In this case, the eigenvalue decomposition of the R N×N matrix yields five for the last eigenvalue and zero for the rest of the eigenvalues.
MEAN PHASE COHERENCE FULL
(b) Five-times copied version of an IMF leads to a R N×N matrix, in which all of its values are equal to one, showing a full phase-synchronization among the oscillators. In this case, all the eigenvalues resulted from the eigenvalue decomposition of the R N×N are close to one. Due to the nearly orthogonal nature of the IMFs extracted from one channel, all the R N×N values are near to zero, showing no phase-synchronization among the oscillators. (a) Five decomposed IMFs from a 1-s, bipolar-derivate ECoG signal using the NA-MEMD process, along with their corresponding mean-phase coherence matrix, eigenvalue spectrum, and the average value of the first 60% lower-index eigenvalues, meanλ 1:60%. All of the values in the mean-phase coherence matrix, R N×N, were normalized and color-coded between zero (black), to one (white). This result suggests that hyper-synchronization of the epileptic network may be an essential self-regulatory mechanism by which the brain terminates seizures.Įvaluating phase-synchrony levels among neuronal oscillators using eigenvalue decomposition of the mean-phase coherence matrix. However, the network phase-synchrony started to increase toward seizure end and achieved its maximum level at seizure offset for both types of epilepsy. Drug-refractory patients with frontal and temporal lobe epilepsy demonstrated a reduction in phase-synchrony around seizure onset. The extracted neuronal oscillators were grouped with respect to their frequency range into wideband (1-600 Hz), ripple (80-250 Hz), and fast-ripple (250-600 Hz) bands in order to investigate the dynamics of ECoG activity in these frequency ranges as seizures evolve. The phase-synchrony dynamics were then assessed using eigenvalue decomposition. Next, the instantaneous phases of the oscillatory functions were extracted using the Hilbert transform in order to be utilized in the mean-phase coherence analysis. A set of finite neuronal oscillators was adaptively extracted from a multi-channel electrocorticographic (ECoG) dataset utilizing noise-assisted multivariate empirical mode de-composition (NA-MEMD). In this paper, a non-linear analytical methodology is proposed to quantitatively evaluate the phase-synchrony dynamics in epilepsy patients. Spatiotemporal evolution of synchrony dynamics among neuronal populations plays an important role in decoding complicated brain function in normal cognitive processing as well as during pathological conditions such as epileptic seizures. We used m * = 1.49 m 0 and v F = 7.5 × 10 5 m s − 1 taken from measurements of bulk samples.
MEAN PHASE COHERENCE FREE
(f) Temperature dependence of the carrier density ( n) (green circles) and the mean free path ( l mf) (blue squares) estimated by the Drude model: l mf = v F τ = m * v F / n e 2 ρ x x, where v F is Fermi velocity, τ is scattering time, m * is the effective mass of electrons, and e is the elementary charge. (e) Hall resistivity ( ρ y x) versus μ 0 H data measured at T = 2 K. (d) Resistivity ( ρ x x) versus T properties of the Hall-bar device under μ 0 H = 0 T and I ac = 10 nA. The triangular patterns of surface morphology were also visible. (c) A SEM image of the HSQ resist (dark region) patterned on PdCo O 2 / c − Al 2 O 3 captured before the Ar-ion milling. L and W stand for the separation between the voltage terminals and the width of the channel, respectively. The longitudinal ( V x x) and transverse voltage ( V y x) were measured using the alternating excitation current ( I ac) under a magnetic field H applied perpendicular to the PdCo O 2 top surface. (b) A schematic of a Hall-bar device fabricated on c − Al 2 O 3 substrates. Magnetic flux penetrating A m n alters the phase difference of the trajectories γ n and γ m. The area surrounded by γ n and γ m is noted as A m n. Two trajectories of electrons, γ n and γ m, are shown as black curves. Right: a schematic drawing of PdCo O 2 channel with Pd + conductive sheets connected to the electrodes. (a) Left: the crystal structure of PdCo O 2.
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