Halo Star Streams in the Solar Neighborhood

We have assembled a sample of halo stars in the solar neighborhood to look for halo substructure in velocity and angular momentum space. Our sample includes red giants, RR Lyrae, and red horizontal branch stars within 2.5 kpc of the Sun with [Fe/H] less than -1.0. It was chosen to include stars with accurate distances, space velocities, and metallicities as well as well-quantified errors. We confirm the existence of the streams found by Helmi and coworkers, which we refer to as the H99 streams. These streams have a double-peaked velocity distribution in the z direction. We use the results of modeling of the H99 streams by Helmi and collaborators to test how one might use v_z velocity information and radial velocity information to detect kinematic substructure in the halo. We find that detecting the H99 streams with radial velocities alone would require a large sample. We use the velocity distribution of the H99 streams to estimate their age. From our model of the progenitor of the H99 streams, we determine that it was accreted between 6 and 9 Gyr ago. The H99 streams have [alpha/Fe] abundances similar to other halo stars in the solar neighborhood, suggesting that the gas that formed these stars were enriched mostly by Type II SNe. We have also discovered in angular momentum space two other possible substructures, which we refer to as the retrograde and prograde outliers. The retrograde outliers are likely to be halo substructure, but the prograde outliers are most likely part of the smooth halo. The retrograde outliers have significant structure in the v_phi direction and show a range of [alpha/Fe]. The methods presented in this paper can be used to exploit the kinematic information present in future large databases like RAVE, SDSSII/SEGUE, and Gaia.Comment: 46 pages, 13 figures, and 9 tables. Minor changes to text to match proofed version of the paper. Low resolution figures. High resolution version at http://www.astro.wisc.edu/~kepley/solar_streams.p

Asymptotic normality of the size of the giant component via a random walk

In this paper we give a simple new proof of a result of Pittel and Wormald concerning the asymptotic value and (suitably rescaled) limiting distribution of the number of vertices in the giant component of $G(n,p)$ above the scaling window of the phase transition. Nachmias and Peres used martingale arguments to study Karp's exploration process, obtaining a simple proof of a weak form of this result. We use slightly different martingale arguments to obtain a much sharper result with little extra work.Comment: 11 pages; slightly expanded, reference adde

On the non-Gaussian fluctuations of the giant cluster for percolation on random recursive trees

We consider a Bernoulli bond percolation on a random recursive tree of size $n\gg 1$, with supercritical parameter $p_n=1-c/\ln n$ for some $c>0$ fixed. It is known that with high probability, there exists then a unique giant cluster of size G_n\sim \e^{-c}, and it follows from a recent result of Schweinsberg \cite{Sch} that $G_n$ has non-gaussian fluctuations. We provide an explanation of this by analyzing the effect of percolation on different phases of the growth of recursive trees. This alternative approach may be useful for studying percolation on other classes of trees, such as for instance regular trees

The phase transition in the configuration model

Let $G=G(d)$ be a random graph with a given degree sequence $d$, such as a random $r$-regular graph where $r\ge 3$ is fixed and $n=|G|\to\infty$. We study the percolation phase transition on such graphs $G$, i.e., the emergence as $p$ increases of a unique giant component in the random subgraph $G[p]$ obtained by keeping edges independently with probability $p$. More generally, we study the emergence of a giant component in $G(d)$ itself as $d$ varies. We show that a single method can be used to prove very precise results below, inside and above the `scaling window' of the phase transition, matching many of the known results for the much simpler model $G(n,p)$. This method is a natural extension of that used by Bollobas and the author to study $G(n,p)$, itself based on work of Aldous and of Nachmias and Peres; the calculations are significantly more involved in the present setting.Comment: 37 page

Central limit theorems in the configuration model

We prove a general normal approximation theorem for local graph statistics in the configuration model, together with an explicit bound on the error in the approximation with respect to the Wasserstein metric. Such statistics take the form $T := \sum_{v \in V} H_v$, where $V$ is the vertex set, and $H_v$ depends on a neighbourhood in the graph around $v$ of size at most $\ell$. The error bound is expressed in terms of $\ell$, $|V|$, an almost sure bound on $H_v$, the maximum vertex degree $d_{\max}$ and the variance of $T$. Under suitable assumptions on the convergence of the empirical degree distributions to a limiting distribution, we deduce that the size of the giant component in the configuration model has asymptotically Gaussian fluctuations.Comment: minor change

Interplay between carotenoids, abscisic acid and jasmonate guides the compatible rice-Meloidogyne graminicola interaction

In this study, we have characterized the role of carotenoids and chlorophyll in the compatible interaction between the sedentary root knot nematode (RKN) Meloidogyne graminicola and the monocot model plant rice (Oryza sativa). Previous transcriptome data showed a differential expression of carotenoid and chlorophyll biosynthesis genes in nematode-induced giant cells and gall tissue. Metabolite measurement showed that galls indeed accumulate chlorophyll a, b and carotenoids, as well as the hormone abscisic acid (ABA). When ABA was externally applied on rice plants, or when ABA-biosynthesis was inhibited, a significant increase in gall formation and nematode development was found, showing the complex role of ABA in this interaction. ABA application suppressed jasmonic acid (JA) levels in the plants, while ABA-biosynthesis inhibition lead to increased JA levels confirming an antagonism between ABA and JA in rice roots. In addition, combined applications of ABA and JA showed that the ABA-effect can overcome JA-induced defense. Based on these observations, we hypothesized that the accumulation of chlorophyll and carotenoid precursors would be beneficial to nematode infection. Indeed, when chemically blocking the carotenoid biosynthesis pathway at different steps, which leads to differential accumulation of carotenoids and chlorophyll in the plants, a positive and clear link between accumulation of carotenoids and chlorophyll and rice susceptibility to RKN was detected