Alex Sheremet

Observations of large infragravity wave runup at Banneg Island, France

On Banneg Island, France, very high water-level events (6.5 m above the astronomical tide) have been observed on the western cliff, exposed to large swells from the North Atlantic. The analysis of hydrodynamic measurements collected during the storm of 10 February 2009 shows unusually high (over 2 m) infragravity wave runup events. By comparing runup observations to measurements in approximately 7 m of water and numerical simulations with a simplified nonlinear model, two distinct infragravity bands may be identified: an 80 s infragravity wave, produced by nonlinear shoaling of the storm swell; and a 300 s wave, trapped on the intertidal platform of the island and generating intermittent, low-frequency inundation. Our analysis shows that the 300 s waves are a key component of the extreme water levels recorded on the island.

Movement Enhances the Nonlinearity of Hippocampal Theta

The nonlinear, metastable dynamics of the brain are essential for large-scale integration of smaller components and for the rapid organization of neurons in support of behavior. Therefore, understanding the nonlinearity of the brain is paramount for understanding the relationship between brain dynamics and behavior. Explicit quantitative descriptions of the properties and consequences of nonlinear neural networks, however, are rare. Because the local field potential (LFP) reflects the total activity across a population of neurons, nonlinearites of the nervous system should be quantifiable by examining oscillatory structure. We used high-order spectral analysis of LFP recorded from the dorsal and intermediate regions of the rat hippocampus to show that the nonlinear character of the hippocampal theta rhythm is directly related to movement speed of the animal. In the time domain, nonlinearity is expressed as the development of skewness and asymmetry in the theta shape. In the spectral domain, nonlinear dynamics manifest as the development of a chain of harmonics statistically phase coupled to the theta oscillation. This evolution was modulated across hippocampal regions, being stronger in the dorsal CA1 relative to more intermediate areas. The intensity and timing of the spiking activity of pyramidal cells and interneurons was strongly correlated to theta nonlinearity. Because theta is known to propagate from dorsal to ventral regions of the hippocampus, these data suggest that the nonlinear character of theta decreases as it travels and supports a hypothesis that activity dissipates along the longitudinal axis of the hippocampus. SIGNIFICANCE STATEMENT We describe the first explicit quantification regarding how behavior enhances the nonlinearity of the nervous system. Our findings demonstrate uniquely how theta changes with increasing speed due to the altered underlying neuronal dynamics and open new directions of research on the relationship between single-neuron activity and propagation of theta through the hippocampus. This work is significant because it will encourage others to consider the nonlinear nature of the nervous system and higher-order spectral analyses when examining oscillatory interactions.

Boat-Wake Statistics at Jensen Beach, Florida

Ship/boat wakes are identified in pressure and flow velocity records as chirp signals, which are also known as sweep signals in sonar and radar applications. A chirp is a signal in which the frequency increases or decreases with time. Wakes are analyzed using time-frequency techniques [windowed Fourier transform (WFT), wavelet transform (WT), and instantaneous frequency]. This approach allows for detecting boat wakes and studying their statistics, even in the presence of a relatively strong broad-banded wind-wave background. Time-frequency methods also open a new direction for the statistical description of wakes, which are applicable to the characterization of the wake climate (e.g., for sites with intense boat traffic). The usefulness of the time-frequency analysis on observations collected in 2010 at Jensen Beach, Florida will be demonstrated.

On the Shoaling of Solitary Waves in the Presence of Short Random Waves

Overhead video from a small number of laboratory tests conducted by Kaihatu et al. at the Tsunami Wave Basin at Oregon State University shows that the breaking point of a shoaling solitary wave shifts to deeper water if random waves are present. The analysis of the laboratory data collected confirms that solitary waves indeed tend to break earlier in the presence of random wave field, and suggests that the effect is the result of the radiationstresses gradientinduced by the randomwavefields.A theoreticalapproachbased on the forced KdV equation is shown to successfully predict the shoaling process of the solitary wave. An ensemble of tests simulated using a state-of-the-art nonhydrostatic model is used to test the statistical significance of the process. The results of this study point to a potentially significant oceanographic process that has so far been ignored and suggest that systematic research into the interaction between tsunami waves and the swell background could increase the accuracy of tsunami forecasting.

Observations of meteotsunami on the Louisiana shelf: a lone soliton with a soliton pack

The paper reports unique high-resolution observations of meteotsunami by a large array of oceanographic instruments deployed on the Atchafalaya Shelf (Louisiana, USA) in 2008 with the primary aim to study wave dissipation in muddy environments. The meteotsunami event on March 7, 2008, was caused by the passage of a cold front which was monitored by the NOAA NEXRAD radar. The observations of water surface elevations on the shelf show a highly detailed textbook picture of an undular bore (solibore) in the process of its disintegration into a train of solitons. The picture has a striking feature never reported before not only for the meteotsunamis but in other contexts of disintegration of a long-wave perturbation into a sequence of solitons as well—the persistent presence of a single soliton, well ahead of the solibore. Data analysis and simulations based on the celebrated variable-coefficient KdV (vKdV) equation first proposed by Ostrovsky and Pelinovsky (Izv Atmos Ocean Phys 11:37–41, 1975) explain the physics of this phenomenon and suggest that the formation of the lone soliton ahead of the solibore is very likely to be the result of the specific interplay of natural meteotsunami forcing and nearshore bathymetry. The analysis strongly suggests that the patterns of coexisting lone solitons and packets of cnoidal waves should be quite common for meteotsunamis. They were not observed before only because of the scarcity of high-resolution observations. The results highlight the effectiveness of the vKdV equation in providing understanding of the fundamental mechanisms of the complex natural phenomenon that would otherwise require computationally very expensive numerical models.

Nonlinear and directional effects on wave predictions over muddy bottoms: central chenier plain coast, Western Louisiana Shelf, USA

The sensitivity of wave-mud interaction on directionality and nonlinearity is investigated. A phase-resolving nonlinear wave model which accounts for directional wave propagation and mud damping is used to simulate wave propagation over a muddy shelf. Field data from an experiment conducted at the central chenier plain coast, western Louisiana, USA are used to validate the model. Recently, verification of a one-dimensional wave model with the field data showed that this model was able to replicate the evolution of wave spectra over muddy bottoms. In this study, unidirectional wave spectra were also run through the parabolic model, but with various initial angles. Linear wave model runs were also performed in order to gauge the effect of nonlinear evolution on the results. Significant wave height and total energy contained in three different spectral bands from the model are compared to the data over the shelf, and correlation metrics calculated. While the model generally performs well no matter the initial angle, at no point does a zero initial angle compare best to the data, indicating that a unidirectional model may be missing some of the dynamical features of wave propagation over a muddy shelf. Furthermore, despite similar correlation scores between linear and nonlinear model comparisons of bulk statistics, it is seen the linear model does not replicate some aspects of the spectral evolution (such as low-frequency generation and amplification) shown in the data and captured by the nonlinear model. Despite the relatively short propagation distance, the effects of both directionality and nonlinearity play a noticeable role in wave evolution over a muddy seabed.

LINEAR ANALYSIS OF HIPPOCAMPAL LFP: SLOW GAMMA VS HIGH THETA

We apply common linear analysis techniques (Fourier and wavelet transforms) to time-series of hippocampal local field potential (LFP) collected from a small population of rats (5 individuals) during awake-behavior in a maze-exploring task, and rest (non-REM sleep). Important characteristics of hippocampal activity, such as the power of the theta rhythm and its harmonics, as well as that of the gamma rhythm, are strongly dependent on the intensity of behavioral activity, as measured by rat speed. A comparison of Fourier and wavelet representation of stationary LFP epochs show that the wavelet representation fails to resolve high-order theta harmonics (24, 32, 40 Hz) that appear well defined in the Fourier analysis and occupy the frequency band of 20–50 Hz, also attributed to the slow gamma rhythm. It seems possible that a misinterpretation of wavelet analysis might be the origin of the identification of the slow gamma rhythm. Such a misidentification would also naturally lead to spurious coupling results between the low gamma and theta oscillations. Theoretically, both transforms can handle arbitrary time-series; however, the Fourier transform is best interpreted for weakly phase-coupled, nearly-Gaussian stochastic processes, while the wavelet transform is most useful when applied to non-stationary, transient processes. Outside their optimal applicability range, both transforms may produce ambiguous, even misleading results. Rather than refuting the existence of slow gamma, our results emphasize the importance of selecting the adequate spectral analysis method for the stochastic process analyzed. To help with the selection, we propose a simple stationarity test based on the integral value of the bicoherence. Further research is needed to separate high order theta harmonics from slow gamma.ABSTRACT Local field potential (LFP) oscillations are the superposition of excitatory/inhibitory postsynaptic potentials. In the hippocampus, the 20-55 Hz range (‘slow gamma’) is proposed to support cognition independent of other frequencies. However, this band overlaps with theta harmonics. We aimed to dissociate the generators of slow gamma versus theta harmonics with current source density and different LFP decompositions. Hippocampal theta harmonic and slow gamma generators were not dissociable. Moreover, comparison of wavelet, ensemble empirical-mode (EEMD), and Fourier decompositions produced distinct outcomes with wavelet and EEMD failing to resolve high-order theta harmonics well defined by Fourier analysis. The varying sizes of the time-frequency atoms used by wavelet distributed the higher-order harmonics over a broader range giving the impression of a low frequency burst (“slow gamma”). The absence of detectable slow gamma refutes a multiplexed model of cognition in favor of the energy cascade hypothesis in which dependency across oscillatory frequencies exists.

Theta-Gamma Cascades and Running Speed

The local field potentials (LFPs) of the hippocampus are primarily generated by the spatiotemporal accretion of electrical currents via activated synapses. Oscillations in the hippocampal LFP at theta and gamma frequencies are prominent during awake-behavior and have demonstrated several behavioral correlates. In particular, both oscillations have been observed to increase in amplitude and frequency as a function of running velocity. Previous investigations, however, have examined the relationship between velocity and each of these oscillation bands separately. Based on energy cascade models where “…perturbations of slow frequencies cause a cascade of energy dissipation at all frequency scales” (Buzsaki 2006), we hypothesized that the cross-frequency interactions between theta and gamma should increase as a function of velocity. We examined these relationships across multiple layers of the CA1 subregion and found a reliable correlation between the power of theta and the power of gamma, indicative of an amplitude-amplitude relationship. Moreover, there was an increase in the coherence between the power of gamma and the phase of theta, demonstrating increased phase-amplitude coupling with velocity. Finally, at higher velocities, phase entrainment between theta and gamma becomes stronger. These results have important implications and provide new insights regarding how theta and gamma are integrated for neuronal circuit dynamics, with coupling strength determined by the excitatory drive within the hippocampus.

TURBULENCE IN THE HIPPOCAMPUS: AN ANSATZ FOR THE ENERGY CASCADEHYPOTHESIS

Mesoscopic neural activity may play an important role in the cross-scale integration of brain activity and in the emergence of cognitive behavior. Mesoscale activity in the cortex can be defined as the organization of activity of large populations of neurons into collective actions, such as traveling waves in the hippocampus. A comprehensive description of collective activity is still lacking, in part because it cannot be built directly with methods and models developed for the microscale (individual neurons): the laws governing mesoscale dynamics are different from those governing a few neurons. To identify the characteristic features of mesoscopic dynamics, and to lay the foundations for a theoretical description of mesoscopic activity in the hippocampus, we conduct a comprehensive examination of observational data of hippocampal local field potential (LFP) recordings. We use the strong correlation between rat running-speed and the LFP power to parameterize the energy input into the hippocampus, and show that both the power, and the nonlinearity of mesoscopic scales of collective action (e.g., theta and gamma rhythms) increase as with energy input. Our results point to a few fundamental characteristics: collective-action dynamics are stochastic (the precise state of a single neuron is irrelevant), weakly nonlinear, and weakly dissipative. These are the principles of the theory of weak turbulence. Therefore, we propose weak turbulence as an ansatz for the development of a theoretical description of mesoscopic activity. The perspective of weak turbulence provides simple and meaningful explanations for the major features observed in the evolution of LFP spectra and bispectra with energy input, such as spectral slopes and their evolution, the increased nonlinear coupling observed between theta and gamma, as well as specific phase lags associated with their interaction. The weak turbulence ansatz is consistent with the theory of self organized criticality, which provides a simple explanation for the existence of the power-law background spectrum, and could provide a unifying approach to modeling the dynamics of mesoscopic activity.

Theta-gamma coupling: a nonlinear dynamical model

Cross-frequency coupling in the hippocampus has been hypothesized to support higher-cognition functions. While gamma modulation by theta is widely accepted, evidence of phase-coupling between the two frequency components is so far unconvincing. Our observations show that theta and gamma energy increases with rat speed, while the overall nonlinearity of the LFP trace also increases, suggesting that energy flow is fundamental for hippocampal dynamics. This contradicts current representations based on the Kuramoto phase model. Therefore, we propose a new approach, based on the three-wave equation, a universally-valid nonlinear-physics paradigm that synthesizes the effects of leading order, quadratic nonlinearity. The paradigm identifies bispectral analysis as the natural tool for investigating LFP cross-frequency coupling. Our results confirm the effectiveness of the approach by showing unambiguous coupling between theta and gamma. Bispectra features agree with predictions of the three-wave model, supporting the conclusion that cross-frequency coupling is a manifestation of nonlinear energy transfers.