### 9129 results for qubit oscillator frequency

Contributors: Eugene Grichuk, Margarita Kuzmina, Eduard Manykin

Date: 2010-09-26

A network of coupled stochastic **oscillators** is
proposed for modeling of a cluster of entangled **qubits** that is
exploited as a computation resource in one-way quantum
computation schemes. A **qubit** model has been designed as a
stochastic **oscillator** formed by a pair of coupled limit cycle
**oscillators** with chaotically modulated limit cycle radii and
**frequencies**. The **qubit** simulates the behavior of electric field of
polarized light beam and adequately imitates the states of two-level
quantum system. A cluster of entangled **qubits** can be associated
with a beam of polarized light, light polarization degree being
directly related to cluster entanglement degree. Oscillatory network,
imitating **qubit** cluster, is designed, and system of equations for
network dynamics has been written. The constructions of one-**qubit**
gates are suggested. Changing of cluster entanglement degree caused
by measurements can be exactly calculated....network of stochastic oscillators...network of stochastic **oscillators**...Network of Coupled Stochastic **Oscillators** and One-way Quantum Computations ... A network of coupled stochastic **oscillators** is
proposed for modeling of a cluster of entangled **qubits** that is
exploited as a computation resource in one-way quantum
computation schemes. A **qubit** model has been designed as a
stochastic **oscillator** formed by a pair of coupled limit cycle
**oscillators** with chaotically modulated limit cycle radii and
**frequencies**. The **qubit** simulates the behavior of electric field of
polarized light beam and adequately imitates the states of two-level
quantum system. A cluster of entangled **qubits** can be associated
with a beam of polarized light, light polarization degree being
directly related to cluster entanglement degree. Oscillatory network,
imitating **qubit** cluster, is designed, and system of equations for
network dynamics has been written. The constructions of one-**qubit**
gates are suggested. Changing of cluster entanglement degree caused
by measurements can be exactly calculated.

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Contributors: Ying-Jie Chen, Hai-Tao Song, Jing-Lin Xiao

Date: 2017-10-14

Temperature effects on polaron in triangular quantum dot **qubit** subjected to an electromagnetic field are studied.
We derive the numerical results and formulate the derivative relationships of the ground and first
excited state energies, the electron probability density and the electron **oscillating** period in the superposition state of
the ground state and the first-excited state with the temperature, the cyclotron **frequency**, the electron-phonon coupling
constant, the electric field strength, the confinement strength and the Coulomb impurity potential, respectively....4-The first excited state energy as functions of the temperature and the electron-phonon coupling constant and etc. in triangular quantum dot **qubit** under an electric field.docx...6-The electron **oscillating** period as functions of the temperature and the cyclotron **frequency** in triangular quantum dot **qubit** under an electric field.docx...Temperature effects on polaron in triangular quantum dot **qubit** subjected to an electromagnetic field are studied.
We derive the numerical results and formulate the derivative relationships of the ground and first
excited state energies, the electron probability density and the electron oscillating period in the superposition state of
the ground state and the first-excited state with the temperature, the cyclotron **frequency**, the electron-phonon coupling
constant, the electric field strength, the confinement strength and the Coulomb impurity potential, respectively....6-The electron oscillating period as functions of the temperature and the cyclotron **frequency** in triangular quantum dot **qubit** under an electric field.docx...Data for: Temperature effects on bound polaron in triangular quantum dot **qubit** subjected to an electromagnetic field...7-The electron **oscillating** period as functions of the temperature and the electron-phonon coupling constant and etc. in triangular quantum dot **qubit** under an electric field.docx...2-The first excited state energy as functions of the temperature and the cyclotron **frequency** in triangular quantum dot **qubit** under an electric field.docx...3-The ground state energy as functions of the temperature and the electron-phonon coupling constant and etc. in triangular quantum dot **qubit** under an electric field.docx...1-The ground state energy as functions of the temperature and the cyclotron **frequency** in triangular quantum dot **qubit** under an electric field.docx ... Temperature effects on polaron in triangular quantum dot **qubit** subjected to an electromagnetic field are studied.
We derive the numerical results and formulate the derivative relationships of the ground and first
excited state energies, the electron probability density and the electron **oscillating** period in the superposition state of
the ground state and the first-excited state with the temperature, the cyclotron **frequency**, the electron-phonon coupling
constant, the electric field strength, the confinement strength and the Coulomb impurity potential, respectively.

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Top results from Data Repository sources. Show only results like these.

Contributors: Tim Byrnes

Date: 2012-03-24

Quantum computation using **qubits** made of two component Bose-Einstein condensates (BECs) is analyzed. We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two **qubit** gate operations that can be performed at a time reduced by a factor of N, where N is the number of bosons per **qubit**. We illustrate the scheme by an application to Deutsch-s and Grover-s algorithms, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed. ... Quantum computation using **qubits** made of two component Bose-Einstein condensates (BECs) is analyzed. We construct a general framework for quantum algorithms to be executed using the collective states of the BECs. The use of BECs allows for an increase of energy scales via bosonic enhancement, resulting in two **qubit** gate operations that can be performed at a time reduced by a factor of N, where N is the number of bosons per **qubit**. We illustrate the scheme by an application to Deutsch-s and Grover-s algorithms, and discuss possible experimental implementations. Decoherence effects are analyzed under both general conditions and for the experimental implementation proposed.

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Contributors: Goldner, Philippe

Date: 2018-12-02

Towards Optically Controlled **Qubits**
in Rare Earth Doped Nanoparticles ... This presentation was given as an invited seminar at the Department of Applied Physics and Materials Science, Caltech, USA, on May 2, 2018, during a visit to the group of Prof. Andrei Faraon. It gives an overview of the current developments on rare earth based nanoscale systems for quantum technologies, focusing on results obtained within the NanOQTech project.

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Contributors: Howan Leung, Cannon X.L. Zhu, Danny T.M. Chan, Wai S. Poon, Lin Shi, Vincent C.T. Mok, Lawrence K.S. Wong

Date: 2015-01-01

An example of the implantation schedule (patient #7) demonstrating areas with conventional frequency ictal patterns, ictal high-frequency oscillations, hyperexcitability, and radiological lesions.
...High-**frequency** oscillations (HFOs, 80–500Hz) from intracranial electroencephalography (EEG) may represent a biomarker of epileptogenicity for epilepsy. We explored the relationship between ictal HFOs and hyperexcitability with a view to improving surgical outcome....High-**frequency** **oscillations**...An example of the implantation schedule (patient #1) demonstrating areas with conventional **frequency** ictal patterns, ictal high-**frequency** **oscillations**, hyperexcitability, and radiological lesions.
...Summary table for statistical analysis. HFO=high frequency oscillations, CFIP=conventional frequency ictal patterns.
...An example of the implantation schedule (patient #7) demonstrating areas with conventional **frequency** ictal patterns, ictal high-**frequency** **oscillations**, hyperexcitability, and radiological lesions.
...High-**frequency** **oscillations** (HFOs, 80–500Hz) from intracranial electroencephalography (EEG) may represent a biomarker of epileptogenicity for epilepsy. We explored the relationship between ictal HFOs and hyperexcitability with a view to improving surgical outcome....Ictal high-**frequency** oscillations and hyperexcitability in refractory epilepsy...An example of the implantation schedule (patient #1) demonstrating areas with conventional frequency ictal patterns, ictal high-frequency oscillations, hyperexcitability, and radiological lesions.
...High-**frequency** oscillations...Summary table for statistical analysis. HFO=high **frequency** **oscillations**, CFIP=conventional **frequency** ictal patterns.
... High-**frequency** **oscillations** (HFOs, 80–500Hz) from intracranial electroencephalography (EEG) may represent a biomarker of epileptogenicity for epilepsy. We explored the relationship between ictal HFOs and hyperexcitability with a view to improving surgical outcome.

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Contributors: Eric Maris, Marieke van Vugt, Michael Kahana

Date: 2011-01-15

Illustration of a tensor decomposition of the four-dimensional array of weighted phase-locking factors (wPLFs). The two spatial maps and the two frequency spectra (see text) are each denoted by a different color (red, yellow, green, and blue) and a different index (i, i', f, f'). The same colors are used both for the boundaries of the panels and the symbols in the formula for the wPLF. In panels a and b, with red and index i, we show the complex-valued spatial map of the high-frequency bursts that are coupled to a common low-frequency oscillation (the coupling oscillation). In panel a, we show the magnitude (absolute value) of this complex-valued spatial map (one colored circle per channel), which expresses the strength of the coupling. In panel b we show the phases of the coupling oscillation to which the high-frequency bursts are locked (one arrow per channel). In panel c, with yellow and index i', we show the spatial map of the coupling oscillation (one colored circle per channel). The more a coefficient bi’ deviates from zero, the more this channel is affected by the coupling oscillation. In panel d, with green and **index f, **we show the frequency spectrum of the phase-coupled bursts (shown on a logarithmic scale). In panel e, with blue and index f', we show the frequency spectrum of the coupling oscillation. The spectra shown in panels a, b, c, d and e are all in arbitrary units (a.u.). This is because the spectra are produced by a tensor decomposition which involves an arbitrary multiplicative scaling (see Supplemental Material). In panels f, h, and j, we show the magnitudes of the complex wPLFs for three selected channel pairs (see text). By means of arrows, we connect the channels in panels a and c for which these wPLFs were calculated, with the corresponding** x-axes (**showing the frequency of the coupling oscillation), respectively, y-axes (showing the frequency of the phase-coupled bursts), in panels f, h, and j. In panels g and i, we show the phases of the complex wPLFs that correspond to panels f and h, respectively.
...Our conclusion about the number of sources involved in PAC depends on our definition of a source. We defined a source in terms of two patterns: (1) a spatial map that specifies how strongly source activity affects the measurements at the sensor level, and (2) its **frequency** spectrum. We showed that, with this source definition, the array of PAC-measures (wPLFs) can be written as a tensor product of two spatial maps (one complex- and one real-valued) and two **frequency** spectra (both real-valued), which is exactly the structure that is extracted by our tensor decomposition (see Supplemental Methods). However, we cannot exclude PAC-generating source configurations that cannot be characterized in this way. In fact, we have argued that PAC-patterns may also be generated by a source configuration that would be considered a single source when viewed from the perspective of the mechanism that generates the physiological signal. This confronts us with the problem that sources can be defined both in terms of their formal characteristics (i.e., in terms of a spatial map and a **frequency** spectrum) and in terms of the neuronal network that generates the physiological signal. The difference between the two definitions is most clear if the physiological mechanism consist of multiple components, such as networks of inhibitory neurons that are connected to one or multiple classes of principal neurons, each with its own network topology. This whole multi-component network may be considered as a single source, but also as multiple sources, each one corresponding to one component. Importantly, if these components differ with respect to their spatial maps and **frequency** spectra, then they can be extracted by means of tensor decomposition. This shows there may be a need for a linking of the set of extracted source configurations on the basis of the neuronal interactions that may have produced them....Localization of components showing a reliable modulation in PAC strength between the activation and the baseline period. The upper panel shows the location of the components with a PAC strength that decreases from the baseline to the activation period. Every component is denoted by a different color. Electrodes are denoted by disks with a diameter proportional to the magnitude of their loadings in the spatial map of the high-frequency bursts. PAC decreases are predominantly observed over the right temporal lobe, but there also decreases over a few left frontal and left temporal areas. The lower panel shows the location of the components with a PAC strength that increases from the baseline to the activation period. PAC increases are predominantly observed over the right temporal and the right parietal lobe, but there are also increases over a few left parietal, left temporal, and right frontal areas.
...Package of figures showing the spatial maps and the **frequency** spectra of a representative set of reliable cross-**frequency** patterns extracted from the activation period wPLFs. The figures belonging to one cross-**frequency** patterns are each in one folder, of which the name refers to the patient. The files that have freqspectra_and_compass as a part of their name contain a figure of which the left panel show the **frequency** spectra of a coupling **oscillation** and the associated phase-coupled bursts, and the right panel shows the preferred phases of the PAC in a compass plots. The files that have _IA_ (instantaneous amplitude) as a part of their name contain figures of the magnitudes of the spatial maps for the phase-coupled bursts. Different figures show different subsets of the electrodes, each from on optimal viewpoint. Electrode subsets on the medial side of the brain are shown from two viewpoints, lateral and occipital. The files that have _AWIP_ (amplitude-weighted instantaneous phase) as a part of their name contain figures of the spatial maps of the coupling **oscillation**. Again, different figures show different subsets of the electrodes, each from on optimal viewpoint.
...Spatial maps of the phase-coupled bursts are smaller than the spatial maps of the associated coupling **oscillation**. Both panels show scatter plots of the extent of the spatial maps of the phase-coupled bursts (horizontal axis) against the extent of the corresponding spatial maps of the coupling **oscillation** (vertical axis). Panels a and b show the scatter plots for, respectively, the baseline and the activation period. Panels a and b show the scatter plots for, respectively, the baseline and the activation period. In both periods, for most of the PAC patterns, the extent of the spatial map of the phase-coupled bursts is substantially smaller than the extent of the spatial map of the associated coupling **oscillation**.
...Our conclusion about the number of sources involved in PAC depends on our definition of a source. We defined a source in terms of two patterns: (1) a spatial map that specifies how strongly source activity affects the measurements at the sensor level, and (2) its frequency spectrum. We showed that, with this source definition, the array of PAC-measures (wPLFs) can be written as a tensor product of two spatial maps (one complex- and one real-valued) and two frequency spectra (both real-valued), which is exactly the structure that is extracted by our tensor decomposition (see Supplemental Methods). However, we cannot exclude PAC-generating source configurations that cannot be characterized in this way. In fact, we have argued that PAC-patterns may also be generated by a source configuration that would be considered a single source when viewed from the perspective of the mechanism that generates the physiological signal. This confronts us with the problem that sources can be defined both in terms of their formal characteristics (i.e., in terms of a spatial map and a frequency spectrum) and in terms of the neuronal network that generates the physiological signal. The difference between the two definitions is most clear if the physiological mechanism consist of multiple components, such as networks of inhibitory neurons that are connected to one or multiple classes of principal neurons, each with its own network topology. This whole multi-component network may be considered as a single source, but also as multiple sources, each one corresponding to one component. Importantly, if these components differ with respect to their spatial maps and frequency spectra, then they can be extracted by means of tensor decomposition. This shows there may be a need for a linking of the set of extracted source configurations on the basis of the neuronal interactions that may have produced them....In the analysis of the activation period wPLFs, 36 reliable PAC patterns were identified: two subjects had four reliable PAC patterns, eight had two, 12 had one, and four had none. In the analysis of the baseline period wPLFs, 17 reliable PAC patterns were identified: four subjects had two reliable PAC patterns, nine had one, and 13 had none. Reliability was defined in terms of the split-half correlation between two independent estimates of the spatial and the frequency spectra produced by the tensor decomposition. All identified PAC patterns had reliabilities much larger than what can be expected under the hypothesis of a random PAC (see Materials and methods). A representative selection of reliable PAC patterns is shown in Supplemental Fig. 3....Spatially distributed coherent **oscillations** provide temporal windows of excitability that allow for interactions between distinct neuronal groups. It has been hypothesized that this mechanism for neuronal communication is realized by bursts of high-**frequency** **oscillations** that are phase-coupled to a low-**frequency** spatially distributed coupling **oscillation**. This mechanism requires multiple physiologically different interacting sources, one generating the low-**frequency** coupling **oscillation** and the others generating phase-coupled high-**frequency** **oscillations**. Using human intracranial EEG (iEEG) data, we provide evidence for multiple oscillatory patterns, as characterized on the basis of their spatial maps (topographies) and their **frequency** spectra. In fact, we show that the spatial maps for the coupling **oscillations** are much more widespread than the ones for the associated phase-coupled bursts. Second, in the majority of the patterns of phase-amplitude coupling (PAC), phase-coupled bursts of high-**frequency** activity are synchronized across brain areas. Third and last, working memory operations affect the PAC strength in a heterogeneous way: in some PAC patterns, working memory operations increase their strength, whereas in others they decrease it....Simulated field potentials with bursts of gamma **oscillations** (60Hz) that are phase-coupled to the rising phase of a theta **oscillation** (5Hz).
...In the analysis of the activation period wPLFs, 36 reliable PAC patterns were identified: two subjects had four reliable PAC patterns, eight had two, 12 had one, and four had none. In the analysis of the baseline period wPLFs, 17 reliable PAC patterns were identified: four subjects had two reliable PAC patterns, nine had one, and 13 had none. Reliability was defined in terms of the split-half correlation between two independent estimates of the spatial and the **frequency** spectra produced by the tensor decomposition. All identified PAC patterns had reliabilities much larger than what can be expected under the hypothesis of a random PAC (see Materials and methods). A representative selection of reliable PAC patterns is shown in Supplemental Fig. 3....Package of figures showing the spatial maps and the frequency spectra of a representative set of reliable cross-frequency patterns extracted from the activation period wPLFs. The figures belonging to one cross-frequency patterns are each in one folder, of which the name refers to the patient. The files that have freqspectra_and_compass as a part of their name contain a figure of which the left panel show the frequency spectra of a coupling oscillation and the associated phase-coupled bursts, and the right panel shows the preferred phases of the PAC in a compass plots. The files that have _IA_ (instantaneous amplitude) as a part of their name contain figures of the magnitudes of the spatial maps for the phase-coupled bursts. Different figures show different subsets of the electrodes, each from on optimal viewpoint. Electrode subsets on the medial side of the brain are shown from two viewpoints, lateral and occipital. The files that have _AWIP_ (amplitude-weighted instantaneous phase) as a part of their name contain figures of the spatial maps of the coupling oscillation. Again, different figures show different subsets of the electrodes, each from on optimal viewpoint.
...Schematic of the calculation of the weighted phase-locking factor (wPLF). Raw signals from channels i and i' are **convolved** with a frequency-indexed wavelet, with indices f and f', producing complex-valued signals. With this convolution we estimate the time-varying amplitudes and the phases for the different frequency bins that are provided by our wavelet filter bank. The wPLF is obtained by taking the average over epochs of the inner products (complex covariances) of an amplitude envelope and a wavelet transform. Prior to calculating the inner product, the amplitude envelopes and the wavelet transform are centered (i.e., their mean is subtracted) and normalized (i.e., dividing the signal by its norm, the square-root of the inner product of the signal with its conjugate transpose). The wPLF is a complex association measure, with absolute value between 0 and 1.
...Illustration of a tensor decomposition of the four-dimensional array of weighted phase-locking factors (wPLFs). The two spatial maps and the two **frequency** spectra (see text) are each denoted by a different color (red, yellow, green, and blue) and a different index (i, i', f, f'). The same colors are used both for the boundaries of the panels and the symbols in the formula for the wPLF. In panels a and b, with red and index i, we show the complex-valued spatial map of the high-**frequency** bursts that are coupled to a common low-**frequency** **oscillation** (the coupling **oscillation**). In panel a, we show the magnitude (absolute value) of this complex-valued spatial map (one colored circle per channel), which expresses the strength of the coupling. In panel b we show the phases of the coupling **oscillation** to which the high-**frequency** bursts are locked (one arrow per channel). In panel c, with yellow and index i', we show the spatial map of the coupling **oscillation** (one colored circle per channel). The more a coefficient bi’ deviates from zero, the more this channel is affected by the coupling **oscillation**. In panel d, with green and index f, we show the **frequency** spectrum of the phase-coupled bursts (shown on a logarithmic scale). In panel e, with blue and index f', we show the **frequency** spectrum of the coupling **oscillation**. The spectra shown in panels a, b, c, d and e are all in arbitrary units (a.u.). This is because the spectra are produced by a tensor decomposition which involves an arbitrary multiplicative scaling (see Supplemental Material). In panels f, h, and j, we show the magnitudes of the complex wPLFs for three selected channel pairs (see text). By means of arrows, we connect the channels in panels a and c for which these wPLFs were calculated, with the corresponding x-axes (showing the **frequency** of the coupling **oscillation**), respectively, y-axes (showing the **frequency** of the phase-coupled bursts), in panels f, h, and j. In panels g and i, we show the phases of the complex wPLFs that correspond to panels f and h, respectively.
...Spectral signature of the PAC patterns. Panels a and b show the results for, respectively, the baseline and the activation period. Both panels show a scatter plot of the central **frequencies** of the phase-coupled bursts (horizontal axis) against the central **frequencies** of the coupling **oscillations** (vertical axis). The central **frequency** of the phase-coupled bursts is always smaller than the one for the associated coupling **oscillation**. For all PAC patterns above the thick black line, the central **frequency** for the phase-coupled bursts is larger than the central **frequency** for the associated coupling **oscillation**. There is not a dominant **frequency**, neither for the phase-coupled bursts, nor for the associated coupling **frequencies**.
...Spectral signature of the PAC patterns. Panels a and b show the results for, respectively, the baseline and the activation period. Both panels show a scatter plot of the central frequencies of the phase-coupled bursts (horizontal axis) against the central frequencies of the coupling oscillations (vertical axis). The central frequency of the phase-coupled bursts is always smaller than the one for the associated coupling oscillation. For all PAC patterns above the thick black line, the central frequency for the phase-coupled bursts is larger than the central frequency for the associated coupling oscillation. There is not a dominant frequency, neither for the phase-coupled bursts, nor for the associated coupling frequencies.
...Spatially distributed coherent oscillations provide temporal windows of excitability that allow for interactions between distinct neuronal groups. It has been hypothesized that this mechanism for neuronal communication is realized by bursts of high-**frequency** oscillations that are phase-coupled to a low-**frequency** spatially distributed coupling oscillation. This mechanism requires multiple physiologically different interacting sources, one generating the low-**frequency** coupling oscillation and the others generating phase-coupled high-**frequency** oscillations. Using human intracranial EEG (iEEG) data, we provide evidence for multiple oscillatory patterns, as characterized on the basis of their spatial maps (topographies) and their **frequency** spectra. In fact, we show that the spatial maps for the coupling oscillations are much more widespread than the ones for the associated phase-coupled bursts. Second, in the majority of the patterns of phase-amplitude coupling (PAC), phase-coupled bursts of high-**frequency** activity are synchronized across brain areas. Third and last, working memory operations affect the PAC strength in a heterogeneous way: in some PAC patterns, working memory operations increase their strength, whereas in others they decrease it....Spatially distributed patterns of oscillatory coupling between high-**frequency** amplitudes and low-**frequency** phases in human iEEG ... Spatially distributed coherent **oscillations** provide temporal windows of excitability that allow for interactions between distinct neuronal groups. It has been hypothesized that this mechanism for neuronal communication is realized by bursts of high-**frequency** **oscillations** that are phase-coupled to a low-**frequency** spatially distributed coupling **oscillation**. This mechanism requires multiple physiologically different interacting sources, one generating the low-**frequency** coupling **oscillation** and the others generating phase-coupled high-**frequency** **oscillations**. Using human intracranial EEG (iEEG) data, we provide evidence for multiple oscillatory patterns, as characterized on the basis of their spatial maps (topographies) and their **frequency** spectra. In fact, we show that the spatial maps for the coupling **oscillations** are much more widespread than the ones for the associated phase-coupled bursts. Second, in the majority of the patterns of phase-amplitude coupling (PAC), phase-coupled bursts of high-**frequency** activity are synchronized across brain areas. Third and last, working memory operations affect the PAC strength in a heterogeneous way: in some PAC patterns, working memory operations increase their strength, whereas in others they decrease it.

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Contributors: Li Wang, Qingmei Kong, Ke Li, Yunai Su, Yawei Zeng, Qinge Zhang, Wenji Dai, Mingrui Xia, Gang Wang, Zhen Jin

Date: 2016-02-12

Brain regions showing significant **group and** frequency (slow-4 and slow-5) interaction effects on ALFF.
...Brain regions showing significant group and **frequency** (slow-4 and slow-5) interaction effects on ALFF.
...The group and **frequency** (slow-4 and slow-5) interaction effects on ALFF. The regions showing significant group and **frequency** interaction effects on ALFF (hot colors): the left ventromedial prefrontal cortex (a), the left inferior frontal gyrus/precentral gyrus (b), and the bilateral posterior cingulate cortex/precuneus (c). The bar maps show the mean ALFF values for these regions.
...Main effects of **group and** frequency on ALFF. (a) The group main effects on ALFF. Hot colors represent increased ALFF in the MDD group compared with HC, while the blue colors represent the opposite. (b) Frequency main effects on ALFF. Hot colors represent increased ALFF in the slow-5 as compared to slow-4 band, while the blue colors represent the opposite. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
...Low-**frequency** **oscillation**...Research paper - **Frequency**-dependent changes in amplitude of low-**frequency** oscillations in depression: A resting-state fMRI study...Low-**frequency** oscillation...**Frequency** dependence...We conducted this fMRI study to examine whether the alterations in amplitudes of low-**frequency** **oscillation** (LFO) of major depressive disorder (MDD) patients were **frequency** dependent....Main effects of group and **frequency** on ALFF. (a) The group main effects on ALFF. Hot colors represent increased ALFF in the MDD group compared with HC, while the blue colors represent the opposite. (b) **Frequency** main effects on ALFF. Hot colors represent increased ALFF in the slow-5 as compared to slow-4 band, while the blue colors represent the opposite. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
...We conducted this fMRI study to examine whether the alterations in amplitudes of low-**frequency** oscillation (LFO) of major depressive disorder (MDD) patients were **frequency** dependent....The **group and** frequency (slow-4 and slow-5) interaction effects on ALFF. The regions showing significant **group and** frequency interaction effects on ALFF (hot colors): the left ventromedial prefrontal cortex (a), the left inferior frontal gyrus/precentral gyrus (b), and the bilateral posterior cingulate cortex/precuneus (c). The bar maps show the mean ALFF values for these regions.
... We conducted this fMRI study to examine whether the alterations in amplitudes of low-**frequency** **oscillation** (LFO) of major depressive disorder (MDD) patients were **frequency** dependent.

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Contributors: White, William C.

Date: 1916-10-01

The pliotron **oscillator** for extreme **frequencies** ... n/a

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Contributors: Duddell, William

Date: 1908-10-31

High-**Frequency** Oscillations ... n/a

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Contributors: George M. Ibrahim, Simeon M. Wong, Ryan A. Anderson, Gabrielle Singh-Cadieux, Tomoyuki Akiyama, Ayako Ochi, Hiroshi Otsubo, Tohru Okanishi, Taufik A. Valiante, Elizabeth Donner

Date: 2014-01-01

Quantification of amplitude-to-phase cycle relationship. (A) Mean amplitudes of high **frequency** **oscillations**, sorted by concurrent low-**frequency** phase into 60 bins of 0.105rad, for an example time window during a seizure; (B) an ideal cosine; and (C) a sine is modeled. (D) Phasor demonstrating the amplitude–phase cycle relationship. (E) The argument (angle) of the example phasor is a single contribution to be incremented onto a cumulative polar histogram spanning multiple subjects for one of ten given time periods in the seizure.
...Individual seizure short-time Fourier transform spectrograms. The seizure onset zone contained predominantly low-frequency power, which was fairly heterogenous across the population. High frequency activity was also evident in all seizures as bursts of high power oscillatory activity.
...Modulation of high frequency amplitude by low-frequency phase. In the seizure-onset zone, significant modulation of high-frequency amplitude (40–300Hz) is observed, mainly by the phase of theta and alpha oscillations during the ictal period. In the interictal period, no specific CFC with slower oscillations is observed. There is also less cross-frequency coupling in the early propagation zone during seizures and no significant coupling is noted in the non-epileptogenic cortex. The z-axis demonstrates the modulation of amplitudes of different narrow-band frequencies (x-axis) by the phases of other narrow-band frequencies (y-axis). Lower and upper planes represent uncorrected and corrected statistical thresholds at p<0.05, respectively.
...Modulation of high **frequency** amplitude by low-**frequency** phase. In the seizure-onset zone, significant modulation of high-**frequency** amplitude (40–300Hz) is observed, mainly by the phase of theta and alpha **oscillations** during the ictal period. In the interictal period, no specific CFC with slower **oscillations** is observed. There is also less cross-**frequency** coupling in the early propagation zone during seizures and no significant coupling is noted in the non-epileptogenic cortex. The z-axis demonstrates the modulation of amplitudes of different narrow-band **frequencies** (x-axis) by the phases of other narrow-band **frequencies** (y-axis). Lower and upper planes represent uncorrected and corrected statistical thresholds at p<0.05, respectively.
...High **frequency** **oscillations**...Dynamic modulation of epileptic high **frequency** oscillations by the phase of slower cortical rhythms...Mean ictal electrode pHFO amplitude and cross-frequency coupling as a function of Cartesian distance from the epileptogenic cortex. Pooled data across all subjects demonstrates that cross-frequency coupling (red trend line) declines sharply relative to pHFO amplitude (blue trend line), indicating that pHFOs and CFC are dissociable measures, which differ in their topographic relation to the epileptogenic cortex. Shaded regions represent standard deviation.
...Individual seizure short-time Fourier transform spectrograms. The seizure onset zone contained predominantly low-**frequency** power, which was fairly heterogenous across the population. High **frequency** activity was also evident in all seizures as bursts of high power oscillatory activity.
...Pathological high **frequency** **oscillations** (pHFOs) have been proposed to be robust markers of epileptic cortex. Oscillatory activity below this **frequency** range has been shown to be modulated by phase of lower **frequency** **oscillations**. Here, we tested the hypothesis that dynamic cross-**frequency** interactions involving pHFOs are concentrated within the epileptogenic cortex. Intracranial electroencephalographic recordings from 17 children with medically-intractable epilepsy secondary to focal cortical dysplasia were obtained. A time-resolved analysis was performed to determine topographic concentrations and dynamic changes in cross-**frequency** amplitude-to-phase coupling (CFC). CFC between pHFOs and the phase of theta and alpha rhythms was found to be significantly elevated in the seizure-onset zone compared to non-epileptic regions (pfrequency **oscillations** at which pHFO amplitudes were maximal was inconsistent at seizure initiation, yet consistently at the trough of the low **frequency** rhythm at seizure termination. Amplitudes of pHFOs were most significantly modulated by the phase of alpha-band **oscillations** (p<0.01). These results suggest that increased CFC between pHFO amplitude and alpha phase may constitute a marker of epileptogenic brain areas and may be relevant for understanding seizure dynamics....Pathological high **frequency** oscillations (pHFOs) have been proposed to be robust markers of epileptic cortex. Oscillatory activity below this **frequency** range has been shown to be modulated by phase of lower **frequency** oscillations. Here, we tested the hypothesis that dynamic cross-**frequency** interactions involving pHFOs are concentrated within the epileptogenic cortex. Intracranial electroencephalographic recordings from 17 children with medically-intractable epilepsy secondary to focal cortical dysplasia were obtained. A time-resolved analysis was performed to determine topographic concentrations and dynamic changes in cross-**frequency** amplitude-to-phase coupling (CFC). CFC between pHFOs and the phase of theta and alpha rhythms was found to be significantly elevated in the seizure-onset zone compared to non-epileptic regions (pfrequency oscillations at which pHFO amplitudes were maximal was inconsistent at seizure initiation, yet consistently at the trough of the low **frequency** rhythm at seizure termination. Amplitudes of pHFOs were most significantly modulated by the phase of alpha-band oscillations (p<0.01). These results suggest that increased CFC between pHFO amplitude and alpha phase may constitute a marker of epileptogenic brain areas and may be relevant for understanding seizure dynamics....Topographic mapping of cross-frequency interactions in a representative subject. (A) Intraoperative image of grid demonstrating seizure onset and early propagation zones. (B) Fast-ripple amplitudes sorted by alpha phase for all grid electrodes. Cosine wave represents alpha phase from −π to π. Increased pHFO-to-low-frequency coupling occurs in the resected cortex (black borders). Values normalized by 95% confidence interval such values above 0 are significant at p0.05. (C) Cross frequency modulation index for all electrodes, where the X-axis represents low frequency phase (1 to 40Hz; left to right), and the Y-axis denotes envelope amplitude (1 to 300Hz; top to bottom). Values exceeding Bonferroni correction threshold shown. Significant modulation of pHFO amplitudes by low-frequency phase is observed in the epileptogenic cortex.
...To characterize the ictal dynamics of relations between pHFO amplitude and low **frequency** phase, we measured the preferred slow oscillatory phase at which high amplitude pHFOs occurred at various times throughout the seizure. When the preferred phases from all bins from all subjects were plotted cumulatively on polar histograms, it was observed that pathological fast-ripple amplitudes preferentially occurred during the trough of alpha oscillations, whereas pathological ripple amplitudes preferentially occurred between 0rad and π/2rad of alpha and theta oscillatory cycles (Fig. 5; p<0.01 and p<0.01, respectively; Rayleigh test). At seizure initiation (i.e. the first bin), there was no preferred phase for coupling between pathological fast-ripple or ripple amplitudes and the phase of alpha or theta oscillations (p=0.14 and p=0.68, respectively). At seizure termination (i.e. the last bin), pHFO amplitudes occurred at the trough of the alpha oscillatory cycle (pathological ripple amplitude: p<0.01; pathological fast-ripple amplitude: p=0.03). Ripple amplitude maxima were also found at the peak of delta phase irrespective of the seizure progression (Supplementary Fig. S9). To ensure that differences in bin length did explain the measures of CFC, a reanalysis of the data with fixed length segments comprised of the first and last 2000ms of seizures, revealed the same pattern....To characterize the ictal dynamics of relations between pHFO amplitude and low **frequency** phase, we measured the preferred slow oscillatory phase at which high amplitude pHFOs occurred at various times throughout the seizure. When the preferred phases from all bins from all subjects were plotted cumulatively on polar histograms, it was observed that pathological fast-ripple amplitudes preferentially occurred during the trough of alpha **oscillations**, whereas pathological ripple amplitudes preferentially occurred between 0rad and π/2rad of alpha and theta oscillatory cycles (Fig. 5; poscillations (p=0.14 and p=0.68, respectively). At seizure termination (i.e. the last bin), pHFO amplitudes occurred at the trough of the alpha oscillatory cycle (pathological ripple amplitude: p<0.01; pathological fast-ripple amplitude: p=0.03). Ripple amplitude maxima were also found at the peak of delta phase irrespective of the seizure progression (Supplementary Fig. S9). To ensure that differences in bin length did explain the measures of CFC, a reanalysis of the data with fixed length segments comprised of the first and last 2000ms of seizures, revealed the same pattern....Simulated data demonstrating expected polar histogram distribution. The high frequency amplitude is represented by the blue solid line, whereas the low-frequency phase is represented by the black dashed line. When the high frequency amplitude is maximal at the peak and trough of the low frequency phase, the polar histograms will indicate pi and 0, respectively.
...Cross-**frequency** coupling...Simulated data demonstrating expected polar histogram distribution. The high **frequency** amplitude is represented by the blue solid line, whereas the low-**frequency** phase is represented by the black dashed line. When the high **frequency** amplitude is maximal at the peak and trough of the low **frequency** phase, the polar histograms will indicate pi and 0, respectively.
...Topographic mapping of cross-**frequency** interactions in a representative subject. (A) Intraoperative image of grid demonstrating seizure onset and early propagation zones. (B) Fast-ripple amplitudes sorted by alpha phase for all grid electrodes. Cosine wave represents alpha phase from −π to π. Increased pHFO-to-low-**frequency** coupling occurs in the resected cortex (black borders). Values normalized by 95% confidence interval such values above 0 are significant at pfrequency modulation index for all electrodes, where the X-axis represents low **frequency** phase (1 to 40Hz; left to right), and the Y-axis denotes envelope amplitude (1 to 300Hz; top to bottom). Values exceeding Bonferroni correction threshold shown. Significant modulation of pHFO amplitudes by low-**frequency** phase is observed in the epileptogenic cortex.
...High **frequency** oscillations ... Pathological high **frequency** **oscillations** (pHFOs) have been proposed to be robust markers of epileptic cortex. Oscillatory activity below this **frequency** range has been shown to be modulated by phase of lower **frequency** **oscillations**. Here, we tested the hypothesis that dynamic cross-**frequency** interactions involving pHFOs are concentrated within the epileptogenic cortex. Intracranial electroencephalographic recordings from 17 children with medically-intractable epilepsy secondary to focal cortical dysplasia were obtained. A time-resolved analysis was performed to determine topographic concentrations and dynamic changes in cross-**frequency** amplitude-to-phase coupling (CFC). CFC between pHFOs and the phase of theta and alpha rhythms was found to be significantly elevated in the seizure-onset zone compared to non-epileptic regions (p<0.01). Data simulations showed that elevated CFC could not be attributed to the presence of sharp transients or other signal properties. The phase of low **frequency** **oscillations** at which pHFO amplitudes were maximal was inconsistent at seizure initiation, yet consistently at the trough of the low **frequency** rhythm at seizure termination. Amplitudes of pHFOs were most significantly modulated by the phase of alpha-band **oscillations** (p<0.01). These results suggest that increased CFC between pHFO amplitude and alpha phase may constitute a marker of epileptogenic brain areas and may be relevant for understanding seizure dynamics.

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