4,139 research outputs found
When trees grow too long: Investigating the causes of highly inaccurate bayesian branch-length estimates
A surprising number of recent Bayesian phylogenetic analyses contain branch-length estimates that are several orders of magnitude longer than corresponding maximum-likelihood estimates. The levels of divergence implied by such branch lengths are unreasonable for studies using biological data and are known to be false for studies using simulated data. We conducted additional Bayesian analyses and studied approximate-posterior surfaces to investigate the causes underlying these large errors. We manipulated the starting parameter values of the Markov chain Monte Carlo (MCMC) analyses, the moves used by the MCMC analyses, and the prior-probability distribution on branch lengths. We demonstrate that inaccurate branch-length estimates result from either 1) poor mixing of MCMC chains or 2) posterior distributions with excessive weight at long tree lengths. Both effects are caused by a rapid increase in the volume of branch-length space as branches become longer. In the former case, both an MCMC move that scales all branch lengths in the tree simultaneously and the use of overdispersed starting branch lengths allow the chain to accurately sample the posterior distribution and should be used in Bayesian analyses of phylogeny. In the latter case, branch-length priors can have strong effects on resulting inferences and should be carefully chosen to reflect biological expectations. We provide a formula to calculate an exponential rate parameter for the branch-length prior that should eliminate inference of biased branch lengths in many cases. In any phylogenetic analysis, the biological plausibility of branch-length output must be carefully considered
The importance of data partitioning and the utility of bayes factors in bayesian phylogenetics
As larger, more complex data sets are being used to infer phylogenies, accuracy of these phylogenies increasingly requires models of evolution that accommodate heterogeneity in the processes of molecular evolution. We investigated the effect of improper data partitioning on phylogenetic accuracy, as well as the type I error rate and sensitivity of Bayes factors, a commonly used method for choosing among different partitioning strategies in Bayesian analyses. We also used Bayes factors to test empirical data for the need to divide data in a manner that has no expected biological meaning. Posterior probability estimates are misleading when an incorrect partitioning strategy is assumed. The error was greatest when the assumed model was underpartitioned. These results suggest that model partitioning is important for large data sets. Bayes factors performed well, giving a 5% type I error rate, which is remarkably consistent with standard frequentist hypothesis tests. The sensitivity of Bayes factors was found to be quite high when the across-class model heterogeneity reflected that of empirical data. These results suggest that Bayes factors represent a robust method of choosing among partitioning strategies. Lastly, results of tests for the inclusion of unexpected divisions in empirical data mirrored the simulation results, although the outcome of such tests is highly dependent on accounting for rate variation among classes. We conclude by discussing other approaches for partitioning data, as well as other applications of Bayes factors. Copyright © Society of Systematic Biologists
Alternative derivation of the relativistic contribution to perihelic precession
An alternative derivation of the first-order relativistic contribution to
perihelic precession is presented. Orbital motion in the Schwarzschild geometry
is considered in the Keplerian limit, and the orbit equation is derived for
approximately elliptical motion. The method of solution makes use of coordinate
transformations and the correspondence principle, rather than the standard
perturbative approach. The form of the resulting orbit equation is similar to
that derived from Newtonian mechanics and includes first-order corrections to
Kepler's orbits due to general relativity. The associated relativistic
contribution to perihelic precession agrees with established first-order
results. The reduced radius for the circular orbit is in agreement to
first-order with that calculated from the Schwarzschild effective potential.
The method of solution is understandable by undergraduate students.Comment: 12 pages, 2 figures. Accepted for publication in the American Journal
of Physic
Flow probe of symmetry energy in relativistic heavy-ion reactions
Flow observables in heavy-ion reactions at incident energies up to about 1
GeV per nucleon have been shown to be very useful for investigating the
reaction dynamics and for determining the parameters of reaction models based
on transport theory. In particular, the elliptic flow in collisions of
neutron-rich heavy-ion systems emerges as an observable sensitive to the
strength of the symmetry energy at supra-saturation densities. The comparison
of ratios or differences of neutron and proton flows or neutron and hydrogen
flows with predictions of transport models favors an approximately linear
density dependence, consistent with ab-initio nuclear-matter theories.
Extensive parameter searches have shown that the model dependence is comparable
to the uncertainties of existing experimental data. Comprehensive new flow data
of high accuracy, partly also through providing stronger constraints on model
parameters, can thus be expected to improve our knowledge of the equation of
state of asymmetric nuclear matter.Comment: 20 pages, 24 figures, review to appear in EPJA special volume on
nuclear symmetry energ
Molecular Density Functional Theory of Water describing Hydrophobicity at Short and Long Length Scales
We present an extension of our recently introduced molecular density
functional theory of water [G. Jeanmairet et al., J. Phys. Chem. Lett. 4, 619,
2013] to the solvation of hydrophobic solutes of various sizes, going from
angstroms to nanometers. The theory is based on the quadratic expansion of the
excess free energy in terms of two classical density fields, the particle
density and the multipolar polarization density. Its implementation requires as
input a molecular model of water and three measurable bulk properties, namely
the structure factor and the k-dependent longitudinal and transverse dielectric
susceptibilities. The fine three-dimensional water structure around small
hydrophobic molecules is found to be well reproduced. In contrast the computed
solvation free-energies appear overestimated and do not exhibit the correct
qualitative behavior when the hydrophobic solute is grown in size. These
shortcomings are corrected, in the spirit of the Lum-Chandler-Weeks theory, by
complementing the functional with a truncated hard-sphere functional acting
beyond quadratic order in density. It makes the resulting functional compatible
with the Van-der-Waals theory of liquid-vapor coexistence at long range.
Compared to available molecular simulations, the approach yields reasonable
solvation structure and free energy of hard or soft spheres of increasing size,
with a correct qualitative transition from a volume-driven to a surface-driven
regime at the nanometer scale.Comment: 24 pages, 8 figure
Neutron Transfer Studied with a Radioactive beam of 24Ne, using TIARA at SPIRAL
A general experimental technique for high resolution studies of nucleon
transfer reactions using radioactive beams is briefly described, together with
the first new physics results that have been obtained with the new TIARA array.
These first results from TIARA are for the reaction 24Ne(d,p)25Ne, studied in
inverse kinematics with a pure radioactive beam of 100,000 pps from the SPIRAL
facility at GANIL. The reaction probes the energies of neutron orbitals
relevant to very neutron rich nuclei in this mass region and the results
highlight the emergence of the N=16 magic number for neutrons and the
associated disappearance of the N=20 neutron magic number for the very neutron
rich neon isotopes.Comment: Proceedings of the Carpathian Summer School of Physics,
Mamaia-Constanta, Romania, 13-24 June 200
Shape oscillations of a charged diamagnetically-levitated droplet
We investigate the effect of electrical charge on the normal mode frequencies
of electrically-charged diamagnetically levitated water droplets with radii
4.5-7.5 mm using diamagnetic levitation. This technique allows us to levitate
almost spherical droplets and therefore to directly compare the measured
vibrational frequencies of the first seven modes of the charged droplet with
theoretical values calculated by Lord Rayleigh, for which we find good
agreement
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