On the origins of approximations for stochastic chemical kinetics

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies

Stochastic simulation of catalytic surface reactions in the fast diffusion limit

The master equation of a lattice gas reaction tracks the probability of visiting all spatial configurations. The large number of unique spatial configurations on a lattice renders master equation simulations infeasible for even small lattices. In this work, a reduced master equation is derived for the probability distribution of the coverages in the infinite diffusion limit. This derivation justifies the widely used assumption that the adlayer is in equilibrium for the current coverages and temperature when all reactants are highly mobile. Given the reduced master equation, two novel and efficient simulation methods of lattice gas reactions in the infinite diffusion limit are derived. The first method involves solving the reduced master equation directly for small lattices, which is intractable in configuration space. The second method involves reducing the master equation further in the large lattice limit to a set of differential equations that tracks only the species coverages. Solution of the reduced master equation and differential equations requires information that can be obtained through short, diffusion-only kinetic Monte Carlo simulation runs at each coverage. These simulations need to be run only once because the data can be stored and used for simulations with any set of kinetic parameters, gas-phase concentrations, and initial conditions. An idealized CO oxidation reaction mechanism with strong lateral interactions is used as an example system for demonstrating the reduced master equation and deterministic simulation techniques

Two classes of quasi-steady-state model reductions for stochastic kinetics

The quasi-steady-state approximation (QSSA) is a model reduction technique used to remove highly reactive species from deterministic models of reaction mechanisms. In many reaction networks the highly reactive intermediates (QSSA species) have populations small enough to require a stochastic representation. In this work we apply singular perturbation analysis to remove the QSSA species from the chemical master equation for two classes of problems. The first class occurs in reaction networks where all the species have small populations and the QSSA species sample zero the majority of the time. The perturbation analysis provides a reduced master equation in which the highly reactive species can sample only zero, and are effectively removed from the model. The reduced master equation can be sampled with the Gillespie algorithm. This first stochastic QSSA reduction is applied to several example reaction mechanisms (including Michaelis-Menten kinetics) [Biochem. Z. 49, 333 (1913)]. A general framework for applying the first QSSA reduction technique to new reaction mechanisms is derived. The second class of QSSA model reductions is derived for reaction networks where non-QSSA species have large populations and QSSA species numbers are small and stochastic. We derive this second QSSA reduction from a combination of singular perturbation analysis and the Omega expansion. In some cases the reduced mechanisms and reaction rates from these two stochastic QSSA models and the classical deterministic QSSA reduction are equivalent; however, this is not usually the case

The stochastic quasi-steady-state assumption: Reducing the model but not the noise

Highly reactive species at small copy numbers play an important role in many biological reaction networks. We have described previously how these species can be removed from reaction networks using stochastic quasi-steady-state singular perturbation analysis (sQSPA). In this paper we apply sQSPA to three published biological models: the pap operon regulation, a biochemical oscillator, and an intracellular viral infection. These examples demonstrate three different potential benefits of sQSPA. First, rare state probabilities can be accurately estimated from simulation. Second, the method typically results in fewer and better scaled parameters that can be more readily estimated from experiments. Finally, the simulation time can be significantly reduced without sacrificing the accuracy of the solution

Mid-infrared selection of quasar-2s in Spitzer's First Look Survey

We present early results from the spectroscopic follow-up of a sample of candidate obscured AGN selected in the mid-infrared from the Spitzer First Look Survey. Our selection allows a direct comparison of the numbers of obscured and unobscured AGN at a given luminosity for the first time, and shows that the ratio of obscured to unobscured AGN at infrared luminosities corresponding to low luminosity quasars is ~1:1 at z~0.5. Most of our optically-faint candidate obscured AGN have the high-ionization, narrow-line spectra expected from type-2 AGN. A composite spectrum shows evidence for Balmer absorption lines, indicating recent star-formation activity in the host galaxies. There is tentative evidence for a decrease in the obscured AGN fraction with increasing AGN luminosity.Comment: To appear in the proceedings of the workshop "Multiband approach to AGN" Bonn October 2004 in Memorie della Societa Astronomica Italian

Near-Infrared Observations of Powerful High-Redshift Radio Galaxies: 4C 40.36 and 4C 39.37

We present near-infrared imaging and spectroscopic observations of two FR II high-redshift radio galaxies (HzRGs), 4C 40.36 (z=2.3) and 4C 39.37 (z=3.2), obtained with the Hubble, Keck, and Hale Telescopes. High resolution images were taken with filters both in and out of strong emission lines, and together with the spectroscopic data, the properties of the line and continuum emissions were carefully analyzed. Our analysis of 4C 40.36 and 4C 39.37 shows that strong emission lines (e.g., [O III] 5007 A and H alpha+[N II]) contribute to the broad-band fluxes much more significantly than previously estimated (80% vs. 20-40%), and that when the continuum sources are imaged through line-free filters, they show an extremely compact morphology with a high surface brightness. If we use the R^1/4-law parametrization, their effective radii (r(e)) are only 2-3 kpc while their restframe B-band surface brightnesses at r(e) are I(B) ~ 18 mag/arcsec^2. Compared with z ~ 1 3CR radio galaxies, the former is x3-5 smaller, while the latter is 1-1.5 mag brighter than what is predicted from the I(B)-r(e) correlation. Although exponential profiles produce equally good fits for 4C 40.36 and 4C 39.37, this clearly indicates that with respect to the z~1 3CR radio galaxies, the light distribution of these two HzRGs is much more centrally concentrated. Spectroscopically, 4C 40.36 shows a flat (fnu=const) continuum while 4C 39.37 shows a spectrum as red as that of a local giant elliptical galaxy. Although this difference may be explained in terms of a varying degree of star formation, the similarities of their surface brightness profiles and the submillimeter detection of 4C 39.37 might suggest that the intrinsic spectra is equally blue (young stars or an AGN), and that the difference is the amount of reddening.Comment: 30 pages, 6 tables, 10 figures; Accepted for publication in Astronomical Journa

NONLINEAR REGRESSION FOR SPLIT PLOT EXPERIMENTS

Split plot experimental designs are common in studies of the effects of air pollutants on crop yields. Nonlinear functions such the Weibull function have been used extensively to model the effect of ozone exposure on yield of several crop species. The usual nonlinear regression model, which assumes independent errors, is not appropriate for data from nested or split plot designs in which there is more than one source of random variation. The nonlinear model with variance components combines a nonlinear model for the mean with additive random effects to describe the covariance structure. We propose an estimated generalized least squares (EGLS) method of estimation for this model. The variance components are estimated two ways: by analysis of variance, and by an approximate MINQUE method. These methods are demonstrated and compared with results from ordinary nonlinear least squares for data from the National Crop Loss Assessment Network (NCLAN) program regarding the effects of ozone on soybeans. In this example all methods give similar point estimates of the parameters of the Weibull function. The advantage of estimated generalized least squares is that it produces proper estimates of the variances of the parameters and of estimated yields, which take the covariance structure into account. A computer program that fits the nonlinear model with variance components by the EGLS method is available from the authors

A Comparative Approach to the Study of Cumulative Cultural Evolution: Where Are We Now, and Where Do We Go?

Evidence for cumulative cultural evolution (CCE) in nonhumans remains rare. Here, we suggest that this results partly from methodological challenges involved in comparative CCE. We discuss two core challenges researchers in the field face: our samples and our protocols. In particular, we encourage more studies that examine diverse species, adopt naturalistic and fair measures, and consider the life stages of participants. Research of this kind is required to fully understand the uniqueness of human CCE

The Optical - Infrared Colors of CORALS QSOs: Searching for Dust Reddening Associated With High Redshift Damped Lyman Alpha Systems

The presence of dust in quasar absorbers, such as damped Lyman alpha (DLA) systems, may cause the background QSO to appear reddened. We investigate the extent of this potential reddening by comparing the optical-to-infrared (IR) colors of QSOs with and without intervening absorbers. Our QSO sample is based on the Complete Optical and Radio Absorption Line System (CORALS) survey of Ellison et al (2001). We have obtained near-simultaneous B and K band magnitudes for subset of the CORALS sample and supplemented our observations with further measurements published in the literature. To account for redshift-related color changes, the B-K colors are normalized using the Sloan Digital Sky Survey (SDSS) QSO composite. The mean normalized B-K color of the DLA sub-sample is +0.12, whereas the mean for the no-DLA sample is -0.10; both distributions have RMS scatters ~0.5. Neither a student's T-test nor a KS test indicate that there is any significant difference between the two color distributions. Based on simulations which redden the colors of QSOs with intervening DLAs, we determine a reddening limit which corresponds to E(B-V) < 0.04 (SMC-like extinction) at 99% confidence (3 sigma), assuming that E(B-V) is the same for all DLAs. Finally, we do not find any general correlation between absorber properties (such as [Fe/Zn] or neutral hydrogen column density) and B-K color. One of these two QSOs shows evidence for strong associated absorption from X-ray observations, an alternative explanation for its very red color. We conclude that the presence of intervening galaxies causes a minimal reddening of the background QSO.Comment: Accepted for publication in A