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.

Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements

We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.

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.

Epidermal iontophoresis: II. Application of the ionic mobility-pore model to the transport of local anesthetics

Purpose, An in vitro study was carried out to determine the iontophoretic permeability of local anesthetics through human epidermis. The relationship between physicochemical structure and the permeability of these solutes was then examined using an ionic mobility-pore model developed to define quantitative relationships. Methods. The iontophoretic permeability of both ester-type anesthetics (procaine, butacaine, tetracaine) and amide-type anesthetics (prilocaine, mepivacaine, lidocaine, bupivacaine, etidocaine, cinchocaine) were determined through excised human epidermis over 2 hrs using a constant d.c. current and Ag/AgCl electrodes. Individual ion mobilities were determined from conductivity measurements in aqueous solutions. Multiple stepwise regression was applied to interrelate the iontophoretic permeability of the solutes with their physical properties to examine the appropriateness of the ionic mobility-pore model and to determine the best predictor of iontophoretic permeability of the local anesthetics. Results. The logarithm of the iontophoretic permeability coefficient (log PCj,iont) for local anesthetics was directly related to the log ionic mobility and MW for the free volume form of the model when other conditions are held constant. Multiple linear regressions confirmed that log PCj,iont was best defined by ionic mobility (and its determinants: conductivity, pK(a) and MW) and MW. Conclusions. Our results suggest that of the properties studied, the best predictors of iontophoretic transport of local anesthetics are ionic mobility (or pK(a)) and molecular size. These predictions are consistent with the ionic mobility pore model determined by the mobility of ions in the aqueous solution, the total current, epidermal permselectivity and other factors as defined by the model.

Localisation of gelatinase activity in epidermal hoof lamellae by in situ zymography

In situ gelatin zymography is a technique, which utilises a gelatin-based emulsion overlay to detect and, more importantly, localise the gelatinase activity in underlying tissue. Gelatinase A [matrix metalloproteinase-2 (MMP-2)] and gelatinase B [matrix metalloproteinase-9 (MMP-9)] are present in equine hoof homogenates and supernatants from cultured hoof explants by SDS-PAGE gelatin zymography, and it has been assumed that the enzymes are derived solely from matrix and epithelia and not from other sources such as leucocytes. Using in situ zymography, gelatinases are shown to be localised within the equine epidermal hoof lamellae and, more specifically, are apparently produced by epidermal basal and/or parabasal cells. The pattern of expression correlates with that expected based on the progression of pathological changes observed during the onset of laminitis, thus providing further evidence that laminitis pathology probably arises as a result of inadequate local MMP regulation.

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.

Predictors of local recurrence after treatment of ductal carcinoma in situ - A meta-analysis

lBACKGROUND. Management of patients with ductal carcinoma in situ (DCIS) is a dilemma, as mastectomy provides nearly a 100% cure rate but at the expense of physical and psychologic morbidity. It would be helpful if we could predict which patients with DCIS are at sufficiently high risk of local recurrence after conservative surgery (CS) alone to warrant postoperative radiotherapy (RT) and which patients are at sufficient risk of local recurrence after CS + RT to warrant mastectomy. The authors reviewed the published studies and identified the factors that may be predictive of local recurrence after management by mastectomy, CS alone, or CS + RT. METHODS. The authors examined patient, tumor, and treatment factors as potential predictors for local recurrence and estimated the risks of recurrence based on a review of published studies. They examined the effects of patient factors (age at diagnosis and family history), tumor factors (sub-type of DCIS, grade, tumor size, necrosis, and margins), and treatment (mastectomy, CS alone, and CS + RT). The 95% confidence intervals (CI) of the recurrence rates for each of the studies were calculated for subtype, grade, and necrosis, using the exact binomial; the summary recurrence rate and 95% CI for each treatment category were calculated by quantitative meta-analysis using the fixed and random effects models applied to proportions. RESULTS, Meta-analysis yielded a summary recurrence rate of 22.5% (95% CI = 16.9-28.2) for studies employing CS alone, 8.9% (95% CI = 6.8-11.0) for CS + RT, and 1.4% (95% CI = 0.7-2.1) for studies involving mastectomy alone. These summary figures indicate a clear and statistically significant separation, and therefore outcome, between the recurrence rates of each treatment category, despite the likelihood that the patients who underwent CS alone were likely to have had smaller, possibly low grade lesions with clear margins. The patients with risk factors of presence of necrosis, high grade cytologic features, or comedo subtype were found to derive the greatest improvement in local control with the addition of RT to CS. Local recurrence among patients treated by CS alone is approximately 20%, and one-half of the recurrences are invasive cancers. For most patients, RT reduces the risk of recurrence after CS alone by at least 50%. The differences in local recurrence between CS alone and CS + RT are most apparent for those patients with high grade tumors or DCIS with necrosis, or of the comedo subtype, or DCIS with close or positive surgical margins. CONCLUSIONS, The authors recommend that radiation be added to CS if patients with DCIS who also have the risk factors for local recurrence choose breast conservation over mastectomy. The patients who may be suitable for CS alone outside of a clinical trial may be those who have low grade lesions with little or no necrosis, and with clear surgical margins. Use of the summary statistics when discussing outcomes with patients may help the patient make treatment decisions. Cancer 1999;85:616-28. (C) 1999 American Cancer Society.

Targeting local tissues by transdermal application: Understanding drug physicochemical properties that best exploit protein binding and blood flow effects

The targeting of topically applied drug molecules into tissues below a site of application requires an understanding of the complex interrelationships between the drug, its formulation, the barrier properties of the skin, and the physiological processes occurring below the skin that are responsible for drug clearance from the site, tissue, and/or systemic distribution and eventual elimination. There is still a certain amount of controversy over the ability of topically applied drugs to penetrate into deeper tissues by diffusion or whether this occurs by redistribution in the systemic circulation. The major focus of our work in this area has been in determining how changes in drug structure and physicochemical properties, such as protein binding and lipophilicity, affect drug clearance into the local dermal microcirculation and lymphatics, as well as subsequent distribution into deeper tissues below an application site. The present study outlines our recent thinking on the drug molecule optimal physical attributes, in terms of plasma and tissue partitioning behaviour, that offer the greatest potential for deep tissue targeting. Drug Dev. Res. 46:309-315, 1999. (C) 1999 Wiley-Liss, Inc.

Life tables of the processionary caterpillar Ochrogaster lunifer Herrich-Schaffer (Lepidoptera : Thaumetopoeidae) at local and regional scales

A major ongoing debate in population ecology has surrounded the causative factors underlying the abundance of phytophagous insects and whether or not these factors limit or regulate herbivore populations. However, it is often difficult to identify mortality agents in census data, and their distribution and relative importance across large spatial scales are rarely understood. Were, we present life tables for egg batches and larval cohorts of the processionary caterpillar Ochrogaster lunifer Herrich-Schaffer, using intensive local sampling combined with extensive regional monitoring to ascertain the relative importance of different mortality factors at different localities. Extinction of entire cohorts (representing the entire reproductive output of one female) at natural localities was high, with 82% of the initial 492 cohorts going extinct. Mortality was highest in the egg and early instar stages due to predation from dermestid beetles, and while different mortality factors (e.g. hatching failure, egg parasitism and failure to establish on the host) were present at many localities, dermestid predation, either directly observed or inferred from indirect evidence, was the dominant mortality factor at 89% of localities surveyed. Predation was significantly higher in plantations than in natural habitats. The second most important mortality factor was resource depletion, with 14 cohorts defoliating their hosts. Egg and larval parasitism were not major mortality agents. A combination of predation and resource depletion consistently accounted for the majority of mortality across localities, suggesting that both factors are important in limiting population abundance. This evidence shows that O. lunifer is not regulated by natural enemies alone, but that resource patches (Acacia trees) ultimately, and frequently, act together to limit population growth.

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.

Exploratory research: Citizen participation, local government and sustainable development in Australia

Exploratory research reported in this paper was undertaken in Adelaide, Australia during 1998/99. The purpose of the research is to explore local development practice as evidenced through the experiences and actions of local citizens, community based groups and local government (Neuman, 1994). Results from this first stage research suggest that sustainability initiatives in Australia might best be implemented through a collaborative approach at the local community level involving local citizens working in partnership with local government. Copyright (C) 2002 John Wiley & Sons, Ltd and ERP Environment.