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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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  • Channels with potential muscle artefacts were excluded from the analysis. This was done by reviewing the SEEG at normal time scale with a filter of 80Hz together with the available epidural, ECG and EMG channels. Muscle artifact can be recognized as a simultaneous high frequency artifact over channels that are potentially outside of the brain, like channels LS6-7 and above, LC5-6 and above and RS5-6 and above in this example. Another clue could be obtained by filtering at lower frequencies as well. If still in doubt, the signal was reviewed at a timescale showing all samples. Muscle artifact shows a less sinusoid shape than HFOs and the frequency spectrum shows relatively more frequencies (Otsubo et al., 2008). Whenever there was doubt, the channel was excluded. ... High frequency oscillations
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  • Typical spontaneous Ca2+ oscillations from the computational study. From top to bottom, the three plots correspond to oscillations in cytoplasmic Ca2+, ER Ca2+, and cytoplasmic IP3. All three variables have the same frequency but different peak times (details are shown in Fig. 4). ... (A) Bifurcation diagram of Ca2+ oscillations as a function of membrane potential. Sustained Ca2+ oscillations occurred in the potential range of −70.0 to −64.9 mV, where the maximum and minimum of Ca2+ oscillations were plotted. The dashed line refers to the unstable steady state. Out of the oscillatory domain, the system evolved into a stable steady state. (B) Frequency of Ca2+ oscillations versus membrane potential. ... Dependence of Ca2+ oscillations on extracellular Ca2+ concentration. Ca2+ oscillations stopped when the extracellular Ca2+ concentration was too low or too high. From 0.1 to 1500 μM, the frequency of Ca2+ oscillations increased with a rise in extracellular Ca2+ concentration. ... Amplitude and frequency of Ca2+ oscillations versus temperature. In the temperature range of 20–37°C, both the amplitude (indicated as an asterisk) and frequency (dotted line) decreased with temperature. ... The occurrence of Ca2+ oscillation depends on the membrane potential. When the membrane potential is −64.9 mV, there is no Ca2+ oscillation. Within −70.0 to −64.9 mV, the frequency and amplitude of Ca2+ oscillations change with the membrane potential.
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  • Relation between the oscillation frequency and the coupling strength. ... Capacitive coupled RC-oscillators. ... RC-oscillators... Coupled oscillators... (a) Single RC oscillator and (b) small-signal equivalent circuit. ... Quadrature oscillator... Simulated frequency. ... Van der Pol oscillators... Frequency of oscillation with the oscillators uncoupled and coupled (CX=20fF).
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  • RANKL-induces Ca2+ oscillations and transient cation currents in RAW 264.7 cells. RAW 264.7 cells were cultured with or without RANKL (30ng/ml) or GST-RANKL (20ng/ml) for 18h and intracellular Ca2+ concentration ([Ca2+]i) and membrane currents were recorded. (A) Spontaneous Ca2+ oscillations in six cells treated with RANKL for 18h were reversibly inhibited by an application of ruthenium red (5μM RR), an inhibitor of TRPV channels. Traces shown in the panel were obtained from six independent cells. (B) Average frequency of [Ca2+]i oscillations (times per 10min) before (control; n=10) and after application of ruthenium red (RR, 5μM; n=10). Each column indicates mean±SEM. Number of cells studied is indicated in parentheses. **PFrequency (times per 1min) of transient inward currents (only counting those with an amplitudes of more than 2pA/pF) before and after application of ruthenium red (RR, 10μM). Each column indicates mean±SEM from number of cells (n) studied. **P<0.01. ... Inhibition of RANKL-induced Ca2+ oscillations by tetracycline-inducible shRNA silencing targeted to store-operated Ca2+ entry associated proteins in RAW264.7/teton/shStim1 or/shOrai1 cells. (A) and (B) RAW264.7/teton/shStim1 (A) or/shOrai1 (B) cells were incubated for 24h in the absence (a) or presence (b) of tetracycline (1μg/ml) and then treated with RANKL (30ng/ml) for 18h, and [Ca2+]i was measured. The changes in [Ca2+]i shown in each graph were simultaneously recorded from four or five cells. Expression of Stim1 (A) or Orai1 (B) protein was reduced in tetracycline treated (tetracycline +) cells as compared to untreated (tetracycline −) cells. ... Effects of PLC inhibitor, U73122, on RANKL-induced [Ca2+]i oscillations and transiently activated cation currents in RAW 264.7/teton/shRNA/TRPV2 cells. Cells treated with RANKL for 18h in the absence of tetracycline were exposed to a phosphlipase C inhibitor, U73343 and its inactive analogue (U73122). (A) Effects of U73343 (10μM) and U73122 (10μM) on Ca2+ oscillations. Recordings were obtained from four cells. (B) Frequency of [Ca2+]i oscillations (times per 10min) before (control; n=12) and 10min after treatment with U73343 (n=5) or U73122 (n=10). Each column indicates mean±SEM. Number of cells studied is indicated in parentheses. **PFrequency (times per 1min) of the transiently activated inward currents (only counting those with amplitude of more than 2pA/pF), before and 15min after treatment with U73343 or U73122. Each column indicates mean±SEM from number of cells (n) studied. **P<0.01. ... Calcium oscillations... Inhibition of RANKL-induced transient activation of cation currents by TRPV2 silencing in RAW 264.7/teton/shTRPV2 cells. RAW 264.7/teton/shTRPV2 cells were cultured with RANKL (30ng/ml) for 18h in the absence (A) or presence (B) of tetracycline (1μg/ml) or doxycycline (10ng/ml) and whole-cell currents (at a membrane potential of −60mV) were recorded using the whole-cell configuration of patch-clamp technique. (C) Frequency (times per 1min) of the transiently activated inward currents (only counting those with amplitudes of more than 2pA/pF) was determined in cells treated with (tetracycline +, closed columns) or without tetracycline (tetracycline −, open columns). Each column indicates mean±SEM. Number of cells studied is indicated in parentheses. **P<0.01. ... Inhibition of RANKL-induced Ca2+ oscillations by tetracycline-inducible shRNA silencing targeted to TRPV2 in RAW264.7/teton/shTRPV2 cells. RAW264.7/teton/shTRPV2 cells were incubated for 24h in the absence (A) or presence (B) of tetracycline (1μg/ml) or doxycycline (10ng/ml) and then treated with RANKL (30ng/ml) for 18h, and their [Ca2+]i was measured. Changes in [Ca2+]i shown in each graph were simultaneously recorded from four cells. (C) Expression of TRPV2 protein was reduced in tetracycline treated (tetracycline +) cells as compared to untreated (tetracycline −) cells. (D) Mean frequency of [Ca2+]i oscillations in cells before (0h) and 18h or 48h after RANKL-treatment in the presence (tetracycline +, closed columns) or absence (tetracycline −, open columns) of tetracycline. Each column indicates mean±SEM. Number of cells studied is indicated in parentheses. **P<0.01.
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  • (a) Time series for the first chrono-mode of the POD, a1(t), for the three different forcings with vin=0.4m/s (Re=3.1in×103, N=0.02). (b) Power spectra of the chrono-modes a1(t). Frequency peaks are found at fPOD=0.027Hz (FL0). The values of the frequency peaks are in reasonable agreement with the frequencies found for the free surface fluctuations, fTS. ... (a–c) Profiles of the turbulence kinetic energy kturb,2D. (d–f) Profiles of the kinetic energy associated with the large-scale oscillations kosc,2D. The inlet velocity is vin=0.4m/s (Rein=3.1×103, N=0.02). ... Amplitude A and frequency fTS of the free surface oscillation at a monitoring point at x=0.175m for the three different forcings (Rein=3.1×103, N=0.02). Dominant frequency fPOD from the power spectrum of the first chrono mode of the POD. ... Self-sustained oscillations
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  • Critical frequency for the one-stage gene circuit. (A) The amplitude of output oscillations decreased with fin. fc was calculated as the intersection between the “average noise level” curve and the “oscillation amplitude” curve. (B) Calculations of fout for varying fin using stochastic simulations. (C) Fraction of stochastic simulations that generated correct fout (i.e., where fout=fin). ... Analysis of frequency signals with noise. (A) A one-stage gene circuit where the output protein P is controlled by a transcription activator, A. (B) An oscillatory input signal can generate an output signal with oscillations compounded with noise. The mean and standard deviation of the output signal of the linearized model can be analytically computed. Here, we define the mean value as the oscillatory component and the standard deviation as the noise component. Alternatively, the stochastic simulations of the output signal for the nonlinear system can be analyzed by the FFT method to obtain its dominant frequency (see Methods for more details). ... Transmission of a multiplexed signal. (A) A multiplexed input signal. (B) The corresponding output signal computed by stochastic simulation. (C) Power spectra of the input signal. (D) Power spectra of the output signal. Power spectra of the output signal indicate that all three frequencies were transmitted with complete fidelity. Even though power spectra decreased when the input frequency increased, they were still at least 10-fold higher than the power spectra of background noise. Three frequencies (0.005/min, 0.0067/min, and 0.01/min) were multiplexed in a composite signal with an amplitude of five molecules for each input frequency.
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  • Flow forces acting on an oscillating cylinder. ... Dimensionless (a) amplitude (A*=A/D) and (b) frequency (f*=fos/fna) of the crossflow oscillations versus the reduced velocity for a curved cylinder in the convex configuration (■) and a vertical cylinder (○). ... Flow visualizations in the wake of a curved cylinder for the fixed (a) convex and (b) concave configurations, and free-to-oscillate (c) convex and (d) concave configurations. Flow is from left to right. ... Dimensionless (a) amplitude (A*=A/D) and (b) frequency (f*=fos/fna) of the crossflow oscillations versus the reduced velocity for a curved cylinder in the concave configuration (▲) and a vertical cylinder (○).
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  • (a) Diffusion signal for different waveforms: square with 90° phase, apodised cosine and apodised trapezoid as a function of oscillation frequency for four different sizes of the restricted compartment; (b) corresponding extracted ADC values. The diffusion signal and ADC for apodised trapezoid and square wave are very similar and are plotted on top of each other. ... Oscillating gradient... (a) Average signal difference between square and sine approximations and the full trapezoidal expressions as a function of α for R=2μm and 10μm. (b) Diffusion signal for R=5μm for the three waveforms with gradient strength G=60mT/m and 200mT/m as a function of oscillation frequency. ... (a) Average signal difference between square and sine approximations and the full trapezoidal expression considering: I – same amplitude, II – same area under the curves, III – same area under the squared curves and IV – same b value per oscillation. (b) Difference between square and sine approximations and the full trapezoidal expressions with SR=200T/m/s as a function of n for all data points with R=5μm. ... Restricted diffusion signal as a function of oscillation frequency for (a) several values of Δ, R=5μm and G=0.1T/m; (b) several gradient strengths, R=5μm and Δ=25ms. In (a) and (b) the filled markers indicate waveforms with integer number of oscillations. Restricted diffusion as a function of (c) gradient strength for several frequencies, R=5μm and Δ=45ms; (d) cylinder radius for several frequencies, G=0.1T/m and Δ=45ms. The markers show the MC simulation and the solid lines are the GPD approximations. The vertical bar separates different scales on the x-axis. ... Square wave oscillations
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  • Oscillation detection in a single electrode with weak alpha. The electrode was selected from the same subject as in Figs. 2 and 4. (A) The 256-electrode array with the selected electrode highlighted in yellow. (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) Oscillations detected across all frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes -closed condition (red) and eyes-open condition (black) that oscillations were detected at each frequency. (E) The raw signal from the chosen electrode, with detected oscillations at the peak alpha frequency (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E, to show the spindle-like appearance of the alpha oscillation. ... Temporal independence of two alpha components. (A) An 8-s epoch from the alpha component shown in Fig. 2, with detected alpha-frequency oscillations highlighted in red. (B) The same time segment as in A, from the alpha component in Fig. 6. Note the alpha oscillation is maximal in B when the oscillation is at a minimum in A, demonstrating why these were extracted as temporally independent components. ... Lateralized alpha component. From the same subject as Figs. 2 and 4–5. (A) The spline-interpolated scalp distribution of an alpha component extracted by ICA. Color scale denotes electrode weight (unitless). (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) Oscillations detected across all frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at each frequency. (E) The time-domain representation of the chosen component, with detected oscillations at the peak alpha frequency (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E. ... Oscillation detection in an ICA alpha component. (A) The spline-interpolated scalp distribution of an alpha component extracted by ICA. Color scale denotes electrode weight (unitless). (B) Background wavelet power spectrum mean and standard deviation (blue) and the linear regression fit to the background (green). (C) Oscillations detected across all frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at each frequency. (E) The time-domain representation of the chosen component, with detected oscillations at the peak alpha frequency (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E, to show the spindle-like appearance of the alpha oscillation. ... Oscillation... Oscillation detection in a single electrode with strong alpha. The electrode was selected from the same subject as in Fig. 2. (A) The 256-electrode array with the selected electrode highlighted in yellow. (B) Background wavelet power spectrum mean and standard deviation (blue), and the linear regression fit to the background (green). (C) Oscillations detected across all frequencies by the oscillatory episode detection method. Red vertical lines indicate when participants were instructed to close their eyes and black vertical lines indicate when participants were instructed to open their eyes. (D) The proportion of time (Pepisode) during the eyes-closed condition (red) and eyes-open condition (black) that oscillations were detected at each frequency. (E) The raw signal from the chosen electrode, with detected oscillations at the peak alpha frequency (9.5Hz) highlighted in red. Vertical lines are the same as above. (F) An expansion of the highlighted section in E to show the spindle-like appearance of the alpha oscillation.
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