An evaluation of the time dependence of the anisotropy of the water diffusion tensor in acute human ischemia

We have performed MRI examinations to determine the water diffusion tensor in the brain of six patients who were admitted to the hospital within 12 h after the onset of cerebral ischemic symptoms. The examinations have been carried out immediately after admission, and thereafter at varying intervals up to 90 days post admission. Maps of the trace of the diffusion tensor, the fractional anisotropy and the lattice index, as well as maps of cerebral blood perfusion parameters, were generated to quantitatively assess the character of the water diffusion tensor in the infarcted area. In patients with significant perfusion deficits and substantial lesion volume changes, four of six cases, our measurements show a monotonic and significant decrease in the diffusion anisotropy within the ischemic lesion as a function of time. We propose that retrospective analysis of this quantity, in combination with brain tissue segmentation and cerebral perfusion maps, may be used in future studies to assess the severity of the ischemic event. (C) 1999 Elsevier Science Inc.

Determination of chemical shielding tensor of an indole carbon and application of tryptophan orientation of a membrane peptide

Using tryptophan C-13-enriched at the C-4 (C epsilon(3)) of the indole, the orientation of the C epsilon(3) chemical shift tensor relative to the C epsilon(3)-H dipolar axis was determined from the C-13 chemical shift/C-13-H-1 dipolar 2D NMR powder pattern. The principal values obtained were 208, 137 and 15 ppm with sigma(33) perpendicular to the indole plane, and sigma(11) (least shielded direction) 5 degrees off the C epsilon(3)-H bond toward C xi(3). The side off the C epsilon(3)-H bond was determined by comparing the reduced chemical shift anisotropies obtained by solid-state NMR and from molecular dynamics calculations of [4-C-13] tryptophans in gramicidin A aligned in phospholipid membranes. (C) 1999 Elsevier Science B.V. All rights reserved.

Loss of connectivity in Alzheimer's disease: an evaluation of white matter tract integrity with colour coded MR diffusion tensor imaging

A novel MRI method-diffusion tensor imaging-was used to compare the integrity of several white matter fibre tracts in patients with probable Alzheimer's disease. Relative to normal controls, patients with probable Alzheimer's disease showed a highly significant reduction in the integrity of the association white matter fibre tracts, such as the splenium of the corpus callosum, superior longitudinal fasciculus, and cingulum. By contrast, pyramidal tract integrity seemed unchanged. This novel finding is consistent with the clinical presentation of probable Alzheimer's disease, in which global cognitive decline is a more prominent feature than motor disturbance.

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Classical simulation of quantum many-body systems with a tree tensor network

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement (Schmidt number) is small for any bipartite split along an edge of the tree. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

Efficient -tensor determination and NH assignment of paramagnetic proteins

Anisotropic magnetic susceptibility tensors chi of paramagnetic metal ions are manifested in pseudocontact shifts, residual dipolar couplings, and other paramagnetic observables that present valuable long-range information for structure determinations of protein-ligand complexes. A program was developed for automatic determination of the chi-tensor anisotropy parameters and amide resonance assignments in proteins labeled with paramagnetic metal ions. The program requires knowledge of the three-dimensional structure of the protein, the backbone resonance assignments of the diamagnetic protein, and a pair of 2D N-15-HSQC or 3D HNCO spectra recorded with and without paramagnetic metal ion. It allows the determination of reliable chi-tensor anisotropy parameters from 2D spectra of uniformly N-15-labeled proteins of fairly high molecular weight. Examples are shown for the 185-residue N-terminal domain of the subunit epsilon from E. coli DNA polymerase III in complex with the subunit theta and La3+ in its diamagnetic and Dy3+, Tb3+, and Er3+ in its paramagnetic form.

Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices

The minimal irreducible representations of U-q[gl(m|n)], i.e. those irreducible representations that are also irreducible under U-q[osp(m|n)] are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra U-q[gl(m|n)((2))]. The U-q[osp(m|n)] invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from U-q[gl(m|n)((2))], which exhibit novel features not previously seen in the untwisted or non-super cases.

Fast Structure-Based Assignment of 15N HSQC Spectra of Selectively 15N-Labeled Paramagnetic Proteins

A novel strategy for fast NMR resonance assignment of N-15 HSQC spectra of proteins is presented. It requires the structure coordinates of the protein, a paramagnetic center, and one or more residue-selectively N-15-labeled samples. Comparison of sensitive undecoupled N-15 HSQC spectra recorded of paramagnetic and diamagnetic samples yields data for every cross-peak on pseudocontact shift, paramagnetic relaxation enhancement, cross-correlation between Curie-spin and dipole-dipole relaxation, and residual dipolar coupling. Comparison of these four different paramagnetic quantities with predictions from the three-dimensional structure simultaneously yields the resonance assignment and the anisotropy of the susceptibility tensor of the paramagnetic center. The method is demonstrated with the 30 kDa complex between the N-terminal domain of the epsilon subunit and the theta subunit of Escherichia Coll DNA polymerase III. The program PLATYPUS was developed to perform the assignment, provide a measure of reliability of the assignment, and determine the susceptibility tensor anisotropy.

High-Frequency Suspended Sediment Flux Measurements in a Small Estuary

In small estuaries, the predictions of scalar dispersion can rarely be predicted accurately because of a lack of fundamental understanding of the turbulence structure. Herein detailed turbulence measurements and suspended sediment concentrations were conducted simultaneously and continuously at high-frequency for 50 hours per investigation in a small subtropical estuary with semi-diurnal tides. The data analyses provided an unique characterisation of the turbulent mixing processes and suspended sediment fluxes. The turbulence was neither homogeneous nor isotropic, and it was not a Gaussian process. The integral time scales for turbulence and suspended sediment concentration were about equal during flood tides, but differed significantly during ebb tides. The field experiences showed that the turbulence measurements must be conducted at high-frequency to characterise the small eddies and the viscous dissipation process, while a continuous sampling was necessary to characterise the time-variations of the instantaneous velocity field, Reynolds stress tensor and suspended sediment flux during the tidal cycles.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules

The graded-fermion algebra and quasispin formalism are introduced and applied to obtain the gl(m\n)down arrow osp(m\n) branching rules for the two- column tensor irreducible representations of gl(m\n), for the case m less than or equal to n(n > 2). In the case m < n, all such irreducible representations of gl(m\n) are shown to be completely reducible as representations of osp(m\n). This is also shown to be true for the case m=n, except for the spin-singlet representations, which contain an indecomposable representation of osp(m\n) with composition length 3. These branching rules are given in fully explicit form. (C) 1999 American Institute of Physics. [S0022-2488(99)04410-2].

Eigenvalues of Casimir invariants for unitary irreps of Uq(gl(m vertical bar n))

A fully explicit formula for the eigenvalues of Casimir invariants for U-q(gl(m/n)) is given which applies to all unitary irreps. This is achieved by making some interesting observations on atypicality indices for irreps occurring in the tensor product of unitary irreps of the same type. These results have applications in the determination of link polynomials arising from unitary irreps of U-q(gl(m/n)).