Temporal and dimensional effects in evolutionary graph theory

The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as N^{(D+1)/D} in D-dimensional hypercubic lattices and as N ln N in fully-connected graphs. It is shown that the surface of the interface between mutants and non-mutants is crucial in predicting the dynamics of the system. Network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction. Includes supplementary information.Comment: 6 pages, 4 figures Replaced after final round of peer revie

Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the Engquist--Osher approximation for the flux and explicit time--stepping. An adaptivemultiresolution scheme with cell averages is then used to speed up CPU time and meet memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for the sake of data compression and to facilitate navigation. Applications to traffic flow with driver reaction and a clarifier--thickener model illustrate the efficiency of this method

Light-cone distribution amplitudes of octet baryons from lattice QCD

We present lattice QCD results for the wave function normalization constants and the first moments of the distribution amplitudes for the lowest-lying baryon octet. The analysis is based on a large number of $N_f=2+1$ ensembles comprising multiple trajectories in the quark mass plane including physical pion (and kaon) masses, large volumes, and, most importantly, five different lattice spacings down to $a=0.039\,\mathrm{fm}$. This allows us to perform a controlled extrapolation to the continuum and infinite volume limits by a simultaneous fit to all available data. We demonstrate that the formerly observed violation of flavor symmetry breaking constraints can, indeed, be attributed to discretization effects that vanish in the continuum limit

Overtones of the Si−H Stretching−Bending Polyad in SiHD₃: Internal Coordinate Force Field, ab initio Dipole Moment Surfaces, and Band Intensities

Overtones of the Si−H stretching−bending polyad of the SiHD3 molecule are studied using an internal coordinate force field model. The potential parameters are optimized by fitting to the experimental band centers. The Fermi resonance between the Si−H stretching and bending motions is insignificant due to cancellation of the contributions from kinetic and potential terms. This suggests a slow redistribution of vibrational energy between these two degrees of freedom and induces local mode character of respective vibrations. Band intensities are calculated by using ab initio one- and three-dimensional dipole moment surfaces (DMS). These agree reasonably well with the observations. The successful reproduction of relative intensities between the (n1 − 1)ʋ1 + 2ʋ5 stretching−bending combination bands and the n1ʋ1 stretching bands establishes the importance of the bending motion in the multidimensional DMS for intensity investigations

Modelling of long term nitrogen retention in surface waters

In order to derive measures to reduce nutrient loadings into waters in Saxony, we calculated nitrogen inputs with the model STOFFBILANZ on the regional scale. Thereby we have to compare our modelling results to measured loadings at the river basin outlets, considering long term nutrient retention in surface waters. The most important mechanism of nitrogen retention is the denitrification in the contact zone of water and sediment, being controlled by hydraulic and micro-biological processes. Retention capacity is derived on the basis of the nutrient spiralling concept, using water residence time (hydraulic aspect) and time-specific N-uptake by microorganisms (biological aspect). Short time related processes of mobilization and immobilization are neglected, because they are of minor importance for the derivation of measures on the regional scale

Stochastic slowdown in evolutionary processes

We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur successively. If the two types have equal fitness the system performs a random walk. If one type has a fitness advantage it is favored by selection, which introduces a bias (asymmetry) in the transition probabilities. How long does it take until advantageous mutants have invaded and taken over? Surprisingly, we find that the average time of such a process can increase, even if the mutant type always has a fitness advantage. We discuss this finding for the Moran process and develop a simplified model which allows a more intuitive understanding. We show that this effect can occur for weak but non--vanishing bias (selection) in the state dependent transition rates and infer the scaling with system size. We also address the Wright-Fisher model commonly used in population genetics, which shows that this stochastic slowdown is not restricted to birth-death processes.Comment: 8 pages, 3 figures, accepted for publicatio

The statistical mechanics of a polygenic characterunder stabilizing selection, mutation and drift

By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as 5 loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.Comment: 35 pages, 8 figure

The effect of a regional increase in ocean surface roughness on the tropospheric circulation: a GCM experiment

The sensitivity of the atmospheric circulation to an increase in ocean surface roughness in the Southern Hemisphere storm track is investigated in a paired general circulation model experiment. Such a change in sea roughness could be induced by ocean waves generated by storms. Two extended permanent-July runs are made. One with standard sea surface roughness, the other with ten times as a large surface roughness over open sea poleward of 40-degrees-S. The regional increase in ocean surface roughness significantly modifies the tropospheric circulation in the Southern Hemisphere. The strongest effect is the reduction of tropospheric winds (by 2 m/s or 100%) above the area with increased roughness. The poleward eddy momentum flux is reduced in the upper troposphere and the meridional eddy sensible heat flux is reduced in the lower troposphere. Zonal mean and eddy kinetic energy are consistently reduced

Survival-extinction phase transition in a bit-string population with mutation

A bit-string model for the evolution of a population of haploid organisms, subject to competition, reproduction with mutation and selection is studied, using mean field theory and Monte Carlo simulations. We show that, depending on environmental flexibility and genetic variability, the model exhibits a phase transtion between extinction and survival. The mean-field theory describes the infinite-size limit, while simulations are used to study quasi-stationary properties.Comment: 11 pages, 5 figure

Observation of large scissors resonance strength in actinides

The orbital M1-scissors resonance (SR) has been measured for the first time in the quasi-continuum of actinides. Particle-gamma coincidences are recorded with deuteron and 3He induced reactions on 232Th. The residual nuclei 231,232,233Th and 232,233Pa show an unexpectedly strong integrated strength of $B_{M1} = 11-15 \mu_{n}^{2}$ in the Egamma=1.0 - 3.5 MeV region. The increased gamma-decay probability in actinides due to the SR is important for cross-section calculations for future fuel cycles of fast nuclear reactors and may also have impact on stellar nucleosynthesis.Comment: 5 pages and 4 figure