ◽

Low Frequency ◽

Theoretical Explanation ◽

Spatial Average ◽

Low Frequency Variability ◽

Zonal Wavenumber ◽

Wavenumber Spectrum ◽

Volume Transports ◽

Analytical Frequency

Abstract The time- and space-scale descriptive power of two-dimensional Fourier analysis is exploited to reanalyze the behavior of midlatitude variability as seen in altimetric data. These data are used to construct a purely empirical and analytical frequency–zonal wavenumber spectrum of ocean variability for periods between about 20 days and 15 yr and on spatial scales of about 200–10 000 km. The spectrum is dominated by motions along a “nondispersive” line, which is a robust feature of the data but for whose prominence a complete theoretical explanation is not available. The estimated spectrum also contains significant energy at all frequencies and wavenumbers in this range, including eastward-propagating motions, which are likely some combination of nonlinear spectral cascades, wave propagation, and wind-forced motions. The spectrum can be used to calculate statistical expectations of spatial average sea level and transport variations. However, because the statistics of trend determination in quantities such as sea level and volume transports depend directly upon the spectral limit of the frequency approaching zero, the appropriate significance calculations remain beyond reach, because low-frequency variability is indistinguishable from trends already present in the data.

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A statistical framework to assess cross-frequency coupling while accounting for confounding analysis effects

eLife ◽

10.7554/elife.44287 ◽

2019 ◽

Vol 8 ◽

Author(s):

Jessica K Nadalin ◽

Louis-Emmanuel Martinet ◽

Ethan B Blackwood ◽

Meng-Chen Lo ◽

Alik S Widge ◽

...

Keyword(s):

High Frequency ◽

Statistical Power ◽

Brain Activity ◽

Low Frequency ◽

Modeling Framework ◽

Frequency Coupling ◽

Phase Amplitude ◽

Cross Frequency Coupling ◽

Frequency Phase

Cross frequency coupling (CFC) is emerging as a fundamental feature of brain activity, correlated with brain function and dysfunction. Many different types of CFC have been identified through application of numerous data analysis methods, each developed to characterize a specific CFC type. Choosing an inappropriate method weakens statistical power and introduces opportunities for confounding effects. To address this, we propose a statistical modeling framework to estimate high frequency amplitude as a function of both the low frequency amplitude and low frequency phase; the result is a measure of phase-amplitude coupling that accounts for changes in the low frequency amplitude. We show in simulations that the proposed method successfully detects CFC between the low frequency phase or amplitude and the high frequency amplitude, and outperforms an existing method in biologically-motivated examples. Applying the method to in vivo data, we illustrate examples of CFC during a seizure and in response to electrical stimuli.

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Theta/delta coupling across cortical laminae contributes to semantic cognition

Journal of Neurophysiology ◽

10.1152/jn.00686.2018 ◽

2019 ◽

Vol 121 (4) ◽

pp. 1150-1161 ◽

Cited By ~ 3

Author(s):

Natalie E. Adams ◽

Catarina Teige ◽

Giovanna Mollo ◽

Theodoros Karapanagiotidis ◽

Piers L. Cornelissen ◽

...

Keyword(s):

Spatial Scales ◽

Rhythmic Activity ◽

Brain Regions ◽

Decision Task ◽

Distributed Network ◽

Spatially Distributed ◽

Semantic Decision ◽

Semantic Decision Task ◽

Frequency Coupling ◽

Cross Frequency Coupling

Rhythmic activity in populations of neurons is associated with cognitive and motor function. Our understanding of the neuronal mechanisms underlying these core brain functions has benefitted from demonstrations of cellular, synaptic, and network phenomena, leading to the generation of discrete rhythms at the local network level. However, discrete frequencies of rhythmic activity rarely occur alone. Despite this, little is known about why multiple rhythms are generated together or what mechanisms underlie their interaction to promote brain function. One overarching theory is that different temporal scales of rhythmic activity correspond to communication between brain regions separated by different spatial scales. To test this, we quantified the cross-frequency interactions between two dominant rhythms—theta and delta activity—manifested during magnetoencephalography recordings of subjects performing a word-pair semantic decision task. Semantic processing has been suggested to involve the formation of functional links between anatomically disparate neuronal populations over a range of spatial scales, and a distributed network was manifest in the profile of theta-delta coupling seen. Furthermore, differences in the pattern of theta-delta coupling significantly correlated with semantic outcome. Using an established experimental model of concurrent delta and theta rhythms in neocortex, we show that these outcome-dependent dynamics could be reproduced in a manner determined by the strength of cholinergic neuromodulation. Theta-delta coupling correlated with discrete neuronal activity motifs segregated by the cortical layer, neuronal intrinsic properties, and long-range axonal targets. Thus, the model suggested that local, interlaminar neocortical theta-delta coupling may serve to coordinate both cortico-cortical and cortico-subcortical computations during distributed network activity. NEW & NOTEWORTHY Here, we show, for the first time, that a network of spatially distributed brain regions can be revealed by cross-frequency coupling between delta and theta frequencies in subjects using magnetoencephalography recording during a semantic decision task. A biological model of this cross-frequency coupling suggested an interlaminar, cell-specific division of labor within the neocortex may serve to route the flow of cortico-cortical and cortico-subcortical information to promote such spatially distributed, functional networks.

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Source-Space Cross-Frequency Amplitude-Amplitude Coupling in Tinnitus

BioMed Research International ◽

10.1155/2015/489619 ◽

2015 ◽

Vol 2015 ◽

pp. 1-15 ◽

Cited By ~ 3

Author(s):

Oliver Zobay ◽

Peyman Adjamian

Keyword(s):

Theta Rhythm ◽

Low Frequency ◽

Hearing Level ◽

Thalamocortical Dysrhythmia ◽

Thalamocortical Oscillations ◽

Frequency Coupling ◽

Auditory Cortices ◽

Frequency Coherence ◽

And Control ◽

Cross Frequency Coupling

The thalamocortical dysrhythmia (TCD) model has been influential in the development of theoretical explanations for the neurological mechanisms of tinnitus. It asserts that thalamocortical oscillations lock a region in the auditory cortex into an ectopic slow-wave theta rhythm (4–8 Hz). The cortical area surrounding this region is hypothesized to generate abnormal gamma (>30 Hz) oscillations (“edge effect”) giving rise to the tinnitus percept. Consequently, the model predicts enhanced cross-frequency coherence in a broad range between theta and gamma. In this magnetoencephalography study involving tinnitus and control cohorts, we investigated this prediction. Using beamforming, cross-frequency amplitude-amplitude coupling (AAC) was computed within the auditory cortices for frequencies (f1,f2) between 2 and 80 Hz. We find the AAC signal to decompose into two distinct components at low (f1,f2<30 Hz) and high (f1,f2>30 Hz) frequencies, respectively. Studying the correlation of AAC with several key covariates (age, hearing level (HL), tinnitus handicap and duration, and HL at tinnitus frequency), we observe a statistically significant association between age and low-frequency AAC. Contrary to the TCD predictions, however, we do not find any indication of statistical differences in AAC between tinnitus and controls and thus no evidence for the predicted enhancement of cross-frequency coupling in tinnitus.

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Transport scaling and trapping

Journal of Plasma Physics ◽

10.1017/s0022377898006631 ◽

1998 ◽

Vol 59 (4) ◽

pp. 707-718 ◽

Cited By ~ 14

Author(s):

M. VLAD ◽

J.-D. REUSS ◽

F. SPINEANU ◽

J. H. MISGUICH

Keyword(s):

Low Frequency ◽

Theoretical Models ◽

Particle Trapping ◽

Gaussian Statistics ◽

Non Gaussian

It is shown that particle trapping plays an important role in the appearance of anomalous or strange diffusion in turbulent fields, mainly by inducing a non-Gaussian statistics of the stochastic displacements. Trapping processes are responsible for the important deviation observed between the traditional prediction of Bohm scaling for diffusion in low-frequency turbulence and the numerically checked prediction by Isichenko. Also, several theoretical models are proposed or reviewed.

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Electrophysiological Low-Frequency Coherence and Cross-Frequency Coupling Contribute to BOLD Connectivity

Neuron ◽

10.1016/j.neuron.2012.09.033 ◽

2012 ◽

Vol 76 (5) ◽

pp. 1010-1020 ◽

Cited By ~ 98

Author(s):

Liang Wang ◽

Yuri B. Saalmann ◽

Mark A. Pinsk ◽

Michael J. Arcaro ◽

Sabine Kastner

Keyword(s):

Low Frequency ◽

Frequency Coupling ◽

Frequency Coherence ◽

Cross Frequency Coupling

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A statistical modeling framework to assess cross-frequency coupling while accounting for confounding effects

10.1101/519470 ◽

2019 ◽

Cited By ~ 2

Author(s):

Jessica Nadalin ◽

Louis-Emmanuel Martinet ◽

Ethan Blackwood ◽

Meng-Chen Lo ◽

Alik S. Widge ◽

...

Keyword(s):

Statistical Modeling ◽

High Frequency ◽

Statistical Power ◽

Brain Activity ◽

Low Frequency ◽

Modeling Framework ◽

Frequency Coupling ◽

Cross Frequency Coupling ◽

Frequency Phase

AbstractCross frequency coupling (CFC) is emerging as a fundamental feature of brain activity, correlated with brain function and dysfunction. Many different types of CFC have been identified through application of numerous data analysis methods, each developed to characterize a specific CFC type. Choosing an inappropriate method weakens statistical power and introduces opportunities for confounding effects. To address this, we propose a statistical modeling framework to estimate high frequency amplitude as a function of both the low frequency amplitude and low frequency phase; the result is a measure of phase-amplitude coupling that accounts for changes in the low frequency amplitude. We show in simulations that the proposed method successfully detects CFC between the low frequency phase or amplitude and the high frequency amplitude, and outperforms an existing method in biologically-motivated examples. Applying the method to in vivo data, we illustrate how CFC evolves during seizures and is affected by electrical stimuli.

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A Time-Series Model of Phase Amplitude Cross Frequency Coupling and Comparison of Spectral Characteristics with Neural Data

BioMed Research International ◽

10.1155/2015/140837 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8 ◽

Cited By ~ 5

Author(s):

Kyle Q. Lepage ◽

Sujith Vijayan

Keyword(s):

Time Series ◽

High Frequency ◽

Spectral Characteristics ◽

Low Frequency ◽

Time Series Model ◽

High Frequency Component ◽

Frequency Oscillation ◽

Low Frequency Oscillation ◽

Frequency Coupling ◽

Cross Frequency Coupling

Stochastic processes that exhibit cross-frequency coupling (CFC) are introduced. The ability of these processes to model observed CFC in neural recordings is investigated by comparison with published spectra. One of the proposed models, based on multiplying a pulsatile function of a low-frequency oscillation (θ) with an unobserved and high-frequency component, yields a process with a spectrum that is consistent with observation. Other models, such as those employing a biphasic pulsatile function of a low-frequency oscillation, are demonstrated to be less suitable. We introduce the full stochastic process time series model as a summation of three component weak-sense stationary (WSS) processes, namely,θ,γ, andη, withηa1/fαnoise process. Theγprocess is constructed as a product of a latent and unobserved high-frequency processxwith a function of the lagged, low-frequency oscillatory component (θ). After demonstrating that the model process is WSS, an appropriate method of simulation is introduced based upon the WSS property. This work may be of interest to researchers seeking to connect inhibitory and excitatory dynamics directly to observation in a model that accounts for known temporal dependence or to researchers seeking to examine what can occur in a multiplicative time-domain CFC mechanism.

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Space–Time Spectral Analysis of the Southern Hemisphere Daily 500-hPa Geopotential Height

Monthly Weather Review ◽

10.1175/mwr-d-12-00019.1 ◽

2012 ◽

Vol 140 (12) ◽

pp. 3844-3856 ◽

Cited By ~ 8

Author(s):

Cheng Sun ◽

Jianping Li

Keyword(s):

Southern Hemisphere ◽

Geopotential Height ◽

Spatial Scales ◽

Temporal Frequency ◽

Low Frequency ◽

Phase Relationship ◽

Space Time ◽

Planetary Scale ◽

Low Frequency Variability ◽

Zonal Wavenumber

Abstract In this paper the authors use the NCEP–Department of Energy (DOE) Reanalysis 2 (NCEP2) data from 1979 to 2004 to expand the daily 500-hPa geopotential height in the Southern Hemisphere (SH, 90°–20°S) into a double Fourier series, and analyze the temporal frequency characteristics of the expansion coefficients over various spatial scales. For the daily series over the whole year, the coefficient series of the extratropical-mean height is characterized by a significant low-frequency (10–30 day) variation. For zonal waves with (k, l) = (1–5, 1), where k and l are the zonal and meridional wavenumbers, respectively, the low-frequency variability is most pronounced for zonal wavenumbers 3 and 4; while the short wave with zonal wavenumber 5 has significant high-frequency (4–8 day) variability. For meridional waves with (k, l) = (0, 2–6), the meridional dipole (l = 2) makes a major contribution to the low-frequency variability, consistent with the intraseasonal space–time features of the southern annular mode (SAM). The meridional tripole (l = 3) also exhibits low-frequency variability. For two-dimensional waves (k, l) = (1–5, 2–6), the dipole is a preferred meridional structure for intraseasonal modes with large zonal scales, indicating an out-of-phase relationship between low-frequency planetary-scale waves at mid- and high latitudes. The diagnostic results outlined above can be explained, to a certain extent, by the dispersion relation for Rossby waves. Theoretical analysis indicates that zonal wavenumber 3, zonally symmetric flow such as SAM, and planetary-scale waves with meridional dipole structures may be interpreted as low-frequency eigenmodes of the atmosphere.

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