The pace of evolution across fitness valleys

How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. If the order of mutations is arbitrary, then there are many ways to evolve to the higher fitness state. We address the time required for fixation in such scenarios and study how it is affected by the order of mutations, the population size, the fitness values and the mutation rate

The Fastest Evolutionary Trajectory

Given two mutants, A and B, separated by n mutational steps, what is the evolutionary trajectory which allows a homogeneous population of A to reach B in the shortest time? We show that the optimum evolutionary trajectory (fitness landscape) has the property that the relative fitness increase between any two consecutive steps is constant. Hence, the optimum fitness landscape between A and B is given by an exponential function. Our result is precise for small mutation rates and excluding back mutations. We discuss deviations for large mutation rates and including back mutations. For very large mutation rates, the optimum fitness landscape is flat and has a single peak at type B.MathematicsOrganismic and Evolutionary Biolog

Datta-Das type spin-field effect transistor in non-ballistic regime

It is revealed that in spin helix state of (001) quantum well system, strong suppression of D'yakonov-Perel' spin relaxation process occurs by an interplay between Rashba and Dresselhaus couplings over a wide range of Rashba coupling strength. Contrary to common belief in early works, this leads to the finding that Datta-Das type spin-field effect transistor is actually applicable to more realistic non-ballistic transport regime in two dimensional electron gas system.Comment: 8 pages, 3 figure

O and Ne K absorption edge structures and interstellar abundance towards Cyg X-2

We have studied the O and Ne absorption features in the X-ray spectrum of Cyg X-2 observed with the Chandra LETG. The O absorption edge is represented by the sum of three absorption-edge components within the limit of the energy resolution and the photon counting statistics. Two of them are due to the atomic O; their energies correspond to two distinct spin states of photo-ionized O atoms. The remaining edge component is considered to represent compound forms of oxide dust grains. Since Cyg X-2 is about 1.4 kpc above the galactic disk, the H column densities can be determined by radio (21 cm and CO emission line) and H alpha observations with relatively small uncertainties. Thus the O abundance relative to H can be determined from the absorption edges. We found that the dust scattering can affect the apparent depth of the edge of the compound forms. We determined the amplitude of the effect, which we consider is the largest possible correction factor. The ratio of column densities of O in atomic to compound forms and the O total abundance were respectively determined to be in the range 1.7^{+3.0}_{-0.9} to 2.8^{+5.1}_{-1.5} (ratio), and 0.63 +/- 0.12 solar to 0.74 +/- 0.14 solar (total), taking into account the uncertainties in the dust-scattering correction and in the ionized H column density. We also determined the Ne abundance from the absorption edge to be 0.75 +/- 0.20 solar. These abundance values are smaller than the widely-used solar values but consistent with the latest estimates of solar abundance.Comment: 20 pages, 3 figures, AASTeX format. Accepted for publication in Ap

A Symmetry of Fixation Times in Evoultionary Dynamics

In this paper, we show that for evolutionary dynamics between two types that can be described by a Moran process, the conditional fixation time of either type is the same irrespective of the selective scenario. With frequency dependent selection between two strategies A and B of an evolutionary game, regardless of whether A dominates B, A and B are best replies to themselves, or A and B are best replies to each other, the conditional fixation times of a single A and a single B mutant are identical. This does not hold for Wright–Fisher models, nor when the mutants start from multiple copies.Human Evolutionary BiologyMathematic

Neural crest stem cells undergo multilineage differentiation in developing peripheral nerves to generate endoneurial fibroblasts in addition to Schwann cells

Neural crest stem cells (NCSCs) persist in peripheral nerves throughout late gestation but their function is unknown. Current models of nerve development only consider the generation of Schwann cells from neural crest, but the presence of NCSCs raises the possibility of multilineage differentiation. We performed Cre-recombinase fate mapping to determine which nerve cells are neural crest derived. Endoneurial fibroblasts, in addition to myelinating and non-myelinating Schwann cells, were neural crest derived, whereas perineurial cells, pericytes and endothelial cells were not. This identified endoneurial fibroblasts as a novel neural crest derivative, and demonstrated that trunk neural crest does give rise to fibroblasts in vivo, consistent with previous studies of trunk NCSCs in culture. The multilineage differentiation of NCSCs into glial and non-glial derivatives in the developing nerve appears to be regulated by neuregulin, notch ligands, and bone morphogenic proteins, as these factors are expressed in the developing nerve, and cause nerve NCSCs to generate Schwann cells and fibroblasts, but not neurons, in culture. Nerve development is thus more complex than was previously thought, involving NCSC self-renewal, lineage commitment and multilineage differentiation

Ground state representations of loop algebras

Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S^1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg.Comment: 22 pages, no figur

Importance of self-interaction-error removal in density functional calculations on water cluster anions

Accurate description of the excess charge in water cluster anions is challenging for standard semi-local and (global) hybrid density functional approximations (DFAs). Using the recent unitary invariant implementation of the Perdew–Zunger self-interaction correction (SIC) method using Fermi-Löwdin orbitals, we assess the effect of self-interaction error on the vertical detachment energies of water cluster anions with the local spin density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation, and the strongly constrained and appropriately normed (SCAN) meta-GGA functionals. Our results show that for the relative energies of isomers with respect to reference CCSD(T) values, the uncorrected SCAN functional has the smallest deviation of 21 meV, better than that for the MP2 method. The performance of SIC-SCAN is comparable to that of MP2 and is better than SIC-LSDA and SIC-PBE, but it reverses the ordering of the two lowest isomers for water hexamer anions. Removing self interaction error (SIE) corrects the tendency of LSDA, PBE, and SCAN to over-bind the extra electron. The vertical detachment energies (VDEs) of water cluster anions, obtained from the total energy differences of corresponding anion and neutral clusters, are significantly improved by removing self-interaction and are better than the hybrid B3LYP functional, but fall short of MP2 accuracy. Removing SIE results in substantial improvement in the position of the eigenvalue of the extra electron. The negative of the highest occupied eigenvalue after SIC provides an excellent approximation to the VDE, especially for SIC-PBE where the mean absolute error with respect to CCSD(T) is only 17 meV, the best among all approximations compared in this work

On the equivalence of two deformation schemes in quantum field theory

Two recent deformation schemes for quantum field theories on the two-dimensional Minkowski space, making use of deformed field operators and Longo-Witten endomorphisms, respectively, are shown to be equivalent.Comment: 14 pages, no figure. The final version is available under Open Access. CC-B