Structure maps for hcp metals from first-principles calculations

The ability to predict the existence and crystal type of ordered structures of materials from their components is a major challenge of current materials research. Empirical methods use experimental data to construct structure maps and make predictions based on clustering of simple physical parameters. Their usefulness depends on the availability of reliable data over the entire parameter space. Recent development of high-throughput methods opens the possibility to enhance these empirical structure maps by ab initio calculations in regions of the parameter space where the experimental evidence is lacking or not well characterized. In this paper we construct enhanced maps for the binary alloys of hcp metals, where the experimental data leaves large regions of poorly characterized systems believed to be phase separating. In these enhanced maps, the clusters of noncompound-forming systems are much smaller than indicated by the empirical results alone. © 2010 The American Physical Society.

Assessment of LD matrix measures for the analysis of biological pathway association.

Complex diseases will have multiple functional sites, and it will be invaluable to understand the cross-locus interaction in terms of linkage disequilibrium (LD) between those sites (epistasis) in addition to the haplotype-LD effects. We investigated the statistical properties of a class of matrix-based statistics to assess this epistasis. These statistical methods include two LD contrast tests (Zaykin et al., 2006) and partial least squares regression (Wang et al., 2008). To estimate Type 1 error rates and power, we simulated multiple two-variant disease models using the SIMLA software package. SIMLA allows for the joint action of up to two disease genes in the simulated data with all possible multiplicative interaction effects between them. Our goal was to detect an interaction between multiple disease-causing variants by means of their linkage disequilibrium (LD) patterns with other markers. We measured the effects of marginal disease effect size, haplotype LD, disease prevalence and minor allele frequency have on cross-locus interaction (epistasis). In the setting of strong allele effects and strong interaction, the correlation between the two disease genes was weak (r=0.2). In a complex system with multiple correlations (both marginal and interaction), it was difficult to determine the source of a significant result. Despite these complications, the partial least squares and modified LD contrast methods maintained adequate power to detect the epistatic effects; however, for many of the analyses we often could not separate interaction from a strong marginal effect. While we did not exhaust the entire parameter space of possible models, we do provide guidance on the effects that population parameters have on cross-locus interaction.

Role of DNA binding sites and slow unbinding kinetics in titration-based oscillators.

Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators.

SMERED: A Bayesian Approach to Graphical Record Linkage and De-duplication

We propose a novel unsupervised approach for linking records across arbitrarily many files, while simultaneously detecting duplicate records within files. Our key innovation is to represent the pattern of links between records as a {\em bipartite} graph, in which records are directly linked to latent true individuals, and only indirectly linked to other records. This flexible new representation of the linkage structure naturally allows us to estimate the attributes of the unique observable people in the population, calculate $k$-way posterior probabilities of matches across records, and propagate the uncertainty of record linkage into later analyses. Our linkage structure lends itself to an efficient, linear-time, hybrid Markov chain Monte Carlo algorithm, which overcomes many obstacles encountered by previously proposed methods of record linkage, despite the high dimensional parameter space. We assess our results on real and simulated data.

Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries.