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Equivalent circuit of the linearized **qubit**–SQUID system. ϕm and ϕp are the two independent variables of a DC SQUID. ϕm correpsonds to the circulating current of the SQUID, and ϕp couples with the ramping current of the SQUID. The capacitances of the inner **oscillator** loop and the external **oscillator** loop are Cm=2CJ and Cp, the shunt capacitance outside the SQUID. Flux of the three loops, q=q0σz, ϕm, and ϕp, are chosen as independent variables in the calculation. Each of the inductances in the three loops interacts by mutual inductances as are indicated by the paired dots near the inductances.
... The measuring circuit of the DC SQUID which surrounds the **qubit**. CJ and I0 are the capacitance and critical current of each of the junctions, and ϕi are the gauge-invariant phases of the junctions. The **qubit** is represented symbolically by a loop with an arrow indicating the magnetic moment of the |0〉 state. The SQUID is shunted by a capacitor Csh and the environmental impedance Z0(ω).

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Diagrammatic representation of time-resolved CARS. Both time-circuit and Feynman diagram are illustrated for a non- overlapping sequence of P, S, P′ pulses, with central **frequency** of the S-pulse chosen to be outside the absorption spectrum of the B←X transition, to ensure that only the P(0,3) component of the third-order polarization is interrogated. In this dominant contribution, all three pulses act on bra (ket) state while the ket (bra) state evolves field free. Note, for the Feynman diagrams, we use the convention of Ref. [6], which is different than that of Ref. [5].
... The wavepacket picture associated with the evolution of the ket-state in the diagram of Fig. 1, for resonant CARS in iodine. The required energy matching condition for the AS radiation, Eq. (10b) of text, can only be met when the packet reaches the inner turning point of the B-surface. Once prepared, ϕ(3)(t) will **oscillate**, radiating periodically every time it reaches the inner turning point.

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Visualization of the ground state |0〉 and the coherent pointer-states |L〉 and |R〉 of the **oscillator** in the potential V(x).

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Behavior of periodically **oscillating** flame with large-scale **oscillation** for Vac=5kV, fac=20Hz, and U0=11m/s.
... **Oscillation** **frequency** in terms of AC **frequency** for U0=11.0m/s and Vac=5kV.
... Low **frequency**... Average amplitude of large-scale **oscillation** with AC **frequency** for U0=11.0m/s and Vac=5kV.
... **Oscillation**... Phase diagrams of HL and dHL/dt for various **oscillation** modes.
... Edge height of lifted flame together with **oscillation** amplitude with AC **frequency** for Vac=5kV and U0=11.0m/s.

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Cross-**frequency** coupling... Steps applied to compute both CFC and CFD. (A) High **frequency** power at **frequency** v is estimated from the original signal by applying a sliding Hanning tapered time window followed by a Fourier transformation (red line). After that, both the original signal and the power envelope of the high **frequency** signal are divided into segments. Within each segment, the original signal and the power envelope of the high **frequency** signal are Fourier-transformed and cross-spectra between them are computed. (B) CFC and CFD quantification. CFC is quantified by coherence and CFD is calculated from the PSI between the phase of slow **oscillation** fi and power of fast **oscillation** vj. The red segment indicates the **frequency** range over which the PSI is calculated. The PSI is calculated for the bandwidth β.
... Statistical assessment of the CFC and CFD when controlling for multiple comparisons over **frequencies**. (A) Observed CFC/D and clustering threshold. All observed CFC/D values were pooled together (i.e. all **frequency** by **frequency** bins) and the threshold is set at the 99.5th percentile of the resulting distribution (right panel). Contiguous CFC/D values exceeding the threshold formed a cluster (left panel). The summed CFC/D values from a given cluster were considered the cluster score. (B) Circular shifted CFC/D and the cluster reference distribution. Random number of the Fourier-transferred phase segment sequences was circular shifted with respect to the amplitude envelope segments and the CFC/D values were recomputed 1000 times. For each randomization, the CFC/D contiguous values exceeding the threshold were used to form reference clusters (e.g., cluster1, cluster2, and so on in the left panel) and the respective cluster scores were calculated. The resulting 1000 maximum cluster scores formed the cluster-level reference distribution. For the observed cluster score, the p value was determined by considering the fraction of cluster scores in the reference distribution exceeding the observed cluster score (right panel).
... Neuronal **oscillations**... Phase spectra between low **frequency** signal and high **frequency** envelope. The red curves represent the envelope of high **frequency** signals. Fig. 1 is adapted from Schoffelen et al. (2005). Left panel: The low **frequency** signal is leading the high **frequency** envelope by 10ms. This constant lead translates into a phase-lead that linearly increases with **frequency** (e.g., 0.25rad for 4Hz, 0.50rad for 8Hz and 0.75rad for 12Hz). Right panel: The low **frequency** signal is lagging the high **frequency** envelope by 10ms. This constant lag translates into a phase-lag that linearly decreases with **frequency** (e.g., −0.25rad for 4Hz, −0.50rad for 8Hz and −0.75rad for 12Hz).
... Cross-**frequency** directionality

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The relational curve of the **oscillating** period T and the electron–LOP coupling constant α.
... **Qubit**... The relational curve of the **oscillating** period T and the confinement length R.

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The phase of the **oscillator** after action of a linearly-chirped pulsed force as a function of the chirp strength. In this case Ω0=4, σ=5.
... The amplitude of a harmonic **oscillator** after the action of a pulsed force with a Gaussian envelope and a linear chirp in dependence on the chirp strength, ΔΩ. In this case Ω0=5 and σ=5, 10, and 20; A=1 in all figures.
... The amplitude of the **oscillator** after the action of a force with an asymmetrical Gaussian envelope, σ1=5, Ω0=5, σ2=10 and 20.
... The amplitude of the **oscillator** vs. ΔΩ in the case of a periodical chirp in the force. The parameters of the force are: Ω0=5, σ=20, b=4.
... Classical **oscillator**... **Frequency** chirp

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Summary of resonance **frequencies** found in all 10 babies (1 and 2 represents first and second run, respectively)
... A screen from our phase analysis program, showing phase analysis performed at four points of the respiratory cycle: top of breath, mid-inspiration, mid-expiration and bottom of breath. Corresponding points from the driving trace and the mouth pressure trace are matched and the phase difference calculated. In this case, the phase difference at the top of breath is 0° at an **oscillating** **frequency** of 20 Hz.
... high-**frequency** **oscillation**

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(a) Spin maser **oscillation** signal observed in a time span of 24 hours. (b) Transient pattern in the initial spin maser **oscillation**. (c) Steady state **oscillation** after the transient settled. The signals shown in the ordinates represent the beat between the spin detection signal and a 36.12 Hz fixed **frequency** reference signal for a lock-in amplifier.
... (a) Fourier spectrum obtained when the newly introduced current source was used for the **oscillator** operation. The measurement time was 3×104 seconds. (b) Fourier spectrum obtained when the previous current source was used for the **oscillator** operation. The measurement time was 1×104 seconds.
... Nuclear spin **oscillator**... Steady state **oscillations** observed at three low **frequencies**: (a) ν0=17.7 Hz, (b) ν0=8.9 Hz, (c) ν0=2.5 Hz. The strength of the static field adopted in the individual operations are indicated in the respective panels.
... **Frequency** precision... **Frequency** precision of the spin **oscillation**. The abscissa represents the standard deviation of the **frequency** ν determined by fitting a function ϕ(t)=2πνt+ϕ0 to the observed precession phases ϕ from t=0 to t=Tm. Solid, dotted and dashed lines are the presentation of three cases with power laws σν∝Tm−3/2, σν∝Tm−1, and σν∝Tm−1/2 respectively.

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