Local Amplitude Research Articles

Offset responses in primary auditory cortex are enhanced after notched noise stimulation.

Sensory "aftereffects" are a subgroup of sensory illusions that can be defined as an illusory phenomenon triggered after prolonged exposure to a given sensory inducer. These phenomena are interesting because they can provide insights into the mechanisms of perception. In auditory modality, there is a special interest in the so-called "Zwicker tone" (ZT), an auditory aftereffect triggered after the presentation of a notched noise (NN, broadband noise with a missing frequency band). The ZT has been considered a plausible model of a specific tinnitus subtype since it presents some key characteristics in common with tinnitus. Indeed, both the tinnitus percept and ZT can be triggered by a relative "sensory deprivation," and their pitch corresponds to the frequency region that has been sensory deprived. The effects of a NN presentation on the central auditory system are still barely investigated, and the mechanisms of the ZT are elusive. In this study, we analyzed the laminar structure of the neural activity in the primary cortex of anesthetized and awake guinea pigs during and after white noise (WN) and NN stimulation. We found significantly increased offset responses, in terms of both spiking activity and local field potential amplitude, after NN compared with WN presentation. The offset responses were circumscribed to the granular and upper infragranular layers (input layers) and were maximal when the neuron's best frequency was within or near the missing frequency band. The mechanisms of the offset response and its putative link with the ZT are discussed.NEW & NOTEWORTHY Notched noise (white noise with embedded spectral gap) causes significant excitatory offset responses in the auditory cortex of awake and anesthetized guinea pigs. The largest offset responses were located in the infragranular/granular layers, and current source density analysis revealed that offset responses were associated with an early current sink localized in the upper infragranular layers. We discuss the possibility that the offset responses might be associated with an auditory phantom percept (Zwicker tone).

Numerical Study of Instability of Medium Interface During Thermonuclear Combustion of a Cylindrical Shelled Microtarget

The study is limited to two-dimensional disturbances of the interface between media. A computational technology based on the explicit interface separation in the form of one of the lines of a regular grid is used. A method for visualizing spontaneous disturbances at an early stage when they cannot yet be seen on the interface profile is proposed. It is shown that the computer rounding error plays an insignificant role in their formation. For the late stage of the disturbance development, a method for obtaining the profile of the local oscillation amplitude along the interface is proposed. The features of spontaneous disturbance at different stages of its development are studied. It is shown that the spontaneous disturbance tends to grid convergence, at least until the beginning of the process of formation of a quasi-stationary shockless combustion wave. It is shown that during the formation of a quasi-stationary wave and its subsequent motion, an additional spontaneous disturbance arises. The interaction of a specified sinusoidal disturbance having an initial amplitude of up to 0.1 of the wavelength with a quasi-stationary combustion wave is studied. It is shown that the Kelvin–Helmholtz instability is the main mechanism for the development of instability at the nonlinear stage. The combustion wave is not destroyed. The profiles of the oscillation amplitude of the given disturbance are obtained, from which it is possible to extract the universal time-independent part.

Accounting for meteorological biases in simulated plumes using smarter metrics

Abstract. In the next few years, numerous satellites with high-resolution instruments dedicated to the imaging of atmospheric gaseous compounds will be launched, to finely monitor emissions of greenhouse gases and pollutants. Processing the resulting images of plumes from cities and industrial plants to infer the emissions of these sources can be challenging. In particular traditional atmospheric inversion techniques, relying on objective comparisons to simulations with atmospheric chemistry transport models, may poorly fit the observed plume due to modelling errors rather than due to uncertainties in the emissions. The present article discusses how these images can be adequately compared to simulated concentrations to limit the weight of modelling errors due to the meteorology used to analyse the images. For such comparisons, the usual pixel-wise ℒ2 norm may not be suitable, since it does not linearly penalise a displacement between two identical plumes. By definition, such a metric considers a displacement as an accumulation of significant local amplitude discrepancies. This is the so-called double penalty issue. To avoid this issue, we propose three solutions: (i) compensate for position error, due to a displacement, before the local comparison; (ii) use non-local metrics of density distribution comparison; and (iii) use a combination of the first two solutions. All the metrics are evaluated using first a catalogue of analytical plumes and then more realistic plumes simulated with a mesoscale Eulerian atmospheric transport model, with an emphasis on the sensitivity of the metrics to position error and the concentration values within the plumes. As expected, the metrics with the upstream correction are found to be less sensitive to position error in both analytical and realistic conditions. Furthermore, in realistic cases, we evaluate the weight of changes in the norm and the direction of the four-dimensional wind fields in our metric values. This comparison highlights the link between differences in the synoptic-scale winds direction and position error. Hence the contribution of the latter to our new metrics is reduced, thus limiting misinterpretation. Furthermore, the new metrics also avoid the double penalty issue.

Spatial Correspondence of LSD-Induced Variations on Brain Functioning at Rest With Serotonin Receptor Expression

BackgroundLysergic acid diethylamide (LSD) is an atypical psychedelic compound that exerts its effects through pleiotropic actions, mainly involving 1A/2A serotoninergic (5-HT) receptor subtypes. However, the mechanisms by which LSD promotes a reorganization of the brain’s functional activity and connectivity are still partially unknown. MethodsOur study analyzed resting-state functional magnetic resonance imaging data acquired from 15 healthy volunteers undergoing LSD single-dose intake. A voxelwise analysis investigated the alterations of the brain’s intrinsic functional connectivity and local signal amplitude induced by LSD or by a placebo. Quantitative comparisons assessed the spatial overlap between these 2 indices of functional reorganization and the topography of receptor expression obtained from a publicly available collection of in vivo, whole-brain atlases. Finally, linear regression models explored the relationships between changes in resting-state functional magnetic resonance imaging and behavioral aspects of the psychedelic experience. ResultsLSD elicited modifications of the cortical functional architecture that spatially overlapped with the distribution of serotoninergic receptors. Local signal amplitude and functional connectivity increased in regions belonging to the default mode and attention networks associated with high expression of 5-HT2A receptors. These functional changes correlate with the occurrence of simple and complex visual hallucinations. At the same time, a decrease in local signal amplitude and intrinsic connectivity was observed in limbic areas, which are dense with 5-HT1A receptors. ConclusionsThis study provides new insights into the neural processes underlying the brain network reconfiguration induced by LSD. It also identifies a topographical relationship between opposite effects on brain functioning and the spatial distribution of different 5-HT receptors.

Three‐dimensional generalized analytic signal associated with linear canonical transform in Clifford biquaternion domain

Analytic signal is a useful mathematical tool. It separates qualitative and quantitative information of a signal in form of the local phase and local amplitude. Clifford Fourier transform (CFT) plays a vital role in the representation of multidimensional signals. By generalizing the CFT to Clifford linear canonical transform (CLCT), we present a new type of Clifford biquaternionic analytic signal. Due to the advantages of more freedom, the envelop detection problems of 3D images, with the help of this new analytic signal, can get a better visual appearance. Synthesis examples are presented to demonstrate these advantages.

Experimental study on the microseismic response characteristics of coal and gas outbursts

A microseismic monitoring simulation experiment of coal and gas outbursts was carried out to study the microseismic response characteristics of the coal and gas outburst process. The microseismic response characteristics were analyzed from the microseismic waveform and time frequency at each stage of the outburst process. The quantitative description of the outburst process was achieved by the statistical analysis of microseismic signals and the determination of the microseismic energy index of outburst hazards. The results showed that the coal and gas outburst process included four stages: preparation, start, development, and stop, and the outburst moment is at the development stage. The protruding hole in the experiment was an ellipsoid with a small mouth and large cavity. Frequency components were complex and extensive and tended to high frequencies at the prominent stage. The frequency of the microseismic response waveform at the moment of prominence was higher than that before and after prominence, but energy at the moment of prominence was not maximum. Sudden changes in amplitudes at the preparation and development stages had more outbursts, and the maximum equivalent energy at the moment of prominence was as high as 45,000 Hz. Compared with the local high amplitude at the preparation stage, the development stage presents an overall high amplitude. Although the start stage is calmer, it is a critical period for predicting outbursts, and the microseismic activity characteristics of the outburst stage differed significantly from those of the other three stages. Quantitative indices reflecting the risk strength of coal and gas outbursts at the breeding stage were defined from microseismic energy, and the outburst risk indices under experimental conditions were established. When L1 < 3.64, L2 < 0.16, and L3 < 5.74, the coal mass had a weak outburst risk; when L1 > 3.64, L2 > 2.33, and L3 > 5.74, it had strong outburst risks. The research results provide an idea for coal and gas outburst precursor information and dynamic early warning.

Continuous ordinal patterns: Creating a bridge between ordinal analysis and deep learning.

We introduce a generalization of the celebrated ordinal pattern approach for the analysis of time series, in which these are evaluated in terms of their distance to ordinal patterns defined in a continuous way. This allows us to naturally incorporate information about the local amplitude of the data and to optimize the ordinal pattern(s) to the problem under study. This last element represents a novel bridge between standard ordinal analysis and deep learning, allowing the achievement of results comparable to the latter in real-world classification problems while also retaining the conceptual simplicity, computational efficiency, and easy interpretability of the former. We test this through the use of synthetic time series, generated by standard chaotic maps and dynamical models, data sets representing brain activity in health and schizophrenia, and the dynamics of delays in the European air transport system. We further show how the continuous ordinal patterns can be used to assess other aspects of the dynamics, like time irreversibility.

Virtual wave based phasor field projection for photoacoustic imaging

The phasor field technique has been demonstrated as a powerful tool to improve imaging performance and reduce computational complexity in time of flight imaging. In this work, we show a similar description and propose phasor field photoacoustics (PAs), a framework for forward acoustic propagation and backward source reconstruction, using phasor representations of acoustic pressure and back projection events. Based on the linear propagation mechanism, this method employs complex phasor filters to decompose the photoacoustic wave into pairs of orthogonal virtual waves, wherein each pair of orthogonal waves corresponds to the real and imaginary parts of the quasi-monochromatic phasor field contribution. By performing phasor field projection (PFP) and thereafter conjugated multiplication in the spatial domain, the complex envelope containing local amplitude and phase information can be faithfully retrieved, attaining rigorous “unipolar” photoacoustic images without ambiguous negative absorption artifacts. Theoretical and experimental results demonstrate that the orthogonal virtual wave based phasor field photoacoustic method can effectively eliminate negative artifacts and improve imaging signal-to-noise ratio (SNR) without excessively increasing computational complexity. This work may pave the way for high-fidelity quantitative imaging, e.g., multispectral and molecular imaging applications.

Degeneration of the Grover search algorithm with depolarization in the oracle-box wires

Grover’s search algorithm and similar techniques are widely used in quantum information science. Communication lines with the so-called oracle are one of inevitable vulnerabilities of quantum search. The impact of localized dephasing and amplitude damping on Grover’s algorithm had already been discussed in recent literature. In this paper, we study the influence of depolarization in the oracle-box wires on the search process. It is shown that even low level of noise is sufficient to degenerate Grover’s algorithm. Complementarity relations between the relative entropy of coherence and the success probability in the presence of depolarization are studied as well.

In vivo pulsed-field ablation in healthy vs. chronically infarcted ventricular myocardium: biophysical and histologic characterization.

Data on ventricular pulsed-field ablation (PFA) are sparse in the setting of chronic myocardial infarction (MI). The objective of this study was to compare the biophysical and histopathologic characteristics of PFA in healthy and MI swine ventricular myocardium. Myocardial infarction swine (n = 8) underwent coronary balloon occlusion and survived for 30 days. We then performed endocardial unipolar, biphasic PFA of the MI border zone and a dense scar with electroanatomic mapping and using an irrigated contact force (CF)-sensing catheter with the CENTAURI System (Galaxy Medical). Lesion and biophysical characteristics were compared with three controls: MI swine undergoing thermal ablation, MI swine undergoing no ablation, and healthy swine undergoing similar PFA applications that included linear lesion sets. Tissues were systematically assessed by gross pathology utilizing 2,3,5-triphenyl-2H-tetrazolium chloride staining and histologically with haematoxylin and eosin and trichrome. Pulsed-field ablation in healthy myocardium generated well-demarcated ellipsoid lesions (7.2 ± 2.1 mm depth) with contraction band necrosis and myocytolysis. Pulsed-field ablation in MI demonstrated slightly smaller lesions (depth 5.3 ± 1.9 mm, P = 0.0002), and lesions infiltrated into the irregular scar border, resulting in contraction band necrosis and myocytolysis of surviving myocytes and extending to the epicardial border of the scar. Coagulative necrosis was present in 75% of thermal ablation controls but only in 16% of PFA lesions. Linear PFA resulted in contiguous linear lesions with no gaps in gross pathology. Neither CF nor local R-wave amplitude reduction correlated with lesion size. Pulsed-field ablation of a heterogeneous chronic MI scar effectively ablates surviving myocytes within and beyond the scar, demonstrating promise for the clinical ablation of scar-mediated ventricular arrhythmias.

Probing large-scale ionizing background fluctuation with Lyman α forest and galaxy cross-correlation at z = 2.4

ABSTRACT The amplitude of the metagalactic ultraviolet background (UVB) at large scales is impacted by two factors. First, it naturally attenuates at scales larger than mean-free path of UVB photons due to the absorption by neutral intergalactic medium. Second, there are discrete and rare ionizing sources distributing in the Universe, emitting the UVB photons, and thus enhancing the local UVB amplitude. Therefore, for cosmological probe that is sensitive to the UVB amplitude and capable of detecting the large scale like Lyman α forest spectrum, the fluctuation due to the clustering of ionizing sources becomes a significant factor for Lyman α flux transmission and leave imprints on Lyman α flux power spectrum at these large scales. In this work, we make use of a radiative transfer model that parametrizes the UVB source distribution by its bias bj and shot noise $\overline{n}_{\rm j}$. We estimate the constraints on this model through the cross-correlation between Lyman α forest survey and galaxy survey, using the DESI Lyman α forest survey and the Roman Space Telescope emission line galaxy survey as an example. We show the detection sensitivity improvement for UVB parameters from disjoint to maximal overlap of DESI + Roman survey strategy. We also show that the degeneracy of two ionizing source parameters can be broken by increasing the overlapping survey area. Our results motivate survey strategies more dedicated to probe the UVB large-scale fluctuations.

Double-function enhancement algorithm for low-illumination images based on retinex theory.

In order to solve the problems of noise amplification and excessive enhancement caused by low contrast and uneven illumination in the process of low-illumination image enhancement, a high-quality image enhancement algorithm is proposed in this paper. First, the total-variation model is used to obtain the smoothed V- and S-channel images, and the adaptive gamma transform is used to enhance the details of the smoothed V-channel image. Then, on this basis, the improved multi-scale retinex algorithms based on the logarithmic function and on the hyperbolic tangent function, respectively, are used to obtain different V-channel enhanced images, and the two images are fused according to the local intensity amplitude of the images. Finally, the three-dimensional gamma function is used to correct the fused image, and then adjust the image saturation. A lightness-order-error (LOE) approach is used to measure the naturalness of the enhanced image. The experimental results show that compared with other classical algorithms, the LOE value of the proposed algorithm can be reduced by 79.95% at most. Compared with other state-of-the-art algorithms, the LOE value can be reduced by 53.43% at most. Compared with some algorithms based on deep learning, the LOE value can be reduced by 52.13% at most. The algorithm proposed in this paper can effectively reduce image noise, retain image details, avoid excessive image enhancement, and obtain a better visual effect while ensuring the enhancement effect.

Amplitude/operator basis in chiral perturbation theory

We establish a systematic construction of the on-shell amplitude/operator basis for Chiral Perturbation Theory (ChPT) in D = 4 spacetime dimensions and with an arbitrary number of flavors Nf. For kinematic factors, we employ spinor-helicity variables to construct the soft blocks, which are local amplitudes satisfying the Adler’s zero condition, as well as to take into account the reduction in the kinematic basis due to the Gram determinant, which arises at O(p10) when the number of multiplicity N in an amplitude becomes large: N > D. For flavor factors, we include group-theoretic relations at small Nf, Nf≤ N, which decreases the flavor basis. The result is obtained by adapting the Young tensor method of constructing the operator basis for generic effective field theories to the case of non-linearly realized symmetries. Working in the massless quark limit, we present purely mesonic operators for both even- and odd-parity at O(p6) and O(p8) for N = 6 and arbitrary Nf, and establish a direct correspondence between the amplitude basis and the operator basis. Furthermore, the redundancy due to the Gram determinant is studied at O(p10) for N = 6, 8 and 10.

Моделирование эквивалентной передаточной функции и импульсного отклика схемы голографии Фурье для высокочастотных голограмм

An approach for modeling the transfer function and approximating the impulse response in the +1 diffraction order of the 4f holography scheme of the Fourier holography under usage of high-frequency holograms characterized by the presence of an inverse section of the dependence of the local diffraction efficiency on the spatial frequency in the frequency range below the frequency of equality of local amplitudes of the reference spectrum and the reference beam by the model of “Difference of Gaussians” is proposed and justified. The expediency of using, when implementing processing models that involve working only with the global maximum of the circuit response, a transfer function that is equivalent in terms of the minimum mean square error of the impulse response, as providing a more accurate approximation of the impulse response compared to the approximation of the direct transfer function, is shown. The validity of the approach is confirmed by comparing the simulation results with experimental data.

Rössler-like Neuronal Firing with Local Amplitude Control

Chaotic neuronal oscillation is fired up when a locally active memristor is introduced into the Rössler system. Such a memristive Rössler system has two independent parameters providing local amplitude control, one of which even adjusts the amplitude and frequency of variables in a specific intermittent mode. Different neuronal firing modes are modified by the system parameter. The coexistence of periodic oscillation and chaos is also captured along with basin of attraction. STM32-based experiment verified the numerical and theoretical results.

Novel Method to Detect Pitfalls of Intracoronary Pressure Measurements by Pressure Waveform Analysis.

Potential pitfalls of fractional flow reserve (FFR) measurements are well-known drawbacks of invasive physiology measurement, e.g., significant drift of the distal pressure trace may lead to the misclassification of stenoses. Thus, a simultaneous waveform analysis of the pressure traces may be of help in the quality control of these measurements by online detection of such artefacts as the drift or the wedging of the catheter. In the current study, we analysed the intracoronary pressure waveform with a dedicated program. In 130 patients, 232 FFR measurements were performed and derivative pressure curves were calculated. Local amplitude around the dicrotic notch was calculated from the distal intracoronary pressure traces (δdPn/dt). A unidimensional arterial network model of blood flow was employed to simulate the intracoronary pressure traces at different flow rates. There was a strong correlation between δdPn/dt values measured during hyperaemia and FFR (r = 0.88). Diagnostic performance of distal δdPn/dt ≤ 3.52 for the prediction of FFR ≤ 0.80 was 91%. The correlation between the pressure gradient and the corresponding δdPn/dt values obtained from all measurements independently of the physiological phase was also significant (r = 0.80). During simulation, the effect of flow rate on δdPn/dt further supported the close correlation between the pressure ratios and δdPn/dt. Discordance between the FFR and the δdPn/dt can be used as an indicator of possible technical problems of FFR measurements. Hence, an online calculation of the δdPn/dt may be helpful in avoiding some pitfalls of FFR evaluation.

The bottom-up EFT: complete UV resonances of the SMEFT operators

The standard model effective field theory (SMEFT) provides systematic parameterization of all possible new physics above the electroweak scale. According to the amplitude-operator correspondence, an effective operator can be decomposed into a linear combination of several j-basis operators, which correspond to local amplitudes carrying certain spin and gauge quantum numbers in a particular scattering channel. Based on the Poincare and gauge symmetries of scattering amplitude, we construct the j-basis using the Casimir method for both the Lorentz and gauge sectors. The quantum numbers of the j-basis operators fix the quantum numbers of any intermediate state in the corresponding amplitudes, such as a UV resonance. This can be re-interpreted as the j-basis/UV correspondence, thus obtaining the j-bases in all partitions of fields for an operator amounts to finding all of its UV origins at tree level, constituting the central part of the bottom-up EFT framework. Applying the j-basis analysis to SMEFT, we obtain a complete list of possible tree-level UV origins of the effective operators at the dimension 5, 6, 7, and all the bosonic operators at dimension 8.

Reservoir characterization using integrated seismic attributes and petrophysical parameters in an onshore field of Niger delta basin

An integrated approach of reservoir characterization of a field was performed using seismic attributes and petrophysical parameters for the evaluation of subsurface geological features and hydrocarbon potential of an onshore field in Niger Delta Basin. Four reservoir intervals were identified within the field wells based on their position within the stratigraphic column, and the reservoir correlation, which was aided using the principle of uniform horizontality, based on the simple rule that sediments are deposited horizontally and basic understanding of sequence stratigraphy. The study revealed that, the four reservoirs were predominantly sand units intercalated with shale within the reservoir units. The petrophysical evaluation revealed the Net to Gross (NTG) values ranges from 79% to 87% within the reservoir units, while the effective porosity ranges from 17% to 21%, the permeability ranges between 1307mD to 1678mD across the reservoir units, while the water saturation ranges from the lowest of 35% (Reservoir C) to 78% in reservoir D. A total of fifteen faults were interpreted using the seismic data, while the surface maps (Time and depth surface maps) revealed the identified closures which are anticlinal structures that are fault dependent. The characterization of the reservoir was further enhanced using the seismic attributes (structural and stratigraphic) extracted such as Reflection intensity, Sweetness, Variance, Envelope, Instantaneous frequency, Time gain, Trace AGC, Local structural dip, Gradient magnitude and RMS amplitude. The results shows moderate to high sweetness (sweet spots) within the zone of interest, while the Envelope attribute show acoustic impedance contrasts indicating discontinuities, lithology changes and possible present of hydrocarbon (Bright spots). The variances and gradient magnitude enhanced the signal to map out discontinuities caused by faults and fractures which are signature that enabled delineation of the zone. The integrated approach validates the lithology discrimination of the elastic properties from the well logs and its effectiveness in optimizing and proper understanding of the subsurface, thus identifying and unmasking hidden features within the reservoir (probable bypass) in the field. The study has revealed that the integration of seismic attributes with petrophysical parameters is a better characterization method for fluid and lithology discrimination of a field in any given reservoir study.

Vortex-Pressure Fluctuation Interaction in the Outlet Duct of Centrifugal Pump as Turbines (PATs)

The outlet duct is the only outlet flow component of the pump as turbines (PATs). The flow state within it not only affects its operation stability but also influences the safe operation of downstream process equipment. The undesirable flow phenomenon of the vortex is the main reason for pressure pulsations and vibrations; therefore, it is important to adopt simulation and experimental methods to reveal the vortex-pressure fluctuation interaction characteristics in the outlet duct of PATs. Firstly, the spatial and temporal evolution of the vortex in the outlet duct under different operation conditions were compared based on the Q-vortex identification criterion. Subsequently, the frequency components corresponding to local high amplitude vorticity and pressure pulsations were clarified. Finally, the relationship between vortex evolution and the pressure pulsations in the outlet duct was established. The results showed that the flow rates of the turbine significantly affected the spatial and temporal evolution of the vortex rope in the outlet duct. The front chamber leakage flow and vortex shedding from the blade trailing edge also influenced the vortex distribution characteristics in the outlet duct. The dominant frequency of the pressure pulsation in the outlet duct was 6 fn under different operating conditions, and the amplitude of the pressure pulsation increased with the flow rates. The effect of vortex evolution on the local pressure pulsation characteristics decreased with increasing flow rates. The results can be used to improve and stabilize the operation and further optimization of PATs.

Inner Belt Wisp Precipitation Measured by ELFIN: Regimes of Energetic Electron Scattering by VLF Transmitter Waves

AbstractMan‐made very low frequency (VLF) transmitter waves play a critical role in energetic electron scattering and precipitation from the inner radiation belt, a type of which is called wisp precipitation. Wisps exhibit dispersive energy‐versus‐L spectra due to the evolution of electron cyclotron resonance conditions with near‐monochromatic VLF transmitter waves. Here, we report on such observations of inner belt wisp precipitation events with full pitch angle resolution in the energy range of 50 to ∼500 keV as measured by Electron Loss and Fields Investigation (ELFIN) at L &lt; ∼2 between March 2021 and April 2022. Statistical observations (82 events) reveal occasional (18 events) wisp precipitation events with local bounce‐loss‐cone electron flux enhancements, which provide new information compared with flux enhancements measured in previous studies only in the drift loss cone. Based on magnetic field and plasmaspheric density models, quasilinear theory, and detailed pitch angle distributions of wisps from ELFIN, we have estimated the wisp electron bounce‐averaged pitch angle diffusion coefficients to be of the order of 10−4 to 10−2 s−1. These are several orders of magnitude larger than the diffusion rates calculated from models using global statistical averages of VLF transmitter wave power. When using our estimated diffusion coefficients to deduce the associated local transmitter wave amplitudes near the equator, based on quasilinear calculations from a transmitter‐induced electron diffusion model, we find these wave amplitudes to be &gt;1 mV/m. Although probable overestimates, such inferred wave amplitudes exceed the theoretical threshold amplitude for nonlinear interactions, strongly suggesting that it is necessary to include nonlinear effects for an accurate evaluation of energetic electron scattering by transmitter waves.