The DOSY Toolbox: A new tool for processing PFG NMR diffusion data

The DOSY Toolbox is a free programme for processing PFG NMR diffusion data (sometimes loosely referred to as DOSY data), distributed under the GNU General Public License. NMR data from three major manufacturers can be imported and all processing is done in a user-friendly graphical user interface. The Toolbox is completely free-standing in the sense that all necessary basic processing of NMR data (e.g., Fourier transformation and phasing) is catered for within the programme, as well as a number of methods specific to DOSY data (e.g., DOSY and SCORE). The programme is written in MATLAB^® and as such can be run on any platform, but can also run independent of MATLAB^® in a free-standing compiled version for Windows, Mac, and Linux.     

Influence of pore structure and architecture of photo-grafted functional layers on separation performance of cellulose-based macroporous membrane adsorbers

New weak cation-exchange membrane adsorbers were prepared via UV-initiated heterogeneous graft copolymerization on Hydrosart^® macroporous regenerated cellulose membranes. The dynamic performance was investigated in detail with respect to the pore size and pore size distribution of the base membranes, ion-exchange capacity and architecture of the grafted functional layers as well as binding of target proteins. Main characterization methods were pore analysis (BET and permporometry), titration, analysis of protein binding under static conditions including visualization by confocal laser scanning microscopy and chromatographic analysis of dynamic protein binding and system dispersion. The trade-off between static binding capacity of the membrane adsorber and its permeability has partially been overcome by adapted architecture of the grafted functional layer achieved via the introduction of uncharged moieties as spacers and via stabilization of the binding layer by chemical cross-linking. The resulting membranes show only negligible effects of flow rate on dynamic binding capacity. There is no considerable size exclusion effect for large proteins due to mesh size of functional cross-linked layers. Investigation of system dispersion based on breakthrough curves confirms that the adapted grafted layer architecture has drastically reduced the contribution of the membrane to total system dispersion. The optimum pore structure of base membranes in combination with the best suited architecture of functional layers was identified in this study.     

Optimal and better transport plans

We consider the Monge-Kantorovich transport problem in a purely measure theoretic setting, i.e. without imposing continuity assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are optimal, provided the cost function c is either lower semi-continuous and finite, or continuous and may possibly attain the value ∞. We show that this is true in a more general setting, in particular for merely Borel measurable cost functions provided that {c=∞} is the union of a closed set and a negligible set. In a previous paper Schachermayer and Teichmann considered strongly c-monotone transport plans and proved that every strongly c-monotone transport plan is optimal. We establish that transport plans are strongly c-monotone if and only if they satisfy a “better” notion of optimality called robust optimality.     

Cohen-Macaulayness and computation of Newton graded toric rings

Let H⊆Z^d be a positive semigroup generated by A⊆H, and let K[H] be the associated semigroup ring over a field K. We investigate heredity of the Cohen-Macaulay property from K[H] to both its A-Newton graded ring and to its face rings. We show by example that neither one inherits in general the Cohen-Macaulay property. On the positive side, we show that for every H there exist generating sets A for which the Newton graduation preserves Cohen-Macaulayness. This gives an elementary proof for an important vanishing result on A-hypergeometric Euler-Koszul homology. As a tool for our investigations we develop an algorithm to compute algorithmically the Newton filtration on a toric ring.     

MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems

We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.