A Symplectic Integrator for Hill's Equations

Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This method is implemented in the parallel N-body code, PKDGRAV and tested on some simple orbits. The method demonstrates a lack of secular changes in orbital elements, making it a very useful technique for integrating Hill's equations over many dynamical times. Furthermore, the method allows for efficient collision searching using linear extrapolation of particle positions.Comment: 15 pages, 2 figures; minor revisions; accepted for publication in the Astronomical Journa

The (In)Stability of Planetary Systems

We present results of numerical simulations which examine the dynamical stability of known planetary systems, a star with two or more planets. First we vary the initial conditions of each system based on observational data. We then determine regions of phase space which produce stable planetary configurations. For each system we perform 1000 ~1 million year integrations. We examine upsilon And, HD83443, GJ876, HD82943, 47UMa, HD168443, and the solar system (SS). We find that the resonant systems, 2 planets in a first order mean motion resonance, (HD82943 and GJ876) have very narrow zones of stability. The interacting systems, not in first order resonance, but able to perturb each other (upsilon And, 47UMa, and SS) have broad regions of stability. The separated systems, 2 planets beyond 10:1 resonance, (we only examine HD83443 and HD168443) are fully stable. Furthermore we find that the best fits to the interacting and resonant systems place them very close to unstable regions. The boundary in phase space between stability and instability depends strongly on the eccentricities, and (if applicable) the proximity of the system to perfect resonance. In addition to million year integrations, we also examined stability on ~100 million year timescales. For each system we ran ~10 long term simulations, and find that the Keplerian fits to these systems all contain configurations which may be regular on this timescale.Comment: 37 pages, 49 figures, 13 tables, submitted to Ap

Differential proportionality - a normalization-free approach to differential gene expression

AbstractGene expression data, such as those generated by next generation sequencing technologies (RNA-seq), are of an inherently relative nature: the total number of sequenced reads has no biological meaning. This issue is most often addressed with various normalization techniques which all face the same problem: once information about the total mRNA content of the origin cells is lost, it cannot be recovered by mere technical means. Additional knowledge, in the form of an unchanged reference, is necessary; however, this reference can usually only be estimated. Here we propose a novel method where sample normalization is unnecessary, but important insights can be obtained nevertheless. Instead of trying to recover absolute abundances, our method is entirely based on ratios, so normalization factors cancel by default. Although the differential expression of individual genes cannot be recovered this way, the ratios themselves can be differentially expressed (even when their constituents are not). Yet, most current analyses are blind to these cases, while our approach reveals them directly. Specifically, we show how the differential expression of gene ratios can be formalized by decomposing log-ratio variance (LRV) and deriving intuitive statistics from it. Although small LRVs have been used to detect proportional genes in gene expression data before, we focus here on the change in proportionality factors between groups of samples (e.g. tissue-specific proportionality). For this, we propose a statistic that is equivalent to the squared t-statistic of one-way ANOVA, but for gene ratios. In doing so, we show how precision weights can be incorporated to account for the peculiarities of count data, and, moreover, how a moderated statistic can be derived in the same way as the one following from a hierarchical model for individual genes. We also discuss approaches to deal with zero counts, deriving an expression of our statistic that is able to incorporate them. In providing a detailed analysis of the connections between the differential expression of genes and the differential proportionality of pairs, we facilitate a clear interpretation of new concepts. The proposed framework is applied to a data set from GTEx consisting of 98 samples from the cerebellum and cortex, with selected examples shown. A computationally efficient implementation of the approach in R has been released as an addendum to the propr package.1</jats:p

Frequency and implications of HIV superinfection

HIV superinfection occurs when an individual with HIV is infected with a new distinct HIV viral strain. Superinfection has been reported throughout the world, and studies have recorded incidence rates of 0–7·7% per year. Use of next-generation sequencing has improved detection of superinfection, which can be transmitted by injecting drug use and sexual intercourse. Superinfection might have incidence rates comparable to those of initial HIV infection. Clinicians should encourage safe sexual and injecting drug use practices for HIV-infected patients because superinfection has detrimental effects on clinical outcomes and could pose a concern for large-scale antiretroviral treatment plans. The occurrence of superinfection has implications for vaccine research, since it seems initial HIV infection is not fully protective against a subsequent infection. Additional collaborative research could benefit care of patients and inform future vaccine design

Recovery from disturbance requires resynchronization of ecosystem nutrient cycles

Nitrogen (N) and phosphorus (P) are tightly cycled in most terrestrial ecosystems, with plant uptake more than 10 times higher than the rate of supply from deposition and weathering. This near-total dependence on recycled nutrients and the stoichiometric constraints on resource use by plants and microbes mean that the two cycles have to be synchronized such that the ratio of N:P in plant uptake, litterfall, and net mineralization are nearly the same. Disturbance can disrupt this synchronization if there is a disproportionate loss of one nutrient relative to the other. We model the resynchronization of N and P cycles following harvest of a northern hardwood forest. In our simulations, nutrient loss in the harvest is small relative to postharvest losses. The low N:P ratio of harvest residue results in a preferential release of P and retention of N. The P release is in excess of plant requirements and P is lost from the active ecosystem cycle through secondary mineral formation and leaching early in succession. Because external P inputs are small, the resynchronization of the N and P cycles later in succession is achieved by a commensurate loss of N. Through succession, the ecosystem undergoes alternating periods of N limitation, then P limitation, and eventually co-limitation as the two cycles resynchronize. However, our simulations indicate that the overall rate and extent of recovery is limited by P unless a mechanism exists either to prevent the P loss early in succession (e.g., P sequestration not stoichiometrically constrained by N) or to increase the P supply to the ecosystem later in succession (e.g., biologically enhanced weathering). Our model provides a heuristic perspective from which to assess the resynchronization among tightly cycled nutrients and the effect of that resynchronization on recovery of ecosystems from disturbance

Tidal stirring and the origin of dwarf spheroidals in the Local Group

N-Body/SPH simulations are used to study the evolution of dwarf irregular galaxies (dIrrs) entering the dark matter halo of the Milky Way or M31 on plunging orbits. We propose a new dynamical mechanism driving the evolution of gas rich, rotationally supported dIrrs, mostly found at the outskirts of the Local Group (LG), into gas free, pressure supported dwarf spheroidals (dSphs) or dwarf ellipticals (dEs), observed to cluster around the two giant spirals. The initial model galaxies are exponential disks embedded in massive dark matter halos and reproduce nearby dIrrs. Repeated tidal shocks at the pericenter of their orbit partially strip their halo and disk and trigger dynamical instabilities that dramatically reshape their stellar component. After only 2-3 orbits low surface brightness (LSB) dIrrs are transformed into dSphs, while high surface brightness (HSB) dIrrs evolve into dEs. This evolutionary mechanism naturally leads to the morphology-density relation observed for LG dwarfs. Dwarfs surrounded by very dense dark matter halos, like the archetypical dIrr GR8, are turned into Draco or Ursa Minor, the faintest and most dark matter dominated among LG dSphs. If disks include a gaseous component, this is both tidally stripped and consumed in periodic bursts of star formation. The resulting star formation histories are in good qualitative agreement with those derived using HST color-magnitude diagrams for local dSphs.Comment: 5 pages, 5 figures, to appear on ApJL. Simulation images and movies can be found at the Local Group web page at http://pcblu.uni.mi.astro.it/~lucio/LG/LG.htm