Tractable diffusion and coalescent processes for weakly correlated loci

Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their computation is extremely difficult. In this paper we derive two new multilocus population genetic models, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates. The diffusion model is based on a central limit theorem for density dependent population processes, and we show that the sampling distribution is a linear combination of moments of Gaussian distributions and hence available in closed-form. The coalescent process is based on a probabilistic coupling of the ancestral recombination graph to a simpler genealogical process which exposes the leading dynamics of the former. We further demonstrate that when we consider the sampling distribution as an asymptotic expansion in inverse powers of the recombination parameter, the sampling distributions of the new models agree with the standard ones up to the first two orders.Comment: 34 pages, 1 figur

Ground state properties of the bond alternating spin-12\frac{1}{2} anisotropic Heisenberg chain

Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and several ground state orders have been obtained. Dimer order and string orders are found to coexist in the ground state. Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain. This spin gap along with the string orders attribute to the Haldane phase. The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.Comment: 16 pages, 6 figures, 1 tabl

Refining structures against reflection rank: an alternative metric for electron crystallography.

A new metric is proposed to improve the fidelity of structures refined against precession electron diffraction data. The inherent dynamical nature of electron diffraction ensures that direct refinement of recorded intensities against structure-factor amplitudes can be prone to systematic errors. Here it is shown that the relative intensity of precessed reflections, their rank, can be used as an alternative metric for refinement. Experimental data from erbium pyrogermanate show that applying precession reduces the dynamical transfer of intensity between reflections and hence stabilizes their rank, enabling accurate and reliable structural refinements. This approach is then applied successfully to an unknown structure of an oxygen-deficient bismuth manganite resulting in a refined structural model that is similar to a calcium analogue.The authors thank the EPSRC for financial support through grant number HO1771

An asymptotic sampling formula for the coalescent with Recombination

Ewens sampling formula (ESF) is a one-parameter family of probability distributions with a number of intriguing combinatorial connections. This elegant closed-form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite-alleles model of mutation. Since its discovery in the early 1970s, the ESF has been used in various biological applications, and has sparked several interesting mathematical generalizations. In the population genetics community, extending the underlying random-mating model to include recombination has received much attention in the past, but no general closed-form sampling formula is currently known even for the simplest extension, that is, a model with two loci. In this paper, we show that it is possible to obtain useful closed-form results in the case the population-scaled recombination rate $\rho$ is large but not necessarily infinite. Specifically, we consider an asymptotic expansion of the two-locus sampling formula in inverse powers of $\rho$ and obtain closed-form expressions for the first few terms in the expansion. Our asymptotic sampling formula applies to arbitrary sample sizes and configurations.Comment: Published in at http://dx.doi.org/10.1214/09-AAP646 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Momentum Broadening in an Anisotropic Plasma

The rates governing momentum broadening in a quark-gluon plasma with a momentum anisotropy are calculated to leading-log order for a heavy quark using kinetic theory. It is shown how the problematic singularity for these rates at leading-oder is lifted by next-to-leading order gluon self-energy corrections to give a finite contribution to the leading-log result. The resulting rates are shown to lead to larger momentum broadening along the beam axis than in the transverse plane, which is consistent with recent STAR results. This might indicate that the quark-gluon-plasma at RHIC is not in equilibrium.Comment: 14 pages, 2 figures, uses revtex4; see source for numerics; v2: typos corrected, note added in appendix, matches published versio

Can my mechanic fix blue cars? A discussion of health clinician\u27s interactions with Aboriginal Australian clients

We expect our professional mechanics to ‘diagnose’ and \u27treat\u27 our cars irrespective of colour, but are we expecting less from our health professionals? There is an increasing focus in the literature on health practitioner decision-making and its influence on the nature and quality of health care. In this article we explore how the basic diagnostic and therapeutic skills that health care practitioners have should be utilised equitably for all clients and propose ways this might be realised. Could the development of Indigenous specific curricula be teaching our medical students to think that Aboriginal patients are different from the norm? We conclude that despite the gains in introducing more comprehensive Aboriginal health curricula there remains considerable work to be done before we can be confident that we are ensuring that health practitioners are no longer contributing to health disparities