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  • A phase-locking model for entrainment of peripheral oscillators to the cyclin–CDK oscillator. (a) Molecular mechanism of the Cdc14 release oscillator. The mitotic phosphatase Cdc14 is activated upon release from sequestration in the nucleolus. This release is controlled by a negative feedback loop in which Cdc14 release, promoted by the polo kinase Cdc5, activates APC-Cdh1, which then promotes Cdc5 degradation, allowing Cdc14 resequestration. This negative-feedback oscillator is entrained to the cyclin–CDK cycle at multiple points: by cyclin–CDK promotion of CDC5 transcription and Cdc5 kinase activation, and by cyclin–CDK inhibition of Cdh1 activity. (b) Schematic of multiple peripheral oscillators coupled to the CDK oscillator in budding yeast. As described above, coupling entrains such peripheral oscillators to cell cycle progression; peripheral oscillators also feed back on the cyclin–CDK oscillator itself. For example, major genes in the periodic transcription program include most cyclins, CDC20, and CDC5; Cdc14 directly promotes establishment of the low-cyclin–CDK positive feedback loop by activating Cdh1 and Sic1 as well as more indirectly antagonizing cyclin–CDK activity by dephosphorylating cyclin–CDK targets; the centrosome and budding cycles could communicate with the cyclin–CDK cycle via the spindle integrity and morphogenesis checkpoints. (c) Oscillator coupling ensures once-per-cell-cycle occurrence of events. Three hypothetical oscillators are shown: a master cycle in black, a faster peripheral cycle in blue, and a slower peripheral cycle in red. In the absence of phase-locking (top), the oscillators trigger events (colored circles) without a coherent phase relationship. In the presence of oscillator coupling (bottom), the peripheral oscillators are slowed or accelerated within their critical periods to produce a locked phase relationship, with events occurring once and only once within each master cycle. ... Positive and negative feedback loops in the cyclin–CDK oscillator. (a) Inset: a negative feedback loop which can give rise to oscillations. Such an oscillator is thought to form the core of eukaryotic cell cycles, with cyclin–Cyclin Dependent Kinase (cyclin–CDK) acting as activator, Anaphase Promoting Complex-Cdc20 (APC-Cdc20) acting as repressor, and non-linearity in APC-Cdc20 activation preventing the system from settling into a steady state. Below is shown the cyclin–CDK machinery in eukaryotic cell cycles. CDKs, present throughout the cell cycle, require the binding of a cyclin subunit for activity. These cyclin partners can also determine the localization of the complex and its specificity for targets. At the beginning of the cell cycle, cyclin–CDK activity is low, and ramps up over most of the cycle. Early cyclins trigger production of later cyclins and these later cyclins then turn off the earlier cyclins, so that control is passed from one set of cyclin–CDKs to the next. The last set of cyclins to be activated, the G2/M-phase cyclins, initiate mitosis, and also initiate their own destruction by activating the APC-Cdc20 negative feedback loop. APC-Cdc20 targets the G2/M-phase cyclins for destruction, resetting the cell to a low-CDK activity state, ready for the next cycle. (b) Positive feedback is added to the oscillator in multiple ways. Left: a highly conserved but non-essential mechanism consists of ‘handoff’ of cyclin proteolysis from APC-Cdc20 to APC-Cdh1. Cdh1 is a relative of Cdc20 which activates the APC late in mitosis and into the ensuing G1. Cdh1 is inhibited by cyclin–CDK activity, resulting in mutual inhibition (which is logically equivalent to positive feedback). Middle: antagonism between cyclin–CDK and stoichiometric CDK inhibitors (CKIs) results in positive feedback. These loops stabilize high- and low-CDK activity states. Right: a double positive feedback loop comprising CDK-mediated inhibition of the Wee1 kinase (which inhibits CDK) and activation of the Cdc25 phosphatase (which activates CDK by removing the phosphorylation added by Wee1) is proposed to stabilize intermediate CDK activity found in mid-cycle, and an alternative stable state of high mitotic CDK activity.
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  • Comparison of the oscillation in Fig. 17 and the basic frequency component L in Fig. 23. The replacement of the feedback channel loops by open areas for vortical flow made the feedback paths slightly shorter (and therefore the frequency higher).... Measured oscillation frequency with different feedback tube lengths of the oscillator shown in Fig. 7, plotted as a function of the supplied flow rate. Surprisingly, the frequency is neither proportional to the flow rate (as is usual in the constant Strouhal-number oscillators, e.g., Tesař et al., 2006) – nor constant (as in the oscillators with resonator channel (Tesař et al., 2013)). ... Fluidic oscillator... Results of measured dependence of oscillation frequency on the supplied flow rate in the layout shown in Figs. 20 and 12. Apart from basic frequency L, the output spectrum exhibited a much higher frequency component H. ... Frequency of generated oscillation plotted as a function of the air flow rate. Similarly as in Fig. 9 this dependence does not the fit the usual (constant Strouhal number) proportionality between frequency and flow rate. ... Basic data on the geometry of the oscillator used in the high-frequency experiments. ... Dependence of bubble natural oscillation frequency on the size – based on the measurements in Tesař (2013b). The line is fitted for constant value of oscillation Weber number We0.
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  • Traveling wave resonator with two ports incorporated into interferometric frequency discriminator for oscillator stabilisation. ... Modified Galani oscillator stabilisation technique utilising travelling wave resonator with standing wave ratio. ... Frequency Standards and Metrology Group, School of Physics, University of Western Australia, 35 Stirling Hwy, Crawley 6009, Australia
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  • Stepped-frequency continuous-wave radar... For the unshifted LPT the first raw frequency-domain sample obtained means of the VNA is aligned with the DFT frequency bin representing frequency Δf. Thus, raw frequency-domain samples do not coincide with the appropriate DFT frequency bins. The negative frequency components are obtained by means of mirroring a conjugated version of the positive ones around DC. Throughout the paper, the positive and negative spectra are depicted by the same individual diagonal patterns. ... The extended array structure with non-zero values only for positive frequencies. Raw data samples are starting at DFT frequency Δf. ... The extended array structure with non-zero values only for negative frequencies. Mirrored conjugated raw data samples are starting at DFT frequency −Δf. ... SNR of the frequency-domain outcome of the FFT for different numbers n of time-domain samples of a sine tone of frequency 2GHz with additive Gaussian noise of standard deviation σ=0.8 sampled with constant sampling frequency, fs=10GHz. ... Department for High-Frequency Technology, Technische Universität Braunschweig, Schleinitzstraße 22, 38106 Braunschweig, Germany... Frequency-domain signal processing... High oscillations for the shifted LPT occurs when fmin is large compared to Δf.
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  • Qubit... The oscillation period T0 changes with the temperature T and Coulomb bound potential β. ... The oscillation period T0 changes with the temperature T and electron phonon coupling strength α .
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  • Spatial frequencies distributions... Ragged oscillation death... The phase synchronization domains (areas enclosed by the red lines) and the OD regions (black areas) in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8}, (b) G={1,4,3,6,2,8,5,7}, and (c) G={1,2,3,6,8,4,7,5}. N=8. The ragged OD sates are clear in (b) and (c) within a certain interval of δω indicated by two vertical dashed lines. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The bifurcation diagram and the largest Lyapunov exponent λ of the coupled Rossler oscillators versus the coupling strength ε with the same spatial arrangement of natural frequencies as in Fig. 1(a)–(c), respectively for δω=0.58. The bifurcation diagram is realized by the soft of XPPAUT [33] where the black dots are fixed points and the red dots are the maximum and minimum values of x1 for the stable periodic solution while the blue dots means the max/min values of x1 for the unstable periodical states. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) ... The critical curves of OD domain from analysis in N coupled Landau–Stuart oscillators for different N’s: (a) N=2, (b) N=3, and (c)–(e) N=4 for G={1,2,3,4},G={1,2,4,3}, and G={1,3,2,4}, respectively. The ragged OD domain is clear in (d). The numerical results with points within the domains perfectly verify the analytical results. ... The OD regions in the parameter space of ε-δω for a ring of coupled Rossler systems with different frequency distributions: (a) G={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30}, (b) G={26,16,25,18,5,14,10,4,6,7,21,12,23,8,1,15,9,29,28,11,2,20,27,30,3,13,17,22,24,19}, and (c) G={19,22,18,13,10,28,7,15,17,8,30,12,26,11,20,9,27,21,25,6,29,1,23,5,3,24,16,14,4,2}. N=30. In all three insets, the values of ωj are plotted for given ω0=0 and δω=N. ... Coupled nonidentical oscillators
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  • Frequency modulation... Frequency modulated Ca2+ oscillations. (A) A computer generated (in silico) oscillating wave with the parameters: period (T), frequency (f), full duration half maximum (FDHM), and duty cycle is depicted. (B) Oscillating wave frequency modulated by agonist concentration. (C) Oscillating wave frequency modulated by the different agonists X, Y, and Z. Three single cell Ca2+ recordings of a Fluo-4/AM-loaded neuroblastoma cell (D), HeLa cell (E), and cardiac cell (F) with the parameters T, f, FDHM, and duty cycle stated. Scale bars are 100s. ... Frequency decoders and host cells. Illustration showing the frequencies and periods that modulate the different frequency decoders and host cells. ... Frequency decoding
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  • Variation of frequency shift due to the amplitude and the rotation rate. ... Conditions for zero frequency shift and zero pressure difference. Broken lines indicate linear fitting lines through the origin. ... Oscillation... Frequency shift
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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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  • 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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