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. Above the coherence length, interference patterns start to fade.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. The length scales above are called coherence lengths. Since all light contains a range of frequencies, it is impossible to have exactly the same frequency, and the effect is noticeable after some length scale. Quantumly, if you're considering photon emission, it satisfies the uncertainty principle $\Delta E \Delta t > \hbar$, which gives you the same thing.
Classically, if you look at an EM wave, it satisfies an uncertainty principle of the form $\Delta \omega \Delta t > 1$ for the same Fourier-transform reasons that the usual uncertainty principle holds. Even if you fix the above problem, light can't have a definite frequency.Each atom in the bulb is wiggling independently, so instead of getting one light wave at some frequency, you get a ton of little wavetrains of the same frequency but independent phases, one from each atom. Light from a fluorescent bulb, which has (roughly) a single frequency, is not coherent.However, it actually stands in for a lot of real world effects that can destroy interference. Naively, that means that two waves are coherent if and only if they have the same frequency, which makes the idea of coherence sound silly. As pointed out, it is more proper to call this the temporal coherence length (how much earlier or later can you look at the beam and find it is still capable of interference) - but since you are measuring time "along the beam", there is a direct relationship between the coherence time and the length along the beam that the light can interfere.Ĭoherence means a constant phase relationship the phase difference could be anything, such as $\pi$ or $7 \pi / 4$. Because of this, if you split light into two branches but make them come back together after they have covered different path lengths, then the interference pattern they will create (a measure of the coherence) will become less.įor this reason, with "monochromatic" light we sometimes talk of the "coherence length" - a measure of how different the path lengths can be before you lose a significant fraction of the coherence (before the interference pattern starts to fade). It is worth noting that typically waves do not consist of a single pure frequency, and that there will be some small drift in frequency over time. If you make a Michelson interferometer where you split an incoming light beam into two arms, and you send half the light through a column of water and the other half through air, then it is possible to get interference between the beams by adjusting the path lengths (according to the refractive index). It is sufficient that they have the same frequency - because that is sufficient to imply a constant phase difference. Waves can be coherent and yet not have the same wavelength.
0 kommentar(er)
