Parallel developmental genetic features underlie stickleback gill raker evolution.

BackgroundConvergent evolution, the repeated evolution of similar phenotypes in independent lineages, provides natural replicates to study mechanisms of evolution. Cases of convergent evolution might have the same underlying developmental and genetic bases, implying that some evolutionary trajectories might be predictable. In a classic example of convergent evolution, most freshwater populations of threespine stickleback fish have independently evolved a reduction of gill raker number to adapt to novel diets. Gill rakers are a segmentally reiterated set of dermal bones important for fish feeding. A previous large quantitative trait locus (QTL) mapping study using a marine × freshwater F2 cross identified QTL on chromosomes 4 and 20 with large effects on evolved gill raker reduction.ResultsBy examining skeletal morphology in adult and developing sticklebacks, we find heritable marine/freshwater differences in gill raker number and spacing that are specified early in development. Using the expression of the Ectodysplasin receptor (Edar) gene as a marker of raker primordia, we find that the differences are present before the budding of gill rakers occurs, suggesting an early change to a lateral inhibition process controlling raker primordia spacing. Through linkage mapping in F2 fish from crosses with three independently derived freshwater populations, we find in all three crosses QTL overlapping both previously identified QTL on chromosomes 4 and 20 that control raker number. These two QTL affect the early spacing of gill raker buds.ConclusionsCollectively, these data demonstrate that parallel developmental genetic features underlie the convergent evolution of gill raker reduction in freshwater sticklebacks, suggesting that even highly polygenic adaptive traits can have a predictable developmental genetic basis

Generalized Background-Field Method

The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than the ordinary background-field gauge, in that even the triple-gluon vertices for internal lines contain only four terms, not the usual six. This reduction simplifies the calculation inspite of the necessity to include other vertices for compensation. Like the ordinary background-field gauge, this generalized background-field gauge also preserves gauge invariance of the external particles. As a check of the result and an illustration for the reduction in labour, an explicit calculation of the two-loop QCD $\beta$-function is carried out in this new gauge. It results in a saving of 45% of computation compared to the ordinary background-field gauge.Comment: 17 pages, Latex, 18 figures in Postscrip

Stability of Filters for the Navier-Stokes Equation

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in a on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise filtering can be performed exactly using the Kalman filter. For nonlinear systems it can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the properties of these ad hoc filters, working in the context of the 2D incompressible Navier-Stokes equation. By working in this infinite dimensional setting we provide an analysis which is useful for understanding high dimensional filtering, and is robust to mesh-refinement. We describe theoretical results showing that, in the small observational noise limit, the filters can be tuned to accurately track the signal itself (filter stability), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics. Numerical results are given which illustrate the theory. In a simplified scenario we also derive, and study numerically, a stochastic PDE which determines filter stability in the limit of frequent observations, subject to large observational noise. The positive results herein concerning filter stability complement recent numerical studies which demonstrate that the ad hoc filters perform poorly in reproducing statistical variation about the true signal

Gradient Echo Quantum Memory for Light using Two-level Atoms

We propose a quantum memory for light that is analogous to the NMR gradient echo. Our proposal is ideally perfectly efficient and provides simplifications to current 3-level quantum memory schemes based on controlled inhomogeneous broadening. Our scheme does not require auxiliary light fields. Instead the input optical pulse interacts only with two-level atoms that have linearly increasing Stark shifts. By simply reversing the sign of the atomic Stark shifts, the pulse is retrieved in the forward direction. We present analytical, numerical and experimental results of this scheme. We report experimental efficiencies of up to 15% and suggest simple realizable improvements to significantly increase the efficiency.Comment: 4 pages, 4 figure

Effects of azimuth-symmetric acceptance cutoffs on the measured asymmetry in unpolarized Drell-Yan fixed target experiments

Fixed-target unpolarized Drell-Yan experiments often feature an acceptance depending on the polar angle of the lepton tracks in the laboratory frame. Typically leptons are detected in a defined angular range, with a dead zone in the forward region. If the cutoffs imposed by the angular acceptance are independent of the azimuth, at first sight they do not appear dangerous for a measurement of the cos(2\phi)-asymmetry, relevant because of its association with the violation of the Lam-Tung rule and with the Boer-Mulders function. On the contrary, direct simulations show that up to 10 percent asymmetries are produced by these cutoffs. These artificial asymmetries present qualitative features that allow them to mimic the physical ones. They introduce some model-dependence in the measurements of the cos(2\phi)-asymmetry, since a precise reconstruction of the acceptance in the Collins-Soper frame requires a Monte Carlo simulation, that in turn requires some detailed physical input to generate event distributions. Although experiments in the eighties seem to have been aware of this problem, the possibility of using the Boer-Mulders function as an input parameter in the extraction of Transversity has much increased the requirements of precision on this measurement. Our simulations show that the safest approach to these measurements is a strong cutoff on the Collins-Soper polar angle. This reduces statistics, but does not necessarily decrease the precision in a measurement of the Boer-Mulders function.Comment: 13 pages, 14 figure