In vivo determination of multiexponential T2 relaxation in the brain of patients with multiple sclerosis

In vivo measurement of T2 relaxation times in multiple sclerosis (MS) lesions by magnetic resonance imaging (MRI) is potentially useful for the evaluation of the disease activity. Seven patients with definite MS were investigated over a period of three years (19 examinations), using a whole-body MRI scanner operating at 0.15 T with a specially designed high-power radio-frequency head coil. A modified CPMG sequence with a 180 degree pulse interval of TE = 6 msec and 128 echoes was used for the T2 relaxation measurement of the areas of increased signal (AIS) and white matter (WM). A biexponential T2 analysis of each pixel of the spin-echo images was computed. The T2 relaxation processes were found to be a monoexponential function in WM. The T2 relaxation times of apparently normal white matter in MS patients was significantly longer than in control subjects. The T2 relaxation curves of the AIS were found in most cases to fit a biexponential function characterized by a short and a long T2. T2 long relaxation times of AIS were spread out over a wide range (150-560 msec). The study of T2 long histograms shows that some AIS can be divided into two or three parts depending on the T2 long values. Each of these parts may correspond to a pathological process such as edema, demyelination and gliosis. Evolution of T2 relaxation times over a period of time cannot as yet be correlated with modifications in the clinical state.     

Geometry of equilibrium configurations in the Ising model

We derive microscopically precise identities for the geometry of small clusters in the equilibrium states of the two-dimensional Ising model with emphasis on near-critical phenomena.     

Synthesis of difluoromethylthio imidazole from methylthio imidazole

Demethylation of methylthio imidazole 1 via a Pummerer rearrangement onto the corresponding sulfoxide 2 afforded imidazole thiol 4 which was then difluoromethylated with the sodium chlorodifluoroacetate/NaI system in 71% overall yield.     

Styrene cis—trans photoisomerisation treated through a Heisenberg non-empirical hamiltonian

Using a recently proposed non-empirical Heisenberg hamiltonian, the ground and excited covalent surfaces of the styrene molecule are calculated as functions of the external double-bond twisting angle θ, including full bond-length optimisation. The lowest excited singlet surface exhibits a barrier at 0 ?~ 45° resulting from a weakly avoided crossing of two neutral diabatic surfaces. The isomerisation should proceed from the twisted funnel. This model and the calculated transition energies are in good agreement with experiment.     

Statistical inference and quantum mechanical measurement

We analyze the quantum mechanical measuring process from the standpoint of information theory. Statistical inference is used in order to define the most likely state of the measured system that is compatible with the readings of the measuring instrument and the a priori information about the correlations between the system and the instrument. This approach has the advantage that no reference to the time evolution of the combined system need be made. It must, however, be emphasized that the result is to be interpreted as the statistically inferred state of the original system rather than the state of the system after measurement. The phenomenon of “reduction of states” appears in this light as a consequence of incomplete information rather than the physical interaction between measured system and measuring instrument.     

CI calculations concerning the styrene cis-trans photoisomerization

Using minimal basis sets, the ionic and diradical excited states of the twisted styrene molecule have been calculated through extended CI, after appropriate SCF procedures. The lowest excited state is a diradical, and the photoisomerization should not involve the ionic state.