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The relation between seizure **frequency** per month and number of channels with (A) ripples (>1/min), (B) fast ripples (>1/min), and (C) more than 20 fast ripples per minute. There were no patients with 0 channels with ripples (>1/min; A), but there were patients with 0 channels with fast ripples (>1 or >20/min; B and C). The seizure **frequency** was shown on a logarithmic scale, because of the distribution. As indicated in the text, there was no correlation between seizure **frequency** per month and the number of channels with more than 1 ripple or fast ripple per minute, but there was a positive correlation between seizure **frequency** and more than 20 fast ripples per minute.
... This table shows the correlation coefficients Rho for different alternative comparisons: seizure **frequency** (seizures/month) compared to the number and percentage of channels with ripples, fast ripples, spikes and ripples and fast ripples without spikes (first two lines), seizure **frequency** compared to number of channels with higher rates of ripples and fast ripples (>5, >10 and >20, lines 3–5) and number of seizure-days/month compared to channels with ripples and fast ripples. All comparisons were done for all patients, all patients with temporal lobe epilepsy and all patients with unilateral mesiotemporal seizure onset.

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Amplitude spectra of our entire data sets for HD 101065 acquired on HJD 2456460 – 6462. Panel (a) clearly shows the principal **frequency** of **oscillation** ν1=1.372867 mHz, and the secondary **frequency** ν2=0.954261 mHz. On pre-whitening ν1, we are left with ν2 in panel (b). Panel (c) gives the residuals after pre-whitening ν2. There is still evidence of further **frequencies** although below the detection criterion.
... Amplitude spectra of HD 101065 data acquired on HJD 2456460 – 6462. Panel (a) clearly shows the principal **frequency** of **oscillation** ν1=1.372867 mHz, and the secondary **frequency** ν2=0.954261 mHz. On pre-whitening ν1, we are left with ν2 in panel (b). Again, on pre-whitening ν2, we are left with low **frequency** residuals peaks in panel (c) which still suggests possible presence of further **oscillation** **frequencies**.
... The Non-linear least-square fit for the principal **frequency** ν1=1.372865 mHz. The JohnsonB amplitude of **oscillation** from year 1978 – 1988 were adopted from Martinez and Kurtz (1990), while that of year 2013 represent the amplitude and phase of **oscillation** secured from our combined data set (HJD 2456404 – 6462). Apart from year 2013 observation which has been analysed using 40-s integrations, 80-s integrations were used in all earlier observations adopted from Martinez and Kurtz (1990)).
... Stars: **oscillations**... The corresponding nightly amplitude spectra of HD 101065 on HJD 2456404 – 6462. Note the presence of resolved secondary **frequencies** ν2 in each panel around the region of 1 mHz. The known principal **oscillation** **frequency** ν1 is also present in all the panels, while 2ν1 which is the harmonic of ν1 appears marginally in panel (b) only.
... Non-linear least-square fit for the **frequencies** secured from our combined data set (HJD 2456404 – 6462).

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Radius and mean surface density for spherical fullerenes and the corresponding CNT radius for stable **oscillations** [33,34].
... **Oscillation** **frequency** of C60-nanotube **oscillator** versus half length of nanotube.
... **Oscillation** **frequency**... **Oscillation** **frequency** against the initial velocity of fullerene (L=70Å).
... **Oscillation** **frequency** against the initial velocity of fullerene (RF=3.55Å).
... Variation of **frequency** with the difference between the amplitude and half length of nanotube (L=70Å).

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Median **frequencies** of the vasomotor **oscillations**, assumed to be associated with baroreceptor activity, for systolic blood pressure (A), diastolic blood pressure (B), and heart rate (C). Means ± SEM. NT, normotensive subjects (n = 33); BHT, borderline hypertensive subjects (n = 29); HT, mildly hypertensive subjects (n = 30); **P < .01 and *P < .05 in pairwise comparisons.

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(a) Basic design conception of the wide operation **frequency** range phase interpolator circuit, and (b) the timing diagram of the DTA phase interpolator with various **oscillation** **frequencies**.
... Circuit architecture of the multiple **frequency** clock generator.
... Microphotograph of the multiple **frequency** clock generator.
... Normalized phase difference error with various **oscillation** **frequencies**.
... Multiple **frequency**... Measured **frequency** spectra of the output **frequency** (a) 88.8MHz (=2/3×133MHz) and (b) 797.8MHz (=6/1×133MHz).
... Voltage-controlled **oscillator**

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Pattern of prevalence of slow-wave activity (SWA*) and pattern of occurrence of activity in the spindle **frequency** range (SFA*), and the corresponding power spectra. The filtered EEG signals (SWA*: low-pass 4.5Hz; SFA*: band-pass 12–15Hz) and standard deviations calculated for consecutive 0.5s epochs are illustrated for 5min episodes of slow-wave sleep (SWA*), and of stage 2 (SFA*). Both time series were smoothed by applying a three-point moving median filter. Average power spectra of the 5min episodes (n=15) calculated for 64s epochs (FFT, Hanning window, detrended with mean value of epoch) shifted by 20s are plotted on a logarithmic **frequency** scale.
... SFA*, pattern of occurrence of spindle **frequency** activity... All-night EEG power spectra of slow-wave sleep (SWS; stages 3 and 4), stage 2 (S2) and REM sleep (REMS). (A) SWS spectra of three individuals; (B,C) mean of eight subjects. In A and B the spectra were computed for 20s episodes (**frequency** resolution 0.05Hz) and are plotted on a linear scale. In C the spectra were computed for 4s episodes (**frequency** resolution 0.25Hz) and plotted on a logarithmic scale (0dB=1μV2/0.25Hz). Bars below the spectra (B,C) depict F-values in those **frequency** bins in which a one-way ANOVA for repeated measures on log-transformed absolute values (factor “sleep stage”; d.f.=2, 14; P<0.05) yielded a significant effect. F-values of 3.74 correspond to a significance level of 0.05, and 6.51 to a significance level of 0.01. On average 319.5 20s epochs contributed to the SWS spectrum, 594.8 to stage 2, and 233.4 to REM sleep. For the individual subjects the values were 232, 292 and 406.
... SFA, spindle **frequency** activity (EEG power in the 12–15Hz range)... Pattern of prevalence of slow-wave activity (SWA*) and pattern of occurrence of activity in the spindle **frequency** range (SFA*). The original EEG, filtered EEG activity (SWA*: low-pass 4.5Hz; SFA*: band-pass 12–15Hz), and the standard deviation calculated for consecutive 0.5s epochs of the filtered signals are illustrated for a 20s epoch of stage 4 (SWA*) and stage 2 (SFA*).
... Average EEG power spectra (n=8) of nonREM sleep episodes 1 to 4. (A–C) 20s episode (**frequency** resolution 0.05Hz), (D–F) 4s episode (**frequency** resolution 0.25Hz). Absolute spectra are plotted on a linear scale (A) and on a logarithmic scale (D; 0dB=1μV2/0.25Hz). In the relative spectra (B,E), values in each **frequency** bin of episodes 2 to 4 are expressed as percentage of the corresponding bin in episode 1. Bars (C,F) depict F-values in those **frequency** bins in which a one-way ANOVA for repeated measures on log-transformed absolute values (factor “episode”; d.f.=3, 21; P<0.05) yielded a significant effect. F-values of 3.07 correspond to a significance level of 0.05, and 4.87 to a significance level of 0.01. On average, 210.9 20s epochs contributed to the spectra of episode 1, 234.6 to episode 2, 175.4 to episode 3, and 181.4 to episode 4.
... Average power spectra of the 0.5s time series (FFT, Hanning window, detrended with mean value of epoch) of SWA* and SFA* of nonREM sleep episodes 1 to 4. The **frequency** axis is plotted on a logarithmic scale. Spectra of 64s epochs shifted by 20s were calculated (**frequency** resolution 0.015625Hz). Only 64s epochs containing identical 20s sleep scores and being devoid of artifacts, were retained for further analysis. A one-way ANOVA for repeated measures on log-transformed absolute values (factor “episode”; d.f.=3, 21; Pfrequency range for the SWA* spectrum, and for the SFA* spectrum up to 0.5Hz. On average 135.3 64s epochs contributed to the spectra of episode 1, 138.8 to episode 2, 127.8 to episode 3, and 143.3 to episode 4.
... slow **oscillation**

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Rotary traveling wave **oscillator**... Comparison of **oscillation** **frequency** between calculation and simulation.
... **Frequency** tuning range... Rotary traveling wave **oscillator**.
... |A4+1|versuse **frequency** for different Ls.
... **Oscillation** **frequency** for two bands, i.e. when switches are on and off.

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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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Van der Pol **oscillator** (18) for a=1,q=1,r=0,ω0=1,s=0.5,x0=0,x˙0=1.
... Ueda **oscillator**; Eq. (1) for p=0.05,q=0,r=1,s=7.5,ω0=1,x0=0,x˙0=1.
... Van der Pol **oscillator** (18) for a=0.05,q=1,r=1,ω0=0.38,s=0.16,x0=0,x˙0=-1.

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Projected phase space of system (30) in the x1–x3 plane with N=10, for two different values q=3 ((a), (c)) and q=5 ((b), (d)), respectively. (a) and (b) describe the 2:1 period **oscillations** for the choice ω1=2 and ω2,ω3,…,ω10=1. (c) and (d) describe the quasiperiodic **oscillations** for the choice ω1=2 and ω2,ω3,…,ω10=1.
... (a) Time series plot of Eq. (15) for q=3 exhibiting periodic **oscillations** with the initial condition x(0)=3 and x˙(0)=0 for ω=1. (b) Phase space portrait of Eq. (15).
... Projected phase space of the almost integrable system (51) in the x1–x2 plane for the choices (a) ω1=1, ω2=2 exhibiting 1:2 period **oscillation**, (b) ω1=2, ω2=1 exhibiting quasiperiodic **oscillation**.
... Nonlinear **oscillators**... (Color online.) (a) Time series plot of Eq. (1) exhibiting periodic **oscillation** for three different initial conditions (three different colors) and ω=1.0. (b) Phase space portrait of Eq. (1).

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