3,402 research outputs found
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 . 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
of the CTMC, its beginning and ending states, and the length of sampling
time . 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 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
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
Two-Particle Microrheology of quasi-2D Viscous Systems
We study the correlated motions of colloidal particles in a quasi-2D system
(Human Serum Albumin (HSA) protein molecules at an air-water interface) for
different surface viscosities . We observe a transition in the
behavior of the correlated motion, from 2-D interface dominated at high
to bulk fluid-dependent at low . The correlated motions
can be scaled onto a master curve which captures the features of this
transition. This master curve also characterizes the spatial dependence of the
flow field of a viscous interface in response to a force. From the flow field
and the correlated particle motions, we calculate a two-particle MSD (mean
square displacement) for direct comparison with rheological measurements.Comment: 4 pages, 4 figures, submitted to PR
The non-random clustering of non-synonymous substitutions and its relationship to evolutionary rate
<p>Abstract</p> <p>Background</p> <p>Protein sequences are subject to a mosaic of constraint. Changes to functional domains and buried residues, for example, are more apt to disrupt protein structure and function than are changes to residues participating in loops or exposed to solvent. Regions of constraint on the tertiary structure of a protein often result in loose segmentation of its primary structure into stretches of slowly- and rapidly-evolving amino acids. This clustering can be exploited, and existing methods have done so by relying on local sequence conservation as a signature of selection to help identify functionally important regions within proteins. We invert this paradigm by leveraging the regional nature of protein structure and function to both illuminate and make use of genome-wide patterns of local sequence conservation.</p> <p>Results</p> <p>Our hypothesis is that the regional nature of structural and functional constraints will assert a positive autocorrelation on the evolutionary rates of neighboring sites, which, in a pairwise comparison of orthologous proteins, will manifest itself as the clustering of non-synonymous changes across the amino acid sequence. We introduce a dispersion ratio statistic to test this and related hypotheses. Using genome-wide interspecific comparisons of orthologous protein pairs, we reveal a strong log-linear relationship between the degree of clustering and the intensity of constraint. We further demonstrate how this relationship varies with the evolutionary distance between the species being compared. We provide some evidence that proteins with a history of positive selection deviate from genome-wide trends.</p> <p>Conclusions</p> <p>We find a significant association between the evolutionary rate of a protein and the degree to which non-synonymous changes cluster along its primary sequence. We show that clustering is a non-redundant predictor of evolutionary rate, and we speculate that conflicting signals of clustering and constraint may be indicative of a historical period of relaxed selection.</p
Photometric Decomposition of Barred Galaxies
We present a non-parametric method for decomposition of the light of disk
galaxies into disk, bulge and bar components. We have developed and tested the
method on a sample of 68 disk galaxies for which we have acquired I-band
photometry. The separation of disk and bar light relies on the single
assumption that the bar is a straight feature with a different ellipticity and
position angle from that of the projected disk. We here present the basic
method, but recognise that it can be significantly refined. We identify bars in
only 47% of the more nearly face-on galaxies in our sample. The fraction of
light in the bar has a broad range from 1.3% to 40% of the total galaxy light.
If low-luminosity galaxies have more dominant halos, and if halos contribute to
bar stability, the luminosity functions of barred and unbarred galaxies should
differ markedly; while our sample is small, we find only a slight difference of
low significance.Comment: Accepted to appear in AJ, 36 pages, 9 figures, full on-line figures
available at http://www.physics.rutgers.edu/~sellwood/Reese.htm
A family-based probabilistic method for capturing de novo mutations from high-throughput short-read sequencing data
Recent advances in high-throughput DNA sequencing technologies and associated statistical analyses have enabled in-depth analysis of whole-genome sequences. As this technology is applied to a growing number of individual human genomes, entire families are now being sequenced. Information contained within the pedigree of a sequenced family can be leveraged when inferring the donors' genotypes. The presence of a de novo mutation within the pedigree is indicated by a violation of Mendelian inheritance laws. Here, we present a method for probabilistically inferring genotypes across a pedigree using high-throughput sequencing data and producing the posterior probability of de novo mutation at each genomic site examined. This framework can be used to disentangle the effects of germline and somatic mutational processes and to simultaneously estimate the effect of sequencing error and the initial genetic variation in the population from which the founders of the pedigree arise. This approach is examined in detail through simulations and areas for method improvement are noted. By applying this method to data from members of a well-defined nuclear family with accurate pedigree information, the stage is set to make the most direct estimates of the human mutation rate to date
Worry as a window into the lives of people who use injection drugs: a factor analysis approach
<p>Abstract</p> <p>Background</p> <p>The concept of risk dominates the HIV/AIDS literature pertaining to People Who Use Injection Drugs (PWUID). In contrast the associated concept of worry is infrequently applied, even though it can produce important perspectives of PWUID's lives. This study asked a sample (n = 105) of PWUID enrolled in a Victoria, British Columbia needle exchange program to evaluate their degree of worry about fourteen factors they may encounter in their daily lives.</p> <p>Methods</p> <p>Exploratory factor analysis was used to analyze their responses.</p> <p>Results</p> <p>Factor analysis delineated three factors: 1) overall personal security, 2) injection drug use-specific risks including overdosing and vein collapse and, 3) contracting infectious diseases associated with injection drug use (e.g. HIV/AIDS and hepatitis C).</p> <p>Conclusion</p> <p>PWUID in this study not only worry about HIV/AIDS but also about stressful factors in their daily life which have been linked to both increased HIV/AIDS risk behaviour and decreased anti-retroviral treatment adherence. The importance PWUID give to this broad range of worry/concerns emphasizes the need to place HIV/AIDS intervention, education, and treatment programs within a broader harm-reduction framework that incorporates their perspectives on both worry and risk.</p
- …