Aluminium

Ohne Zusammenfassung     

Variational optimization of the 2DM: approaching three-index accuracy using extended cluster constraints

The reduced density matrix is variationally optimized for the two-dimensional Hubbard model. Exploiting all symmetries present in the system, we have been able to study 6 × 6 lattices at various fillings and different values for the on-site repulsion, using the highly accurate but computationally expensive three-index conditions. To reduce the computational cost we study the performance of imposing the three-index constraints on local clusters of 2 × 2 and 3 × 3 sites. We subsequently derive new constraints which extend these cluster constraints to incorporate the open-system nature of a cluster on a larger lattice. The feasibility of implementing these new constraints is demonstrated by performing a proof-of-principle calculation on the 6 × 6 lattice. It is shown that a large portion of the three-index result can be recovered using these extended cluster constraints, at a fraction of the computational cost.     

Design, fabrication and demonstration of a magnetophoresis chamber with 25 output fractions

Our goal is to develop an instrument for parallel and multiplexed bioassay using magnetic labels. Toward this end we are developing a multi-outlet magnetophoresis instrument incorporating a fluidic flow chamber placed inside a magnetic field gradient. Magnetic microparticles are sorted by their magnetic moment for eventual use as biological labels based on magnetic signature. In this paper, we concentrate on developments in our flow chamber fabrication methods that have allowed us to scale the number of sorting channels from 8 to 25. We present data for instrument performance and reproducibility of sorting.     

Parameter optimization and uncertainty analysis in a model of oceanic CO2 uptake using a hybrid algorithm and algorithmic differentiation

Methods and results for parameter optimization and uncertainty analysis for a one-dimensional marine biogeochemical model of NPZD type are presented. The model, developed by Schartau and Oschlies, simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column and is driven by ocean circulation data. Our aim is to identify parameters and fit the model output to given observational data. For this model, it has been shown that a satisfactory fit could not be obtained, and that parameters with comparable fits can vary significantly. Since these results were obtained by evolutionary algorithms (EA), we used a wider range of optimization methods: A special type of EA (called quantum-EA) with coordinate line search and a quasi-Newton SQP method, where exact gradients were generated by Automatic/Algorithmic Differentiation. Both methods are parallelized and can be viewed as instances of a hybrid, mixed evolutionary and deterministic optimization algorithm that we present in detail. This algorithm provides a flexible and robust tool for parameter identification and model validation. We show how the obtained parameters depend on data sparsity and given data error. We present an uncertainty analysis of the optimized parameters w.r.t. Gaussian perturbed data. We show that the model is well suited for parameter identification if the data are attainable. On the other hand, the result that it cannot be fitted to the real observational data without extension or modification, is confirmed.     

Calibration-less multi-coil MR image reconstruction

In parallel magnetic resonance imaging (MRI), the problem is to reconstruct an image given the partial K-space scans from all the receiver coils. Depending on its position within the scanner, each coil has a different sensitivity profile. All existing parallel MRI techniques require estimation of certain parameters pertaining to the sensitivity profile, e.g., the sensitivity map needs to be estimated for the SENSE and SMASH and the interpolation weights need to be calibrated for GRAPPA and SPIRiT. The assumption is that the estimated parameters are applicable at the operational stage. This assumption does not always hold, consequently the reconstruction accuracies of existing parallel MRI methods may suffer. We propose a reconstruction method called Calibration-Less Multi-coil (CaLM) MRI. As the name suggests, our method does not require estimation of any parameters related to the sensitivity maps and hence does not require a calibration stage. CaLM MRI is an image domain method that produces a sensitivity encoded image for each coil. These images are finally combined by the sum-of-squares method to yield the final image. It is based on the theory of Compressed Sensing (CS). During reconstruction, the constraint that "all the coil images should appear similar" is introduced within the CS framework. This leads to a CS optimization problem that promotes group-sparsity. The results from our proposed method are comparable (at least for the data used in this work) with the best results that can be obtained from state-of-the-art methods.