### 21982 results for qubit oscillator frequency

Contributors: György Buzsáki, Fernando Lopes da Silva

Date: 2012-09-01

Spontaneously occurring fast ‘ripple’ **oscillations** (400–500Hz) in the neocortex of the rat during high-voltage spindles. (A) Averaged high-voltage spindles and associated unit firing histograms from layers IV–VI. (B) Wide-band (a and a′; 1Hz–5kHz), filtered field (b and b′; 200–800Hz), and filtered unit (c and c′; 0.5–5kHz) traces from layers IV and V, respectively. (C) Averaged fast waves and corresponding unit histograms. The field ripples are filtered (200–800Hz) derivatives of the wide-band signals recorded from 16 sites. Note the sudden phase-reversal of the **oscillating** waves (arrows) but locking of unit discharges (dashed lines). These phase reversed dipoles likely reflect synchronous discharge of layer 5 neurons in the vicinity of the recording electrode.
...Self-organized burst of activity in the CA3 region of the hippocampus produces a sharp wave sink in the apical dendrites of CA1 pyramidal neurons and also discharge interneurons. The interactions between the discharging pyramidal cells and interneurons give rise to a short-lived fast **oscillation** (‘ripple’; 140–200Hz), which can be detected as a field potential in the somatic layer. The strong CA1 population burst brings about strongly synchronized activity in the target populations of parahippocampal structures as well. These parahippocampal ripples are slower and less synchronous, compared to CA1 ripples.
...High **frequency** **oscillations** (HFOs) constitute a novel trend in neurophysiology that is fascinating neuroscientists in general, and epileptologists in particular. But what are HFOs? What is the **frequency** range of HFOs? Are there different types of HFOs, physiological and pathological? How are HFOs generated? Can HFOs represent temporal codes for cognitive processes? These questions are pressing and this symposium volume attempts to give constructive answers. As a prelude to this exciting discussion, we summarize the physiological high **frequency** patterns in the intact brain, concentrating mainly on hippocampal patterns, where the mechanisms of high **frequency** **oscillations** are perhaps best understood. ... High **frequency** **oscillations** (HFOs) constitute a novel trend in neurophysiology that is fascinating neuroscientists in general, and epileptologists in particular. But what are HFOs? What is the **frequency** range of HFOs? Are there different types of HFOs, physiological and pathological? How are HFOs generated? Can HFOs represent temporal codes for cognitive processes? These questions are pressing and this symposium volume attempts to give constructive answers. As a prelude to this exciting discussion, we summarize the physiological high **frequency** patterns in the intact brain, concentrating mainly on hippocampal patterns, where the mechanisms of high **frequency** **oscillations** are perhaps best understood.

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Contributors: Olivier Audouin, Jacques Bodin

Date: 2007-02-20

Extensive slug-test experiments have been performed at the Hydrogeological Experimental Site (HES) of Poitiers in France, made up of moderately fractured limestones. All data are publicly available through the “H+” database, developed within the scope of the ERO program (French Environmental Research Observatory, http://hplus.ore.fr). Slug-test responses with high-**frequency** (>0.12Hz) **oscillations** have been consistently observed in wells equipped with multiple concentric casing. These **oscillations** are interpreted as the result of inertia-induced fluctuations of the water level in the annular space between the inner and outer casing. In certain cases, these high-**frequency** **oscillations** overlap with lower **frequency** (**oscillations**, which leads to complex responses that cannot be interpreted using conventional models. Slug-test data have been processed in the Fourier-**frequency** domain, in order to remove the high-**frequency** component by a signal-filtering method. The corrected signals have been interpreted with the model of [McElwee, C.D., Zenner, M., 1998. A nonlinear model for analysis of slug-test data. Water Resour. Res. 34 (1), 55–66.], which accounts for the inertia of the water-column above the well screen, non-linear head losses in the well, and neglects the aquifer storage (quasi-steady-state approximation). Hydraulic conductivity values interpreted from dual-**frequency** slug-tests compare well to those interpreted from “standard” overdamped or underdamped slug-test responses....**Frequency** spectrum of the slug-test response in HES well M05, for an initial head displacement H0=0.2m (slug-test reference=STM5_02).
...Filtering of high-**frequency** **oscillations**: example of processing of the slug test STM5_02 (HES well M05, initial head displacement H0=0.2m).
...High-**frequency** **oscillations**...Filter shape in the **frequency** domain for ρ=0.9.
...Interpretation of high-**frequency** **oscillations**: inertia-induced water level fluctuations in the annular space between the inner PVC casing and the outer steel casing.
...Typical slug-test responses in HES wells. (a) “Standard” overdamped response; (b) “standard” underdamped response with low-**frequency** **oscillations**; (c) overdamped response with high-**frequency** **oscillations**; (d) underdamped response with dual-**frequency** **oscillations**.
... Extensive slug-test experiments have been performed at the Hydrogeological Experimental Site (HES) of Poitiers in France, made up of moderately fractured limestones. All data are publicly available through the “H+” database, developed within the scope of the ERO program (French Environmental Research Observatory, http://hplus.ore.fr). Slug-test responses with high-**frequency** (>0.12Hz) **oscillations** have been consistently observed in wells equipped with multiple concentric casing. These **oscillations** are interpreted as the result of inertia-induced fluctuations of the water level in the annular space between the inner and outer casing. In certain cases, these high-**frequency** **oscillations** overlap with lower **frequency** (<0.05Hz) **oscillations**, which leads to complex responses that cannot be interpreted using conventional models. Slug-test data have been processed in the Fourier-**frequency** domain, in order to remove the high-**frequency** component by a signal-filtering method. The corrected signals have been interpreted with the model of [McElwee, C.D., Zenner, M., 1998. A nonlinear model for analysis of slug-test data. Water Resour. Res. 34 (1), 55–66.], which accounts for the inertia of the water-column above the well screen, non-linear head losses in the well, and neglects the aquifer storage (quasi-steady-state approximation). Hydraulic conductivity values interpreted from dual-**frequency** slug-tests compare well to those interpreted from “standard” overdamped or underdamped slug-test responses.

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Contributors: Yulia P. Emelianova, Alexander P. Kuznetsov, Ludmila V. Turukina, Igor R. Sataev, Nikolai Yu. Chernyshov

Date: 2014-04-01

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.
...A structure of the **oscillation** **frequencies** parameter space for three and four dissipatively coupled van der Pol **oscillators** is discussed. Situations of different codimension relating to the configuration of the full synchronization area as well as a picture of different modes in its neighborhood are revealed. An organization of quasi-periodic areas of different dimensions is considered. The results for the phase model and for the original system are compared....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).
... A structure of the **oscillation** **frequencies** parameter space for three and four dissipatively coupled van der Pol **oscillators** is discussed. Situations of different codimension relating to the configuration of the full synchronization area as well as a picture of different modes in its neighborhood are revealed. An organization of quasi-periodic areas of different dimensions is considered. The results for the phase model and for the original system are compared.

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Contributors: Fatema F. Ghasia, Aasef G. Shaikh

Date: 2014-01-01

(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.
...Most common eye movements, oblique saccades, feature rapid velocity, precise amplitude, but curved trajectory that is variable from trial-to-trial. In addition to curvature and inter-trial variability, the oblique saccade trajectory also features high-**frequency** **oscillations**. A number of studies proposed the physiological basis of the curvature and inter-trial variability of the oblique saccade trajectory, but kinematic characteristics of high-**frequency** **oscillations** are yet to be examined. We measured such **oscillations** and compared their properties with orthogonal pure horizontal and pure vertical **oscillations** generated during pure vertical and pure horizontal saccades, respectively. We found that the **frequency** of **oscillations** during oblique saccades ranged between 15 and 40 Hz, consistent with the **frequency** of orthogonal saccadic **oscillations** during pure horizontal or pure vertical saccades. We also found that the amplitude of oblique saccade **oscillations** was larger than pure horizontal and pure vertical saccadic **oscillations**. These results suggest that the superimposed high-**frequency** sinusoidal **oscillations** upon the oblique saccade trajectory represent reverberations of disinhibited circuit of reciprocally innervated horizontal and vertical burst generators....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.
... Most common eye movements, oblique saccades, feature rapid velocity, precise amplitude, but curved trajectory that is variable from trial-to-trial. In addition to curvature and inter-trial variability, the oblique saccade trajectory also features high-**frequency** **oscillations**. A number of studies proposed the physiological basis of the curvature and inter-trial variability of the oblique saccade trajectory, but kinematic characteristics of high-**frequency** **oscillations** are yet to be examined. We measured such **oscillations** and compared their properties with orthogonal pure horizontal and pure vertical **oscillations** generated during pure vertical and pure horizontal saccades, respectively. We found that the **frequency** of **oscillations** during oblique saccades ranged between 15 and 40 Hz, consistent with the **frequency** of orthogonal saccadic **oscillations** during pure horizontal or pure vertical saccades. We also found that the amplitude of oblique saccade **oscillations** was larger than pure horizontal and pure vertical saccadic **oscillations**. These results suggest that the superimposed high-**frequency** sinusoidal **oscillations** upon the oblique saccade trajectory represent reverberations of disinhibited circuit of reciprocally innervated horizontal and vertical burst generators.

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Contributors: Markku Penttonen, György Buzsáki

Date: 2003-04-01

**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**...Behaviorally relevant brain **oscillations** relate to each other in a specific manner to allow neuronal networks of different sizes with wide variety of connections to cooperate in a coordinated manner. For example, thalamo-cortical and hippocampal **oscillations** form numerous **frequency** bands, which follow a general rule. Specifically, the center **frequencies** and **frequency** ranges of **oscillation** bands with successively faster **frequencies**, from ultra-slow to ultra-fast **frequency** **oscillations**, form an arithmetic progression on the natural logarithmic scale. Due to mathematical properties of natural logarithm, the cycle lengths (periods) of **oscillations**, as an inverse of **frequency**, also form an arithmetic progression after natural logarithmic transformation. As a general rule, the neuronal excitability is larger during a certain phase of the **oscillation** period. Because the intervals between these activation phases and the temporal window of activation vary in proportion to the length of the **oscillation** period, lower **frequency** **oscillations** allow for an integration of neuronal effects with longer delays and larger variability in delays and larger areas of involvement. Neural representations based on these **oscillations** could therefore be complex. In contrast, high **frequency** **oscillation** bands allow for a more precise and spatially limited representation of information by incorporating synaptic events from closely located regions with short synaptic delays and limited variability. The large family of **oscillation** **frequency** bands with a constant relation may serve to overcome the information processing limitations imposed by the synaptic delays. ... Behaviorally relevant brain **oscillations** relate to each other in a specific manner to allow neuronal networks of different sizes with wide variety of connections to cooperate in a coordinated manner. For example, thalamo-cortical and hippocampal **oscillations** form numerous **frequency** bands, which follow a general rule. Specifically, the center **frequencies** and **frequency** ranges of **oscillation** bands with successively faster **frequencies**, from ultra-slow to ultra-fast **frequency** **oscillations**, form an arithmetic progression on the natural logarithmic scale. Due to mathematical properties of natural logarithm, the cycle lengths (periods) of **oscillations**, as an inverse of **frequency**, also form an arithmetic progression after natural logarithmic transformation. As a general rule, the neuronal excitability is larger during a certain phase of the **oscillation** period. Because the intervals between these activation phases and the temporal window of activation vary in proportion to the length of the **oscillation** period, lower **frequency** **oscillations** allow for an integration of neuronal effects with longer delays and larger variability in delays and larger areas of involvement. Neural representations based on these **oscillations** could therefore be complex. In contrast, high **frequency** **oscillation** bands allow for a more precise and spatially limited representation of information by incorporating synaptic events from closely located regions with short synaptic delays and limited variability. The large family of **oscillation** **frequency** bands with a constant relation may serve to overcome the information processing limitations imposed by the synaptic delays.

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Contributors: Gabriel H. Paissan, Damián H. Zanette

Date: 2008-05-15

**Frequency** clustering...The effective **frequency** ωi′ as a function of the natural **frequency** ωi of individual **oscillators** in single realizations for constant coupling, ki=1.5 for all i, with constant weights (upper right), and uniformly distributed weights (upper left), and for uniformly distributed couplings, 0frequency distributions is displayed.
...Synchronization region (gray shaded), obtained analytically for anti-correlated couplings and weights, Eq. (40), in the (Kmax,|λ|) parameter plane. The inserts show plots of individual effective **frequencies** versus natural **frequencies** (cf. Fig. 2), for single realizations of the system at the indicated points of the parameter plane. Scales in all the inserts vary from −0.4 to 0.4 on both axes.
...Coupled **oscillators**...Upper panel: Numerical results for the fraction ns of synchronized **oscillators** in the case of constant couplings, ki=K for all i, with constant weights, qi=1 for all i (solid dots), and with uniformly distributed weights (open dots). Lower panel: The same, for the case of uniformly distributed couplings, 0<ki<Kmax. Full and dotted curves stand for the analytical calculation of ns and the collective amplitude σ, respectively.
...The fraction ns of synchronized **oscillators** for the case of anti-correlated couplings and weights, as a function of Kmax, for four values of |λ|. Full curves stand for the analytical prediction, and dotted curves are plotted as a guide to the eye in the region of **frequency** clustering.
...We consider an extension of Kuramoto’s model of coupled phase **oscillators** where **oscillator** pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated to an **oscillator**, Kuramoto’s theory for the transition to synchronization can be explicitly generalized, and the effects of coupling heterogeneity on synchronized states can be analytically studied. The two factors are respectively interpreted as the weight of the contribution of each **oscillator** to the mean field, and the coupling of each **oscillator** to that field. We explicitly analyze the effects of correlations between those weights and couplings, and show that synchronization can be completely inhibited when they are strongly anti-correlated. Numerical results validate the theory, but suggest that finite-size effect are relevant to the collective dynamics close to the synchronization transition, where **oscillators** become entrained in synchronized **frequency** clusters....Upper panel: Fraction ns of synchronized **oscillators** as a function of |λ|, for Kmax=4. The full curve is the analytical prediction, and the dotted curve has been added as a guide to the eye in the clustering regime. Lower panel: The corresponding number of clusters, C. The dotted curve is a spline approximation.
... We consider an extension of Kuramoto’s model of coupled phase **oscillators** where **oscillator** pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated to an **oscillator**, Kuramoto’s theory for the transition to synchronization can be explicitly generalized, and the effects of coupling heterogeneity on synchronized states can be analytically studied. The two factors are respectively interpreted as the weight of the contribution of each **oscillator** to the mean field, and the coupling of each **oscillator** to that field. We explicitly analyze the effects of correlations between those weights and couplings, and show that synchronization can be completely inhibited when they are strongly anti-correlated. Numerical results validate the theory, but suggest that finite-size effect are relevant to the collective dynamics close to the synchronization transition, where **oscillators** become entrained in synchronized **frequency** clusters.

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Contributors: Lucas C. Monteiro, A.V. Dodonov

Date: 2016-04-08

We consider the interaction between a single cavity mode and N≫1 identical **qubits**, assuming that any system parameter can be rapidly modulated in situ by external bias. It is shown that, for the **qubits** initially in the ground states, three photons can be coherently annihilated in the dispersive regime for harmonic modulation with **frequency** 3ω0−Ω0, where ω0 (Ω0) is the bare cavity (**qubit**) **frequency**. This phenomenon can be called “Anti-dynamical Casimir effect”, since a pair of excitations is destroyed without dissipation due to the external modulation. For the initial vacuum cavity state, three **qubit** excitations can also be annihilated for the modulation **frequency** 3Ω0−ω0. ... We consider the interaction between a single cavity mode and N≫1 identical **qubits**, assuming that any system parameter can be rapidly modulated in situ by external bias. It is shown that, for the **qubits** initially in the ground states, three photons can be coherently annihilated in the dispersive regime for harmonic modulation with **frequency** 3ω0−Ω0, where ω0 (Ω0) is the bare cavity (**qubit**) **frequency**. This phenomenon can be called “Anti-dynamical Casimir effect”, since a pair of excitations is destroyed without dissipation due to the external modulation. For the initial vacuum cavity state, three **qubit** excitations can also be annihilated for the modulation **frequency** 3Ω0−ω0.

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Contributors: Atsushi Tomeda, Shogo Morisaki, Kenichi Watanabe, Shigeki Kuroki, Isao Ando

Date: 2003-07-24

The plots of 1H signal width for the crystalline region of polyethylene thin film on the surface of on an piezoelectric **oscillator** plate against **oscillation** **frequency** in the range from 1 Hz to 2 MHz (a) and in the expanded range from 1 Hz to 100 kHz (b) at 40 °C.
...The plots of 1H signal width for the non-crystalline region of polyethylene thin film on the surface of on a piezoelectric **oscillator** plate against **oscillation** **frequency** in the range from 1 Hz to 2 MHz (a) in the expanded range from 1 Hz to 100 kHz (b) at 40 °C.
...A diagram of an NMR glass tube with an piezoelectric **oscillator** plate. The polyethylene thin film was molten and adhered on the surface of piezoelectric **oscillator** plate. The **oscillation** of an piezoelectric **oscillator** plate is generated by AD alternator.
...The 1H NMR spectrum of polyethylene thin film on an piezoelectric **oscillator** plate made of inorganic material was observed, which is **oscillated** with high **frequency** by application of AD electric current in the Hz–MHz range. From these experimental results, it is shown that dipolar interactions in solid polyethylene are remarkably reduced by high **frequency** **oscillation** and then the signal width of the crystalline component is significantly reduced with an increase in **oscillation** **frequency**. This means that the introduction of the high **frequency** **oscillation** for solids has large potentiality of obtaining the high resolution NMR spectrum. ... The 1H NMR spectrum of polyethylene thin film on an piezoelectric **oscillator** plate made of inorganic material was observed, which is **oscillated** with high **frequency** by application of AD electric current in the Hz–MHz range. From these experimental results, it is shown that dipolar interactions in solid polyethylene are remarkably reduced by high **frequency** **oscillation** and then the signal width of the crystalline component is significantly reduced with an increase in **oscillation** **frequency**. This means that the introduction of the high **frequency** **oscillation** for solids has large potentiality of obtaining the high resolution NMR spectrum.

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Contributors: K.M. EL-Naggar

Date: 2009-06-01

Low-**frequency** **oscillations**...Undamped swing curve: one **oscillation** mode.
...Un-damped swing curve with two **oscillation** modes: f1=0.4, f2=0.5Hz and σ1=−0.025, σ2=+0.037s−1.
...Low-**frequency** **oscillations** in the interconnected power systems are observed all around the electrical grids. This paper presents a novel technique for analyzing the low-**frequency** **oscillations** in power system networks. The proposed technique is a dynamic estimator based on stochastic estimation theory which is suitable for estimating parameters on-line. The method uses digital set of measurements for power system swings to perform the analysis process digitally. The goal is to estimate the amount of damping in the swing curve as well as the **oscillation** **frequency**. The problem is formulated and presented as a stochastic dynamic estimation problem. The proposed technique is used to perform the estimation process. The algorithm tested using different study cases including practical data. Results are evaluated and compared to those obtained using other conventional methods to show the capabilities of the proposed method. ... Low-**frequency** **oscillations** in the interconnected power systems are observed all around the electrical grids. This paper presents a novel technique for analyzing the low-**frequency** **oscillations** in power system networks. The proposed technique is a dynamic estimator based on stochastic estimation theory which is suitable for estimating parameters on-line. The method uses digital set of measurements for power system swings to perform the analysis process digitally. The goal is to estimate the amount of damping in the swing curve as well as the **oscillation** **frequency**. The problem is formulated and presented as a stochastic dynamic estimation problem. The proposed technique is used to perform the estimation process. The algorithm tested using different study cases including practical data. Results are evaluated and compared to those obtained using other conventional methods to show the capabilities of the proposed method.

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Contributors: Ting Wang, Xiaoguang Wang, Zhe Sun

Date: 2007-09-15

We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the **oscillations** of the ground-state and the first-excited-state entanglements are out of phase or in phase....The thermal concurrences between **qubits** 1 and 2 in the 2–6-**qubit** spin-half open Heisenberg chains.
... We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the **oscillations** of the ground-state and the first-excited-state entanglements are out of phase or in phase.

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