Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation

Self-consistent correlation potentials for H$_2$ and LiH for various inter-atomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations. We find that the RPA misses the derivative discontinuity at odd integer particle numbers but explicitly eliminates the fractional spin error in the exact-exchange functional. The latter finding explains the accurate total energy in the dissociation limit.Comment: 9 pages, 10 figure

Severity of disease and risk of malignant change in hereditary multiple exostoses. A genotype-phenotype study

We performed a prospective genotype-phenotype study using molecular screening and clinical assessment to compare the severity of disease and the risk of sarcoma in 172 individuals (78 families) with hereditary multiple exostoses. We calculated the severity of disease including stature, number of exostoses, number of surgical procedures that were necessary, deformity and functional parameters and used molecular techniques to identify the genetic mutations in affected individuals. Each arm of the genotype-phenotype study was blind to the outcome of the other. Mutations EXT1 and EXT2 were almost equally common, and were identified in 83% of individuals. Non-parametric statistical tests were used. There was a wide variation in the severity of disease. Children under ten years of age had fewer exostoses, consistent with the known age-related penetrance of this condition. The severity of the disease did not differ significantly with gender and was very variable within any given family. The sites of mutation affected the severity of disease with patients with EXT1 mutations having a significantly worse condition than those with EXT2 mutations in three of five parameters of severity (stature, deformity and functional parameters). A single sarcoma developed in an EXT2 mutation carrier, compared with seven in EXT1 mutation carriers. There was no evidence that sarcomas arose more commonly in families in whom the disease was more severe. The sarcoma risk in EXT1 carriers is similar to the risk of breast cancer in an older population subjected to breast-screening, suggesting that a role for regular screening in patients with hereditary multiple exostoses is justifiable. ©2004 British Editorial Society of Bone and Joint Surgery

Categorisation of continuous risk factors in epidemiological publications: a survey of current practice

BACKGROUND: Reports of observational epidemiological studies often categorise (group) continuous risk factor (exposure) variables. However, there has been little systematic assessment of how categorisation is practiced or reported in the literature and no extended guidelines for the practice have been identified. Thus, we assessed the nature of such practice in the epidemiological literature. Two months (December 2007 and January 2008) of five epidemiological and five general medical journals were reviewed. All articles that examined the relationship between continuous risk factors and health outcomes were surveyed using a standard proforma, with the focus on the primary risk factor. Using the survey results we provide illustrative examples and, combined with ideas from the broader literature and from experience, we offer guidelines for good practice. RESULTS: Of the 254 articles reviewed, 58 were included in our survey. Categorisation occurred in 50 (86%) of them. Of those, 42% also analysed the variable continuously and 24% considered alternative groupings. Most (78%) used 3 to 5 groups. No articles relied solely on dichotomisation, although it did feature prominently in 3 articles. The choice of group boundaries varied: 34% used quantiles, 18% equally spaced categories, 12% external criteria, 34% other approaches and 2% did not describe the approach used. Categorical risk estimates were most commonly (66%) presented as pairwise comparisons to a reference group, usually the highest or lowest (79%). Reporting of categorical analysis was mostly in tables; only 20% in figures. CONCLUSIONS: Categorical analyses of continuous risk factors are common. Accordingly, we provide recommendations for good practice. Key issues include pre-defining appropriate choice of groupings and analysis strategies, clear presentation of grouped findings in tables and figures, and drawing valid conclusions from categorical analyses, avoiding injudicious use of multiple alternative analyses

Exchange and Correlation Kernels at the Resonance Frequency -- Implications for Excitation Energies in Density-Functional Theory

Specific matrix elements of exchange and correlation kernels in time-dependent density-functional theory are computed. The knowledge of these matrix elements not only constraints approximate time-dependent functionals, but also allows to link different practical approaches to excited states, either based on density-functional theory, or on many-body perturbation theory, despite the approximations that have been performed to derive them.Comment: Submitted to Phys. Rev. Lett. (February 4, 1999). Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Asymptotically exact dispersion relations for collective modes in a confined charged Fermi liquid

Using general local conservations laws we derive dispersion relations for edge modes in a slab of electron liquid confined by a symmetric potential. The dispersion relations are exact up to $\lambda^{2} q^{2}$, where $q$ is a wave vector and $\lambda$ is an effective screening length. For a harmonic external potential the dispersion relations are expressed in terms of the {\em exact} static pressure and dynamic shear modulus of a homogeneous liquid with the density taken at the slab core. We also derive a simple expression for the frequency shift of the dipole (Kohn) modes in nearly parabolic quantum dots in a magnetic field.Comment: RevTeX4, 4 pages. Revised version with new results on quantum qots and wires. Published in Phys.Rev.

Time-dependent density functional theory beyond the adiabatic local density approximation

In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of viscoelastic stresses in the electron fluid. Complex and frequency-dependent viscosity/elasticity coefficients are microscopically derived and expressed in terms of properties of the homogeneous electron gas. As a first consequence of this formalism, we provide an explicit formula for the linewidths of collective excitations in electronic systems.Comment: RevTeX, 4 page

Sequential, structural and functional properties of protein complexes are defined by how folding and binding intertwine.

Intrinsically Disordered Proteins (IDPs) fulfill critical biological roles without having the potential to fold on their own. While lacking inherent structure, the majority of IDPs do reach a folded state via interaction with a protein partner, presenting a deep entanglement of the folding and binding process. Protein disorder has been recognized as a major determinant in several properties of proteins, such as sequence, adopted structure upon binding, and function. Yet, the way the binding process is reflected in these features in general lacks a detailed description. Here, we defined three categories of protein complexes depending on the unbound structural state of the interactors, and analyzed them in detail. We found that strikingly, the properties of interactors in terms of sequence and adopted structure are defined not only by the intrinsic structural state of the protein itself, but also to a comparable extent by the structural state of the binding partner. The three different types of interactions are also regulated through divergent molecular tactics of post-translational modifications. This not only widens the range of biologically relevant sequence and structure spaces defined by ordered proteins, but also presents distinct molecular mechanisms compatible with specific biological processes, separately for each interaction type. The distinct attributes of different binding modes identified in this study can help to understand how various types of interactions serve as building blocks for the assembly of tightly regulated and highly intertwined regulatory networks

Pupil mobility, attainment and progress in secondary school

This paper is the second of two articles arising from a study of the association between pupil mobility and attainment in national tests and examinations in an inner London borough. The first article (Strand & Demie, 2006) examined the association of pupil mobility with attainment and progress during primary school. It concluded that pupil mobility had little impact on performance in national tests at age 11, once pupils’ prior attainment at age 7 and other pupil background factors such as age, sex, special educational needs, stage of fluency in English and socio-economic disadvantage were taken into account. The present article reports the results for secondary schools (age 11-16). The results indicate that pupil mobility continues to have a significant negative association with performance in public examinations at age 16, even after including statistical controls for prior attainment at age 11 and other pupil background factors. Possible reasons for the contrasting results across school phases are explored. The implications for policy and further research are discussed

Center of mass and relative motion in time dependent density functional theory

It is shown that the exchange-correlation part of the action functional $A_{xc}[\rho (\vec r,t)]$ in time-dependent density functional theory , where $\rho (\vec r,t)$ is the time-dependent density, is invariant under the transformation to an accelerated frame of reference $\rho (\vec r,t) \to \rho ' (\vec r,t) = \rho (\vec r + \vec x (t),t)$, where $\vec x (t)$ is an arbitrary function of time. This invariance implies that the exchange-correlation potential in the Kohn-Sham equation transforms in the following manner: $V_{xc}[\rho '; \vec r, t] = V_{xc}[\rho; \vec r + \vec x (t),t]$. Some of the approximate formulas that have been proposed for $V_{xc}$ satisfy this exact transformation property, others do not. Those which transform in the correct manner automatically satisfy the ``harmonic potential theorem", i.e. the separation of the center of mass motion for a system of interacting particles in the presence of a harmonic external potential. A general method to generate functionals which possess the correct symmetry is proposed

The Kohn mode for trapped Bose gases within the dielectric formalism

The presence of undamped harmonic center of mass oscillations of a weakly interacting Bose gas in a harmonic trap is demonstrated within the dielectric formalism for a previously introduced finite temperature approximation including exchange. The consistency of the approximation with the Kohn theorem is thereby demonstrated. The Kohn modes are found explicitly, generalizing an earlier zero-temperature result found in the literature. It is shown how the Kohn mode disappears from the single-particle spectrum, while remaining in the density oscillation spectrum, when the temperature increases from below to above the condensation temperature.Comment: 6 pages revte