On the nonlinear stability of symplectic integrators

The modified Hamiltonian is used to study the nonlinear stability of symplectic integrators, especially for nonlinear oscillators. We give conditions under which an initial condition on a compact energy surface will remain bounded for exponentially long times for sufficiently small time steps. For example, the implicit midpoint rule achieves this for the critical energy surface of the H´enon- Heiles system, while the leapfrog method does not. We construct explicit methods which are nonlinearly stable for all simple mechanical systems for exponentially long times. We also address questions of topological stability, finding conditions under which the original and modified energy surfaces are topologically equivalent

Viscous Dark Energy Models with Variable G and Lambda

We consider a cosmological model with bulk viscosity ($\eta$) and variable cosmological $(\Lambda\propto \rho^{-\alpha}, \alpha=\rm const.$) and gravitational ($G$) constants. The model exhibits many interesting cosmological features. Inflation proceeds du to the presence of bulk viscosity and dark energy without requiring the equation of state $p=-\rho$. During the inflationary era the energy density ($\rho$) does not remain constant, as in the de-Sitter type. Moreover, the cosmological and gravitational constants increase exponentially with time, whereas the energy density and viscosity decrease exponentially with time. The rate of mass creation during inflation is found to be very huge suggesting that all matter in the universe was created during inflation.Comment: 6 Latex page

Opportunities for future supernova studies of cosmic acceleration

We investigate the potential of a future supernova dataset, as might be obtained by the proposed SNAP satellite, to discriminate among different ``dark energy'' theories that describe an accelerating Universe. We find that many such models can be distinguished with a fit to the effective pressure-to-density ratio, $w$, of this energy. More models can be distinguished when the effective slope, $dw/dz$, of a changing $w$ is also fit, but only if our knowledge of the current mass density, $\Omega_m$, is improved. We investigate the use of ``fitting functions'' to interpret luminosity distance data from supernova searches, and argue in favor of a particular preferred method, which we use in our analysis.Comment: Four pages including figures. Final published version. No significant changes from v

Phantom Energy Accretion by Stringy Charged Black Hole

We investigate the dynamical behavior of phantom energy near stringy magnetically charged black hole. For this purpose, we derive equations of motion for steady-state spherically symmetric flow of phantom energy onto the stringy magnetically charged black hole. It is found that phantom energy accreting onto black hole decreases its mass. Further, the location of critical points of accretion is explored, which yields mass to charge ratio. This ratio implies that accretion process cannot transform a black hole into an extremal black hole or a naked singularity, hence cosmic censorship hypothesis remains valid here.Comment: 7 pages, no figur

Zeldovich flow on cosmic vacuum background: new exact nonlinear analytical solution

A new exact nonlinear Newtonian solution for a plane matter flow superimposed on the isotropic Hubble expansion is reported. The dynamical effect of cosmic vacuum is taken into account. The solution describes the evolution of nonlinear perturbations via gravitational instability of matter and the termination of the perturbation growth by anti-gravity of vacuum at the epoch of transition from matter domination to vacuum domination. On this basis, an `approximate' 3D solution is suggested as an analog of the Zeldovich ansatz.Comment: 9 pages, 1 figure

Positive Selection and Horizontal Gene Transfer in the Genome of a Male-Killing Wolbachia

Wolbachia are a genus of widespread bacterial endosymbionts in which some strains can hijack or manipulate arthropod host reproduction. Male killing is one such manipulation in which these maternally transmitted bacteria benefit surviving daughters in part by removing competition with the sons for scarce resources. Despite previous findings of interesting genome features of microbial sex ratio distorters, the population genomics of male-killers remain largely uncharacterized. Here, we uncover several unique features of the genome and population genomics of four Arizonan populations of a male-killing Wolbachia strain, wInn, that infects mushroom-feeding Drosophila innubila. We first compared the wInn genome with other closely related Wolbachia genomes of Drosophila hosts in terms of genome content and confirm that the wInn genome is largely similar in overall gene content to the wMel strain infecting D. melanogaster. However, it also contains many unique genes and repetitive genetic elements that indicate lateral gene transfers between wInn and non-Drosophila eukaryotes. We also find that, in line with literature precedent, genes in the Wolbachia prophage and Octomom regions are under positive selection. Of all the genes under positive selection, many also show evidence of recent horizontal transfer among Wolbachia symbiont genomes. These dynamics of selection and horizontal gene transfer across the genomes of several Wolbachia strains and diverse host species may be important underlying factors in Wolbachia’s success as a male-killer of divergent host species

Multi-Color Light Curves of Type Ia Supernovae on the Color-Magnitude Diagram: a Novel Step Toward More Precise Distance and Extinction Estimates

We show empirically that fits to the color-magnitude relation of Type Ia supernovae after optical maximum can provide accurate relative extragalactic distances. We report the discovery of an empirical color relation for Type Ia light curves: During much of the first month past maximum, the magnitudes of Type Ia supernovae defined at a given value of color index have a very small magnitude dispersion; moreover, during this period the relation between $B$ magnitude and $B-V$ color (or $B-R$ or $B-I$ color) is strikingly linear, to the accuracy of existing well-measured data. These linear relations can provide robust distance estimates, in particular, by using the magnitudes when the supernova reaches a given color. After correction for light curve strech factor or decline rate, the dispersion of the magnitudes taken at the intercept of the linear color-magnitude relation are found to be around 0$^m$.08 for the sub-sample of supernovae with \BVm $\le 0^m.05$, and around 0$^m$.11 for the sub-sample with \BVm $\le 0^m.2$. This small dispersion is consistent with being mostly due to observational errors. The method presented here and the conventional light curve fitting methods can be combined to further improve statistical dispersions of distance estimates. It can be combined with the magnitude at maximum to deduce dust extinction. The slopes of the color-magnitude relation may also be used to identify intrinsically different SN Ia systems. The method provides a tool that is fundamental to using SN Ia to estimate cosmological parameters such as the Hubble constant and the mass and dark energy content of the universe.Comment: ApJ, in pres

A single synonymous nucleotide change impacts the male-killing phenotype of prophage WO gene wmk

Wolbachia are the most widespread bacterial endosymbionts in animals. Within arthropods, these maternally transmitted bacteria can selfishly hijack host reproductive processes to increase the relative fitness of their transmitting females. One such form of reproductive parasitism called male killing, or the selective killing of infected males, is recapitulated to degrees by transgenic expression of the prophage WO-mediated killing (wmk) gene. Here, we characterize the genotype-phenotype landscape of wmk-induced male killing in D. melanogaster using transgenic expression. While phylogenetically distant wmk homologs induce no sex-ratio bias, closely-related homologs exhibit complex phenotypes spanning no death, male death, or death of all hosts. We demonstrate that alternative start codons, synonymous codons, and notably a single synonymous nucleotide in wmk can ablate killing. These findings reveal previously unrecognized features of transgenic wmk-induced killing and establish new hypotheses for the impacts of post-transcriptional processes in male killing variation. We conclude that synonymous sequence changes are not necessarily silent in nested endosymbiotic interactions with life-or-death consequences

Geodesic Warps by Conformal Mappings

In recent years there has been considerable interest in methods for diffeomorphic warping of images, with applications e.g.\ in medical imaging and evolutionary biology. The original work generally cited is that of the evolutionary biologist D'Arcy Wentworth Thompson, who demonstrated warps to deform images of one species into another. However, unlike the deformations in modern methods, which are drawn from the full set of diffeomorphism, he deliberately chose lower-dimensional sets of transformations, such as planar conformal mappings. In this paper we study warps of such conformal mappings. The approach is to equip the infinite dimensional manifold of conformal embeddings with a Riemannian metric, and then use the corresponding geodesic equation in order to obtain diffeomorphic warps. After deriving the geodesic equation, a numerical discretisation method is developed. Several examples of geodesic warps are then given. We also show that the equation admits totally geodesic solutions corresponding to scaling and translation, but not to affine transformations