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

Geographical Assessment of Microalgae Biofuels Potential Incorporating Resource Availability

Previous assessments of the economic feasibility and large-scale productivity of microalgae biofuels have not considered the impacts of land and carbon dioxide (CO2) availability on the scalability of microalgae-based biofuels production. To accurately assess the near-term productivity potential of large-scale microalgae biofuel in the US, a geographically realized growth model was used to simulate microalgae lipid yields based on meteorological data. The resulting lipid productivity potential of Nannochloropsis under large-scale cultivation is combined with land and CO2 resource availability illustrating current geographically feasible production sites and corresponding productivity in the US. Baseline results show that CO2 transport constraints will limit US microalgae based bio-oil production to 4% of the 2030 Department of Energy (DOE) alternative fuel goal. The discussion focuses on synthesis of this large-scale productivity potential results including a sensitivity analysis to land and CO2 resource assumptions, an evaluation of previous modeling efforts and their assumptions regarding the transportation of CO2, the feasibility of microalgae to meet DOE 2030 alternative fuel goals, and a comparison of the productivity potential in several key regions of the US

N-Body Simulations of Growth from 1 km Planetesimals at 0.4 AU

We present N-body simulations of planetary accretion beginning with 1 km radius planetesimals in orbit about a 1 solar mass star at 0.4 AU. The initial disk of planetesimals contains too many bodies for any current N-body code to integrate; therefore, we model a sample patch of the disk. Although this greatly reduces the number of bodies, we still track in excess of 10^5 particles. We consider three initial velocity distributions and monitor the growth of the planetesimals. The masses of some particles increase by more than a factor of 100. Additionally, the escape speed of the largest particle grows considerably faster than the velocity dispersion of the particles, suggesting impending runaway growth, although no particle grows large enough to detach itself from the power law size-frequency distribution. These results are in general agreement with previous statistical and analytical results. We compute rotation rates by assuming conservation of angular momentum around the center of mass at impact and that merged planetesimals relax to spherical shapes. At the end of our simulations, the majority of bodies that have undergone at least one merger are rotating faster than the breakup frequency. This implies that the assumption of completely inelastic collisions (perfect accretion), which is made in most simulations of planetary growth at sizes 1 km and above, is inappropriate. Our simulations reveal that, subsequent to the number of particles in the patch having been decreased by mergers to half its initial value, the presence of larger bodies in neighboring regions of the disk may limit the validity of simulations employing the patch approximation.Comment: 19 pages, 32 figures, 5 tables, accepted to Icaru

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