51 research outputs found
Conformally Invariant Fractals and Potential Theory
The multifractal (MF) distribution of the electrostatic potential near any
conformally invariant fractal boundary, like a critical O(N) loop or a
-state Potts cluster, is solved in two dimensions. The dimension of the boundary set with local wedge angle is , with the central charge of the
model. As a corollary, the dimensions
of the external perimeter and of the hull of a Potts cluster obey
the duality equation . A related covariant
MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.Comment: 5 pages, 1 figur
Divergent Cortical Generators of MEG and EEG during Human Sleep Spindles Suggested by Distributed Source Modeling
Background: Sleep spindles are,1-second bursts of 10–15 Hz activity, occurring during normal stage 2 sleep. In animals, sleep spindles can be synchronous across multiple cortical and thalamic locations, suggesting a distributed stable phaselocked generating system. The high synchrony of spindles across scalp EEG sites suggests that this may also be true in humans. However, prior MEG studies suggest multiple and varying generators. Methodology/Principal Findings: We recorded 306 channels of MEG simultaneously with 60 channels of EEG during naturally occurring spindles of stage 2 sleep in 7 healthy subjects. High-resolution structural MRI was obtained in each subject, to define the shells for a boundary element forward solution and to reconstruct the cortex providing the solution space for a noise-normalized minimum norm source estimation procedure. Integrated across the entire duration of all spindles, sources estimated from EEG and MEG are similar, diffuse and widespread, including all lobes from both hemispheres. However, the locations, phase and amplitude of sources simultaneously estimated from MEG versus EEG are highly distinct during the same spindles. Specifically, the sources estimated from EEG are highly synchronous across the cortex, whereas those from MEG rapidly shift in phase, hemisphere, and the location within the hemisphere. Conclusions/Significance: The heterogeneity of MEG sources implies that multiple generators are active during huma
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