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. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

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.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Ca2+ sensitivity of phospholipid scrambling in human red cell ghosts

The phospholipids in plasma membranes of erythrocytes, as well as platelets, lymphocytes and other cells are asymmetrically distributed, with sphingomyelin and phosphatidylcholine residing predominantly in the outer leaflet of the bilayer, and phosphatidylserine and phosphatidylethanolamine in the inner leaflet. It is known that Ca2+ can disrupt the phospholipid asymmetry by activation of a protein known as phospholipid scramblase, which affects bidirectional phospholipid movement in a largely non-selective manner. As Ca2+ also inhibits aminophospholipid translocase, whose Mg2+-ATPase activity is responsible for active translocation of aminophospholipids from the outer to the inner leaflet, it is important to accurately determine the sensitivity of scramblase to intracellular free Ca2+. In the present study we have utilized the favourable K-d, of Mag-fura-2 for calcium in the high micromolar range to determine free Ca2+ levels associated with lipid scrambling in resealed human red cell ghosts. The Ca2+ sensitivity was measured in parallel to the translocation of a fluorescent-labelled lipid incorporated into the ghost bilayer. The phospholipid scrambling was found to be half-maximally activated at 63-88 mu M free intracellular Ca2+. The wider applicability of the method and the physiological implications of the calcium sensitivity determined is discussed.

Sensitivity of multiple frequency bioelectrical impedance analysis to changes in ion status

Bioelectrical impedance analysis has found extensive application as a simple noninvasive method for the assessment of body fluid volumes, The measured impedance is, however, not only related to the volume of fluid but also to its inherent resistivity. The primary determinant of the resistivities of body fluids is the concentration of ions. The aim of this study was to investigate the sensitivity of bioelectrical impedance analysis to bodily ion status. Whole body impedance over a range of frequencies (4-1012 kHz) of rats was measured during infusion of various concentrations of saline into rats concomitant with measurement of total body and intracellular water by tracer dilution techniques. Extracellular resistance (R-o), intracellular resistance (R-i) and impedance at the characteristic frequency (Z(c)) were calculated. R-o and Z(c) were used to predict extracellular and total body water respectively using previously published formulae. The results showed that whilst R-o and Z(c) decreased proportionately to the amount of NaCl infused, R-i increased only slightly. Impedances at the end of infusion predicted increases iu TBW and ECW of approximately 4-6% despite a volume increase of less than 0.5% in TBW due to the volume of fluid infused. These data are discussed in relation to the assumption of constant resistivity in the prediction of fluid volumes from impedance data.

Sensitivity to measurement perturbation of single-atom dynamics in cavity QED

We consider continuous observation of the nonlinear dynamics of single atom trapped in an optical cavity by a standing wave with intensity modulation. The motion of the atom changes the phase of the field which is then monitored by homodyne detection of the output field. We show that the conditional Hilbert space dynamics of this system, subject to measurement-induced perturbations, depends strongly on whether the corresponding classical dynamics is regular or chaotic. If the classical dynamics is chaotic, the distribution of conditional Hilbert space vectors corresponding to different observation records tends to be orthogonal. This is a characteristic feature of hypersensitivity to perturbation for quantum chaotic systems.

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying U-q(sl (2/1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.

Altered kinetics and benzodiazepine sensitivity of a GABA(A) receptor subunit mutation [gamma(2)(R43Q)] found in human epilepsy

The gamma-aminobutyric acid type A (GABA(A)) receptor mediates fast inhibitory synaptic transmission in the CNS. Dysfunction of the GABA(A) receptor would be expected to cause neuronal hyperexcitability, a phenomenon linked with epileptogenesis. We have investigated the functional consequences of an arginine-to-glutamine mutation at position 43 within the GABA(A) gamma(2)-subunit found in a family with childhood absence epilepsy and febrile seizures. Rapid-application experiments performed on receptors expressed in HEK-293 cells demonstrated that the mutation slows GABA(A) receptor deactivation and increases the rate of desensitization, resulting in an accumulation of desensitized receptors during repeated, short applications. In Xenopus laevis oocytes, two-electrode voltage-clamp analysis of steady-state currents obtained from alpha(1)beta(2)gamma(2) or alpha(1)beta(2)gamma(2)(R43Q) receptors did not reveal any differences in GABA sensitivity. However, differences in the benzodiazepine pharmacology of mutant receptors were apparent. Mutant receptors expressed in oocytes displayed reduced sensitivity to diazepam and flunitrazepam but not the imiclazopyricline zolpidem. These results provide evidence of impaired GABA(A) receptor function that could decrease the efficacy of transmission at inhibitory synapses, possibly generating a hyperexcitable neuronal state in thalamocortical networks of epileptic patients possessing the mutant subunit.

The interaction of metal ions and Marimastat with matrix metalloproteinase 9

The effect of a range of metal ions on the ability of Marimastat to inhibit matrix metalloproteinase 9 (MMP-9) was examined in a fluorescence based proteolytic assay. Whilst none of the metals examined significantly affected the inhibitory ability of Marimastat, several metal ions did have a significant effect on MMP-9 activity itself. In the absence of Marimastat, Zn(II) and Fe(II) significantly inhibited MMP-9 activity at metal ion concentrations of 10 and 100 muM, respectively. In both the absence and presence of Marimastat, Cd(II) significantly inhibited MMP-9 at 100 muM. In contrast, 1 mM Co(II) significantly upregulated MMP-9 proteolytic activity. (C) 2003 Elsevier Science Inc. All rights reserved.

'You can criticise because you care': Identification, constructiveness, and the intergroup sensitivity effect

Group criticisms judged to be reasonable in the mouth of an ingroup member are aggressively rejected when they stem from an outgroup member (the intergroup sensitivity effect). Mediational analyses suggest that this phenomenon is underpinned by an attributional bias; criticisms from insiders are more likely to be perceived as being motivated for constructive reasons than are criticisms from outsiders, thus arousing lower levels of defensiveness. But what if group members were to receive information that called into question the ingroup critic's commitment to the group? For example, if the ingroup critic was known to be a low identifier with their group, or used language to suggest that they were psychologically distancing themselves from their group, we might expect that ingroup critics will be downgraded as strongly as outgroup critics. Furthermore, it might be possible for people to turn an outgroup criticism into an ingroup criticism by making salient their shared identity at the superordinate level. Three experiments are described that provide support for each of these propositions.