Space Representation of Stochastic Processes with Delay

We show that a time series $x_t$ evolving by a non-local update rule $x_t = f (x_{t-n},x_{t-k})$ with two different delays $k<n$ can be mapped onto a local process in two dimensions with special time-delayed boundary conditions provided that $n$ and $k$ are coprime. For certain stochastic update rules exhibiting a non-equilibrium phase transition this mapping implies that the critical behavior does not depend on the short delay $k$. In these cases, the autocorrelation function of the time series is related to the critical properties of directed percolation.Comment: 6 pages, 8 figure

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas, and the conserved threshold transfer process. It is believed that the transitions in these models belong to an autonomous universality class of nonequilibrium phase transitions, the so-called Manna class. Contrarily, the present numerical study of selected (1+1)-dimensional models in this class suggests that their critical behavior converges to directed percolation after very long time, questioning the existence of an independent Manna class.Comment: article (4 pages, 9 eps figures) + Supplement (8 pages, 9 eps figures); Phys. Rev. Lett. 201

Molecular Phylogenetics of Mole Crabs (Hippidae : Emerita)

Mole crabs of the genus Emerita (Family Hippidae) inhabit many of the temperate and tropical sandy beaches of the world. The nine described species of this genus are rarely sympatric, and most are endemic to broad biogeographic regions. The phylogenetic relationships among the species have not yet been investigated. Based on presumed morphological synapomorphics, it has been suggested that the species inhabiting the New World constitute a monophyletic group, as do the species inhabiting the Old World, The relationships within the New World species were previously studied using sequence data from Cytochrome Oxidase I and 16S rRNA mitochondrial genes; the results strongly suggested that one of the species, Emerita analoga, was very divergent from the other taxa examined. This observation prompted uncertainty about monophyly of the New World species. The goal of the present study was to elucidate the relationships among the species within the genus Emerita. Partial sequences for the mitochondrial COI and 16S rRNA genes for all nine species of the genus (and several outgroups) were examined. Phylogenetic analyses suggest that E. analoga is closer to the Old World taxa than to the other New World species; thus the New World Emerita species do not constitute a monophyletic group

On Matrix Product Ground States for Reaction-Diffusion Models

We discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a coagulation-decoagulation model explicit four-dimensional representations are given and exact expressions for various physical quantities are recovered. We also find the general structure of $n$-point correlation functions at the phase transition.Comment: LaTeX source, 7 pages, no figure

Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input

We investigate with the help of analytical and numerical methods the reaction A+A->A on a one-dimensional lattice opened at one end and with an input of particles at the other end. We show that if the diffusion rates to the left and to the right are equal, for large x, the particle concentration c(x) behaves like As/x (x measures the distance to the input end). If the diffusion rate in the direction pointing away from the source is larger than the one corresponding to the opposite direction the particle concentration behaves like Aa/sqrt(x). The constants As and Aa are independent of the input and the two coagulation rates. The universality of Aa comes as a surprise since in the asymmetric case the system has a massive spectrum.Comment: 27 pages, LaTeX, including three postscript figures, to appear in J. Stat. Phy

Correlated Initial Conditions in Directed Percolation

We investigate the influence of correlated initial conditions on the temporal evolution of a (d+1)-dimensional critical directed percolation process. Generating initial states with correlations ~r^(sigma-d) we observe that the density of active sites in Monte-Carlo simulations evolves as rho(t)~t^kappa. The exponent kappa depends continuously on sigma and varies in the range -beta/nu_{||}<=kappa<=eta. Our numerical results are confirmed by an exact field-theoretical renormalization group calculation.Comment: 10 pages, RevTeX, including 5 encapsulated postscript figure

Variation in levels of acceptance, developmental success, and abortion of Halyomorpha halys eggs by native North American parasitoids

Using native North American parasitoid species (Hymenoptera: Scelionidae) that often unsuccessfully attack the eggs of the invasive brown marmorated stink bug Halyomorpha halys (Hemiptera: Pentatomidae), we assessed variation in traits that may determine the parasitoids’ ability to adapt to the invasive host by either exploiting or avoiding H. halys eggs (acceptance, developmental success). We also assessed variation in the parasitoids’ ability to induce H. halys host egg abortion, which may contribute to biological control of H. halys in invaded areas. The first set of experiments evaluated intra- and interspecific variation using standardized laboratory tests with iso-female lines of Telenomus podisi and Trissolcus euschisti that included matching of detailed behavioural observations of acceptance with developmental outcomes. In a second set of experiments, we assessed how variation in developmental ability and abortion induction may affect levels of biological control by indigenous parasitoid species. We examined a broader sample of parasitoids that emerged from field collections of egg masses of an indigenous north American stink bug Podisus maculiventris in a region newly invaded by H. halys. Results from the first set of experiments showed high levels of acceptance of H. halys eggs among iso-female lines of parasitoids, but offspring development success was almost zero. H. halys egg abortion due to unsuccessful parasitism was often very low and varied among iso-female lines only for T. podisi. In the second set of experiments we never observed increases in abortion levels of Halyomorpha halys eggs above natural levels, even for the two species (T. euschisti and T. podisi) that were observed to oviposit in and abort H. halys eggs in the first set of experiments. We conclude that while there may be some variation in behavioural and physiological parameters mediating acceptance and abortion of H. halys eggs by native North American egg parasitoids, there does not appear to be significant variation in developmental success. Moreover, current biological control impact of H. halys eggs via host egg abortion is likely very low