Decoding coalescent hidden Markov models in linear time

In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population.Comment: 18 pages, 5 figures. To appear in the Proceedings of the 18th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2014). The final publication is available at link.springer.co

Ab Initio studies of the atomic structure and electronic density of states of pure and hydrogenated a-Si

We propose a method to simulate a-Si and a-Si:H using an ab initio approach based on the Harris functional and thermally amorphisized periodically continued cells with at least 64 atoms, and calculate their radial distribution functions. Hydrogen incorporation was achieved via diffusive random addition. The electronic density of states (DOS) is obtained using density functional theory with the aid of both the Harris-functional and Kohn-Sham-LDA approaches. Two time steps are used, 2.44 and 10 fs for the pure, and 0.46 and 2 fs for the hydrogenated, to see their effect on the topological and DOS structure of the samples. The calculated long time-step radial features of a-Si are in very good agreement with experiment whereas for a-Si:H the short time-step partial and total radial features agree well; for the long time-step simulation molecular hydrogen appears during annealing.The long time-step a-Si has a well defined gap with two dangling bonds, that clears and increases upon hydrogen addition and relaxation, as expected. The short time-step structures have more defects, both dangling and floating bonds, that are less characteristic of a good sample; however the radial structures of a-Si:H are in better agreement with experiment indicating that the experimental work was done on defective samples.Comment: 11 pages, RevTeX, 16 figures, submitted to Phys. Rev. B 16 June 200

3D Micron-scale Imaging of the Cortical Bone Canal Network in Human Osteogenesis Imperfecta (OI)

Osteogenesis imperfecta (OI) is a genetic disorder leading to increased bone fragility. Recent work has shown that the hierarchical structure of bone plays an important role in determining its mechanical properties and resistance to fracture. The current study represents one of the first attempts to characterize the 3D structure and composition of cortical bone in OI at the micron-scale. A total of 26 pediatric bone fragments from 18 individuals were collected during autopsy (Nc=5) or routing orthopaedic procedures (NOI=13) and imaged by microtomography with a synchrotron light source (SRµCT) for several microstructural parameters including cortical porosity (Ca.V/TV), canal surface to tissue volume (Ca.S/TV), canal diameter (Ca.Dm), canal separation (Ca.Sp), canal connectivity density (Ca.ConnD), and volumetric tissue mineral density (TMD). Results indicated significant differences in all imaging parameters between pediatric controls and OI tissue, with OI bone showing drastically increased cortical porosity, canal diameter, and connectivity. Preliminary mechanical testing revealed a possible link between cortical porosity and strength. Together these results suggest that the pore network in OI contributes greatly to its reduced mechanical properties

Two-Libron Spectrum of Solid H\u3csub\u3e2\u3c/sub\u3e and D\u3csub\u3e2\u3c/sub\u3e

It is shown that the two-libron lines in the Raman spectrum of solid hydrogen result from the large cubic anharmonicity of the quadrupole-quadrupole Hamiltonian. A localized picture is used to describe the interaction of two librational excitations on neighboring molecules, and dynamic interactions with other molecules are treated perturbatively. In this approximation the average single-libron energy agrees with the anharmonic calculation in the accompanying paper. Using a value of the quadrupole-coupling constant obtained from the single-libron spectrum, the resulting two-libron energies and Raman transition probabilities are in excellent agreement with the observed spectrum

High-Temperature Expansion for the Orientational Specific Heat of Solid H\u3csub\u3e2\u3c/sub\u3e and D\u3csub\u3e2\u3c/sub\u3e

Terms up to order (Γ/kBT)5 in the high-temperature expansion of the orientational specific heat of ortho-para alloys of solid H2 or D2 are evaluated. Good agreement is obtained between theory and experiment using a Padé approximant and effective values of the quadrupolar coupling constant, Γeff/Γ0=0.83 for D2 and Γeff/Γ0=0.80 for H2, where Γ0 is the value for a rigid lattice. These values agree with other determinations of Γeff, whereas the T−2 approximation for the specific heat yields anomalously small values of Γeff

Orientational Phases of Hydrogen Molecules on a Triangular Lattice

A mean-field theory for the ordering of hydrogen molecules on a triangular net is derived in terms of the quadrupole coupling constant Γ, the crystal field Vc, and the temperature T. The phase diagram consists of six regions, separated by first- and second-order transitions. For almost all values of Vc/Γ for which ordering occurs, the disordered to ordered phase transition is continuous. At T=0 K, all phases have energy gaps except for a ferrorotational phase which behaves like an XY model

Theoretical Analysis of Inelastic Neutron Scattering in Solid Hydrogen

The inelastic-neutron-scattering cross section of (J=1) solid hydrogen is studied and the experimental data of Stein and co-workers analyzed. The rms displacement ⟨u2⟩1/2 is deduced from the data via different methods and mutually consistent values of order 0.65 Å are obtained. The enhancement of the cross section at the libron energy due to libron-phonon interactions is found to be the same, about 40% each for both one-and two-libron processes, in agreement with the neutron scattering data. The rms splitting at the libron-phonon crossovers is found to be about 1 cm−1, somewhat smaller than found by Mertens and Biem. A sum rule for the J=1 to J=0 cross section is given which relates the average energy of this transition to the orientational internal energy. Using high-temperature expansions and experimental data for the specific heat, we obtain a qualitative fit to the neutron scattering data in the orientationally disordered phase. In the ordered phase both the sum rule and a direct calculation indicate the existence of a libron sideband above the main J=1 to J=0 line having an intensity of 10% of the main line. The energy of the main line at zero temperature is calculated including (a) tipping corrections, (b) virtual excitations with J not conserved, and (c) modified zero-point energy. The value of the electrostatic quadrupole-quadrupole coupling constant deduced from the data of Stein and co-workers using this calculation is in agreement with that obtained from other experiments