Stuttgart 2012 – wissenschaftliches Programm

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A: Fachverband Atomphysik

A 24: Poster: Interaction with VUV and X-ray light

A 24.8: Poster

Mittwoch, 14. März 2012, 16:30–19:00, Poster.V

Ordering of randomly orientated diffraction patterns with diffusion map — •Martin Winter, Ulf Saalmann, and Jan-Michael Rost — Max-Planck-Institut für Physik komplexer Systeme, Dresden

By means of manifold embedding techniques we recover the orientations of an ensemble of diffraction patterns from a randomly orientated molecule, which would be the outcome of experiments at X-ray free-electron lasers. Since the mapping of the orientation to the diffraction pattern is highly non-linear, we use an algorithm capable of dealing with non-linear data, like diffusion map [1].

Diffusion map can handle a certain degree of non-linearity. Problems arise especially when multiple parameters/angles get mixed up in the mapping/formation of the diffraction patterns [2]. This is illustrated with some simple examples which reveal the applicability of diffusion map for scattering problems.

[1] Ronald R. Coifman, Stéphane Lafon, Diffusion maps, Appl. Comp. Harm. Anal. 21 (2006) 5-30

[2] Amit Singer, Ronald R. Coifman, Non-linear independent component analysis with diffusion maps, Appl. Comp. Harm. Anal. 25 (2008) 226-239