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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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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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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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Microwave spectroscopy of a one-electron double dot. (a) Charge occupancy of the left dot, M, as a function of ε for several microwave **frequencies**. (b) One-half of the resonance peak splitting as a function of f for several values of VT. Solid lines are best fits to the experimental data using the theory outlined in the text. Inset: Two-level system energy level diagram. (c) Amplitude of the resonance, expressed as Mmax(τ)/Mmax(τ=5ns), as a function of chopped cw period, τ, with f=19GHz. Theory gives a best fit T1=16ns (solid line, see text). Inset: Single photon peak shown in a plot of M as a function of ε for τ=5ns and 1μs. (d) Power dependence of the resonance for f=24GHz. Widths are used to extract the ensemble-averaged charge dephasing time T2*. At higher microwave powers multiple photon processes occur. Curves are offset by 0.3 for clarity.
... Rabi **oscillation**... Spin **qubit**... Charge **qubit**

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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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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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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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Adaptive **frequency** **oscillator**... The left plot of this figure represents the evolution of ω(t) when the adaptive Hopf **oscillator** is coupled to the z variable of the Lorenz attractor. The right plot represents the z variable of the Lorenz attractor. We clearly see that the adaptive Hopf **oscillators** can correctly learn the pseudo-**frequency** of the Lorenz attractor. See the text for more details.
... Plots of the **frequency** of the **oscillations** of the Van der Pol **oscillator** according to ω. Here α=50. There are two plots, for the dotted line the **oscillator** is not coupled and for the plain line the **oscillator** is coupled to F=sin30t. The strength of coupling is ϵ=2. We clearly see basins of phase-locking, the main one for **frequency** of **oscillations** 30. The other major basins appear each 30n (dotted horizontal lines). We also notice small entrainment basins for some **frequencies** of the form 30pq. For a more detailed discussion of these results refer to the text.
... We show the adaptation of the Van der Pol **oscillator** to the **frequencies** of various input signals: (a) a simple sinusoidal input (F=sin(40t)), (b) a sinusoidal input with uniformly distributed noise (F=sin(40t)+uniform noise in [−0.5,0.5]), (c) a square input (F=square(40t)) and (d) a sawtooth input (F=sawtooth(40t)). For each experiment, we set ϵ=0.7 and α=100 and we show three plots. The right one shows the evolution of ω(t). The upper left graph is a plot of the **oscillations**, x, of the system, at the beginning of the learning. The lower graph shows the **oscillations** at the end of learning. In both graphs, we also plotted the input signal (dashed). In each experiment, ω converges to ω≃49.4, which corresponds to **oscillations** with a **frequency** of 40 rad s−1 like the input and thus the **oscillator** correctly adapts its **frequency** to the **frequency** of the input.
... **Frequency** spectra of the Van der Pol **oscillator**, both plotted with ω=10. The left figure is an **oscillator** with α=10 and on the right the nonlinearity is higher, α=50. On the y-axis we plotted the square root of the power intensity, in order to be able to see smaller **frequency** components.
... This figure shows the convergence of ω for several initial **frequencies**. The Van der Pol **oscillator** is perturbed by F=sin(30t), with coupling ϵ=0.7, α=50. We clearly see that the convergence directly depends on the initial conditions and as expected the different kinds of convergence correspond to the several entrainment basins of Fig. 7.

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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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