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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Tree-Based Methods And A Mixed Ridge Estimator For Analyzing Longitudinal Data With Correlated Predictors, Melissa Nicole Eliot
Tree-Based Methods And A Mixed Ridge Estimator For Analyzing Longitudinal Data With Correlated Predictors, Melissa Nicole Eliot
Open Access Dissertations
Due to recent advances in technology that facilitate acquisition of multi-parameter defined phenotypes, new opportunities have arisen for predicting patient outcomes based on individual specific cell subset changes. The data resulting from these trials can be a challenge to analyze, as predictors may be highly correlated with each other or related to outcome within levels of other predictor variables. As a result, applying traditional methods like simple linear models and univariate approaches such as odds ratios may be insufficient. In this dissertation, we describe potential solutions including tree-based methods, ridge regression, mixed modeling, and a new estimator called a mixed …
Spatial Evolutionary Game Theory: Deterministic Approximations, Decompositions, And Hierarchical Multi-Scale Models, Sung-Ha Hwang
Spatial Evolutionary Game Theory: Deterministic Approximations, Decompositions, And Hierarchical Multi-Scale Models, Sung-Ha Hwang
Open Access Dissertations
Evolutionary game theory has recently emerged as a key paradigm in various behavioral science disciplines. In particular it provides powerful tools and a conceptual framework for the analysis of the time evolution of strategic interdependence among players and its consequences, especially when the players are spatially distributed and linked in a complex social network. We develop various evolutionary game models, analyze these models using appropriate techniques, and study their applications to complex phenomena. In the second chapter, we derive integro-differential equations as deterministic approximations of the microscopic updating stochastic processes. These generalize the known mean-field ordinary differential equations and provide …
A Mathematical Growth Model Of The Viral Population In Early Hiv-1 Infections, Elena Edi Giorgi
A Mathematical Growth Model Of The Viral Population In Early Hiv-1 Infections, Elena Edi Giorgi
Open Access Dissertations
In this thesis we develop a mathematical model to describe HIV-1 evolution during the first stages of infection (approximately within 40-60 days since onset), when one can assume exponential growth and random accumulation of mutations under a neutral drift. We analyze the Hamming distance (HD) distribution under different models (synchronous and asynchronous) in the absence of selection and recombination. In the second part of the thesis, we introduce recombination and develop a combinatorial approach to estimate the new HD distribution. We conclude describing a T statistic to test significance differences between the HD of two genetic samples, which we derive …
Knot Contact Homology And Open Strings, Jason Frederick Mcgibbon
Knot Contact Homology And Open Strings, Jason Frederick Mcgibbon
Open Access Dissertations
In this thesis, we give a topological interpretation of knot contact homology, by considering intersections of a particular class of chains of open strings with the knot itself. In doing so, we provide evidence toward a differential graded algebra structure on the algebra generated by chains of open strings.
Statistical Methods For Nonlinear Dynamic Models With Measurement Error Using The Ricker Model, David Joseph Resendes
Statistical Methods For Nonlinear Dynamic Models With Measurement Error Using The Ricker Model, David Joseph Resendes
Open Access Dissertations
In ecological population management, years of animal counts are fit to nonlinear, dynamic models (e.g. the Ricker model) because the values of the parameters are of interest. The yearly counts are subject to measurement error, which inevitably leads to biased estimates and adversely affects inference if ignored. In the literature, often convenient distribution assumptions are imposed, readily available estimated measurement error variances are not utilized, or the measurement error is ignored entirely. In this thesis, ways to estimate the parameters of the Ricker model and perform inference while accounting for measurement error are investigated where distribution assumptions are minimized and …