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  • Ictal EEG recorded at a sampling rate of 10kHz (Patient 1). (A) Ictal EEG shown using conventional filter settings (low-pass filter 120Hz, time constant 0.1s). Only 10 channels are shown. Ictal EEG shows initial spike burst at HI1–4/HS1–4 and spike-and-waves at A5–6, followed by electrodecremental pattern and low amplitude fast activities at HI1–3/HS1. Filled circle and straight line indicate the presence of VHFO. The EEG at B, C, and D is shown using VHFO filter settings. (B and C) Preictal VHFO detected visually using low-pass filter of 3kHz and time constant of 0.001s. Preictal VHFO of 1000–2500Hz are observed at HI1 and HI2 electrodes (underlined). They appear intermittently before the start of seizures, and are interrupted by spikes. The amplitudes are 3.5–22.1μV (note the calibrations), and the durations were 12–27ms. These activities are not observed at other electrodes. HFO of 350–550Hz are seen at HS1–2 and HI1–2 electrodes, with durations of HFO of 10–14ms and the amplitudes of 22.6–234.7μV. Representative HFO peaks are marked by triangles (B). (D) VHFO recorded at HI1, HI2 (both electrodes also record preictal VHFO) and HS1 electrodes become sustained at the start of seizure. The frequencies of VHFO are 1000–2000Hz and the amplitudes are around 8.8–14.1μV. These activities superimpose on the slower rhythmic activities (70–90Hz) (marked by triangles). Sustained VHFO lasted approximately 10s. Again, these activities are not observed at other electrodes, although rhythmic activities are recorded. ... Very high frequency oscillations
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  • Normalized primary-mode frequencies of the drag and lift coefficients a... Time history of lift coefficient spanning three oscillation periods for a deeply submerged cylinder oscillating with A=0.4 and fe/fo=1.1 and 1.15. The dashed lines indicate the times when the cylinder moves to the highest position. ... Transverse oscillation... Definition of problem. U: inflow velocity, g: gravitational acceleration, D: cylinder diameter, A: amplitude of oscillation, fe: frequency of oscillation, h: distance between still fluid surface and cylinder top when the cylinder moves to the equilibrium position, ρi: mass density of the i-th fluid phase, μi: dynamic viscosity of the i-th fluid phase. ... Normalized beating frequency of lift coefficient (fb/fe), normalized vortex shedding frequency (fv/fe), and vortex structure number sequence (NS) for a deeply submerged cylinder oscillating with selected frequency ratios. The individual number in NS denotes the number of vortices which merge in the middle wake. ... Lift and drag coefficients as function of time for three frequency ratios with Fr=0.5, h=0.4, and A=0.4. Also shown is the time history of the vertical coordinate of the cylinder center. Te=1/fe is the prescribed oscillation period and tref some reference time when the cylinder reaches the highest position.
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  • Entrainment of spontaneous oscillation by an external stimulus. (A) Sinusoidal forces were applied to a spontaneously oscillating hair cell bundle for three different stimulation conditions: one at the frequency of the spontaneous oscillations (FO=4kHz) and two for slightly lower frequency (3.5kHz). Thick lines are bundle tip displacements and thin red lines are external stimuli. Initial states of the bundle for the three simulations were the same and selected to have the opposite phase to the stimulus. (B) Bundle displacement in response to the three different stimuli in (A) averaged over 160 presentations (top two records) and 80 presentations (bottom record). Note that the response at FO (4kHz, top) builds up with a time constant of 0.7ms, indicative of a sharply tuned resonator. The bundle entrained poorly to the 3.5kHz stimulus at low level (middle), but at the higher level the force was sufficient to suppress the spontaneous movement and the bundle movement was entrained to the external stimulus. (C) A single cycle of bundle displacement (red line) averaged over 200ms of response compared to the force stimulus (black line), which was scaled for comparison with displacements. The bundle compliance obtained by dividing the displacement amplitude by the force amplitude is given beside each trace. (D) PSD plots for each response showing a sharply tuned response at FO (top). At 3.5kHz, the spectral density contains frequency components (both the spontaneous oscillation and the stimulus; middle). For the larger stimulus level at 3.5kHz, the spectral density is now dominated by the stimulus frequency. ... Effects of Ca2+ on the spontaneous oscillation. Different levels of the calcium concentration at the fast adaptation site were simulated. The bundle oscillated when the Ca2+ concentration at the fast adaptation site was between 12 and 30μM. Other parameters were identical to those given in Table 1. The hair bundle oscillated most strongly at 4kHz with Ca2+ of 20μM. The oscillation frequency increased from 3kHz to 4.5kHz as the Ca2+ concentration increased from 12 to 30μM. Note the “twitch-like” behavior at low Ca2+. ... Compressive nonlinearity demonstrated by entrainment to an external stimulus. The hair cell bundle was stimulated with sinusoidal forces with different frequencies (1–16kHz) and magnitudes (0.1–1000 pN). (A) Representative examples of average bundle tip displacements (solid lines) and force stimuli (broken lines) scaled for comparison with displacements for one stimulus cycle. Displacements were averaged cycle by cycle over 200ms of response. (B) Bundle displacement plotted against stimulation frequency for three different force magnitudes. Note the sharp tuning for small 1 pN stimuli and the broad tuning for the largest 100 pN stimuli. (C) Bundle displacement plotted against force magnitude at the frequency of the spontaneous oscillations, FO=4kHz. Note that the relationship displays a compressive nonlinearity for intermediate stimulus levels, is linear at low stimulus levels, and again approaches linearity (denoted by dashed line) at the highest levels. (D) Gain plotted against stimulation frequency for three different force magnitudes. Gain is defined as the ratio of the compliance under the stimulus conditions to the passive compliance with the MT channel blocked. (E) Gain plotted against force magnitude at the frequency of the spontaneous oscillations, FO=4kHz. The gain declines from a maximum of 50 at the lowest levels, approaching 1 (passive) at the highest levels. ... Determinant of frequency: KD, Ca2+ dissociation constant. (A) The hair bundle morphology of a rat high-frequency hair cell was used to create a new FE model. The hair bundle had more stereocilia of smaller maximum height, (2.4μm compared to 4.2μm) than the low-frequency bundle. (B) Spontaneous oscillations of bundle position and open probability. (C) PSD plots indicating sharply tuned oscillations at 23kHz. For these simulations, KD and CFA, the Ca2+ concentration near the open channel, were elevated five times. Other values as in Table 1 except: fCa=8 pN and f0, the intrinsic force difference between open and closed states=−15 pN. ... Effects of loading the hair bundle with a tectorial membrane mass. (A) Passive resonance of a low-frequency (solid circles) and a high-frequency (open circles) hair bundle in the absence of the tectorial membrane mass with MT channels blocked. The system behaves as a low-pass filter with corner frequency of 23kHz (solid circles) and 88kHz (open circles). The hair bundle was driven with a sinusoidal force stimulus of 100 pN amplitude at different frequencies. (B) Passive behavior of the same two hair bundles surmounted by a block of tectorial membrane. The block of tectorial membrane had a mass of 6.2×10−12 kg for the low-frequency location, which was decreased fourfold for the high-frequency location. The MT channels were blocked, so the system was not spontaneously active. Resonant frequencies: 5.1kHz (solid circles) and 21kHz (open circles). (C). The active hair bundles, incorporating MT channel gating, combined with the tectorial membrane mass generated narrow-band spontaneous oscillations. PSD function is plotted against frequency, giving FO=2.9kHz, Q=40 for the low-frequency location, and FO=14kHz, Q =110 for the high-frequency location.
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  • Generic level schemes of atoms for optical qubits (left) and radio-frequency qubits (right). In addition to the two qubit levels {|0〉,|1〉} usually a third rapidly decaying level is used for laser cooling and state read-out. While the optical qubit is typically manipulated on a quadrupole transition, radio-frequency qubit levels are connected with Raman-transitions. ... Rabi oscillations of a single Ca+ ion. Each dot represents 1000 experiments, each consisting of initialization, application of laser light on the qubit transition and state detection. ... Normal modes of a three-ion crystal along the axial direction with motional frequencies ωi. ... Energy level scheme of a single trapped ion with a ground (|g〉) and an excited (|e〉) level in a harmonic trap (oscillator states are labeled |0〉,|1〉,|2〉,…). Ω denotes the carrier Rabi frequency. The Rabi frequency on the blue sideband transition |0,e〉↔|1,g〉 transition is reduced by the Lamb-Dicke factor η as compared to the carrier transition (see Eq. (5)). The symbols ωqubit and ωt denote the qubit and the trap frequency, respectively. ... Rabi oscillation on the blue sideband of the center-of-mass mode. The data were taken on a string of two 40Ca+ ions whose center-of-mass mode was cooled to the ground state. Only one of the ions was addressed. The population oscillates between the |S,0〉 and the |D,1〉 state of the addressed ion.
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  • (a) Time-averaged drag coefficients, (b) r.m.s. of drag coefficients, and (c) r.m.s. of lift coefficients as a function of frequency ratio and distance between two cylinders. ... Instantaneous vorticity contours of two oscillating cylinders at Re=160, go=2, Ae=0.2, and fe/fo**=1.0. (a) present result, (b) results from Mahir and Rockwell (1996). ... Peak values of Fourier transforms of lift coefficients of two oscillating cylinders ... Drag and lift coefficients as a function of time for one oscillating. ... Wake patterns of two oscillating cylinders ... Forced oscillation
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  • (A) The reduction in the frequency of the oscillations as a function of thiopental concentration. (B) The reduction in the frequency of the oscillations as a function of propofol concentration. (C) The reduction in the frequency of the oscillations as a function of ketamine concentration. Each point represents the mean of data from an average of 6 slices and the error bars are standard errors. The lines are least squares regressions. The data have been normalised such that the control frequency in the absence of anaesthetic is unity. The frequency (mean ± s.e.m) of the control response was 36.0 ± 0.1 Hz (n = 11) for the thiopental data, 38.0 ± 0.7 Hz (n = 21) for the propofol data and 33.8 ± 0.7 Hz (n = 38) for the ketamine data. ... 40 Hz oscillations... The effect of the optical isomers of etomidate on the oscillations. Each point represents the mean of data from an average of 5 slices and the error bars are standard errors. The inactive S(−)-enantiomer had no significant effect on the oscillation frequency at concentrations up to 2.5 μM. The lines have been drawn by eye and have no theoretical significance. The data have been normalised such that the control frequency in the absence of anaesthetic is unity. The frequency (mean ± s.e.m) of the control response was 38.9 ± 0.6 Hz (n = 54). ... (A) Representative traces from the same brain slice showing control oscillations (upper trace), oscillations in the presence of 1.4 vol% isoflurane (middle trace) and oscillations after washout of isoflurane (lower trace). (B) Power spectra of data from the same slice as in (A) showing the reduction in frequency in the presence of 1.4 vol% isoflurane. ... (A) Representative traces from the same brain slice showing control oscillations at 26 and 30 °C. (B) Power spectra of data from the same slice as in (A) showing the reduction in oscillation frequency at 26 °C compared to 30 °C. (C) Plot of oscillation frequency as a function of temperature. The line is a least squares regression. The data were recorded from 4 slices. ... Percentage change in carbachol-evoked gamma oscillation frequency and prolongation of IPSC time-course at clinical concentrations of anaesthetic
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  • Quantification of amplitude-to-phase cycle relationship. (A) Mean amplitudes of high frequency oscillations, sorted by concurrent low-frequency phase into 60 bins of 0.105rad, for an example time window during a seizure; (B) an ideal cosine; and (C) a sine is modeled. (D) Phasor demonstrating the amplitude–phase cycle relationship. (E) The argument (angle) of the example phasor is a single contribution to be incremented onto a cumulative polar histogram spanning multiple subjects for one of ten given time periods in the seizure. ... Cross-frequency coupling... Modulation of high frequency amplitude by low-frequency phase. In the seizure-onset zone, significant modulation of high-frequency amplitude (40–300Hz) is observed, mainly by the phase of theta and alpha oscillations during the ictal period. In the interictal period, no specific CFC with slower oscillations is observed. There is also less cross-frequency coupling in the early propagation zone during seizures and no significant coupling is noted in the non-epileptogenic cortex. The z-axis demonstrates the modulation of amplitudes of different narrow-band frequencies (x-axis) by the phases of other narrow-band frequencies (y-axis). Lower and upper planes represent uncorrected and corrected statistical thresholds at p<0.05, respectively. ... High frequency oscillations... Simulated data demonstrating expected polar histogram distribution. The high frequency amplitude is represented by the blue solid line, whereas the low-frequency phase is represented by the black dashed line. When the high frequency amplitude is maximal at the peak and trough of the low frequency phase, the polar histograms will indicate pi and 0, respectively. ... Individual seizure short-time Fourier transform spectrograms. The seizure onset zone contained predominantly low-frequency power, which was fairly heterogenous across the population. High frequency activity was also evident in all seizures as bursts of high power oscillatory activity. ... Topographic mapping of cross-frequency interactions in a representative subject. (A) Intraoperative image of grid demonstrating seizure onset and early propagation zones. (B) Fast-ripple amplitudes sorted by alpha phase for all grid electrodes. Cosine wave represents alpha phase from −π to π. Increased pHFO-to-low-frequency coupling occurs in the resected cortex (black borders). Values normalized by 95% confidence interval such values above 0 are significant at pfrequency modulation index for all electrodes, where the X-axis represents low frequency phase (1 to 40Hz; left to right), and the Y-axis denotes envelope amplitude (1 to 300Hz; top to bottom). Values exceeding Bonferroni correction threshold shown. Significant modulation of pHFO amplitudes by low-frequency phase is observed in the epileptogenic cortex. ... To characterize the ictal dynamics of relations between pHFO amplitude and low frequency phase, we measured the preferred slow oscillatory phase at which high amplitude pHFOs occurred at various times throughout the seizure. When the preferred phases from all bins from all subjects were plotted cumulatively on polar histograms, it was observed that pathological fast-ripple amplitudes preferentially occurred during the trough of alpha oscillations, whereas pathological ripple amplitudes preferentially occurred between 0rad and π/2rad of alpha and theta oscillatory cycles (Fig. 5; poscillations (p=0.14 and p=0.68, respectively). At seizure termination (i.e. the last bin), pHFO amplitudes occurred at the trough of the alpha oscillatory cycle (pathological ripple amplitude: p<0.01; pathological fast-ripple amplitude: p=0.03). Ripple amplitude maxima were also found at the peak of delta phase irrespective of the seizure progression (Supplementary Fig. S9). To ensure that differences in bin length did explain the measures of CFC, a reanalysis of the data with fixed length segments comprised of the first and last 2000ms of seizures, revealed the same pattern.
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  • Frequency domain analysis in CAD ... Frequency domain analysis in ischemic stroke ... low frequency oscillations
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  • System frequency and load demand on September 15, 2011 KEPCO system rolling blackout. ... Power flow and frequency for 10min between 17:00 and 17:10. ... Power flow for 10s with a significant oscillation. ... Low frequency oscillation
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  • qy,ave/qy,cond for various frequencies (p1/pm=0.01, ks1/kf=1/12, ks2/kf=1/2). ... Oscillating flow... uave for various frequencies (p1/pm=0.01, ks1/kf=1/12, ks2/kf=1/2).
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