Simulation from endpoint-conditioned, continuous-time Markov chains on a finite state space, with applications to molecular evolution

Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete and finite state space. Specifically, we consider the generation of sample paths, including intermediate states and times of transition, from a CTMC whose beginning and ending states are known across a time interval of length $T$. We first unify the literature through a discussion of the three predominant approaches: (1) modified rejection sampling, (2) direct sampling, and (3) uniformization. We then give analytical results for the complexity and efficiency of each method in terms of the instantaneous transition rate matrix $Q$ of the CTMC, its beginning and ending states, and the length of sampling time $T$. In doing so, we show that no method dominates the others across all model specifications, and we give explicit proof of which method prevails for any given $Q,T,$ and endpoints. Finally, we introduce and compare three applications of CTMCs to demonstrate the pitfalls of choosing an inefficient sampler.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS247 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nucleon-Nucleon Interactions from the Quark Model

We report on investigations of the applicability of non-relativistic constituent quark models to the low-energy nucleon-nucleon (NN) interaction. The major innovations of a resulting NN potential are the use of the $^3$P$_0$ decay model and quark model wave functions to derive nucleon-nucleon-meson form-factors, and the use of a colored spin-spin contact hyperfine interaction to model the repulsive core rather than the phenomenological treatment common in other NN potentials. We present the results of the model for experimental free NN scattering phase shifts, S-wave scattering lengths and effective ranges and deuteron properties. Plans for future study are discussed.Comment: 5 pages, 4 figures, 2 tables. To appear in Proceedings of XIII International Conference on Hadron Spectroscopy, November 29 - December 4, 2009, Florida State Universit

Pheromone-induced polarization is dependent on the Fus3p MAPK acting through the formin Bni1p

During mating, budding yeast cells reorient growth toward the highest concentration of pheromone. Bni1p, a formin homologue, is required for this polarized growth by facilitating cortical actin cable assembly. Fus3p, a pheromone-activated MAP kinase, is required for pheromone signaling and cell fusion. We show that Fus3p phosphorylates Bni1p in vitro, and phosphorylation of Bni1p in vivo during the pheromone response is dependent on Fus3p. fus3 mutants exhibited multiple phenotypes similar to bni1 mutants, including defects in actin and cell polarization, as well as Kar9p and cytoplasmic microtubule localization. Disruption of the interaction between Fus3p and the receptor-associated Gα subunit caused similar mutant phenotypes. After pheromone treatment, Bni1p-GFP and Spa2p failed to localize to the cortex of fus3 mutants, and cell wall growth became completely unpolarized. Bni1p overexpression suppressed the actin assembly, cell polarization, and cell fusion defects. These data suggest a model wherein activated Fus3p is recruited back to the cortex, where it activates Bni1p to promote polarization and cell fusion.</jats:p

Human impacts on soil carbon dynamics of deep-rooted Amazonian forests and effect of land use change on the carbon cycle in Amazon soils

The main objective of these NASA-funded projects is to improve our understanding of land-use impacts on soil carbon dynamics in the Amazon Basin. Soil contains approximately one half of tropical forest carbon stocks, yet the fate of this carbon following forest impoverishment is poorly studied. Our mechanistics approach draws on numerous techniques for measuring soil carbon outputs, inputs, and turnover time in the soils of adjacent forest and pasture ecosystems at our research site in Paragominas, state of Para, Brazil. We are scaling up from this site-specific work by analyzing Basin-wide patterns in rooting depth and rainfall seasonality, the two factors that we believe should explain much of the variation in tropical soil carbons dynamics. In this report, we summarize ongoing measurements at our Paragominas study site, progress in employing new field data to understand soil C dynamics, and some surprising results from our regional, scale-up work

Three-dimensional flows in slowly-varying planar geometries

We consider laminar flow in channels constrained geometrically to remain between two parallel planes; this geometry is typical of microchannels obtained with a single step by current microfabrication techniques. For pressure-driven Stokes flow in this geometry and assuming that the channel dimensions change slowly in the streamwise direction, we show that the velocity component perpendicular to the constraint plane cannot be zero unless the channel has both constant curvature and constant cross-sectional width. This result implies that it is, in principle, possible to design "planar mixers", i.e. passive mixers for channels that are constrained to lie in a flat layer using only streamwise variations of their in-plane dimensions. Numerical results are presented for the case of a channel with sinusoidally varying width

Sampling the Grains: Pollen Samples from Hummingbirds

Hummingbirds transmit pollen both actively and passively while feeding or moving through the landscape. They play a largely undocumented role in plant pollination on their breeding grounds. Many hummingbirds also migrate thousands of miles, potentially transporting pollen greater distances than other pollinators. To investigate the role of hummingbirds in both short- and long-distance pollen transfer, we collected pollen samples from the heads and bills of hummingbirds during migration and throughout the breeding season. We identified the pollen from 44 hummingbirds captured during the 2016 and 2017 field season in western Montana. We also solicited and analyzed 9 samples from southwestern Idaho. Pollen analysis revealed 18 different genera of pollen on sampled hummingbirds, including genera (e.g., Pinus, Larix) that passively broadcast pollen. We detected some pollen from plant species not locally available, suggesting that hummingbirds do transfer pollen long distances, and may serve as vectors for plant genetic diversity. Pollen grains differed in their anatomy and potential for adhesion to hummingbird feathers and bills, suggesting that some pollen is better suited for long-distance dispersal. We plan to continue collecting pollen samples from ours and other sites in the future. We also hope to perform experiments that investigate the role pollen morphology may play in adhesion longevity