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

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 $\eta_{s}$. We observe a transition in the behavior of the correlated motion, from 2-D interface dominated at high $\eta_{s}$ to bulk fluid-dependent at low $\eta_{s}$. 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

Extracting Radiant Cooling From Building Exhaust Air Using the Maisotsenko Cycle Principle

Indirect evaporative cooling has exciting implications for air based thermal comfort. With recent advances in the research and commercialization of Maisotsenko Cycle (M-Cycle), or dew-point, evaporative cooling, thermodynamics can be fully leveraged to provide effectively free air cooling. However, few studies seek to generate cool surfaces by evaporation for radiant cooling. As a method to reduce building energy consumption, such an evapo-radiative system would maintain occupant thermal comfort at higher ventilation air temperatures and provide cooling at low cost. This study explores an analytical model for an M-Cycle evapo-radiative cooling system that derives a 1-D temperature profile throughout an experimental module and compares the outputs to experimental data to begin the model validation process