Browsing by Subject "model"
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Item Open Access Bias correction and Bayesian analysis of aggregate counts in SAGE libraries(2010) Zaretzki, Russell L; Gilchrist, Michael A; Briggs, William M; Armagan, ArtinBackground: Tag-based techniques, such as SAGE, are commonly used to sample the mRNA pool of an organism's transcriptome. Incomplete digestion during the tag formation process may allow for multiple tags to be generated from a given mRNA transcript. The probability of forming a tag varies with its relative location. As a result, the observed tag counts represent a biased sample of the actual transcript pool. In SAGE this bias can be avoided by ignoring all but the 3' most tag but will discard a large fraction of the observed data. Taking this bias into account should allow more of the available data to be used leading to increased statistical power. Results: Three new hierarchical models, which directly embed a model for the variation in tag formation probability, are proposed and their associated Bayesian inference algorithms are developed. These models may be applied to libraries at both the tag and aggregate level. Simulation experiments and analysis of real data are used to contrast the accuracy of the various methods. The consequences of tag formation bias are discussed in the context of testing differential expression. A description is given as to how these algorithms can be applied in that context. Conclusions: Several Bayesian inference algorithms that account for tag formation effects are compared with the DPB algorithm providing clear evidence of superior performance. The accuracy of inferences when using a particular non-informative prior is found to depend on the expression level of a given gene. The multivariate nature of the approach easily allows both univariate and joint tests of differential expression. Calculations demonstrate the potential for false positive and negative findings due to variation in tag formation probabilities across samples when testing for differential expression.Item Open Access Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans(2010) Dai, Shu; Schaeffer, David GInstabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria-Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3456058]Item Open Access Computational and Analytic Perspectives on the Drift Paradox(2010) Pasour, VB; Ellner, SPThe fact that many small aquatic and marine organisms manage to persist in their native environments in the presence of constant advection into unfavorable habitat is known as the "drift paradox." Although advection may determine large scale biological patterns, individual behavior such as predation or vertical/horizontal migration can dominate at smaller scales. Using both computational and analytical methods to model flow in an idealized channel, we explore the extent to which biological processes can counteract physical drivers. In particular, we investigate how different zooplankton migration behaviors affect biological retention time under a variety of flow regimes and whether a combination of physical/biological regimes exists that can resolve the drift paradox, i.e., allow the zooplankton to avoid washout for time periods much greater than the hydrologic retention time. The computational model is a three-dimensional semi-implicit hydrodynamic model which is coupled with an individual-based model for zooplankton behavior, while the analytical model is a simple partial differential equation containing both advective and behavioral components. The only behavior exhibited by the zooplankton is diel vertical migration. Our studies show that the interaction of zooplankton behavior and exchange flow can significantly influence zooplankton residence time. For a channel without vegetation, the analytical methods give biological residence times that vary by at most a day from the computational results.Item Open Access On Population Structure and Marriage Dynamics(2010) Giolito, EugenioI develop an equilibrium, a two-sided search model of marriage with endogenous population growth, to study the interaction between fertility, the age structure of the population and the age of men and women at first marriage. Within a simple two-period overlapping generation model, I show that given an increase of the desired number of children age at marriage is affected through two different channels. First, as population growth increases, the age structure of the population produces a thicker market for young people, inducing early marriages. The second channel comes from differential fecundity: if the desired number of children is not feasible for older women, women tend to marry younger and men older, with single men outnumbering single women in equilibrium. Using an extended version of the model to a finite number of periods and fertility data, I show that two mechanisms described above may have acted as persistence mechanisms after the U. S. Baby Boom. Specifically, I find that the demographic transitional dynamics after the Baby Boom may account for approximately 23 percent of the increase in men's age of marriage between 1985 and 2009, although the impact on women's age is small.