Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection

Matrix functions are a central topic of linear algebra, and problems of their numerical approximation appear increasingly often in scientific computing. We review various rational Krylov methods for the computation of large-scale matrix functions. Emphasis is put on the rational Arnoldi method and variants thereof, namely, the extended Krylov subspace method and the shift-and-invert Arnoldi method, but we also discuss the nonorthogonal generalized Leja point (or PAIN) method. The issue of optimal pole selection for rational Krylov methods applied for approximating the resolvent and exponential function, and functions of Markov type, is treated in some detail

Fungal ecological strategies reflected in gene transcription - a case study of two litter decomposers.

Microbial communities interplay with their environment through their functional traits that can be a response or an effect on the environment. Here, we explore how a functional trait-the decomposition of organic matter, can be addressed based on genetic markers and how the expression of these markers reflect ecological strategies of two fungal litter decomposer Gymnopus androsaceus and Chalara longipes. We sequenced the genomes of these two fungi, as well as their transcriptomes at different steps of Pinus sylvestris needles decomposition in microcosms. Our results highlighted that if the gene content of the two species could indicate similar potential decomposition abilities, the expression levels of specific gene families belonging to the glycoside hydrolase category reflected contrasting ecological strategies. Actually, C. longipes, the weaker decomposer in this experiment, turned out to have a high content of genes involved in cell wall polysaccharides decomposition but low expression levels, reflecting a versatile ecology compare to the more competitive G. androsaceus with high expression levels of keystone functional genes. Thus, we established that sequential expression of genes coding for different components of the decomposer machinery indicated adaptation to chemical changes in the substrate as decomposition progressed

Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model

We present a computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model of diblock copolymers. The model is a fourth-order parabolic partial differential equation subject to homogeneous Neumann boundary conditions, which contains as a special case the celebrated Cahn-Hilliard equation. While the attractor structure of the latter model is completely understood for one-dimensional domains, the diblock copolymer extension exhibits considerably richer long-term dynamical behavior, which includes a high level of multistability. In this paper, we establish the existence of certain heteroclinic connections between the homogeneous equilibrium state, which represents a perfect copolymer mixture, and all local and global energy minimizers. In this way, we show that not every solution originating near the homogeneous state will converge to the global energy minimizer, but rather is trapped by a stable state with higher energy. This phenomenon can not be observed in the one-dimensional Cahn-Hillard equation, where generic solutions are attracted by a global minimizer

Covariant transport approach for strongly interacting partonic systems

The dynamics of partons, hadrons and strings in relativistic nucleus-nucleus collisions is analyzed within the novel Parton-Hadron-String Dynamics (PHSD) transport approach, which is based on a dynamical quasiparticle model for partons (DQPM) matched to reproduce recent lattice-QCD results - including the partonic equation of state - in thermodynamic equilibrium. Scalar- and vector-interaction densities are extracted from the DQPM as well as effective scalar- and vector-mean fields for the partons. The transition from partonic to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs or three quarks (antiquarks), respectively, obeying flavor current-conservation, color neutrality as well as energy-momentum conservation. Since the dynamical quarks and antiquarks become very massive close to the phase transition, the formed resonant 'pre-hadronic' color-dipole states ($q\bar{q}$ or $qqq$) are of high invariant mass, too, and sequentially decay to the groundstate meson and baryon octets increasing the total entropy. When applying the PHSD approach to Pb+Pb colllisions at 158 A$\cdot$GeV we find a significant effect of the partonic phase on the production of multi-strange antibaryons due to a slightly enhanced $s{\bar s}$ pair production from massive time-like gluon decay and a larger formation of antibaryons in the hadronization process.Comment: 12 pages, 6 figures, to be published in the Proceedings of the 26th Winter Workshop on `Nuclear Dynamics', Ochto Rios, Jamaica, 2-9 January, 2010

Nucleon-Nucleon interaction, charge symmetry breaking and renormalization

We study the interplay between charge symmetry breaking and renormalization in the NN system for s-waves. We find a set of universality relations which disentangle explicitly the known long distance dynamics from low energy parameters and extend them to the Coulomb case. We analyze within such an approach the One-Boson-Exchange potential and the theoretical conditions which allow to relate the proton-neutron, proton-proton and neutron-neutron scattering observables without the introduction of extra new parameters and providing good phenomenological success.Comment: 15 pages, 6 figure

Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian

We present and apply a novel scheme for studying photon- and pion-nucleon scattering beyond the threshold region. Partial-wave amplitudes for the $\gamma\, N$ and $\pi N$ states are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. Based on the chiral Lagrangian we recover the empirical s- and p-wave amplitudes up to energies $\sqrt{s}\simeq 1300$ MeV in terms of the parameters relevant at order $Q^3$.Comment: 76 pages, 23 figures, one additional figure, Tables 4,5 and Figure 4 are corrected, a few references and comments are added. The role of higher partial waves in pion photoproduction is clarifie