Mathematics and Statisticshttp://hdl.handle.net/11122/9742019-07-20T21:10:30Z2019-07-20T21:10:30ZAn exploration of two infinite families of snarksVer Hoef, Landerhttp://hdl.handle.net/11122/105472019-07-08T11:04:32Z2019-05-01T00:00:00ZAn exploration of two infinite families of snarks
Ver Hoef, Lander
In this paper, we generalize a single example of a snark that admits a drawing with even rotational symmetry into two infinite families using a voltage graph construction techniques derived from cyclic Pseudo-Loupekine snarks. We expose an enforced chirality in coloring the underlying 5-pole that generated the known example, and use this fact to show that the infinite families are in fact snarks. We explore the construction of these families in terms of the blowup construction. We show that a graph in either family with rotational symmetry of order m has automorphism group of order m2m⁺¹. The oddness of graphs in both families is determined exactly, and shown to increase linearly with the order of rotational symmetry.
Thesis (M.S.) University of Alaska Fairbanks, 2019
2019-05-01T00:00:00ZOn the Klein-Gordon equation originating on a curve and applications to the tsunami run-up problemGaines, Jodyhttp://hdl.handle.net/11122/104902019-06-29T11:05:57Z2019-05-01T00:00:00ZOn the Klein-Gordon equation originating on a curve and applications to the tsunami run-up problem
Gaines, Jody
Our goal is to study the linear Klein-Gordon equation in matrix form, with initial conditions originating on a curve. This equation has applications to the Cross-Sectionally Averaged Shallow Water equations, i.e. a system of nonlinear partial differential equations used for modeling tsunami waves within narrow bays, because the general Carrier-Greenspan transform can turn the Cross-Sectionally Averaged Shallow Water equations (for shorelines of constant slope) into a particular form of the matrix Klein-Gordon equation. Thus the matrix Klein-Gordon equation governs the run-up of tsunami waves along shorelines of constant slope. If the narrow bay is U-shaped, the Cross-Sectionally Averaged Shallow Water equations have a known general solution via solving the transformed matrix Klein-Gordon equation. However, the initial conditions for our Klein-Gordon equation are given on a curve. Thus our goal is to solve the matrix Klein-Gordon equation with known conditions given along a curve. Therefore we present a method to extrapolate values on a line from conditions on a curve, via the Taylor formula. Finally, to apply our solution to the Cross-Sectionally Averaged Shallow Water equations, our numerical simulations demonstrate how Gaussian and N-wave profiles affect the run-up of tsunami waves within various U-shaped bays.
Thesis (M.S.) University of Alaska Fairbanks, 2019
2019-05-01T00:00:00ZSpecies network inference under the multispecies coalescent modelBaños Cervantes, Hector Danielhttp://hdl.handle.net/11122/104822019-06-29T11:05:53Z2019-05-01T00:00:00ZSpecies network inference under the multispecies coalescent model
Baños Cervantes, Hector Daniel
Species network inference is a challenging problem in phylogenetics. In this work, we present two results on this. The first shows that many topological features of a level-1 network are identifable under the network multispecies coalescent model (NMSC). Specifcally, we show that one can identify from gene tree frequencies the unrooted semidirected species network, after suppressing all cycles of size less than 4. The second presents the theory behind a new, statistically consistent, practical method for the inference of level-1 networks under the NMSC. The input for this algorithm is a collection of unrooted topological gene trees, and the output is an unrooted semidirected species network.
Thesis (Ph.D.) University of Alaska Fairbanks, 2019
2019-05-01T00:00:00ZTesting multispecies coalescent simulators with summary statisticsBaños Cervantes, Hector Danielhttp://hdl.handle.net/11122/101782019-05-24T11:05:20Z2018-12-01T00:00:00ZTesting multispecies coalescent simulators with summary statistics
Baños Cervantes, Hector Daniel
The Multispecies coalescent model (MSC) is increasingly used in phylogenetics to describe the formation of gene trees (depicting the direct ancestral relationships of sampled lineages) within species trees (depicting the branching of species from their common ancestor). A number of MSC simulators have been implemented, and these are often used to test inference methods built on the model. However, it is not clear from the literature that these simulators are always adequately tested. In this project, we formulated tools for testing these simulators and use them to show that of four well-known coalescent simulators, Mesquite, Hybrid-Lambda, SimPhy, and Phybase, only SimPhy performs correctly according to these tests.
Master's Project (M.S.) University of Alaska Fairbanks, 2018.
2018-12-01T00:00:00ZThe treatment of missing data on placement tools for predicting success in college algebra at the University of AlaskaCrawford, Alyssahttp://hdl.handle.net/11122/97622019-01-30T12:05:30Z2014-05-01T00:00:00ZThe treatment of missing data on placement tools for predicting success in college algebra at the University of Alaska
Crawford, Alyssa
This project investigated the statistical significance of baccalaureate student placement tools such as tests scores and completion of a developmental course on predicting success in a college level algebra course at the University of Alaska (UA). Students included in the study had attempted Math 107 at UA for the first time between fiscal years 2007 and 2012. The student placement information had a high percentage of missing data. A simulation study was conducted to choose the best missing data method between complete case deletion, and multiple imputation for the student data. After the missing data methods were applied, a logistic regression with fitted with explanatory variables consisting of tests scores, developmental course grade, age (category) of scores and grade, and interactions. The relevant tests were SAT math, ACT math, AccuPlacer college level math, and the relevant developmental course was Devm /Math 105. The response variable was success in passing Math 107 with grade of C or above on the first attempt. The simulation study showed that under a high percentage of missing data and correlation, multiple imputation implemented by the R package Multivariate Imputation by Chained Equations (MICE) produced the least biased estimators and better confidence interval coverage compared to complete cases deletion when data are missing at random (MAR) and missing not at random (MNAR). Results from multiple imputation method on the student data showed that Devm /Math 105 grade was a significant predictor of passing Math 107. The age of Devm /Math 105, age of tests, and test scores were not significant predictors of student success in Math 107. Future studies may consider modeling with ALEKS scores, and high school math course information.
Master's Project (M.S.) University of Alaska Fairbanks, 2014
2014-05-01T00:00:00ZAnalyzing tree distribution and abundance in Yukon-Charley Rivers National Preserve: developing geostatistical Bayesian models with count dataWinder, Samanthahttp://hdl.handle.net/11122/97352019-01-11T12:04:59Z2018-05-01T00:00:00ZAnalyzing tree distribution and abundance in Yukon-Charley Rivers National Preserve: developing geostatistical Bayesian models with count data
Winder, Samantha
Species distribution models (SDMs) describe the relationship between where a species occurs and underlying environmental conditions. For this project, I created SDMs for the five tree species that occur in Yukon-Charley Rivers National Preserve (YUCH) in order to gain insight into which environmental covariates are important for each species, and what effect each environmental condition has on that species' expected occurrence or abundance. I discuss some of the issues involved in creating SDMs, including whether or not to incorporate spatially explicit error terms, and if so, how to do so with generalized linear models (GLMs, which have discrete responses). I ran a total of 10 distinct geostatistical SDMs using Markov Chain Monte Carlo (Bayesian methods), and discuss the results here. I also compare these results from YUCH with results from a similar analysis conducted in Denali National Park and Preserve (DNPP).
Master's Project (M.S.) University of Alaska Fairbanks, 2018
2018-05-01T00:00:00ZToward an optimal solver for the obstacle problemHeldman, Maxhttp://hdl.handle.net/11122/97272019-01-10T12:04:47Z2018-04-01T00:00:00ZToward an optimal solver for the obstacle problem
Heldman, Max
An optimal algorithm for solving a problem with m degrees of freedom is one that computes a solution in O (m) time. In this paper, we discuss a class of optimal algorithms for the numerical solution of PDEs called multigrid methods. We go on to examine numerical solvers for the obstacle problem, a constrained PDE, with the goal of demonstrating optimality. We discuss two known algorithms, the so-called reduced space method (RSP) [BM03] and the multigrid-based projected full-approximation scheme (PFAS) [BC83]. We compare the performance of PFAS and RSP on a few example problems, finding numerical evidence of optimality or near-optimality for PFAS.
Master's Project (M.S.) University of Alaska Fairbanks, 2018
2018-04-01T00:00:00ZReliability analysis of reconstructing phylogenies under long branch attraction conditionsDissanayake, Ranjanhttp://hdl.handle.net/11122/97262019-01-10T12:04:42Z2018-05-01T00:00:00ZReliability analysis of reconstructing phylogenies under long branch attraction conditions
Dissanayake, Ranjan
In this simulation study we examined the reliability of three phylogenetic reconstruction techniques in a long branch attraction (LBA) situation: Maximum Parsimony (M P), Neighbor Joining (NJ), and Maximum Likelihood. Data were simulated under five DNA substitution models-JC, K2P, F81, HKY, and G T R-from four different taxa. Two branch length parameters of four taxon trees ranging from 0.05 to 0.75 with an increment of 0.02 were used to simulate DNA data under each model. For each model we simulated DNA sequences with 100, 250, 500 and 1000 sites with 100 replicates. When we have enough data the maximum likelihood technique is the most reliable of the three methods examined in this study for reconstructing phylogenies under LBA conditions. We also find that MP is the most sensitive to LBA conditions and that Neighbor Joining performs well under LBA conditions compared to MP.
Master's Project (M.S.) University of Alaska Fairbanks, 2018.
2018-05-01T00:00:00ZStreetlight HalosTape, Walterhttp://hdl.handle.net/11122/97052018-12-11T12:05:15Z2010-01-01T00:00:00ZStreetlight Halos
Tape, Walter
The book treats streetlight halos, that is, atmospheric halos whose light source is nearby, rather than being the sun. Also see the elegant simulations of streetlight halos by Nicolas Lefaudeux at
http://opticsaround.blogspot.com/2013/07/la-simulation-des-halos-divergent.html
2010-01-01T00:00:00ZThe linear algebra of interpolation with finite applications giving computational methods for multivariate polynomialsOlmsted, Coert D.http://hdl.handle.net/11122/93432018-08-08T11:07:55Z1988-01-01T00:00:00ZThe linear algebra of interpolation with finite applications giving computational methods for multivariate polynomials
Olmsted, Coert D.
Linear representation and the duality of the biorthonormality relationship express the linear algebra of interpolation by way of the evaluation mapping. In the finite case the standard bases relate the maps to Gramian matrices. Five equivalent conditions on these objects are found which characterize the solution of the interpolation problem. This algebra succinctly describes the solution space of ordinary linear initial value problems. Multivariate polynomial spaces and multidimensional node sets are described by multi-index sets. Geometric considerations of normalization and dimensionality lead to cardinal bases for Lagrange interpolation on regular node sets. More general Hermite functional sets can also be solved by generalized Newton methods using geometry and multi-indices. Extended to countably infinite spaces, the method calls upon theorems of modern analysis.
Thesis (Ph.D.) University of Alaska Fairbanks, 1988
1988-01-01T00:00:00Z