Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies

A study of fermion nodes for spin-polarized states of a few-electron ions and molecules with $s,p,d$ one-particle orbitals is presented. We find exact nodes for some cases of two electron atomic and molecular states and also the first exact node for the three-electron atomic system in $^4S(p^3)$ state using appropriate coordinate maps and wavefunction symmetries. We analyze the cases of nodes for larger number of electrons in the Hartree-Fock approximation and for some cases we find transformations for projecting the high-dimensional node manifolds into 3D space. The node topologies and other properties are studied using these projections. We also propose a general coordinate transformation as an extension of Feynman-Cohen backflow coordinates to both simplify the nodal description and as a new variational freedom for quantum Monte Carlo trial wavefunctions.Comment: 7 pages, 7 figure

Menelaus relation and Fay's trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte

Does sticky blood predict a sticky end? Associations of blood viscosity, haematocrit and fibrinogen with mortality in the West of Scotland

There is increasing evidence that blood viscosity and its major determinants (haematocrit, plasma viscosity and fibrinogen) are associated with an increased risk of incident cardiovascular events; however, their associations with mortality are not established. We therefore studied the associations of these variables with cardiovascular events and total mortality in 1238 men and women aged 25-64 years, followed for 13 years in the first North Glasgow MONICA (MONItoring CArdiovascular disease) survey and West of Scotland centres in the Scottish Heart Health Study. After adjustment for age and sex, increasing whole blood viscosity, plasma viscosity, haematocrit and fibrinogen (analysed by both von Clauss and heat precipitation assays) were significantly associated with mortality. Only the association for fibrinogen (von Clauss assay) remained significant after adjustment for major cardiovascular risk factors. We conclude that clottable fibrinogen may be independently associated with mortality. However, the significance of this association, and the extent to which viscosity is associated with mortality, remain to be established in larger studies and meta-analyses

C-reactive protein: associations with haematological variables, cardiovascular risk factors and prevalent cardiovascular disease

C-reactive protein (CRP) has been proposed as a risk factor for cardiovascular disease; however, this association is confounded by mutual relationships with both classical and haematological cardiovascular risk factors. We, therefore, measured CRP with a high-sensitivity assay in stored plasma samples from 414 men and 515 women in the north Glasgow MONICA (MONItoring trends in CArdiovascular diseases) survey, to study its correlation with haematological variables, classical risk factors and prevalent cardiovascular disease. CRP correlated with age, oral contraceptive use, menopause and most classical cardiovascular risk factors (except blood pressure). CRP also correlated with plasma levels of the pro-inflammatory cytokine interleukin 6, and haematocrit, viscosity, red cell aggregation, white cell count, and coagulation factors [fibrinogen, factor (F) VII in women, FVIII, FIX] and inhibitors (antithrombin and protein C in women; protein S) but not coagulation activation markers. CRP was significantly associated with prevalent cardiovascular disease in both men (P = 0.03) and women (P = 0.009), however, the association became non-significant after adjustment for firstly classical risk factors, then fibrinogen. We conclude that correlations with classical and haematological risk factors account for a substantial component of the association of CRP with prevalent cardiovascular disease, but there is evidence of a residual, independent effect among women

Asymptotic singularities of planar parallel 3-RPR manipulators

We study the limits of singularities of planar parallel 3-RPR manipulators as the lengths of their legs tend to infinity, paying special attention to the presence of cusps. These asymptotic singularities govern the kinematic behavior of the manipulator in a rather large portion of its workspace

Menelaus' theorem, Clifford configurations and inversive geometry of the Schwarzian KP hierarchy

It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal mappings encapsulates nothing but a fundamental theorem of ancient Greek geometry. Thus, it is demonstrated that the connection with Menelaus' theorem and, more generally, Clifford configurations renders the dSKP equation a natural object of inversive geometry on the plane. The geometric and algebraic integrability of dSKP lattices and their reductions to lattices of Menelaus-Darboux, Schwarzian KdV, Schwarzian Boussinesq and Schramm type is discussed. The dSKP and discrete Schwarzian Boussinesq equations are shown to represent discretizations of families of quasi-conformal mappings.Comment: 26 pages, 9 figure

Generalized isothermic lattices

We study multidimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isthermic lattices using Steiner's projective structure of conics and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem.Comment: 19 pages, 11 figures; v2. some typos corrected; v3. new references added, higlighted similarities and differences with recent papers on the subjec

Stroke risk estimation across nine European countries in the MORGAM project.

Previous tools for stroke risk assessment have either been developed for specific populations or lack data on non-fatal events or uniform data collection. The purpose of this study was to develop a stepwise model for the estimation of 10 year risk of stroke in nine different countries across Europe.Using data from the MOnica Risk, Genetics, Archiving and Monograph (MORGAM) Project, sex-specific models estimating 10 year risk of stroke were developed using a Cox regression model stratified by country and including modelling of competing risks. Models were developed in a stepwise manner first using only data from questionnaires, and then adding data from physical examinations and finally data from blood samples.During 1,176,296 years of observation, 2928 incident fatal and non-fatal events of stroke were registered. The developed model showed good calibration and accuracy of prediction. The discrimination of the model varied between sex and country but increased with increasing number of variables used (area under the receiver operating characteristic curve between 0.77 and 0.79 in men and between 0.75 and 0.80 in women).The present study shows that using a large multicountry cohort from nine European countries it is possible to develop a stepwise risk estimation model for 10 year risk of stroke tailored to different availability of risk factors and still obtain valid measures of risk even in the simplest form of the model, with increasing performance of the model following increasing complexity. The methods chosen which separate this model from previous models (competing risk and stepwise approach) should be considered for future risk estimation models

Exploring the equity of GP practice prescribing rates for selected coronary heart disease drugs: a multiple regression analysis with proxies of healthcare need

Background There is a small, but growing body of literature highlighting inequities in GP practice prescribing rates for many drug therapies. The aim of this paper is to further explore the equity of prescribing for five major CHD drug groups and to explain the amount of variation in GP practice prescribing rates that can be explained by a range of healthcare needs indicators (HCNIs). Methods The study involved a cross-sectional secondary analysis in four primary care trusts (PCTs 1–4) in the North West of England, including 132 GP practices. Prescribing rates (average daily quantities per registered patient aged over 35 years) and HCNIs were developed for all GP practices. Analysis was undertaken using multiple linear regression. Results Between 22–25% of the variation in prescribing rates for statins, beta-blockers and bendrofluazide was explained in the multiple regression models. Slightly more variation was explained for ACE inhibitors (31.6%) and considerably more for aspirin (51.2%). Prescribing rates were positively associated with CHD hospital diagnoses and procedures for all drug groups other than ACE inhibitors. The proportion of patients aged 55–74 years was positively related to all prescribing rates other than aspirin, where they were positively related to the proportion of patients aged >75 years. However, prescribing rates for statins and ACE inhibitors were negatively associated with the proportion of patients aged >75 years in addition to the proportion of patients from minority ethnic groups. Prescribing rates for aspirin, bendrofluazide and all CHD drugs combined were negatively associated with deprivation. Conclusion Although around 25–50% of the variation in prescribing rates was explained by HCNIs, this varied markedly between PCTs and drug groups. Prescribing rates were generally characterised by both positive and negative associations with HCNIs, suggesting possible inequities in prescribing rates on the basis of ethnicity, deprivation and the proportion of patients aged over 75 years (for statins and ACE inhibitors, but not for aspirin)