Morphological Image Analysis of Quantum Motion in Billiards

Morphological image analysis is applied to the time evolution of the probability distribution of a quantum particle moving in two and three-dimensional billiards. It is shown that the time-averaged Euler characteristic of the probability density provides a well defined quantity to distinguish between classically integrable and non-integrable billiards. In three dimensions the time-averaged mean breadth of the probability density may also be used for this purpose.Comment: Major revision. Changes include a more detailed discussion of the theory and results for 3 dimensions. Now: 10 pages, 9 figures (some are colored), 3 table

Beyond the poor man's implementation of unconditionally stable algorithms to solve the time-dependent Maxwell Equations

For the recently introduced algorithms to solve the time-dependent Maxwell equations (see Phys.Rev.E Vol.64 p.066705 (2001)), we construct a variable grid implementation and an improved spatial discretization implementation that preserve the property of the algorithms to be unconditionally stable by construction. We find that the performance and accuracy of the corresponding algorithms are significant and illustrate their practical relevance by simulating various physical model systems.Comment: 18 pages, 16 figure

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Myelination and voltage-gated ion channel clustering at the nodes of Ranvier are essential for the rapid saltatory conduction of action potentials. Whether myelination influences the structural organization of the axon initial segment (AIS) and action potential initiation is poorly understood. Using the cuprizone mouse model, we combined electrophysiological recordings with immunofluorescence of the voltage-gated Nav1.6 and Kv7.3 subunits and anchoring proteins to analyze the functional and structural properties of single demyelinated neocortical L5 axons. Whole-cell recordings demonstrated that neurons with demyelinated axons were intrinsically more excitable, characterized by increased spontaneous suprathreshold depolarizations as well as antidromically propagating action potentials ectopically generated in distal parts of the axon. Immunofluorescence examination of demyelinated axons showed that βIV-spectrin, Nav1.6, and the Kv7.3 channels in nodes of Ranvier either dissolved or extended into the paranodal domains. In contrast, while the AIS in demyelinated axons started more closely to the soma, ankyrin G, βIV-spectrin, and the ion channel expression were maintained. Structure-function analysis and computational modeling, constrained by the AIS location and realistic dendritic and axonal morphologies, confirmed that a more proximal onset of the AIS slightly reduced the efficacy of action potential generation, suggesting a compensatory role. These results suggest that oligodendroglial myelination is not only important for maximizing conduction velocity, but also for limiting hyperexcitability of pyramidal neurons