An Infinitesimal Probabilistic Model for Principal Component Analysis of Manifold Valued Data

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean PCA procedure, we show how PCA can be generalized to manifolds in an intrinsic way that does not resort to linearization of the data space. The underlying probability model is constructed by mapping a Euclidean stochastic process to the manifold using stochastic development of Euclidean semimartingales. The construction uses a connection and bundles of covariant tensors to allow global transport of principal eigenvectors, and the model is thereby an example of how principal fiber bundles can be used to handle the lack of global coordinate system and orientations that characterizes manifold valued statistics. We show how curvature implies non-integrability of the equivalent of Euclidean principal subspaces, and how the stochastic flows provide an alternative to explicit construction of such subspaces. We describe estimation procedures for inference of parameters and prediction of principal components, and we give examples of properties of the model on embedded surfaces

Topological susceptibility and the sampling of field space in Nf=2N_f=2 lattice QCD simulations

We present a measurement of the topological susceptibility in two flavor QCD. In this observable, large autocorrelations are present and also sizable cutoff effects have to be faced in the continuum extrapolation. Within the statistical accuracy of the computation, the result agrees with the expectation from leading order chiral perturbation theory.Comment: 22 pages, 7 figures; References added, minor clarifications in the text, results unchange

Dissolved methane pluming mapping using Membrane Inlet Mass-Spectrometry (MIMS) at a blowout site in the North Sea

A blow out site in the North Sea (well 22/4-b, UK EEZ) in a water depth of 83 m, served as a test area to demonstrate MIMS as a powerful tool for the continuous measurement of dissolved methane simultaneously to the partial pressure of carbon dioxide, nitrogen and oxygen as well as other gases. A pump-CTD arrangement was used to generate a continuous water stream through a 2.5 cm thick tube to the ship laboratory and was analyzed using a membrane inlet quadrupole mass spectrometer (GAM 200, InProcessInstruments). The pump-CTD was further equipped with calibrated HydroC CH4/CO2 sensors. The MIMS measurements were conducted under fully controlled temperature conditions and were calibrated for CH4, N2, O2, and pCO2. The pump-CTD arrangement was towed along transects across the blow out and dissolved gas concentrations as well as physical water column data were synchronized and geo-referenced. The transects were repeated in three different depth layers, including a bottom layer of � 2 m above the sea floor, 60 m above the sea floor just below the thermocline and a third plane in 10 m water depth. During the tows water samples were taken for later onboard methane analysis and cross-calibration with the MIMS and HydroC data. After data selection under consideration of the tidal regime lateral and vertical plume dimensions of dissolved methane were constructed. Dissolved methane concentrations ranged between background and up to about 18�M. Below the thermocline, which represents an effective barrier for the vertical distribution of dissolved methane, methane distinctively spreads laterally. Only at locations were the gas bubble stream and concurrently advected water from below the thermocline reaches the sea surface enhanced methane emission into the atmosphere took place

2. Wochenbericht M92

Meteor Reise M92, Callao-­‐Callao, 2. Jan. – 3. Feb. 2. Wochenbericht, 13. Januar [2013

5. Wochenbericht M92

Meteor Reise M92, Callao-­‐Callao, 2. Jan. – 3. Feb. 5. Wochenbericht, 03. Februar [2013

3. Wochenbericht Meteor Reise M137

Callao – Callao, 06. – 29. Ma

4. Wochenbericht M92

Meteor Reise M92, Callao-­‐Callao, 2. Jan. – 3. Feb. 4. Wochenbericht, 27. Janua

3. Wochenbericht M92

Meteor Reise M92, Callao-­‐Callao, 2. Jan. – 3. Feb. 3. Wochenbericht, 20. Janua