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Amplitude and Intertrial Phase Coherence of Theta and Gamma Oscillations ... theta oscillations... The amplitude of stimulus-driven gamma oscillations is modulated by the phase of ongoing theta oscillations. This cross-frequency coupling indicates a hierarchical organization of cortical oscillatory dynamics in both healthy control subjects (black line) and schizophrenia patients (red line). The x axis indicates theta phase. The y axis indicates gamma amplitude. ... Heuristic model of phase-amplitude cross-frequency coupling. Gamma oscillations (red and blue lines) are largest in the excitatory versus inhibitory phase of ongoing theta oscillations (black line). Note that excitatory and inhibitory phase may vary according to tasks and neural sources. ... cross-frequency coupling... gamma oscillations... Schizophrenia patients have normal theta-phase/gamma-amplitude cross-frequency coupling. The modulation index demonstrates the relative strength of cross-frequency coupling via comparison of observed (O) versus resampled or surrogate (S) electroencephalography data in healthy control subjects (black circle) and schizophrenia patients (red squares). The y axis indicates log transform of modulation index. ... neural oscillations... Schizophrenia patients (SZ) have increased theta amplitude and decreased gamma synchrony. The left column shows time-frequency maps from healthy control subjects (HC) and the middle column shows time-frequency maps from schizophrenia patients. The x axis indicates time in milliseconds and the y axis indicates frequency. Color indicates amplitude in the top row and intertrial phase coherence (ITC) in the bottom row. The right column shows difference between schizophrenia patients and healthy control subjects. Difference maps show only time-frequency points at p < .01.
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Detection and parameters of ictal high frequency oscillations in 19 patients. ... Ictal EEG and HFO in Patient 1. (A) Conventional EEG (low-pass filter 120Hz, time constant 0.1s) reveals periodic sharp waves at LH1-3. The periodic sharp waves are followed by more repetitive sharp waves in the left hippocampus and amygdala. Filled circles indicate the presence of HFO. (B) HFO waveforms (low-pass filter 300Hz, time constant 0.003s). 200–250Hz high frequency activities are detected at LH1-3. Note the calibration, which shows that HFO waves have very small amplitude and short duration. ... Ictal EEG and HFO in Patient 2. (A) On conventional EEG (low-pass filter 120Hz, time constant 0.1s), ictal EEG starts with repetitive spikes at LA1, LH2, LH3, and LH4, as well as rhythmic alpha activity at LH1 at the same time. The spikes spread widely in the left temporal area, and are replaced by rhythmic beta waves at LH1, LH2, LH3, and LH4. The right hemispheric electrodes do not show clear ictal activities throughout. Filled circles and bold line indicate the presence of HFO. (B) HFO waveforms before conventional EEG onset, and around onset (low-pass filter 300Hz, time constant 0.003s). 200–333Hz high frequency activities are recorded at 1 to 3 electrodes on the right side (RA1, RH1, and RH2). Circles indicate the locations of HFO. Although spikes are seen on the left side, HFO is not recorded at the left-sided electrodes. ... Ictal EEG and HFO in Patient 7. (A) On conventional EEG (low-pass filter 120Hz, time constant 0.1s), ictal EEG starts with a large positive sharp wave at RH1 and RH2, followed by beta activities at the same electrodes. Seven seconds later, rhythmic beta waves start at RA1 and RA2 with gradual evolution. Approximately 45s later, left-sided electrodes (LH1-4 and LA1-4) start showing small spikes, followed by beta activities in the same electrodes Filled circles and the bold line indicate the presence of HFO. (B) HFO waveforms before conventional EEG onset, around onset, and around conventional EEG onset at the left hemisphere (low-pass filter 300Hz, time constant 0.003s). These demonstrate 200–333Hz high-frequency activities at 1–4 electrodes in the right side (RA1, RA2, RH1 and RH2). These also demonstrate high-frequency activities at LA1-2 and LH1 around the conventional EEG onset on the left side. Circles indicate the locations of HFO. ... High frequency oscillations... Detection and parameters of interictal high frequency oscillations.
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Pressure fluctuations in the 8-in. burner for the stable combustion case ((A), Φ=0.7) and for the oscillating case ((B), Φ=1.0) under the fixed air flow rate condition Qa=800m3/h. ... Pressure fluctuations spectra of the 12-in. burner for the stable combustion case ((A), part (a) of Fig. 11A), and for the oscillating case ((B), part (a) of Fig. 11B), and for the early stage of the high frequency oscillation ((C), part (b) of Fig. 11B). ... Pressure fluctuations spectra of the 8-in. burner for the stable combustion case ((A), part (a) of Fig. 8A), and for the oscillating case ((B), part (a) of Fig. 8B), and for the early stage of the high frequency oscillation ((C), part (b) of Fig. 8B). ... Natural frequencies of tangential/radial mode oscillations of the 12-in. burner (A) and the experimental peak frequencies (B) (peak frequencies (c)–(h) in Fig 12B). ... Natural frequencies of tangential/radial mode oscillations of the 8-in. burner (A) and the experimental peak frequencies (B) (peak frequencies (c)–(h) in Fig 10B).
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Oscillator... Oscillation frequencies against bias currents in the proposed circuit for various capacitances. ... Proposed current-mode quadrature oscillator.
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Representative time-frequency spectra and the corresponding electroencephalography (EEG) traces. Parts of the temporally expanded and filtered EEG traces are shown in the left column (low-cut filtered at 0.5Hz in blue and filtered at 70Hz in red). A ripple with a frequency above 100Hz occurs in temporal association with the positive peak, the ascending slope, and/or the negative peak of the spike; it is barely visible near the spike-peak in the trace with a 0.5-Hz filter (magnification in box). The resulting time-frequency spectra in the right column show spectral spots (yellow arrows) in association with the spikes in the overlaid traces from the EEGs with CSWS (B corresponding to A with a peak frequency of 128.9Hz; (D) corresponding to (C) with a peak frequency of 125.0Hz). ... Ictal discharges associated with epileptic spasms. (A) Ictal ECoG traces are shown with a low-frequency filter of 53Hz and a high-frequency filter of 300Hz. Ictal augmentation of HFOs occurred at channel 1 and quickly involved the surrounding channels. The end of HFOs augmentation occurred at channel 1 and sequentially involved the surrounding channels; this observation was referred to as the “ictal doughnut phenomenon”. The trigger point for time-frequency analysis was placed at the EMG onset detected at right deltoid muscles. (B) Time-frequency plots derived from 62 spasms are shown. Augmentation of HFOs preceded the EMG onset (denoted as ±0ms). (C) The amplitudes of HFOs associated with spasms are shown. ... Ripples recorded with surface EEG. Example of ripples recorded on surface EEG. The upper section shows ripple oscillations co-occurring with a spike, with oscillations visible during the spike. The middle section shows a ripple co-occurring with a spike with oscillations not visible during the spike, but visible after filtering. In the bottom section a ripple independent of any spike can be observed. (A) Raw EEG. (B) Raw EEG with expanded time. (C) EEG filtered with high-pass filter of 80Hz.
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Time-frequency analysis... Multivariate modulated oscillations... The partitioned frequency domain with the multivariate bandwidth given by Bl,m, where l corresponds to the level of the frequency band and m is the frequency band index. ... Time-frequency analysis of Doppler radar data. (a) The time domain waveforms of both the high gain and low gain Doppler radar data. (b) The time-frequency representation of Doppler radar data using the proposed multivariate extension of the SST (left panel) and the MPWD algorithm (right panel). A window length 1063 was used for the MPWD. ... Amplitude and frequency modulated signal... Instantaneous frequency... The time-frequency representations for both the proposed method (left panels) and the MWPD (right panels) for a bivariate AM/FM signal, with input SNR of (a) 10dB, (b) 5dB and (c) 0dB. The window length used for MPWD was 681 samples. ... Time-frequency analysis of real world float drift data. (a) The time domain waveforms of bivariate float velocity data. (b) The time-frequency representation of float data using the proposed multivariate extension of the SST (left panel) and the MPWD algorithm (right panel). A window length 501 was used for the MPWD. ... A comparison between the localization ratios B, for both the proposed method and the MPWD, evaluated for a bivariate oscillation with the following joint instantaneous frequencies: (a) 10.5Hz, (b) 40.5Hz, and (c) 100.5Hz. A window length of 1001 samples was used for the MPWD.
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Microbubble oscillation... The bubble’s natural frequency as a function of bubble radius for bubbles lying in the center of compliable vessels with L = 100 μm: (a) dimensional natural frequency; (b) dimensionless natural frequency. ... Natural frequency... The natural frequency of a bubble with a0 = 4 μm as a function of the rigidity index k of the blood vessel in compliable vessel with R0 = 5 μm and L = 500 μm: (a) dimensional natural frequency; (b) dimensionless natural frequency. ... The bubble’s natural frequency as a function of the vessel inner radius for bubbles lying in the center of compliable vessels with L = 100 μm: (a) dimensional natural frequency; (b) dimensionless natural frequency. ... The bubble’s natural frequency as a function of bubble radius for bubbles lying in the center of rigid vessels with L = 500 μm: (a) dimensional natural frequency; (b) dimensionless natural frequency. ... The bubble’s natural frequency as a function of the vessel inner radius for bubbles lying in the center of rigid vessels with L = 500 μm: (a) dimensional natural frequency; (b) dimensionless natural frequency, which is the normalized natural frequency of a bubble in the corresponding unbounded field predicted by the Rayleigh-Plesset equation f0=12π3κ(p0+2σ/a0)ρa0  2 − 2σρa0  3. ... Nonlinear oscillation
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Frequency encoding... Parameter values corresponding to the simple oscillations and the various types of complex oscillatory behavior in the Ca2+ oscillations model ... Effects of cytosolic Ca2+ oscillations on the fraction of active phosphorylase. (a) Average fraction of active phosphorylase as a function of average Ca2+ concentration for different VM5, the dot line by the response of 〈X〉 to the regulation by a sustained Ca2+ concentration. (b) Average fraction of active phosphorylase as a function of period of Ca2+ oscillations, A and B correspond to these as marked in Fig. 1b, and period of Ca2+ oscillations at A or B is the largest for a given VM5. ... (a) Temporal evolution of fraction of active phosphorylase regulated by simple Ca2+ oscillations at a fixed stimulation level β=0.5 for different VM5. (b) Different relationships between the frequency of Ca2+ oscillations and the level of stimulation for VM5=5 μMmin−1 (solid line), VM5=15 μMmin−1 (dash line) and VM5=30 μMmin−1 (dot line). h1, h2 and h3 correspond to the smaller supercritical Hopf bifurcation points of Ca2+ kinetics for different VM5, and A and B correspond to the smallest frequency of Ca2+ oscillations, respectively. The other parameter values are given by the first column in Table 1. ... Effects of bursting Ca2+ oscillations on the fraction of active phosphorylase. (a) The relationship between average fraction of active phosphorylase (solid line) and frequency of Ca2+ oscillations (solid circle) as a function of β. Points A and C (open circles) correspond to the two supercritical Hopf bifurcation points of Ca2+ dynamics. Note that some frequencies of bursting Ca2+ oscillations jump located B (open circle). (b) Average fraction of active phosphorylase as a function of the period of bursting Ca2+ oscillations. ... Calcium oscillations... Effect of complex Ca2+ oscillation on the fraction of active phosphorylase. (a) 〈X〉 vs. β for complex Ca2+ oscillations: bursting (curve a), chaos (curve b, ϵ=11 min−1), chaos (curve c, ϵ=13 min−1) and quasiperiodicity (curve d). (b) 〈X〉 vs. 〈Z〉 for different Ca2+ oscillation types: bursting (curve a), chaos (curve b, ϵ=11 min−1), chaos (curve c, ϵ=13 min−1) and quasiperiodicity (curve d). The open circles are the response of 〈X〉 to the regulation by a sustained Ca2+ concentration.
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When analyzing the nonlinear Duffing oscillator, the weak nonlinearity is basically dependent on the amplitude range of the input excitation. The nonlinear differential equation models of such nonlinear oscillators, which can be transformed into the frequency domain, can generally only provide Volterra modeling and analysis in the frequency-domain over a fraction of the entire framework of weak nonlinearity. When the amplitude of the excitation exceeds a certain value, the underlying nonlinear differential equation will become invalid in the frequency domain. This paper discusses the problem of using a new non-parametric routine to extend the capability of Volterra analysis, in the frequency domain, to weakly nonlinear Duffing systems at a much wider range of excitation amplitude range which the current underlying nonlinear differential equation models fail to address.
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Dependency of the computed oscillator parameters as a function of the normalized frequency. ... Variations of the computed self-starting oscillations frequency versus normalized s parameter. ... Dependence of the amplitude and frequency of oscillations on bias voltage for the first stage of the oscillator. ... Variation of frequency and amplitude of oscillations on the load resistor for the circuit oscillator with single TD. ... Self-starting oscillation... Variations of the amplitude and frequency of oscillations as a function of external capacitor values, and positions. ... Millimeter wave oscillators... Cascaded oscillator networks
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