Comparison of fast field-cycling magnetic resonance imaging methods and future perspectives

ABSTRACT

Fast field-cycling (FFC) nuclear magnetic resonance relaxometry is a well-established method to determine the relaxation rates as a function of magnetic field strength. This so-called nuclear magnetic relaxation dispersion gives insight into the underlying molecular dynamics of a wide range of complex systems and has gained interest especially in the characterisation of biological tissues and diseases. The combination of FFC techniques with magnetic resonance imaging (MRI) offers a high potential for new types of image contrast more specific to pathological molecular dynamics. This article reviews the progress in FFC-MRI over the last decade and gives an overview of the hardware systems currently in operation. We discuss limitations and error correction strategies specific to FFC-MRI such as field stability and homogeneity, signal-to-noise ratio, eddy currents and acquisition time. We also report potential applications with impact in biology and medicine. Finally, we discuss the challenges and future applications in transferring the underlying molecular dynamics into novel types of image contrast by exploiting the dispersive properties of biological tissue or MRI contrast agents.     

The combinatorics of the bar resolution in group cohomology

We study a combinatorially defined double complex structure on the ordered chains of any simplicial complex. Its columns are related to the cell complex K_n whose face poset is isomorphic to the subword ordering on words without repetition from an alphabet of size n. This complex is shellable and as an application we give a representation theoretic interpretation for derangement numbers and a related symmetric function considered by Désarménien and Wachs [11].

We analyze the two spectral sequences arising from the double complex in the case of the bar resolution for a group. This spectral sequence converges to the cohomology of the group and provides a method for computing group cohomology in terms of the cohomology of subgroups. Its behavior is influenced by the complex of oriented chains of the simplicial complex of finite subsets of the group, and we examine the Ext class of this complex.     

A Deformation-Theoretical Approach to Weyl Quantization on Riemannian Manifolds

By using a sheaf-theoretical language, we introduce a notion of deformation quantization allowing not only for formal deformation parameters but also for real or complex ones as well. As a model for this approach to deformation quantization, we construct a quantization scheme for cotangent bundles of Riemannian manifolds. Here, we essentially use a complete symbol calculus for pseudodifferential operators on a Riemannian manifold. Depending on a scaling parameter, our quantization scheme corresponds to normally ordered, Weyl or antinormally ordered quantization. Finally, it is shown that our quantization scheme induces a family of pairwise isomorphic strongly closed star products on a cotangent bundle.     

A stable approach to the equivariant Hopf theorem

Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner [S. Waner, Equivariant RO(G)-graded bordism theories, Topology and its Applications 17 (1984) 1-26], the homotopy classes of G-equivariant maps into a G-sphere are described in terms of their degrees, and the degrees occurring are characterised in terms of congruences. This is first shown to be a stable problem, and then solved using methods of equivariant stable homotopy theory with respect to a semi-free G-universe.     

Diastereoselective formation of 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines: An X-ray crystallographic and H NMR study

N-Arylsulfonamides of (R)- and (S)-2-amino-1-butanol, on condensation with aromatic aldehydes produced diastereomerically pure 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines. The absolute configurations of one enantiomeric pair have been determined from two fully refined X-ray structures, supplemented by nmr data.