### 25677 results for qubit oscillator frequency

Contributors: F.K. Wilhelm, S. Kleff, J. von Delft

Date: 2004-01-26

Visualization of the ground state |0〉 and the coherent pointer-states |L〉 and |R〉 of the oscillator in the potential V(x).
...Visualization of the ground state |0〉 and the coherent pointer-states |L〉 and |R〉 of the **oscillator** in the potential V(x).
...In the spin-boson model, the properties of the **oscillator** bath are fully characterized by the spectral density of **oscillators** J(ω). We study the case when this function is of Breit–Wigner shape and has a sharp peak at a **frequency** Ω with width Γ≪Ω. We use a number of approaches such as the weak-coupling Bloch–Redfield equation, the non-interacting blip approximation (NIBA) and the flow-equation renormalization scheme. We show, that if Ω is much larger than the **qubit** energy scales, the dynamics corresponds to an ohmic spin-boson model with a strongly reduced tunnel splitting. We also show that the direction of the scaling of the tunnel splitting changes sign when the bare splitting crosses Ω. We find good agreement between our analytical approximations and numerical results. We illuminate how and why different approaches to the model account for these features and discuss the interpretation of this model in the context of an application to quantum computation and read-out. ... In the spin-boson model, the properties of the **oscillator** bath are fully characterized by the spectral density of **oscillators** J(ω). We study the case when this function is of Breit–Wigner shape and has a sharp peak at a **frequency** Ω with width Γ≪Ω. We use a number of approaches such as the weak-coupling Bloch–Redfield equation, the non-interacting blip approximation (NIBA) and the flow-equation renormalization scheme. We show, that if Ω is much larger than the **qubit** energy scales, the dynamics corresponds to an ohmic spin-boson model with a strongly reduced tunnel splitting. We also show that the direction of the scaling of the tunnel splitting changes sign when the bare splitting crosses Ω. We find good agreement between our analytical approximations and numerical results. We illuminate how and why different approaches to the model account for these features and discuss the interpretation of this model in the context of an application to quantum computation and read-out.

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Contributors: D. Sugny, M. Ndong, D. Lauvergnat, Y. Justum, M. Desouter-Lecomte

Date: 2007-08-15

We examine the effect of dissipation on the laser control of a process that transforms a state into a superposed state. We consider a two-dimensional double well of a single potential energy surface. In the context of reactivity, the objective of the control is the localization in a given well, for instance the creation of an enantiomeric form whereas for quantum gates, this control corresponds to one of the transformation of the Hadamard gate. The environment is either modelled by coupling few harmonic **oscillators** (up to five) to the system or by an effective interaction with an Ohmic bath. In the discrete case, dynamics is carried out exactly by using the coupled harmonic adiabatic channels. In the continuous case, Markovian and non-Markovian dynamics are considered. We compare two laser control strategies: the Stimulated Raman Adiabatic Passage (STIRAP) method and the optimal control theory. Analytical estimations for the control by adiabatic passage in a Markovian environment are also derived....Dynamics controlled by f-STIRAP strategy for the preparation of the superposed state |R〉. Panels (a) and (b) show, respectively, the evolution of the localization in the right well for different values of λ and the Rabi **frequencies** of the different pulses. Rabi **frequencies** are in atomic units. The solid line of panel (b) corresponds to the Stokes pulse and the dashed one to the pump pulse. The total duration of the process is of the order of 4.5ps.
...**Qubit**...Half-live time τ1/2 in fs and the time τmax for which C(t) (Eq. (12)) vanishes for the two reference **frequencies** (Eq. (7)) and temperatures used in the simulations
...Robustness of the f-STIRAP process as a function of the peak Rabi **frequency** and the delay between the pulses for a total duration of 4.5ps of the overall field. Rabi **frequency** and delay are in atomic units. The upper and the lower part of the figure correspond, respectively, to λ=5×10−4 and λ=2×10−3.
...Half-live time τ1/2 in fs and the time τmax for which C(t) (Eq. (12)) vanishes for the two reference frequencies (Eq. (7)) and temperatures used in the simulations
...Robustness of the f-STIRAP process as a function of the peak Rabi frequency and the delay between the pulses for a total duration of 4.5ps of the overall field. Rabi frequency and delay are in atomic units. The upper and the lower part of the figure correspond, respectively, to λ=5×10−4 and λ=2×10−3.
...Dynamics controlled by f-STIRAP strategy for the preparation of the superposed state |R〉. Panels (a) and (b) show, respectively, the evolution of the localization in the right well for different values of λ and the Rabi frequencies of the different pulses. Rabi frequencies are in atomic units. The solid line of panel (b) corresponds to the Stokes pulse and the dashed one to the pump pulse. The total duration of the process is of the order of 4.5ps.
... We examine the effect of dissipation on the laser control of a process that transforms a state into a superposed state. We consider a two-dimensional double well of a single potential energy surface. In the context of reactivity, the objective of the control is the localization in a given well, for instance the creation of an enantiomeric form whereas for quantum gates, this control corresponds to one of the transformation of the Hadamard gate. The environment is either modelled by coupling few harmonic **oscillators** (up to five) to the system or by an effective interaction with an Ohmic bath. In the discrete case, dynamics is carried out exactly by using the coupled harmonic adiabatic channels. In the continuous case, Markovian and non-Markovian dynamics are considered. We compare two laser control strategies: the Stimulated Raman Adiabatic Passage (STIRAP) method and the optimal control theory. Analytical estimations for the control by adiabatic passage in a Markovian environment are also derived.

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Contributors: A.G. Khachatryan, F.A. van Goor, K.-J. Boller

Date: 2006-12-18

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 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 motion of a classical (harmonic) **oscillator** is studied in the case where the **oscillator** is driven by a pulsed **oscillating** force with a **frequency** varying in time (**frequency** chirp). The amplitude and phase of the **oscillations** left after the pulsed force in dependence on the profile and strength of chirp, **frequency** and duration of the force is investigated....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**...Classical **oscillator** driven by an oscillating chirped force...The motion of a classical (harmonic) **oscillator** is studied in the case where the **oscillator** is driven by a pulsed oscillating force with a **frequency** varying in time (**frequency** chirp). The amplitude and phase of the oscillations left after the pulsed force in dependence on the profile and strength of chirp, **frequency** and duration of the force is investigated....**Frequency** chirp ... The motion of a classical (harmonic) **oscillator** is studied in the case where the **oscillator** is driven by a pulsed **oscillating** force with a **frequency** varying in time (**frequency** chirp). The amplitude and phase of the **oscillations** left after the pulsed force in dependence on the profile and strength of chirp, **frequency** and duration of the force is investigated.

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Contributors: Yun-Fei Liu, Jing-Lin Xiao

Date: 2008-09-01

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.
...In this paper, we study the influence of LO phonon (LOP) on the charge **qubit** in a quantum dot (QD), and find that the eigenenergies of the ground and first excited states are reduced due to the electron–LOP interaction. At the same time, the time evolution of the electron probability density is obtained, the dependence of the **oscillating** period on electron–LOP coupling constant is found, the relation of between the **oscillating** period and the confinement length of the QD is calculated. Finally, we consider the effects of the electron–LOP coupling constant on pure dephasing factor under considering the correction of electron–LOP interaction for the wave functions. Our results suggest that electron–LOP interaction has very important effects on charge **qubit**....In this paper, we study the influence of LO phonon (LOP) on the charge **qubit** in a quantum dot (QD), and find that the eigenenergies of the ground and first excited states are reduced due to the electron–LOP interaction. At the same time, the time evolution of the electron probability density is obtained, the dependence of the oscillating period on electron–LOP coupling constant is found, the relation of between the oscillating period and the confinement length of the QD is calculated. Finally, we consider the effects of the electron–LOP coupling constant on pure dephasing factor under considering the correction of electron–LOP interaction for the wave functions. Our results suggest that electron–LOP interaction has very important effects on charge **qubit**....The effects of LO phonons on charge **qubit** ... In this paper, we study the influence of LO phonon (LOP) on the charge **qubit** in a quantum dot (QD), and find that the eigenenergies of the ground and first excited states are reduced due to the electron–LOP interaction. At the same time, the time evolution of the electron probability density is obtained, the dependence of the **oscillating** period on electron–LOP coupling constant is found, the relation of between the **oscillating** period and the confinement length of the QD is calculated. Finally, we consider the effects of the electron–LOP coupling constant on pure dephasing factor under considering the correction of electron–LOP interaction for the wave functions. Our results suggest that electron–LOP interaction has very important effects on charge **qubit**.

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Contributors: Mina Amiri, Jean-Marc Lina, Francesca Pizzo, Jean Gotman

Date: 2016-01-01

Examples of a spike without HFOs (left) and a spike with HFOs (right), as defined with the Analytic Morse wavelet in the time–**frequency** domain.
...High **Frequency** **Oscillations**...To demonstrate and quantify the occurrence of false High **Frequency** Oscillations (HFOs) generated by the filtering of sharp events. To distinguish real HFOs from spurious ones using analysis of the raw signal....Parameter selection for the Analytic Morse Wavelet; top: time–**frequency** presentation for different values of n (m=40), bottom: raw signal and filtered signal (80–250Hz). Blue lines represent HFO interval marked visually.
...Examples of detection errors. Left: HFO without isolated blob but having **oscillation** in the raw signal. Right: HFO without visible **oscillation** in the raw signal but representing an isolated peak. Blue lines show the HFO interval marked by reviewers.
...Parameter selection for the Analytic Morse **Wavelet; **top: time–**frequency** presentation for different values of n (m=40), bottom: raw signal and filtered signal (80–250Hz). Blue lines represent HFO interval marked visually.
...Time–**frequency**...High **Frequency** Oscillations and spikes: Separating real HFOs from false oscillations...High **Frequency** Oscillations...To demonstrate and quantify the occurrence of false High **Frequency** **Oscillations** (HFOs) generated by the filtering of sharp events. To distinguish real HFOs from spurious ones using analysis of the raw signal. ... To demonstrate and quantify the occurrence of false High **Frequency** **Oscillations** (HFOs) generated by the filtering of sharp events. To distinguish real HFOs from spurious ones using analysis of the raw signal.

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Contributors: Ludovic Righetti, Jonas Buchli, Auke Jan Ijspeert

Date: 2006-04-15

Nonlinear **oscillators** are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for **oscillators** which adapts their **frequency** to the **frequency** of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of **oscillators**, from phase **oscillators** to relaxation **oscillators** and strange attractors with a generic learning rule. One major feature of our learning rule is that the **oscillators** constructed can adapt their **frequency** without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive **oscillator**. The convergence of the learning is proved for the Hopf **oscillator**, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic **oscillators** like relaxation **oscillators** and strange attractors....Adaptive **frequency** **oscillator**...Dynamic Hebbian learning in adaptive **frequency** **oscillators**...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.
...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.
...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.
...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.
...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.
...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.
...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.
... Nonlinear **oscillators** are widely used in biology, physics and engineering for modeling and control. They are interesting because of their synchronization properties when coupled to other dynamical systems. In this paper, we propose a learning rule for **oscillators** which adapts their **frequency** to the **frequency** of any periodic or pseudo-periodic input signal. Learning is done in a dynamic way: it is part of the dynamical system and not an offline process. An interesting property of our model is that it is easily generalizable to a large class of **oscillators**, from phase **oscillators** to relaxation **oscillators** and strange attractors with a generic learning rule. One major feature of our learning rule is that the **oscillators** constructed can adapt their **frequency** without any signal processing or the need to specify a time window or similar free parameters. All the processing is embedded in the dynamics of the adaptive **oscillator**. The convergence of the learning is proved for the Hopf **oscillator**, then numerical experiments are carried out to explore the learning capabilities of the system. Finally, we generalize the learning rule to non-harmonic **oscillators** like relaxation **oscillators** and strange attractors.

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Contributors: B.M.R. Schneider, C. Gollub, K.-L. Kompa, R. de Vivie-Riedle

Date: 2007-09-25

Quantum gates are optimized for the IR active high **frequency** modes of MnBr(CO)5-complexes. We investigate whether the selectivity for quantum gates is conserved for energetically close lying **qubits** of different symmetry that are nevertheless simultaneously addressable with the same laser pulse. The **qubits** are encoded in different vibrational normal modes, which are separated only by 50cm−1. Furthermore the influence of additional non-**qubit** modes on the efficiency of the quantum gates optimized for the pure **qubit** system is studied. Potential perturbers are low **frequency** vibrational modes highly populated at room temperature or vibrational modes that seems predestined to interfere during the gate operation. To prevent translational motion, the possibility of spatial localization is explored by incorporation of the carbonyl complex in the unit cell of a MFI zeolite....PES of the **qubit** system (a) and total dipole surface (b). For both surfaces: −52.8 pm⩽rA1⩽+52.8pm and −37.4pm⩽rE⩽+37.4pm.
...Normal modes included in the quantum dynamical calculation. (a) Coordinates of the **qubit** modes, (b) coordinates of the non-**qubit** modes.
...Spectral analysis of the NOT (top) and CNOT (bottom) gate. The solid lines correspond to the spectra of the optimized pulses, the dashed lines to the spectra of the sub pulses. The vertical lines indicate the relevant qubit basis transition frequencies for the quantum gates.
...spectroscopical** data** of the qubit vibrational modes E** and **A1** and **the non-qubit modes, the δ-deformation mode (E) and the dissociative mode (A1)
...Robustness of quantum gates operating on the high **frequency** modes of MnBr(CO)5...Spectral analysis of the NOT (top) and CNOT (bottom) gate. The solid lines correspond to the spectra of the optimized pulses, the dashed lines to the spectra of the sub pulses. The vertical lines indicate the relevant **qubit** basis transition **frequencies** for the quantum gates.
...Normal modes included in the quantum dynamical calculation. (a) Coordinates of the qubit modes, (b) coordinates of the non-qubit modes.
...spectroscopical data of the **qubit** vibrational modes E and A1 and the non-**qubit** modes, the δ-deformation mode (E) and the dissociative mode (A1)
...PES of the qubit system (a) and total dipole surface (b). For both surfaces: −52.8 pm⩽rA1⩽+52.8pm and −37.4pm⩽rE⩽+37.4pm.
... Quantum gates are optimized for the IR active high **frequency** modes of MnBr(CO)5-complexes. We investigate whether the selectivity for quantum gates is conserved for energetically close lying **qubits** of different symmetry that are nevertheless simultaneously addressable with the same laser pulse. The **qubits** are encoded in different vibrational normal modes, which are separated only by 50cm−1. Furthermore the influence of additional non-**qubit** modes on the efficiency of the quantum gates optimized for the pure **qubit** system is studied. Potential perturbers are low **frequency** vibrational modes highly populated at room temperature or vibrational modes that seems predestined to interfere during the gate operation. To prevent translational motion, the possibility of spatial localization is explored by incorporation of the carbonyl complex in the unit cell of a MFI zeolite.

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Contributors: Alberto Pretel, John H. Reina, William R. Aguirre-Contreras

Date: 2008-03-01

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**...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.
...Within the density matrix formalism, we report on the quantum control of the excitonic coherences in quantum dots coupled to a single mode field resonant semiconductor cavity. We use an external classical laser field to drive the dynamical response of the excitonic states. Dissipation mechanisms associated with the cavity field and the excitonic states are explicitly included in the model. Our numerical simulations of the excitonic dynamics are in good agreement with recent experimental reports. Furthermore, we compute and show how to tailor such a dynamics in the presence of the laser field by means of controlling the detuning between the laser and the cavity field **frequencies**. The results are analyzed with a view to implementing quantum control of local **qubit** operations. ... Within the density matrix formalism, we report on the quantum control of the excitonic coherences in quantum dots coupled to a single mode field resonant semiconductor cavity. We use an external classical laser field to drive the dynamical response of the excitonic states. Dissipation mechanisms associated with the cavity field and the excitonic states are explicitly included in the model. Our numerical simulations of the excitonic dynamics are in good agreement with recent experimental reports. Furthermore, we compute and show how to tailor such a dynamics in the presence of the laser field by means of controlling the detuning between the laser and the cavity field **frequencies**. The results are analyzed with a view to implementing quantum control of local **qubit** operations.

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Contributors: Erik Smedler, Per Uhlén

Date: 2014-03-01

**Frequency** modulation...Calcium (Ca2+) **oscillations** are ubiquitous signals present in all cells that provide efficient means to transmit intracellular biological information. Either spontaneously or upon receptor ligand binding, the otherwise stable cytosolic Ca2+ concentration starts to **oscillate**. The resulting specific oscillatory pattern is interpreted by intracellular downstream effectors that subsequently activate different cellular processes. This signal transduction can occur through **frequency** modulation (FM) or amplitude modulation (AM), much similar to a radio signal. The decoding of the oscillatory signal is typically performed by enzymes with multiple Ca2+ binding residues that diversely can regulate its total phosphorylation, thereby activating cellular program. To date, NFAT, NF-κB, CaMKII, MAPK and calpain have been reported to have **frequency** decoding properties....Frequen...**Frequency** decoders and host cells. Illustration showing the frequencies and periods that modulate the different **frequency** decoders and host cells.
...**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.
...Review - **Frequency** decoding of calcium oscillations...**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.
...Calcium (Ca2+) oscillations are ubiquitous signals present in all cells that provide efficient means to transmit intracellular biological information. Either spontaneously or upon receptor ligand binding, the otherwise stable cytosolic Ca2+ concentration starts to oscillate. The resulting specific oscillatory pattern is interpreted by intracellular downstream effectors that subsequently activate different cellular processes. This signal transduction can occur through **frequency** modulation (FM) or amplitude modulation (AM), much similar to a radio signal. The decoding of the oscillatory signal is typically performed by enzymes with multiple Ca2+ binding residues that diversely can regulate its total phosphorylation, thereby activating cellular program. To date, NFAT, NF-κB, CaMKII, MAPK and calpain have been reported to have **frequency** decoding properties....**Frequency** decoders and host cells. Illustration showing the **frequencies** and periods that modulate the different **frequency** decoders and host cells.
...**Frequency** decoding ... Calcium (Ca2+) **oscillations** are ubiquitous signals present in all cells that provide efficient means to transmit intracellular biological information. Either spontaneously or upon receptor ligand binding, the otherwise stable cytosolic Ca2+ concentration starts to **oscillate**. The resulting specific oscillatory pattern is interpreted by intracellular downstream effectors that subsequently activate different cellular processes. This signal transduction can occur through **frequency** modulation (FM) or amplitude modulation (AM), much similar to a radio signal. The decoding of the oscillatory signal is typically performed by enzymes with multiple Ca2+ binding residues that diversely can regulate its total phosphorylation, thereby activating cellular program. To date, NFAT, NF-κB, CaMKII, MAPK and calpain have been reported to have **frequency** decoding properties.

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Contributors: S Lee, R Blowes, A.D Milner

Date: 1998-09-01

Phase analysis in high-**frequency** oscillation...high-**frequency** oscillation...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.
...Summary of resonance **frequencies** found in all 10 babies (1 and 2 represents first and second run, respectively)
...In an oscillating system driven by a sine wave pump, the resonance **frequency** of the respiratory system can be determined using phase analysis. At resonance **frequency**, when elastance and inertance cancel out, flow becomes in-phase with resistance. In premature infants with respiratory distress syndrome, owing to surfactant deficiency, localized areas of hyperinflation and collapse develop, resulting in complex changes in overall pulmonary mechanics. We investigated the effect of measuring resonance **frequency** of the respiratory system by phase analysis at different points of the respiratory cycle: end of inspiration, end of expiration, mid-inspiration and mid-expiration. Ten ventilated premature infants with respiratory distress syndrome were studied, gestational age ranged from 24 to 30 weeks (mean 27.6 weeks) and birth weight ranged from 0.7 to 1.505 kg (mean 0.984 kg). Results: The resonance **frequency** was consistently higher when measured at the end of inspiration compared with the end of expiration. The expected trend of phase variation, that is, negative below the resonance **frequency** and positive above, was most consistently found when analysis was done at the end of inspiration. Conclusions: These findings were most likely a result of the complexity of pulmonary mechanics in the surfactant-deficient lungs, rendering the single compartment model we based our theory on inadequate. However, phase analysis performed at the end of inspiration seemed to produce the most reliable and consistent results....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**...In an **oscillating** system driven by a sine wave pump, the resonance **frequency** of the respiratory system can be determined using phase analysis. At resonance **frequency**, when elastance and inertance cancel out, flow becomes in-phase with resistance. In premature infants with respiratory distress syndrome, owing to surfactant deficiency, localized areas of hyperinflation and collapse develop, resulting in complex changes in overall pulmonary mechanics. We investigated the effect of measuring resonance **frequency** of the respiratory system by phase analysis at different points of the respiratory cycle: end of inspiration, end of expiration, mid-inspiration and mid-expiration. Ten ventilated premature infants with respiratory distress syndrome were studied, gestational age ranged from 24 to 30 weeks (mean 27.6 weeks) and birth weight ranged from 0.7 to 1.505 kg (mean 0.984 kg). Results: The resonance **frequency** was consistently higher when measured at the end of inspiration compared with the end of expiration. The expected trend of phase variation, that is, negative below the resonance **frequency** and positive above, was most consistently found when analysis was done at the end of inspiration. Conclusions: These findings were most likely a result of the complexity of pulmonary mechanics in the surfactant-deficient lungs, rendering the single compartment model we based our theory on inadequate. However, phase analysis performed at the end of inspiration seemed to produce the most reliable and consistent results. ... In an **oscillating** system driven by a sine wave pump, the resonance **frequency** of the respiratory system can be determined using phase analysis. At resonance **frequency**, when elastance and inertance cancel out, flow becomes in-phase with resistance. In premature infants with respiratory distress syndrome, owing to surfactant deficiency, localized areas of hyperinflation and collapse develop, resulting in complex changes in overall pulmonary mechanics. We investigated the effect of measuring resonance **frequency** of the respiratory system by phase analysis at different points of the respiratory cycle: end of inspiration, end of expiration, mid-inspiration and mid-expiration. Ten ventilated premature infants with respiratory distress syndrome were studied, gestational age ranged from 24 to 30 weeks (mean 27.6 weeks) and birth weight ranged from 0.7 to 1.505 kg (mean 0.984 kg). Results: The resonance **frequency** was consistently higher when measured at the end of inspiration compared with the end of expiration. The expected trend of phase variation, that is, negative below the resonance **frequency** and positive above, was most consistently found when analysis was done at the end of inspiration. Conclusions: These findings were most likely a result of the complexity of pulmonary mechanics in the surfactant-deficient lungs, rendering the single compartment model we based our theory on inadequate. However, phase analysis performed at the end of inspiration seemed to produce the most reliable and consistent results.

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