Stochastic methods for modeling hydrodynamics of dilute gases

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.Includes bibliographical references (leaf 18).When modeling small scale sub-micron gas flows, continuum methods, i.e. Navier Stokes equations, no longer apply. Molecular Dynamics (MD) approaches are then more appropriate. For dilute gases, where particles travel in straight lines for the overwhelming majority of the time, MD methods are inefficient compared to kinetic theory approaches because they require the explicit calculation of each particle's trajectory. An effective way to model the hydrodynamics of dilute gases is a stochastic particle method known as Direct Simulation Monte Carlo (DSMC). In DSMC the motion and collision of particles are decoupled to increase computational efficiency. The purpose of this thesis is to evaluate a variant of the DSMC algorithm, in which particles have discrete velocities. The most important modification to the DSMC algorithm is the treatment of collisions between particles with discrete velocities in a way which ensures strict conservation of momentum and energy. To achieve that an algorithm that finds all possible pairs of discrete post-collision velocities given a pair of discrete pre-collision velocities was developed and coded.(cont.) Two important discretization ingredients were introduced: the number of discrete velocities and the maximum discrete velocity allowed. A number of simulations were performed to compare the discrete DSMC (IDSMC) and the regular DSMC method. Our results show that the difference between the two methods is small when the allowed discrete velocity spectrum extends to high speeds. In this case the error is fairly insensitive to the number of discrete velocities used. On the other hand, when the maximum velocity allowed is small compared to the most probably particle speed (approximately equivalent to the speed of sound), large errors are observed (in our case up to 450% in the stress).by Tristan J. Hayeck.S.B

Development, Calibration, and Validation of a U.S. White Male Population-Based Simulation Model of Esophageal Adenocarcinoma

The incidence of esophageal adenocarcinoma (EAC) has risen rapidly in the U.S. and western world. The aim of the study was to begin the investigation of this rapid rise by developing, calibrating, and validating a mathematical disease simulation model of EAC using available epidemiologic data.The model represents the natural history of EAC, including the essential biologic health states from normal mucosa to detected cancer. Progression rates between health states were estimated via calibration, which identified distinct parameter sets producing model outputs that fit epidemiologic data; specifically, the prevalence of pre-cancerous lesions and EAC cancer incidence from the published literature and Surveillance, Epidemiology, and End Results (SEER) data. As an illustrative example of a clinical and policy application, the calibrated and validated model retrospectively analyzed the potential benefit of an aspirin chemoprevention program.Model outcomes approximated calibration targets; results of the model's fit and validation are presented. Approximately 7,000 cases of EAC could have been prevented over a 30-year period if all white males started aspirin chemoprevention at age 40 in 1965.The model serves as the foundation for future analyses to determine a cost-effective screening and management strategy to prevent EAC morbidity and mortality

The impact of patterns in linkage disequilibrium and sequencing quality on the imprint of balancing selection

Regions under balancing selection are characterized by dense polymorphisms and multiple persistent haplotypes, along with other sequence complexities. Successful identification of these patterns depends on both the statistical approach and the quality of sequencing. To address this challenge, at first, a new statistical method called LD-ABF was developed, employing efficient Bayesian techniques to effectively test for balancing selection. LD-ABF demonstrated the most robust detection of selection in a variety of simulation scenarios, compared against a range of existing tests/tools (Tajima\u27s D, HKA, Dng, BetaScan, and BalLerMix). Furthermore, the impact of the quality of sequencing on detection of balancing selection was explored, as well, using: (i) SNP genotyping and exome data, (ii) targeted high-resolution HLA genotyping (IHIW), and (iii) whole-genome long-read sequencing data (Pangenome). In the analysis of SNP genotyping and exome data, we identified known targets and 38 new selection signatures in genes not previously linked to balancing selection. To further investigate the impact of sequencing quality on detection of balancing selection, a detailed investigation of the MHC was performed with high-resolution HLA typing data. Higher quality sequencing revealed the HLA-DQ genes consistently demonstrated strong selection signatures otherwise not observed from the sparser SNP array and exome data. The HLA-DQ selection signature was also replicated in the Pangenome samples using considerably less samples but, with high-quality long-read sequence data. The improved statistical method, coupled with higher quality sequencing, leads to more consistent identification of selection and enhanced localization of variants under selection, particularly in complex regions

14 Schizophrenia Working Group of the Psychiatric Genomics Consortium, Discovery, Biology, and Risk of Inherited Variants in Breast Cancer (DRIVE) study

Polygenic risk scores have shown great promise in predicting complex disease risk and will become more accurate as training sample sizes increase. The standard approach for calculating risk scores involves linkage disequilibrium (LD)-based marker pruning and applying a p value threshold to association statistics, but this discards information and can reduce predictive accuracy. We introduce LDpred, a method that infers the posterior mean effect size of each marker by using a prior on effect sizes and LD information from an external reference panel. Theory and simulations show that LDpred outperforms the approach of pruning followed by thresholding, particularly at large sample sizes. Accordingly, predicted R 2 increased from 20.1% to 25.3% in a large schizophrenia dataset and from 9.8% to 12.0% in a large multiple sclerosis dataset. A similar relative improvement in accuracy was observed for three additional large disease datasets and for non-European schizophrenia samples. The advantage of LDpred over existing methods will grow as sample sizes increase

Mixed model with correction for case-control ascertainment increases association power

We introduce a liability-threshold mixed linear model (LTMLM) association statistic for case-control studies and show that it has a well-controlled false-positive rate and more power than existing mixed-model methods for diseases with low prevalence. Existing mixed-model methods suffer a loss in power under case-control ascertainment, but no solution has been proposed. Here, we solve this problem by using a chi(2) score statistic computed from posterior mean liabilities (PMLs) under the liability-threshold model. Each individual's PML is conditional not only on that individual's case-control status but also on every individual's case-control status and the genetic relationship matrix (GRM) obtained from the data. The PMLs are estimated with a multivariate Gibbs sampler; the liability-scale phenotypic covariance matrix is based on the GRM, and a heritability parameter is estimated via Haseman-Elston regression on case-control phenotypes and then transformed to the liability scale. In simulations of unrelated individuals, the LTMLM statistic was correctly calibrated and achieved higher power than existing mixed-model methods for diseases with low prevalence, and the magnitude of the improvement depended on sample size and severity of case-control ascertainment. In a Wellcome Trust Case Control Consortium 2 multiple sclerosis dataset with >10,000 samples, LTMLM was correctly calibrated and attained a 4.3% improvement (p = 0.005) in chi(2) statistics over existing mixed-model methods at 75 known associated SNPs, consistent with simulations. Larger increases in power are expected at larger sample sizes. In conclusion, case-control studies of diseases with low prevalence can achieve power higher than that in existing mixed-model methods

De Novo Mutation in an Enhancer of EBF3 in simplex autism

AbstractPrevious research in autism and other neurodevelopmental disorders (NDDs) has indicated an important contribution of de novo protein-coding variants within specific genes. The role of de novo noncoding variation has been observable as a general increase in genetic burden but has yet to be resolved to individual functional elements. In this study, we assessed whole-genome sequencing data in 2,671 families with autism, with a specific focus on de novo variation in enhancers with previously characterized in vivo activity. We identified three independent de novo mutations limited to individuals with autism in the enhancer hs737. These mutations result in similar phenotypic characteristics, affect enhancer activity in vitro, and preferentially occur in AAT motifs in the enhancer with predicted disruptions of transcription factor binding. We also find that hs737 is enriched for copy number variation in individuals with NDDs, is dosage sensitive in the human population, is brain-specific, and targets the NDD gene EBF3 that is genome-wide significant for protein coding de novo variants, demonstrating the importance of understanding all forms of variation in the genome.One Sentence SummaryWhole-genome sequencing in thousands of families reveals variants relevant to simplex autism in a brain enhancer of the well-established neurodevelopmental disorder gene EBF3