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High-frequency oscillations... Time–frequency distributions. On the left side, the full 20–1000 Hz range is displayed for three exemplary subjects. The two graphs per subject show the ERG and VEP activity, respectively. The high-frequency oscillations appear as a distinct area which in most cases is around or above 100 Hz. The flash was given at t=0. Those parts of the time–frequency diagram which would be contaminated by edge effects are displayed in white. Their spread is due to the inevitable frequency-dependent finite time resolution, which also causes the spurious pre-stimulus activity at low frequencies. The white rectangles in the diagrams mark the regions of interest, which are shown enlarged on the right side for all 7 subjects. The arrows link the high-frequency maxima of ERG and VEP. Most subjects produced activity around or above 100 Hz in both VEP and ERG. However, only in one subject (S1) the frequencies matched. Asterisks indicate the significance levels of frequency differences in standard notation, based on a sequential Bonferroni adjustment. No significance value could be obtained for subject S3.
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Dependence of the phase shift α on the two parameters ng and Φe. The qubit is irradiated by microwaves with a frequency of 8.0GHz. The periodic circular structure is due to the variation of the total interferometer-tank impedance caused by transitions from the lower to the upper energy band. The “crater ridges” (solid-line ellipse) correspond to all combinations of the parameters ng and Φe that give the same energy gap (8.0GHz) between the respective states [14]. ... Tank phase shift α dependence on gate parameter ng for different magnetic flux applied to the qubit loop . The data correspond to the flux Φ/Φ0=0.5, 0.53, 0.54, 0.56, 0.57. 0.61, 0.62, 0.65 (from bottom to top). For clarity, the upper curves are shifted. ... Superconducting qubits... Integrated design: Al qubit fabricated in the middle of the Nb coil (left-hand side), and single-Cooper-pair transistor (right-hand side). ... Left-hand side: tank phase shift α dependence on gate parameter ng without microwave power (lowest curve) and with microwave power at different excitation frequencies. The data correspond to the frequency of the microwave ΩMW/2π=8.9, 7.5, 6.0GHz (from top to bottom) [14]. Here the applied external magnetic flux was fixed Φdc=Φ0/2. For clarity, the upper curves are shifted. Right-hand side: energy gap Δ between the ground and upper states of the qubit determined from the experimental data for the case δ=π (Φdc=Φ0/2) [14]. The dots represent the experimental data, the solid line corresponds to the fit (cf. text). ... Calculated dependence of the tank voltage phase shift α on the phase difference δ. The curves correspond to the fixed frequency Ω/2π=7.05GHz with the different amplitude of the excitation (from bottom to top n˜g is: 0.1, 0.2, 0.4) [11]. For clarity, the upper curves are shifted.
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Driven qubit
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Charts of the Lyapunov exponents for the four dissipatively coupled phase oscillators on the frequency detunings parameter plane (Δ1,Δ3). Values of the parameters are μ=0.4, (а) Δ2=0.4, (b) Δ2=2.4. Resonance conditions in the chain of oscillators are shown by arrows. ... Examples of phase portraits for the system (2). (a) Two-frequency resonance regime of the type 1:3 for Δ1=−1.5, Δ2=1, μ=0.6; (b) three-frequency regime for Δ1=−1, Δ2=1, μ=0.25. ... Chart of the Lyapunov exponents for three coupled van der Pol oscillators on the frequency detunings parameter plane. Numbers correspond to cycle periods in the Poincaré section. Values of the parameters are λ=0.1,μ=0.04. ... Chart of the Lyapunov exponents for three coupled van der Pol oscillators on the frequency detunings parameter plane. Numbers correspond to cycle periods in the Poincaré section. Values of the parameters are λ=1,μ=0.4. ... Chain of van der Pol oscillators... Full synchronization area for the four phase oscillators on the frequency detunings parameter space (Δ1,Δ2,Δ3).
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In all plots the decay rates κ/g=0.1, γr/g=4.35×10-2, and cavity factor Q=1400. The quantum dot excitonic Bohr frequency is assumed to be in resonance with the cavity field frequency, i.e., ωqd=ωc. The amplitude of the external laser field to the cavity decay rate ratio is fixed to I/κ=631. The coherence ρ01≡ρ(0,1) dynamics is plotted for: (a) Δωcl=0.4g; (b) Δωcl=g; (c) Δωcl=100g; (d) Δωcl=1000g. The cavity photons mean number is plotted in (e) and (f). We have used a logarithmic scale for the time axis and the values: (i) Δωcl=g; (ii) Δωcl=1000g, for the solid and dotted curves, respectively. ... Rabi oscillations
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(A) Comparison of the frequency of oscillations during oblique, pure horizontal and pure vertical saccades. Number of observations is plotted on y-axis, while x-axis represents bins of oscillation frequency. Each data point represents the number of observations in a given frequency bin. Black trace suggests oblique saccade, Gray traces with circular symbols are horizontal saccades and triangular symbols represent vertical saccade. Dashed lines depict median oscillation frequency. (B) Comparison of frequency oblique saccade oscillations with the frequency of orthogonal saccadic oscillations during pure horizontal and vertical saccades. Each data point depicts one subject. Black data points are comparison with pure horizontal saccade, gray data points are comparison with vertical saccade. Dashed gray line is an equality line. (C) Comparison of the amplitude of the sinusoidal modulation of oblique, horizontal, and vertical saccade trajectories. Number of samples is plotted on y-axis, while x-axis represents the amplitude bins. Each data point depicts number of observations in a given bin of the histogram. Black trace shows oblique saccade, Gray trace with circuit symbol is a horizontal saccade and the triangular symbol is a vertical saccade. Dashed lines represent median values. ... An example of horizontal, vertical, and oblique saccade from one healthy subject. The left column depicts horizontal saccade; central column vertical, and right column is oblique saccade. Panels A, B and C illustrate eye position vector plotted along y-axis. Panels D, E and F represent eye velocity vector plotted along y-axis while ordinate in panels G, H and I illustrate eye acceleration. In each panel, x-axis represents corresponding time. Arrows in panels C, F, I show oscillations in oblique saccade trajectory.
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Free oscillation response of pendulum mechanism. ... Free oscillation response... Low frequency
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Oscillation bands form an arithmetic progression on the logarithmic scale. For each band the frequency (Hz) or period ranges are shown together with their commonly used names. ... Brain oscillators... Alpha, gamma and theta oscillations
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Theory and simulation results of the normalized digital frequency fD as a function of the f0/fS ratio and ρ=0.01. The r and δ values which identify each f0/fS segment are also specified. ... Oscilloscope screen captures of resonator position, input pulses (D6), delayed comparator output (D3) and sample clock (D0), for a PDO topology with m=1 and a ‘not perfect’ frequency fS=46.093kHz (r=2). ... Pulsed digital oscillators, MEMS, Oscillators, Sigma-delta... Oscilloscope screen captures of resonator position, input pulses (D6), delayed comparator output (D3 and D1) and sample clock (D0), for a PDO topology with m=2 and the ‘perfect’ frequency fS=44.052kHz (r=2).
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High-frequency oscillations... An example of the implantation schedule (patient #1) demonstrating areas with conventional frequency ictal patterns, ictal high-frequency oscillations, hyperexcitability, and radiological lesions. ... An example of the implantation schedule (patient #7) demonstrating areas with conventional frequency ictal patterns, ictal high-frequency oscillations, hyperexcitability, and radiological lesions. ... Summary table for statistical analysis. HFO=high frequency oscillations, CFIP=conventional frequency ictal patterns.
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