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.

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons are studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local magnetic moments of the impurities are presented as non-trivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, the model Hamiltonian is diagonalized and the Bethe ansatz equations are derived. It is interesting to note that our model exhibits a free parameter in the bulk Hamiltonian but no free parameter exists on the boundaries. This is in sharp contrast to the impurity models arising from the supersymmetric t-J and extended Hubbard models where there is no free parameter in the bulk but there is a free parameter on each boundary.

The continuum of quasi-psychotic beliefs and experiences in the Australian general public

When surveyed, many individuals without psychosis report a range of beliefs and experiences that are shared by patients with psychosis. This study aimed to examine quasi-psychotic beliefs and experiences in a sample of well Australians. 303 individuals were recruited from a defined catchment area as part of the Brisbane Psychosis Study. All subjects were screened with a modified SCAN in order to exclude psychoses. The Peters Delusional Inventory (PDI 40 items), items from the Chapmans' Psychosis Proneness Scale (PPS), the Communication Awareness Scale (CAS: a measure of awareness of thought disorder), items related to perceptions and beliefs from various schizotypy questionnaires and the Social Desirability (SD) items from the EPQ were administered. There was a significant negative correlation between age and total score on the PDI. There were significant positive correlations between the PDI, the PPS, the CAS and the items related to perception. There were no significant gender differences on any of the scores apart from SD (females had higher scores). Those with a positive family history of mental illness other than schizophrenia (n = 118) scored significantly higher on the PDI and scores related to perception, however they were no different on SD or the Psychosis Proneness items. There were no group differences on any of these items when those with a positive family history of schizophrenia (n = 27) were compared to the rest of the group. Well individuals who endorse delusional beliefs also tend to endorse items related to abnormal perceptions and awareness of thought disorder. The results of the study support the concept of a 'continuum of beliefs and experiences' in the general community that should inform our neurocognitive models of the symptoms of psychosis. The Stanley Foundation supported this project.

The relationship between cannabis use and other substance use in the general population

This study examined if (1) there is an association in the general population between cannabis use, DSM-IV abuse and dependence, and other substance use and DSM-IV substance abuse/dependence; (2) if so, is it explained by demographic characteristics or levels of neuroticism? It used data from the Australian National Survey of Mental Health and Well-Being (NSMHWB), a stratified, multistage probability sample of 10641 adults, representative of the general population. DSM-IV diagnoses of substance abuse and dependence were derived using the Composite International Diagnostic Interview (CIDI). There was a strong bivariate association between involvement with cannabis use in the past 12 months and other substance use, abuse and dependence. In particular, cannabis abuse and dependence were highly associated with increased risks of other substance dependence. These associations remained after including other variables in multiple regression. Cannabis use without disorder was strongly related to other drug use, an association that was not explained by other variables considered here. The high likelihood of other substance use and substance use disorders needs to be considered among persons seeking treatment for cannabis use problems. (C) 2001 Elsevier Science Ireland Ltd. All rights reserved.

The role of the church in developing the law: response to commentators

Three of the four commentators endorse our concerns about intervention by the Roman Catholic church as an omicus curiae in civil litigation, with few reservations. One commentary rejects our arguments in We deal first with the three commentaries that support our arguments; secondly, with the reservations and qualifications in those commentaries, and thirdly, with the commentary that totally rejects our arguments.

APOE polymorphism is associated with lipid profile, but not with arterial stiffness in the general population

Background: Cardiovascular diseases (CVD) are the main cause of death and disability in developed countries. In most cases, the progress of CVD is influenced by environmental factors and multifactorial inheritance. The purpose of this study was to investigate the association between APOE genotypes, cardiovascular risk factors, and a noninvasive measure of arterial stiffness in the Brazilian population. Methods: A total of 1493 urban Brazilian individuals were randomly selected from the general population of the Vitoria City Metropolitan area. Genetic analysis of the APOE polymorphism was conducted by PCR-RFLP and pulse wave velocity analyzed with a noninvasive automatic device. Results: Age, gender, body mass index, triglycerides, creatinine, uric acid, blood glucose, blood pressure phenotypes were no different between epsilon 2, epsilon 3 and epsilon 4 alleles. The epsilon 4 allele was associated with higher total-cholesterol (p < 0.001), LDL-C (p < 0.001), total-cholesterol/HDL-C ratio (p < 0.001), LDL/HDL-C ratio (p < 0.001), lower HDL-C values (p < 0.001) and higher risk to obesity (OR = 1.358, 95% CI = 1.019-1.811) and hyperuricemia (OR = 1.748, 95% CI = 1.170-2.611). Nevertheless, pulse wave velocity (p = 0.66) measures were no different between genotypes. The significant association between APOE genotypes and lipid levels persisted after a 5-year follow-up interval, but no interaction between time and genotype was observed for lipids longitudinal behavior. Conclusion: The epsilon 4 allele of the APOE gene is associated with a worse lipid profile in the Brazilian urban population. In our relatively young sample, the observed effect of APOE genotype on lipid levels was not translated into significant effects in arterial wall stiffness.

Screening for serious mental illness in the general population with the K6 screening scale: results from the WHO World Mental Health (WMH) survey initiative

Data are reported on the background and performance of the K6 screening scale for serious mental illness (SMI) in the World Health Organization (WHO) World Mental Health (WMH) surveys. The K6 is a six-item scale developed to provide a brief valid screen for Diagnostic and Statistical Manual of Mental Disorders 4th edition (DSM-IV) SMI based on the criteria in the US ADAMHA Reorganization Act. Although methodological studies have documented good K6 validity in a number of countries, optimal scoring rules have never been proposed. Such rules are presented here based on analysis of K6 data in nationally or regionally representative WMH surveys in 14 countries (combined N = 41,770 respondents). Twelve-month prevalence of DSM-IV SMI was assessed with the fully-structured WHO Composite International Diagnostic Interview. Nested logistic regression analysis was used to generate estimates of the predicted probability of SMI for each respondent from K6 scores, taking into consideration the possibility of variable concordance as a function of respondent age, gender, education, and country. Concordance, assessed by calculating the area under the receiver operating characteristic curve, was generally substantial (median 0.83; range 0.76-0.89; inter-quartile range 0.81-0.85). Based on this result, optimal scaling rules are presented for use by investigators working with the K6 scale in the countries studied. Copyright (c) 2010 John Wiley & Sons, Ltd.

A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

The role of the church in developing the law

The church and other community organisations have a legitimate role to play in influencing public policy. However, intervention by the church and other religious bodies in recent litigation in Australia and the United Kingdom raises questions about the appropriateness of such bodies being permitted to intervene directly in the court process as amici curiae. We argue that there are dangers in such bodies insinuating their doctrine under the guise of legal argument in civil proceedings, but find it difficult to enunciate a principled distinction between doctrine and legal argument. We advise that judges should exercise caution in dealing with amicus submissions.

Some new killing trick: Welfare reform and drug markets in a U.S. urban ghetto

Ethnographic data collected over a 5-year period is analyzed to determine how the Personal Responsibility & Work Opportunity Reconciliation Act of 1996 (PRWORA) has affected the lives of young male drug dealers from AIDS-afflicted families residing in Detroit. The data analysis indicated that the participants perceived drug dealing as the only viable employment opportunity for meeting the quotidian & health care needs of their families. The findings also revealed that the participants were highly aware of local political processes & the necessities of caring for relatives living with AIDS. Additional attention is dedicated to exploring the state of MI's rationale for ending the General Assistance Program, the sociocultural foundations of the PRWORA, various stipulations of the PRWORA, & how the PRWORA has augmented the legal vulnerability of welfare recipients. It is concluded that the PRWORA will force many welfare recipients to engage in illicit activities & will generally decrease recipients' health. 59 References. J. W. Parker