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 $Q$ -state Potts cluster, is solved in two dimensions. The dimension $\hat f(\theta)$ of the boundary set with local wedge angle $\theta$ is $\hat f(\theta)=\frac{\pi}{\theta} -\frac{25-c}{12} \frac{(\pi-\theta)^2}{\theta(2\pi-\theta)}$, with $c$ the central charge of the model. As a corollary, the dimensions $D_{\rm EP} =sup_{\theta}\hat f(\theta)$ of the external perimeter and $D_{\rm H}$ of the hull of a Potts cluster obey the duality equation $(D_{\rm EP}-1)(D_{\rm H}-1)={1/4}$. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.Comment: 5 pages, 1 figur

Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

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

Early Category-Specific Cortical Activation Revealed by Visual Stimulus Inversion

Visual categorization may already start within the first 100-ms after stimulus onset, in contrast with the long-held view that during this early stage all complex stimuli are processed equally and that category-specific cortical activation occurs only at later stages. The neural basis of this proposed early stage of high-level analysis is however poorly understood. To address this question we used magnetoencephalography and anatomically-constrained distributed source modeling to monitor brain activity with millisecond-resolution while subjects performed an orientation task on the upright and upside-down presented images of three different stimulus categories: faces, houses and bodies. Significant inversion effects were found for all three stimulus categories between 70–100-ms after picture onset with a highly category-specific cortical distribution. Differential responses between upright and inverted faces were found in well-established face-selective areas of the inferior occipital cortex and right fusiform gyrus. In addition, early category-specific inversion effects were found well beyond visual areas. Our results provide the first direct evidence that category-specific processing in high-level category-sensitive cortical areas already takes place within the first 100-ms of visual processing, significantly earlier than previously thought, and suggests the existence of fast category-specific neocortical routes in the human brain

Quasibound states at thresholds in multichannel impurity scattering.

We investigate the threshold behaviour of transmission resonances and quasibound states in the multichannel scattering problems of a one-dimensional (1D) time-dependent impurity potential, and the related problem of a single impurity in a quasi-1D wire. It was claimed before in the literature that a quasibound state disappears when a transmission zero collides with the subband boundary. However, the transmission line shape, the Friedel sum rule, and the delay time show that the quasibound states still survive and affect the physical quantities. We discuss the relation between threshold behaviour of transmission resonances, and quasibound states and their boundary conditions in the general context of multichannel scatterings

Previous exposure to measles, mumps, and rubella--but not vaccination during adolescence--correlates to the prevalence of pancreatic and thyroid autoantibodies.

OBJECTIVE: This study was designed to determine whether a relationship exists between previous exposure to measles, mumps, and rubella (MMR) by natural infection or vaccination or by new immunization with MMR vaccine, and either the presence or levels of autoantibodies against thyroid cell and pancreatic beta-cell antigens. METHODS: Antibodies against MMR and autoantibodies against thyroglobulin, thyroid peroxidase, pancreas islet cells (ICA), islet cell surface, glutamic acid decarboxylase 65k autoantibodies, and insulin were studied before, and 3 months after, vaccination with combined MMR vaccine in 386 school children between 11 and 13 years of age. RESULTS: The vaccination changed neither the prevalence nor the level of autoantibodies. Children with rubella antibodies before vaccination had higher levels of ICA than did the rubella seronegative children. In contrast, thyroid autoantibody levels and prevalence were lower in children with antibodies against measles, mumps, or both before vaccination than in children without those antibodies. CONCLUSIONS: Previous natural infection or vaccination against measles, mumps, or both seemed to have an inhibitory effect on the development of thyroid autoantibodies. In contrast, children with previous exposure to rubella had higher levels of ICA. No evidence was found that MMR vaccination during adolescence may trigger autoimmunity