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A major challenge in computational finance is the pricing of options that depend on a large number of risk factors. Prominent examples are basket or index options where dozens or even hundreds of stocks constitute the underlying asset and determine the dimensionality of the corresponding degenerate parabolic equation. The objective of this article is to… (More)

Two-photon microscopy in combination with novel fluorescent labeling techniques enables imaging of three-dimensional neuronal morphologies in intact brain tissue. In principle it is now possible to automatically reconstruct the dendritic branching patterns of neurons from 3-D fluorescence image stacks. In practice however, the signal-to-noise ratio can be… (More)

For elliptic partial diierential equations with periodically oscillating coeecients (which may have large jumps) we prove robust convergence of a two-grid algorithm using a prolonga-tion motivated by homogenization theory. The corresponding Galerkin operator on the coarse grid turns out to be a discretization of a diiusion operator with homogenized… (More)

The shape of neuronal cells strongly resembles botanical trees or roots of plants. To analyze and compare these complex three-dimensional structures it is important to develop suitable methods. We review the so called tree-edit-distance known from theoretical computer science and use this distance to define dissimilarity measures for neuronal cells. This… (More)