Dissecting Trait Heterogeneity: a Comparison of Three Clustering Methods Applied to Genotypic Data

Background: Trait heterogeneity, which exists when a trait has been defined with insufficient specificity such that it is actually two or more distinct traits, has been implicated as a confounding factor in traditional statistical genetics of complex hu man disease. In the absence of de tailed phenotypic data collected consistently in combination with genetic data, unsupervised computational methodologies offer the potential for discovering underlying trait heteroge neity. The performance of three such methods – Bayesian Classification, Hyperg raph-Based Clustering, and Fuzzy k -Modes Clustering – appropriate for categorical data were comp ared. Also tested was the ability of these methods to detect trait heterogeneity in the presence of locus heteroge neity and/or gene-gene interaction , which are two other complicating factors in discovering genetic models of complex human disease. To dete rmine the efficacy of applying the Bayesian Classification method to re al data, the reliability of its intern al clustering metr ics at finding good clusterings was evaluated using permutation testing. Results: Bayesian Classifica tion outperformed the other two method s, with the exception that the Fuzzy k -Modes Clustering performed best on the most comp lex genetic model. Bayesian Classificati on achieved excellent recovery for 75% of the da tasets simulated under the simplest genetic model, while it achieved moderate recovery for 56% of datase ts with a sample size of 500 or more (across all simulated models) and for 86% of datasets with 10 or fewer nonfuncti onal loci (across all si mulated models). Neither Hypergraph Clustering nor Fuzzy k -Modes Clustering achieved good or excellent cluster recovery for a majority of datasets even under a re stricted set of conditions. When usin g the average log of class strength as the internal clustering metric, th e false positive rate was controlled very well, at three percent or less for all three significance levels (0. 01, 0.05, 0.10), and the false negative rate was acceptably low (18 percent) for the least stringent sign ificance level of 0.10. Conclusion: Bayesian Classificati on shows promise as an unsuper vised computational method for dissecting trait hetero geneity in genotypic data. Its control of fa lse positive and false negative rates lends confidence to the validity of its results. Further investigation of how differ ent parameter settings may improve the performance of Bayesian Classification, especi ally under more comp lex genetic models, is ongoing

A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization

We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons is bounded above by 2Z+1 + c sqrt{B}. We follow Lieb's strategy in which convexity plays a critical role. For the case of two electrons and fractional nuclear charge, we also discuss the critical value at which the nuclear charge becomes too weak to bind two electrons.Comment: 23 pages, 5 figures. J. Phys. A: Math and General (in press) 199

Shapley Supercluster Survey (ShaSS): Galaxy Evolution from Filaments to Cluster Cores

We present an overview of a multi-wavelength survey of the Shapley supercluster (SSC; z~0.05) covering a contiguous area of 260 h^-2_70 Mpc^2 including the supercluster core. The project main aim is to quantify the influence of cluster-scale mass assembly on galaxy evolution in one of the most massive structures in the local Universe. The Shapley supercluster survey (ShaSS) includes nine Abell clusters (A3552, A3554, A3556, A3558, A3559, A3560, A3562, AS0724, AS0726) and two poor clusters (SC1327- 312, SC1329-313) showing evidence of cluster-cluster interactions. Optical (ugri) and near-infrared (K) imaging acquired with VST and VISTA allow us to study the galaxy population down to m*+6 at the supercluster redshift. A dedicated spectroscopic survey with AAOmega on the Anglo-Australian Telescope provides a magnitude-limited sample of supercluster members with 80% completeness at ~m*+3. We derive the galaxy density across the whole area, demonstrating that all structures within this area are embedded in a single network of clusters, groups and filaments. The stellar mass density in the core of the SSC is always higher than 9E09 M_sun Mpc^-3, which is ~40x the cosmic stellar mass density for galaxies in the local Universe. We find a new filamentary structure (~7 Mpc long in projection) connecting the SSC core to the cluster A3559, as well as previously unidentified density peaks. We perform a weak-lensing analysis of the central 1 sqdeg field of the survey obtaining for the central cluster A3558 a mass of M_500=7.63E14 M_sun, in agreement with X-ray based estimates.Comment: 22 pages, 11 figures. Accepted for publication on MNRA

Hydrogen atom moving across a strong magnetic field: analytical approximations

Analytical approximations are constructed for binding energies, quantum-mechanical sizes and oscillator strengths of main radiative transitions of hydrogen atoms arbitrarily moving in magnetic fields 10^{12}-10^{13} G. Examples of using the obtained approximations for determination of maximum transverse velocity of an atom and for evaluation of absorption spectra in magnetic neutron star atmospheres are presented.Comment: 17 pages, 3 figures, 5 tables, LaTeX with IOP style files (included). In v.2, Fig.1 and Table 5 have been corrected. In v.3, a misprint in the fit for oscillator strengths, Eq.(21), has been correcte

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Hydrogen and Helium Atoms and Molecules in an Intense Magnetic Field

We calculate the atomic structure of hydrogen and helium, atoms and molecules in an intense magnetic field, analytically and numerically with a judiciously chosen basis.Comment: 16 pages, 5 figures, to appear in Phys. Rev.

Auto-calibration of ultrasonic lubricant-film thickness measurements

The measurement of oil film thickness in a lubricated component is essential information for performance monitoring and design. It is well established that such measurements can be made ultrasonically if the lubricant film is modelled as a collection of small springs. The ultrasonic method requires that component faces are separated and a reference reflection recorded in order to obtain a reflection coefficient value from which film thickness is calculated. The novel and practically useful approach put forward in this paper and validated experimentally allows reflection coefficient measurement without the requirement for a reference. This involves simultaneously measuring the amplitude and phase of an ultrasonic pulse reflected from a layer. Provided that the acoustic properties of the substrate are known, the theoretical relationship between the two can be fitted to the data in order to yield reflection coefficient amplitude and phase for an infinitely thick layer. This is equivalent to measuring a reference signal directly, but importantly does not require the materials to be separated. The further valuable aspect of this approach, which is demonstrated experimentally, is its ability to be used as a self-calibrating routine, inherently compensating for temperature effects. This is due to the relationship between the amplitude and phase being unaffected by changes in temperature which cause unwanted changes to the incident pulse. Finally, error analysis is performed showing how the accuracy of the results can be optimized. A finding of particular significance is the strong dependence of the accuracy of the technique on the amplitude of reflection coefficient input data used. This places some limitations on the applicability of the technique. © 2008 IOP Publishing Ltd

Clinical examination for hyperlinear palms to determine filaggrin genotype:a diagnostic test accuracy study

BackgroundPalmar hyperlinearity is a feature of ichthyosis vulgaris, the monogenic skin disorder caused by FLG loss-of-function mutations.ObjectiveTo investigate how well the presence or absence of hyperlinear palms (HLP) detect FLG genotype in children.MethodsSTARD criteria are used to report this diagnostic accuracy study. Phenotype and genotype data (four most prevalent FLG null mutations) were obtained from a total of 3656 children in three studies: the UK CLOTHES trial (children 1–5 years with moderate–severe atopic eczema); UK BEEP trial (2 year olds at high risk of developing atopic eczema); UK-Irish eczema case collection (0–16 year olds with atopic eczema). All participants included in analyses of HLP as the index test and FLG genotype as the reference were of white European ancestry.ResultsThirty-two percent of participants (1159/3656) had FLG null mutation(s) and 37% (1347/3656) had HLP. In 13% (464/3656), HLP was recorded as ‘unsure’ or not recorded. The sensitivity and specificity of HLP for detecting FLG mutations in each of the studies was: 67% (95% CI 55–78%) and 75% (67–82%) in CLOTHES; 46% (36–55%) and 89% (86–91%) in BEEP; 72% (68–75%) and 60% (57–62%) in the UK-Irish case collection. Positive and negative likelihood ratios were: 2.73 (1.95–3.81) and 0.44 (0.31–0.62) in CLOTHES; 4.02 (2.99–5.40) and 0.61 (0.52–0.73) in BEEP; 1.79 (1.66–1.93) and 0.47 (0.42–0.53) in the UK-Irish collection.DiscussionTrained observers were able to define palmar hyperlinearity in the majority (3191/3656, 87%) of cases. The presence of HLP is not a reliable sign to detect FLG mutations, but the absence of HLP excludes FLG null genotype with a reasonable degree of certainty