12,947 research outputs found
Single-trial multiwavelet coherence in application to neurophysiological time series
A method of single-trial coherence analysis is presented, through the application of continuous muldwavelets. Multiwavelets allow the construction of spectra and bivariate statistics such as coherence within single trials. Spectral estimates are made consistent through optimal time-frequency localization and smoothing. The use of multiwavelets is considered along with an alternative single-trial method prevalent in the literature, with the focus being on statistical, interpretive and computational aspects. The multiwavelet approach is shown to possess many desirable properties, including optimal conditioning, statistical descriptions and computational efficiency. The methods. are then applied to bivariate surrogate and neurophysiological data for calibration and comparative study. Neurophysiological data were recorded intracellularly from two spinal motoneurones innervating the posterior,biceps muscle during fictive locomotion in the decerebrated cat
Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods
We derive a correct first-order perturbation theory in electromagnetism for
cases where an interface between two anisotropic dielectric materials is
slightly shifted. Most previous perturbative methods give incorrect results for
this case, even to lowest order, because of the complicated discontinuous
boundary conditions on the electric field at such an interface. Our final
expression is simply a surface integral, over the material interface, of the
continuous field components from the unperturbed structure. The derivation is
based on a "localized" coordinate-transformation technique, which avoids both
the problem of field discontinuities and the challenge of constructing an
explicit coordinate transformation by taking a limit in which a coordinate
perturbation is infinitesimally localized around the boundary. Not only is our
result potentially useful in evaluating boundary perturbations, e.g. from
fabrication imperfections, in highly anisotropic media such as many
metamaterials, but it also has a direct application in numerical
electromagnetism. In particular, we show how it leads to a sub-pixel smoothing
scheme to ameliorate staircasing effects in discretized simulations of
anisotropic media, in such a way as to greatly reduce the numerical errors
compared to other proposed smoothing schemes.Comment: 10 page
Correlation functions of scattering matrix elements in microwave cavities with strong absorption
The scattering matrix was measured for microwave cavities with two antennas.
It was analyzed in the regime of overlapping resonances. The theoretical
description in terms of a statistical scattering matrix and the rescaled
Breit-Wigner approximation has been applied to this regime. The experimental
results for the auto-correlation function show that the absorption in the
cavity walls yields an exponential decay. This behavior can only be modeled
using a large number of weakly coupled channels. In comparison to the
auto-correlation functions, the cross-correlation functions of the diagonal
S-matrix elements display a more pronounced difference between regular and
chaotic systems
- …