You searched for +publisher:"University of Colorado" +contributor:("Jem Corcoran").
Showing records 1 – 29 of
29 total matches.
University of Colorado
1.
Woytarowicz, Nicole.
Discretizing Continuous Attributes of a Bayesian Network With a Birth and Death Process Based on Minimum Description Length.
Degree: MS, Applied Mathematics, 2018, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/98 
► A Bayesian network is a graphical model that can be used to represent potentially complex relationships between a large number of random variables. Given…
(more)
▼ A Bayesian network is a graphical model that can be used to represent potentially complex relationships between a large number of random variables. Given data consisting of realizations of the nodes (variables) of a network with unknown structure, much work has been done in recent years to recover the directed edges that describe the joint behavior of the nodes. The underlying assumption for such recovery algorithms is that the data are either from discrete or Gaussian distributions. In the event that neither hold, structure recovery algorithms are usually run after a discretization of the data. Unfortunately, if the discretization is not performed in a thoughtful way, the very structure that one is trying to recover may be obscured.
In this thesis, we extend the work of Friedman and Goldszmidt [Proceedings of the Thirteenth International Conference on Machine Learning, pp. 157–165, (1996)] where a principled approach was developed based on the idea of minimum description length. Although their approach gives a scoring mechanism that appears to be able to recover a good discretization, actually finding high-scoring discretizations is difficult due to the large number of possibilities that need to be checked. We propose and implement a Monte Carlo search procedure based on a birth-and-death process to maximize discretization score. This allows for different discretization thresholds to be inserted into and removed from the data, creating a random walk around the ``discretization space" in a way that ensures visitation to high-scoring discretizations.
Advisors/Committee Members: Jem Corcoran.
Subjects/Keywords: bayesian networks; birth and death process; Applied Statistics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Woytarowicz, N. (2018). Discretizing Continuous Attributes of a Bayesian Network With a Birth and Death Process Based on Minimum Description Length. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/98
Chicago Manual of Style (16th Edition):
Woytarowicz, Nicole. “Discretizing Continuous Attributes of a Bayesian Network With a Birth and Death Process Based on Minimum Description Length.” 2018. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/98.
MLA Handbook (7th Edition):
Woytarowicz, Nicole. “Discretizing Continuous Attributes of a Bayesian Network With a Birth and Death Process Based on Minimum Description Length.” 2018. Web. 25 Jan 2021.
Vancouver:
Woytarowicz N. Discretizing Continuous Attributes of a Bayesian Network With a Birth and Death Process Based on Minimum Description Length. [Internet] [Masters thesis]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/98.
Council of Science Editors:
Woytarowicz N. Discretizing Continuous Attributes of a Bayesian Network With a Birth and Death Process Based on Minimum Description Length. [Masters Thesis]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/98
University of Colorado
2.
Sidrow, Evan.
Network Structure Sampling in Bayesian Networks via Perfect Sampling from Linear Extensions.
Degree: MS, Applied Mathematics, 2018, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/98
► Bayesian networks are widely considered as powerful tools for modeling risk assessment, uncertainty, and decision making. They have been extensively employed to develop decision…
(more)
▼ Bayesian networks are widely considered as powerful tools for modeling risk assessment, uncertainty, and decision making. They have been extensively employed to develop decision support systems in a variety of domains including medical diagnosis, risk assessment and management, human cognition, industrial process and procurement, pavement and bridge management, and system reliability. Bayesian networks are convenient graphical expressions for high dimensional probability distributions which are used to represent complex relationships between a large number of random variables. A Bayesian network is a directed acyclic graph consisting of nodes which represent random variables and arrows which correspond to probabilistic dependencies between them. The ability to recover Bayesian network structures from data is critical to enhance their application in modeling real-world phenomena.
Many research efforts have been done on this topic to identify the specific network structure. Friedman and Koller suggest an approach based on the assumption that every Bayesian network has a corresponding ordering of its vertices. An order associated with a Bayesian network can be thought of as a logical ordering of causality, with random variables earlier in the order causing random variables later in the order.
The Friedman and Koller (FK) algorithm itself is comprised of two steps: (1) Use Markov Chain Monte Carlo (MCMC) methods to sample the order of a Bayesian network and then (2) sample the parent set for each vertex independently using Bayesian methods. However, since some Bayesian networks are compatible with more orders than others, the FK algorithm is biased towards these networks. The algorithm presented in this thesis corrects this bias while adding minimal algorithmic complexity to the FK algorithm by uniformly drawing linear extensions of the partial ordering of vertices implied by any Bayesian network.
Advisors/Committee Members: Jem Corcoran.
Subjects/Keywords: Bayesian Networks; Partially Ordered Sets; Perfect Simulation; Directed Acyclic Graphs; Applied Statistics; Probability
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Sidrow, E. (2018). Network Structure Sampling in Bayesian Networks via Perfect Sampling from Linear Extensions. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/98
Chicago Manual of Style (16th Edition):
Sidrow, Evan. “Network Structure Sampling in Bayesian Networks via Perfect Sampling from Linear Extensions.” 2018. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/98.
MLA Handbook (7th Edition):
Sidrow, Evan. “Network Structure Sampling in Bayesian Networks via Perfect Sampling from Linear Extensions.” 2018. Web. 25 Jan 2021.
Vancouver:
Sidrow E. Network Structure Sampling in Bayesian Networks via Perfect Sampling from Linear Extensions. [Internet] [Masters thesis]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/98.
Council of Science Editors:
Sidrow E. Network Structure Sampling in Bayesian Networks via Perfect Sampling from Linear Extensions. [Masters Thesis]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/98
University of Colorado
3.
Kazakov, Denis.
State Denoised Recurrent Neural Networks.
Degree: MS, 2018, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/112
► We investigate the use of attractor neural networks for denoising the internal states of another neural network, thereby boosting its generalization performance. Denoising is most…
(more)
▼ We investigate the use of attractor neural networks for denoising the internal states of another neural network, thereby boosting its generalization performance. Denoising is most promising for recurrent sequence-processing networks (i.e. recurrent neural networks), in which noise can accumulate in the hidden states over the elements of a sequence. We call our architecture <i>state- denoised recurrent neural network</i> (SD-RNN). We conduct a series of experiments to demonstrate the benefit of internal denoising, from small experiments like detecting parity of a binary sequence to larger natural language processing data sets. We characterize the behavior of the network using an information theoretic analysis, and we show that internal denoising causes the network to learn better on less data.
Advisors/Committee Members: Michael C. Mozer, Jem Corcoran, Stephen Becker.
Subjects/Keywords: recurrent sequence-processing; denoising; information theoretic analysis; binary sequence; behavior; Applied Mathematics; Computer Sciences
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kazakov, D. (2018). State Denoised Recurrent Neural Networks. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/112
Chicago Manual of Style (16th Edition):
Kazakov, Denis. “State Denoised Recurrent Neural Networks.” 2018. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/112.
MLA Handbook (7th Edition):
Kazakov, Denis. “State Denoised Recurrent Neural Networks.” 2018. Web. 25 Jan 2021.
Vancouver:
Kazakov D. State Denoised Recurrent Neural Networks. [Internet] [Masters thesis]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/112.
Council of Science Editors:
Kazakov D. State Denoised Recurrent Neural Networks. [Masters Thesis]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/112
University of Colorado
4.
Char, Ian Guo-fan.
Algorithmic Construction and Stochastic Analysis of Optimal Automata for Generalized Strings.
Degree: MS, 2018, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/115
► In many applications, the need arises to search a text for appearances of a given set of keywords. As an example, in bioinformatics one…
(more)
▼ In many applications, the need arises to search a text for appearances of a given set of keywords. As an example, in bioinformatics one may wish to search a DNA sequence to find so-called <i>biological motifs</i>. A standard approach to this problem is to leverage a <i>deterministic finite automaton</i> – a graph structure which is traversed as letters of the text are read in. However, depending on the number and length of the keywords being sought in the text, the graph may be too large to fit in computer memory, making this approach fruitless. In this thesis, we first present a novel algorithm that, under the assumption that the keywords take the form of a so-called <i>generalized string</i>, constructs the minimal DFA recognizing those keywords. Importantly, the algorithm is iterative and allows one to build the automaton directly, without any use of buffer memory. Not only does this mean that the algorithm is efficient regarding memory consumption, but it also provides useful insight to help facilitate analysis for the size of such DFA. Using this new algorithm and pairing it with the assumption that the generalized strings are drawn at random from some class of probability distributions, we develop bounds on the size of the minimal automaton that are true with high probability. Furthermore, using synthetic data, we provide evidence that the size of the minimal automaton grows linearly in expectation for many cases.
Advisors/Committee Members: Manuel E. Lladser, Jem Corcoran, Anne Dougherty.
Subjects/Keywords: aho-corasick automaton; biological motifs; deterministic finite automata; generalized strings; stochastic analysis; Applied Mathematics; Computer Sciences
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Char, I. G. (2018). Algorithmic Construction and Stochastic Analysis of Optimal Automata for Generalized Strings. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/115
Chicago Manual of Style (16th Edition):
Char, Ian Guo-fan. “Algorithmic Construction and Stochastic Analysis of Optimal Automata for Generalized Strings.” 2018. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/115.
MLA Handbook (7th Edition):
Char, Ian Guo-fan. “Algorithmic Construction and Stochastic Analysis of Optimal Automata for Generalized Strings.” 2018. Web. 25 Jan 2021.
Vancouver:
Char IG. Algorithmic Construction and Stochastic Analysis of Optimal Automata for Generalized Strings. [Internet] [Masters thesis]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/115.
Council of Science Editors:
Char IG. Algorithmic Construction and Stochastic Analysis of Optimal Automata for Generalized Strings. [Masters Thesis]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/115
University of Colorado
5.
Border, Richard.
Stochastic Lanczos Likelihood Estimation of Genomic Variance Components.
Degree: MS, Applied Mathematics, 2018, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/120
► Genomic variance components analysis seeks to estimate the extent to which interindividual variation in a given trait can be attributed to genetic similarity. Likelihood…
(more)
▼ Genomic variance components analysis seeks to estimate the extent to which interindividual variation in a given trait can be attributed to genetic similarity. Likelihood estimation of such models involves computationally expensive operations on large, dense, and unstructured matrices of high rank. As a result, standard estimation procedures relying on direct matrix methods become prohibitively expensive as sample sizes increase. We propose a novel estimation procedure that uses the Lanczos process and stochastic Lanczos quadrature to approximate the likelihood for an initial choice of parameter values. Then, by identifying the variance components parameter space with a family of shifted linear systems, we are able to exploit the Krylov subspace shift-invariance property to efficiently compute the likelihood for all additional parameter values of interest in linear time. Numerical experiments using simulated data demonstrate increased performance relative to conventional methods with little loss of accuracy.
Advisors/Committee Members: Stephen Becker, Jem Corcoran, Matthew Keller.
Subjects/Keywords: variance components; likelihood estimation; numerical linear algebra; krylov subspaces; genomics; Biostatistics; Numerical Analysis and Computation
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Border, R. (2018). Stochastic Lanczos Likelihood Estimation of Genomic Variance Components. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/120
Chicago Manual of Style (16th Edition):
Border, Richard. “Stochastic Lanczos Likelihood Estimation of Genomic Variance Components.” 2018. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/120.
MLA Handbook (7th Edition):
Border, Richard. “Stochastic Lanczos Likelihood Estimation of Genomic Variance Components.” 2018. Web. 25 Jan 2021.
Vancouver:
Border R. Stochastic Lanczos Likelihood Estimation of Genomic Variance Components. [Internet] [Masters thesis]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/120.
Council of Science Editors:
Border R. Stochastic Lanczos Likelihood Estimation of Genomic Variance Components. [Masters Thesis]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/120
University of Colorado
6.
Lee, Kwan Ho.
Simulation of Nonstationary Gaussian Process by Consecutive Conditioning.
Degree: MS, 2018, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/136
► This thesis aims to develop the method of consecutive conditioning, which is used to directly simulate a stochastic process given an arbitrary covariance function.…
(more)
▼ This thesis aims to develop the method of consecutive conditioning, which is used to directly simulate a stochastic process given an arbitrary covariance function. As a method for simulating stochastic processes, consecutive conditioning is useful in at least in three respects. While most methods require modeling of the covariance function prior to simulation, consecutive conditioning can be used with any arbitrary covariance function, thus introducing less error into the simulation than other methods. Second, consecutive conditioning allows us to perform very fast computations during simulation and can be used even by people who are not experts in modeling, unlike other methods which require substantial statistical work prior to simulation. Finally, this method can be used to simulate both stationary and nonstationary processes, which is particularly useful since the majority of real-world physical processes are nonstationary. With the Kullback-Leibler divergence in hand, we validate the consecutive conditioning method as follows. After executing our method on a simulated distribution, we compare the resulting distribution with the true distribution for calculating the KL values. Then, we demonstrate that the consecutive conditioning works well on different covariance functions by applying it to a different series of simulations. First, we use a consecutive conditioning with several different covariance functions to simulate two time points of a stochastic process, then compare the results to determine the best covariance function for our method. Finally, we use our method to generate five time points from a stochastic process in both uninitialized and initialized cases, then evaluate the results.
Advisors/Committee Members: William Kleiber, Jem Corcoran, Brian Zaharatos.
Subjects/Keywords: conditional simulatioin; kriging; nonstationary; covariance function; physical processes; Applied Mathematics; Physical Processes
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Lee, K. H. (2018). Simulation of Nonstationary Gaussian Process by Consecutive Conditioning. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/136
Chicago Manual of Style (16th Edition):
Lee, Kwan Ho. “Simulation of Nonstationary Gaussian Process by Consecutive Conditioning.” 2018. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/136.
MLA Handbook (7th Edition):
Lee, Kwan Ho. “Simulation of Nonstationary Gaussian Process by Consecutive Conditioning.” 2018. Web. 25 Jan 2021.
Vancouver:
Lee KH. Simulation of Nonstationary Gaussian Process by Consecutive Conditioning. [Internet] [Masters thesis]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/136.
Council of Science Editors:
Lee KH. Simulation of Nonstationary Gaussian Process by Consecutive Conditioning. [Masters Thesis]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/136
University of Colorado
7.
Lewis, Owen Ardron.
A Review of Mathematical Techniques in Machine Learning.
Degree: MS, Applied Mathematics, 2010, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/7
► As machine learning has developed, its methodologies have become increasingly mathematically sophisticated. For example, sampling and variational methods that were originally developed for application…
(more)
▼ As machine learning has developed, its methodologies have become increasingly mathematically sophisticated. For example, sampling and variational methods that were originally developed for application to mathematically diffcult problems in statistical mechanics are now commonplace in machine learning. Similarly, machine learning has co-opted many ideas from statistics, such as nonparametric Bayesian methods like Gaussian processes, Dirichlet processes, and completely random measures. In addition, graphical models and their associated inference techniques have emerged as a very important tool in a wide variety contexts. There are also interesting ideas that originated in machine learning rather than coming from other fields, ideas such as the kernelization of linear algorithms, and ideas in reinforcement and hierarchical reinforcement learning. This thesis reviews machine learning techniques of the types mentioned above that are of particular mathematical interest.
Advisors/Committee Members: Michael Mozer, Jem Corcoran, Matthew Jones.
Subjects/Keywords: machine learning techniques; Applied Mathematics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Lewis, O. A. (2010). A Review of Mathematical Techniques in Machine Learning. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/7
Chicago Manual of Style (16th Edition):
Lewis, Owen Ardron. “A Review of Mathematical Techniques in Machine Learning.” 2010. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/7.
MLA Handbook (7th Edition):
Lewis, Owen Ardron. “A Review of Mathematical Techniques in Machine Learning.” 2010. Web. 25 Jan 2021.
Vancouver:
Lewis OA. A Review of Mathematical Techniques in Machine Learning. [Internet] [Masters thesis]. University of Colorado; 2010. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/7.
Council of Science Editors:
Lewis OA. A Review of Mathematical Techniques in Machine Learning. [Masters Thesis]. University of Colorado; 2010. Available from: https://scholar.colorado.edu/appm_gradetds/7
University of Colorado
8.
Carpenter, Marshall.
Statistical Properties of Avalanches on Complex Networks.
Degree: MS, Applied Mathematics, 2012, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/25
► We characterize the distribution of sizes and durations of avalanches propagating in complex networks. We find that the statistics of avalanches can be characterized…
(more)
▼ We characterize the distribution of sizes and durations of avalanches propagating in complex networks. We find that the statistics of avalanches can be characterized in terms of the Perron-Frobenius eigenvalue and eigenvectors of an appropriate adjacency matrix which encodes the structure of the network. By using mean-field analyses, previous studies of avalanches in networks have not considered the effect of network structure on the distribution of size and duration of avalanches in all cases. Our results are specific to individual networks and allow us to find expressions for the distribution of size and duration of avalanches starting at particular nodes. These findings apply more broadly to branching processes in networks such as cascading power grid failures and critical brain dynamics. In particular, our results show that some experimental signatures of critical brain dynamics (i.e., power-law distributions of neuronal avalanches sizes and durations), are robust to complex underlying network topologies. We model avalanches in complex networks by considering a collection of connected nodes where the connection strength between two nodes determines the probability that an excitation is passed from one node to the next. Networks of size N can be identified with a N x N adjacency matrix where the ijth entry represents the connection strength from node i to node j. Networks are separated into three classes: subcritical, critical, and supercritical based on the largest eigenvalue of the adjacency matrix. We are able to determine the distribution for avalanche size and duration for each type of network.
Advisors/Committee Members: Juan G. Restrepo, Jem Corcoran, Anne Dougherty.
Subjects/Keywords: Adjacency Matrix; Avalanches; Degree Distribution; Networks; Perron-Frobenius; Power-law; Mathematics; Neurosciences
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Carpenter, M. (2012). Statistical Properties of Avalanches on Complex Networks. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/25
Chicago Manual of Style (16th Edition):
Carpenter, Marshall. “Statistical Properties of Avalanches on Complex Networks.” 2012. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/25.
MLA Handbook (7th Edition):
Carpenter, Marshall. “Statistical Properties of Avalanches on Complex Networks.” 2012. Web. 25 Jan 2021.
Vancouver:
Carpenter M. Statistical Properties of Avalanches on Complex Networks. [Internet] [Masters thesis]. University of Colorado; 2012. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/25.
Council of Science Editors:
Carpenter M. Statistical Properties of Avalanches on Complex Networks. [Masters Thesis]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/appm_gradetds/25
University of Colorado
9.
Hampton, Jerrad Davis.
Dissimilarity and Optimal Sampling in Urn Ensembles.
Degree: PhD, Applied Mathematics, 2012, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/27
► We study an ensemble of urns with unknown compositions inferred from initial samples with replacement from each urn. This model fits diverse situations. For…
(more)
▼ We study an ensemble of urns with unknown compositions inferred from initial samples with replacement from each urn. This model fits diverse situations. For instance, in microbial ecology studies each urn represents an environment, each ball within an urn corresponds to an individual bacterium, and a ball's color represents its taxonomic label. In a different context, each urn could represent a random RNA pool and each colored ball a possible solution to a particular binding site problem over that pool. The main parameter of this study is dissimilarity, which we define as the probability that a draw from one urn is not seen in a sample of size k from a possibly different urn. We estimate this parameter with a U-statistic, shown to be the uniformly minimum variance unbiased estimator (UMVUE) of dissimilarity over a range for k determined by initial sample sizes. Furthermore, despite the non-Markovian nature of our estimator when applied sequentially over k, we provide conditions that guarantee uniformly consistent estimates of variances via a jackknife method, and show uniform convergence in probability as well as approximately normal marginal distributions. We apply our U-statistics and a restricted exponential regression to extrapolate dissimilarity over a range beyond that determined by initial sample sizes, which we use to identify an allocation of draws for subsequent sampling that minimizes a measure of pair-wise dissimilarities over the whole ensemble. This is motivated by the challenge faced by microbiome projects worldwide to effectively allocate additional samples for a more robust and reliable estimation of UniFrac distances between pairs of environments. Similar methods are applied to measures of sample quality of the ensemble derived from alpha-diversity and coverage. We test our methods against simulated data, where we compare optimal and inferred draw allocations when considering these three measures, and analyze 16S ribosomal RNA data from the Human Microbiome Project.
Advisors/Committee Members: Manuel E. Lladser, Rob Knight, Jem Corcoran.
Subjects/Keywords: Alpha-Diversity; Coverage; Dissimilarity; Urn Models; Applied Mathematics; Statistics and Probability
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Hampton, J. D. (2012). Dissimilarity and Optimal Sampling in Urn Ensembles. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/27
Chicago Manual of Style (16th Edition):
Hampton, Jerrad Davis. “Dissimilarity and Optimal Sampling in Urn Ensembles.” 2012. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/27.
MLA Handbook (7th Edition):
Hampton, Jerrad Davis. “Dissimilarity and Optimal Sampling in Urn Ensembles.” 2012. Web. 25 Jan 2021.
Vancouver:
Hampton JD. Dissimilarity and Optimal Sampling in Urn Ensembles. [Internet] [Doctoral dissertation]. University of Colorado; 2012. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/27.
Council of Science Editors:
Hampton JD. Dissimilarity and Optimal Sampling in Urn Ensembles. [Doctoral Dissertation]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/appm_gradetds/27
University of Colorado
10.
Aicher, Christopher Vinyu.
The Weighted Stochastic Block Model.
Degree: MS, Applied Mathematics, 2014, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/50
► Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar…
(more)
▼ Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network's large-scale structure, which can facilitate its scientific interpretation and the prediction of unknown or future interactions. Popular approaches, including the stochastic block model, assume edges are unweighted, which limits their utility by throwing away potentially useful information. We introduce the weighted stochastic block model (WSBM), which generalizes the stochastic block model to networks with edge weights drawn from any exponential family distribution. This model learns from both the presence and weight of edges, allowing it to discover structure that would otherwise be hidden when weights are discarded or thresholded. We describe a Bayesian variational algorithm for efficiently approximating this model's posterior distribution over latent block structures. We then evaluate the WSBM's performance on both edge-existence and edge-weight prediction tasks for both synthetic and real-world weighted networks. In all cases, the WSBM performs as well or better than the best alternatives on these tasks.
Advisors/Committee Members: Aaron Clauset, Jem Corcoran, Vanja Dukic.
Subjects/Keywords: Bayesian; Community Detection; Generative Models; Machine Learning; Networks; Variational Inference; Applied Mathematics; Computer Sciences; Statistics and Probability; Theory and Algorithms
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Aicher, C. V. (2014). The Weighted Stochastic Block Model. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/50
Chicago Manual of Style (16th Edition):
Aicher, Christopher Vinyu. “The Weighted Stochastic Block Model.” 2014. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/50.
MLA Handbook (7th Edition):
Aicher, Christopher Vinyu. “The Weighted Stochastic Block Model.” 2014. Web. 25 Jan 2021.
Vancouver:
Aicher CV. The Weighted Stochastic Block Model. [Internet] [Masters thesis]. University of Colorado; 2014. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/50.
Council of Science Editors:
Aicher CV. The Weighted Stochastic Block Model. [Masters Thesis]. University of Colorado; 2014. Available from: https://scholar.colorado.edu/appm_gradetds/50
University of Colorado
11.
Olson, Branden.
Stochastic Weather Generation with Approximate Bayesian Computation.
Degree: MS, Applied Mathematics, 2016, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/74
► Stochastic weather generators (SWGs) are designed to create simulations of synthetic weather data and are frequently used as input into physical models throughout many…
(more)
▼ Stochastic weather generators (SWGs) are designed to create simulations of synthetic weather data and are frequently used as input into physical models throughout many scientific disciplines. While the field of SWGs is vast, the search for better methods of spatiotemporal simulation of meteorological variables persists. We propose techniques to estimate SWG parameters based on an emerging set of methods called Approximate Bayesian Computation (ABC), which bypass the evaluation of a likelihood function. In this thesis, we begin with a review of the current state of ABC methods, including their advantages, drawbacks, and variations, and then apply ABC to the simulation of daily local maximum temperature, daily local precipitation occurrence, and daily precipitation occurrence over a spatial domain.
For temperature, we model the mean and variance as following a sinusoidal pattern which depends on the previous day. A similar approach is used for precipitation, but instead use a probit regression to model the probability that it rains on a given day of the year, based on an oscillatory mean function. For spatiotemporal precipitation occurrence, we employ a thresholded Gaussian process which reduces to our methods for local occurrence. In each scenario, we identify appropriate ABC penalization criteria to produce simulations whose statistical characteristics closely resemble those of the data. For our numerical case studies, we use daily temperature and precipitation records
Colorado and Iowa, collected over the course of hundreds of years.
Advisors/Committee Members: William Kleiber, Jem Corcoran, Vanja Dukic.
Subjects/Keywords: Approximate Bayesian Computation; Gaussian processes; Geostatistics; Markov chain Monte Carlo; Precipitation Modeling; Stochastic Weather Generators; Applied Mathematics; Applied Statistics; Atmospheric Sciences; Hydrology; Meteorology
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Olson, B. (2016). Stochastic Weather Generation with Approximate Bayesian Computation. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/74
Chicago Manual of Style (16th Edition):
Olson, Branden. “Stochastic Weather Generation with Approximate Bayesian Computation.” 2016. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/74.
MLA Handbook (7th Edition):
Olson, Branden. “Stochastic Weather Generation with Approximate Bayesian Computation.” 2016. Web. 25 Jan 2021.
Vancouver:
Olson B. Stochastic Weather Generation with Approximate Bayesian Computation. [Internet] [Masters thesis]. University of Colorado; 2016. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/74.
Council of Science Editors:
Olson B. Stochastic Weather Generation with Approximate Bayesian Computation. [Masters Thesis]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/appm_gradetds/74
University of Colorado
12.
Driggs, Derek T.
Optimization for High-Dimensional Data Analysis.
Degree: MS, Applied Mathematics, 2017, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/86
► As modern datasets continue to grow in size, they are also growing in complexity. Data are more often being recorded using multiple sensors, creating large,…
(more)
▼ As modern datasets continue to grow in size, they are also growing in complexity. Data are more often being recorded using multiple sensors, creating large, multidimensional datasets that are difficult to analyze. In this thesis, we explore methods to accelerate low-rank recovery algorithms for data analysis, with an emphasis on Robust Principal Component Analysis (RPCA). We also develop a tensor-based approach to RPCA that preserves the inherent structure of multidimensional datasets, allowing for improved analysis. Both of our approaches use nuclear-norm regularization with Burer-Monteiro factorization (or higher-order generalizations thereof) to transform convex but expensive programs into non-convex programs that can be solved efficiently. We supplement our non-convex programs with a certificate of optimality that can be used to bound the suboptimality of each iterate. We demonstrate that both of these approaches allow for new applications of RPCA in fields involving multidimensional datasets; for example, we show that our methods can be used for real-time video processing as well as the analysis of fMRI brain-scans. Traditionally, these tasks have been considered too demanding for low-rank recovery algorithms.
Advisors/Committee Members: Stephen Becker, Lijun Chen, Jem Corcoran.
Subjects/Keywords: Low-rank regularization; Parallel programming; RPCA; Tensor; Applied Mathematics; Numerical Analysis and Scientific Computing
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Driggs, D. T. (2017). Optimization for High-Dimensional Data Analysis. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/86
Chicago Manual of Style (16th Edition):
Driggs, Derek T. “Optimization for High-Dimensional Data Analysis.” 2017. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/86.
MLA Handbook (7th Edition):
Driggs, Derek T. “Optimization for High-Dimensional Data Analysis.” 2017. Web. 25 Jan 2021.
Vancouver:
Driggs DT. Optimization for High-Dimensional Data Analysis. [Internet] [Masters thesis]. University of Colorado; 2017. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/86.
Council of Science Editors:
Driggs DT. Optimization for High-Dimensional Data Analysis. [Masters Thesis]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/appm_gradetds/86
University of Colorado
13.
Mink, Jacob.
Twitter and Movies: Can Important Users Influence the Industry?.
Degree: MS, Applied Mathematics, 2017, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/91
► Over the past decade, social media has become an increasingly powerful tool for economic and social analysis. Specifically, Twitter has been used in a variety…
(more)
▼ Over the past decade, social media has become an increasingly powerful tool for economic and social analysis. Specifically, Twitter has been used in a variety of fields to predict and analyze human behavior and the effects that behavior has on marketing and product sales. In this study, I attempt to find a predictive model for movie box office revenue using well-connected, film industry critics and other Twitter users, natural language processing, and statistical analysis.
Advisors/Committee Members: Brian Keegan, Jem Corcoran, Manuel Lladser.
Subjects/Keywords: box office; NLP; Twitter; user graph; Applied Mathematics; Social Media
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Mink, J. (2017). Twitter and Movies: Can Important Users Influence the Industry?. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/91
Chicago Manual of Style (16th Edition):
Mink, Jacob. “Twitter and Movies: Can Important Users Influence the Industry?.” 2017. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/91.
MLA Handbook (7th Edition):
Mink, Jacob. “Twitter and Movies: Can Important Users Influence the Industry?.” 2017. Web. 25 Jan 2021.
Vancouver:
Mink J. Twitter and Movies: Can Important Users Influence the Industry?. [Internet] [Masters thesis]. University of Colorado; 2017. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/91.
Council of Science Editors:
Mink J. Twitter and Movies: Can Important Users Influence the Industry?. [Masters Thesis]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/appm_gradetds/91
University of Colorado
14.
Medley, Gavin Christopher.
Detection and Characterization of Ice Surface Elevation Profiles from Micropulse Photon-Counting Lidar Data.
Degree: MS, Applied Mathematics, 2016, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/100
► Quantitative analysis of the cryosphere relies on accurate and very precise data describing the ice surfaces of the earth. These data can be used to…
(more)
▼ Quantitative analysis of the cryosphere relies on accurate and very precise data describing the ice surfaces of the earth. These data can be used to study surfaces of the Earth to better understand the dynamics that govern our planet. As technology improves, these data become more readily available but with more data, the analysis inevitably becomes more complex. We present an analysis and application of data collected by NASA’s Slope Imaging Multi-Polarization Photon Counting LiDAR (SIMPL) instrument using a density dimension algorithm (DDA) in conjunction with geostatistical classification methods. SIMPL is an airborne predecessor instrument of the next-generation multi-beam micropulse photon-counting LiDAR instrument – the Advanced Topographic Laser Altimeter System (ATLAS) – that will be used during NASA’s Ice Cloud and Land Elevation Satellite (ICESat)-2 mission. SIMPL uses four spatially distinct beams at two wavelength and in two polarization modes. High-resolution elevation profiles of ice surfaces in western Greenland are constructed from SIMPL photon return data obtained during preliminary test flights conducted in August, 2015. Using a density dimension algorithm, noise is filtered out and the photon returns from the true ice surface are retained. The retained points are then weighted to estimate the surface elevation profile along the flight track. We present an estimate of optimal parameters for each of the 16 channels and show the estimated surface from each. Further, we make observations about data and discuss its characteristics in different conditions. Finally, to demonstrate the potential usefulness of the SIMPL data, we perform a surface classification study using geostatistical methods.
Advisors/Committee Members: Ute C. Herzfeld, William Kleiber, Jem Corcoran.
Subjects/Keywords: altimetry; glacier; greenland; icesat; lidar; simpl; Applied Mathematics; Geographic Information Sciences; Remote Sensing
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Medley, G. C. (2016). Detection and Characterization of Ice Surface Elevation Profiles from Micropulse Photon-Counting Lidar Data. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/100
Chicago Manual of Style (16th Edition):
Medley, Gavin Christopher. “Detection and Characterization of Ice Surface Elevation Profiles from Micropulse Photon-Counting Lidar Data.” 2016. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/100.
MLA Handbook (7th Edition):
Medley, Gavin Christopher. “Detection and Characterization of Ice Surface Elevation Profiles from Micropulse Photon-Counting Lidar Data.” 2016. Web. 25 Jan 2021.
Vancouver:
Medley GC. Detection and Characterization of Ice Surface Elevation Profiles from Micropulse Photon-Counting Lidar Data. [Internet] [Masters thesis]. University of Colorado; 2016. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/100.
Council of Science Editors:
Medley GC. Detection and Characterization of Ice Surface Elevation Profiles from Micropulse Photon-Counting Lidar Data. [Masters Thesis]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/appm_gradetds/100
University of Colorado
15.
Slattum, Victoria Anne.
Feature-Based Calibration of a Global Magnetosphere-Ionosphere Model for Geomagnetic Storms.
Degree: MS, Applied Mathematics, 2017, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/101
► Geomagnetic storms play a significant role in space weather physics and have the potential to impact our daily lives. Widespread impacts of space weather physics…
(more)
▼ Geomagnetic storms play a significant role in space weather physics and have the potential to impact our daily lives. Widespread impacts of space weather physics can include power grid outages, air traffic rerouting, and disruption of GPS signals. The Lyon-Fedder-Mobarry global magnetosphere–ionosphere coupled model (LFM-MIX) is a computer model used at the Center for Integrated Space Weather Modeling (CISM) to study Sun-Earth interactions by simulating geomagnetic storms. LFM-MIX uses solar wind observations to perform a magnetohydrodynamic (MHD) simulation of the magnetosphere (LFM) and couples it with an electrostatic model of the ionosphere (MIX). Given a set of input parameters and solar wind data, LFM-MIX numerically solves the MHD equations and outputs a large bivariate spatiotemporal field of ionospheric energy and flux. These input parameters are unknown and we focus on quantifying them. The currently available methods are insufficient for our data set due to its high dimensionality, thus we develop our own method based on statistical calibration. Here, statistical calibration refers to the process of fitting a model to observed data by adjusting the input parameters. Our approach, which we call feature-based calibration, involves calculating some goodness of fit criterion between model output and observed data, then predicting its value over the entire feasible parameter space and locating the minimum of the predicted surface. We apply this approach to several goodness of fit criteria based on different defining features of the data.
Advisors/Committee Members: William Kleiber, Jem Corcoran, Manuel Lladser.
Subjects/Keywords: calibration; computer experiments; geomagnetic storms; kriging; multivariate computer model; Applied Mathematics; Applied Statistics; Atmospheric Sciences
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Slattum, V. A. (2017). Feature-Based Calibration of a Global Magnetosphere-Ionosphere Model for Geomagnetic Storms. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/101
Chicago Manual of Style (16th Edition):
Slattum, Victoria Anne. “Feature-Based Calibration of a Global Magnetosphere-Ionosphere Model for Geomagnetic Storms.” 2017. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/101.
MLA Handbook (7th Edition):
Slattum, Victoria Anne. “Feature-Based Calibration of a Global Magnetosphere-Ionosphere Model for Geomagnetic Storms.” 2017. Web. 25 Jan 2021.
Vancouver:
Slattum VA. Feature-Based Calibration of a Global Magnetosphere-Ionosphere Model for Geomagnetic Storms. [Internet] [Masters thesis]. University of Colorado; 2017. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/101.
Council of Science Editors:
Slattum VA. Feature-Based Calibration of a Global Magnetosphere-Ionosphere Model for Geomagnetic Storms. [Masters Thesis]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/appm_gradetds/101
University of Colorado
16.
Dao, Raymond.
Probabilistic and Statistical Methods for Target Tracking.
Degree: MS, Applied Mathematics, 2015, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/69
► Accurate and efficient tracking of objects through frames of a video is important in a wide range of areas including surveillance, military, and medical…
(more)
▼ Accurate and efficient tracking of objects through frames of a video is important in a wide range of areas including surveillance, military, and medical imaging applications, as well the understanding of social interactions of biological populations such as swarming insects. In this thesis, we review some of the most popular deterministic template matching algorithms for tracking, including the seminal Lucas-Kanade algorithm. We also review a Monte Carlo method and introduce a simple probabilistic algorithm for parameter learning. Additionally, we offer some improvements for existing algorithms, including a template stabilizer, formed from a principle components analysis, and an additional stopping rule for iterative attempts at matching that improves the speed of existing algorithms and in some cases results in better accuracy. Existing and new methods are compared on simulated images and on real video. In several cases, R code is provided.
Advisors/Committee Members: Jem Corcoran, Anne Dougherty, Yermal Bhat.
Subjects/Keywords: Image Alignment; Target Tracking; Applied Mathematics; Applied Statistics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Dao, R. (2015). Probabilistic and Statistical Methods for Target Tracking. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/69
Chicago Manual of Style (16th Edition):
Dao, Raymond. “Probabilistic and Statistical Methods for Target Tracking.” 2015. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/69.
MLA Handbook (7th Edition):
Dao, Raymond. “Probabilistic and Statistical Methods for Target Tracking.” 2015. Web. 25 Jan 2021.
Vancouver:
Dao R. Probabilistic and Statistical Methods for Target Tracking. [Internet] [Masters thesis]. University of Colorado; 2015. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/69.
Council of Science Editors:
Dao R. Probabilistic and Statistical Methods for Target Tracking. [Masters Thesis]. University of Colorado; 2015. Available from: https://scholar.colorado.edu/appm_gradetds/69
University of Colorado
17.
Zetterlund, Erika Henning.
Fuel for the Star Formation Engine: Dense Molecular Cloud Clumps in the Northern Galactic Plane.
Degree: PhD, 2018, University of Colorado
URL: https://scholar.colorado.edu/astr_gradetds/55
► The interstellar medium (ISM) is a confusing, muddled place. It provides the fuel for star formation, but before that can occur, the ISM must…
(more)
▼ The interstellar medium (ISM) is a confusing, muddled place. It provides the fuel for star formation, but before that can occur, the ISM must cool and condense into molecular clouds. Even this is not enough, however. It is only the cores, contained within the clumps, contained within the clouds, which form stars. With all these nested structures, it takes an optically thin, yet still bright, tracer to uncover the processes which convert the molecular clouds into stars. Luckily, the ISM is dusty. I use the <i>Herschel</i> infrared GALactic plane survey (Hi-GAL) to study molecular cloud clumps through their thermal dust emission at 500 μm. For adapting and testing the clump identification and distance techniques – developed for the Bolocam Galactic Plane Survey (BGPS) – I used six Hi-GAL maps at a representative sample of Galactic longitudes. I found many more clumps per square degree with Hi-GAL than were identified with BGPS, particularly at longitudes farther from the Galactic center, where Hi-GAL's increased sensitivity truly shines. Where I found the same clumps as BGPS, my distances and physical properties aligned well. Notably, clumps are slightly larger in Hi-GAL, where the diffuse edges are not overtaken by atmospheric noise, as was the case with BGPS. The application of these techniques to 10°<
Advisors/Committee Members: Jason Glenn, Jem Corcoran, Ann-Marie Madigan, Jeremy Darling, Benjamin Brown.
Subjects/Keywords: interstellar medium; milky way galaxy; herschel infrared galactic; galactic plane; molecular; Astrophysics and Astronomy; Stars, Interstellar Medium and the Galaxy
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Zetterlund, E. H. (2018). Fuel for the Star Formation Engine: Dense Molecular Cloud Clumps in the Northern Galactic Plane. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/astr_gradetds/55
Chicago Manual of Style (16th Edition):
Zetterlund, Erika Henning. “Fuel for the Star Formation Engine: Dense Molecular Cloud Clumps in the Northern Galactic Plane.” 2018. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/astr_gradetds/55.
MLA Handbook (7th Edition):
Zetterlund, Erika Henning. “Fuel for the Star Formation Engine: Dense Molecular Cloud Clumps in the Northern Galactic Plane.” 2018. Web. 25 Jan 2021.
Vancouver:
Zetterlund EH. Fuel for the Star Formation Engine: Dense Molecular Cloud Clumps in the Northern Galactic Plane. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/astr_gradetds/55.
Council of Science Editors:
Zetterlund EH. Fuel for the Star Formation Engine: Dense Molecular Cloud Clumps in the Northern Galactic Plane. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/astr_gradetds/55
University of Colorado
18.
Fairbanks, Hillary Ruth.
Low-Rank, Multi-Fidelity Methods for Uncertainty Quantification of High-Dimensional Systems.
Degree: PhD, 2018, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/114
► Characterizing and incorporating uncertainties when simulating physical phenomena is essential for improving model-based predictions. These uncertainties may stem from a lack of knowledge regarding…
(more)
▼ Characterizing and incorporating uncertainties when simulating physical phenomena is essential for improving model-based predictions. These uncertainties may stem from a lack of knowledge regarding the underlying physical processes or from imprecise measurements of quantities that describe properties of the physical system. Uncertainty quantification (UQ) is a tool that seeks to characterize the impact of these uncertainties on solutions of computational models, resulting in improved predictive models. In practice, these uncertainties are either treated as random parameters to inform the statistics of the solution of interest (forward UQ), or their statistics are inferred from noisy observations of the solutions (inverse UQ). For systems exhibiting high-dimensional uncertainty, performing either forward or inverse UQ presents a significant computational challenge, as these methods require a large number forward solves of the high-fidelity model, that is, the model that accurately captures the physics of the problem. For large-scale problems, this may result in the need for a possibly infeasible number of simulations. Prominent methods have been developed to reduce the burdens related to these challenges, including multilevel Monte Carlo (for forward UQ) and low-rank approximations to the posterior covariance (for inverse UQ). However, these methods may still require many forward solves of the high-fidelity model. To reduce the cost of performing UQ on high-dimensional systems, we apply multi-fidelity strategies to both the forward problem, in order to estimate moments of the quantity of interest, and inverse problem, to approximate the posterior covariance. In particular, we formulate multi-fidelity methods that exploit the low-rank structure of the solution of interest and utilize models of lower fidelity (which are computationally cheaper to simulate) than the intended high-fidelity model, in a nonintrusive manner. Doing so results in surrogate models that may have accuracies closer to that of the high-fidelity model, yet have computational costs comparable to that of the low-fidelity models. Theoretical error analysis, cost comparisons, and numerical examples are provided to to show the promise of these novel methods.
Advisors/Committee Members: Alireza Doostan, Gregory Beylkin, Stephen Becker, Jem Corcoran, Chris Ketelsen.
Subjects/Keywords: bi-fidelity approximations; low-rank approximations; multi-fidelity approximations; parametric model reduction; uncertainty quantification; Applied Mathematics; Models and Methods
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Fairbanks, H. R. (2018). Low-Rank, Multi-Fidelity Methods for Uncertainty Quantification of High-Dimensional Systems. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/114
Chicago Manual of Style (16th Edition):
Fairbanks, Hillary Ruth. “Low-Rank, Multi-Fidelity Methods for Uncertainty Quantification of High-Dimensional Systems.” 2018. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/114.
MLA Handbook (7th Edition):
Fairbanks, Hillary Ruth. “Low-Rank, Multi-Fidelity Methods for Uncertainty Quantification of High-Dimensional Systems.” 2018. Web. 25 Jan 2021.
Vancouver:
Fairbanks HR. Low-Rank, Multi-Fidelity Methods for Uncertainty Quantification of High-Dimensional Systems. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/114.
Council of Science Editors:
Fairbanks HR. Low-Rank, Multi-Fidelity Methods for Uncertainty Quantification of High-Dimensional Systems. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/114
University of Colorado
19.
Coston, Natalie A.
Spectral Properties of Products of Independent Random Matrices.
Degree: PhD, 2018, University of Colorado
URL: https://scholar.colorado.edu/math_gradetds/62
► In the field of random matrix theory, there are many matrix models one may choose to study. This thesis focuses on independent and identically…
(more)
▼ In the field of random matrix theory, there are many matrix models one may choose to study. This thesis focuses on independent and identically distributed (iid) random matrices. Given a random variable ξ, we say that a matrix is an iid random matrix if each entry is an iid copy of ξ, and we call ξ the atom random variable. Given a positive constant integer <i>m</i>, consider <i>m</i> random variables ξ
1,...,ξ
m, and create an independent <i>n</i> ✕ <i>n</i> iid random matrix for each of these random variables. The results presented in this thesis focus on the limiting behavior of the eigenvalues of the product of these <i>m</i> independent iid random matrices. Call this product <i>P
n</i> and note that <i>P
n</i> is also an <i>n</i> ✕ <i>n</i> random matrix, but the entries are no longer independent. [object Object] This thesis is comprised of two main results. First, we examine the locations of eigenvalues of matrix products as the size of the matrices tend to infinity. From the previous results by O'Rourke, Renfrew, Soshnikov, and Vu, we see that under certain moment assumptions on the atom random variables, as <i>n</i> tends to infinity, the empirical spectral measure of the eigenvalues of the rescaled product <i>n</i><sup>-<i>m</i>/2</sup><i>P
n</i> converges to a measure supported on a disk centered at the origin in the complex plane with radius depending on the atom random variables. In this work, we study the asymptotic location of eigenvalues which can fall outside of this disk. These outlying eigenvalues may be present when the random matrix product <i>P
n</i> is additively perturbed by a low rank, small norm deterministic matrix. We also consider multiplicative perturbations, and perturbations in any order. By studying these various perturbations, we characterize when a perturbed matrix product has outliers, and the asymptotic locations of these outlying eigenvalues. The second result of this thesis studies the fluctuation of the eigenvalues of the rescaled product <i>n</i><sup>-<i>m</i>/2</sup><i>P
n</i> . In particular, we define a linear statistic and use this to study the spectrum, or the collection of eigenvalues, of <i>n</i><sup>-<i>m</i>/2</sup><i>P
n</i> . We see that the limiting distribution of the unnormalized linear statistic is a mean-zero Gaussian distribution with variance depending on the the linear statistic. The explicit variance formula is computed as well.
Advisors/Committee Members: Sean O'Rourke, Philip Wood, Sergei Kuznetsov, Janos Englander, Jem Corcoran.
Subjects/Keywords: probability; random matrix; eigenvalues; product; gaussian distribution; Mathematics; Statistics and Probability
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Coston, N. A. (2018). Spectral Properties of Products of Independent Random Matrices. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/62
Chicago Manual of Style (16th Edition):
Coston, Natalie A. “Spectral Properties of Products of Independent Random Matrices.” 2018. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/math_gradetds/62.
MLA Handbook (7th Edition):
Coston, Natalie A. “Spectral Properties of Products of Independent Random Matrices.” 2018. Web. 25 Jan 2021.
Vancouver:
Coston NA. Spectral Properties of Products of Independent Random Matrices. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/math_gradetds/62.
Council of Science Editors:
Coston NA. Spectral Properties of Products of Independent Random Matrices. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/math_gradetds/62
University of Colorado
20.
Matviychuk, Yevgen.
Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing.
Degree: PhD, Electrical, Computer & Energy Engineering, 2016, University of Colorado
URL: https://scholar.colorado.edu/ecen_gradetds/124
► While the field of image processing has been around for some time, new applications across many diverse areas, such as medical imaging, remote sensing,…
(more)
▼ While the field of image processing has been around for some time, new applications across many diverse areas, such as medical imaging, remote sensing, astrophysics, cellular imaging, computer vision, and many others, continue to demand more and more sophisticated image processing techniques. These areas inherently rely on the development of novel methods and algorithms for their success. Many important cases in these applications can be posed as problems of reversing the action of certain linear operators. Recently, patch-based methods for image reconstruction have been shown to work exceptionally well in addressing these inverse problems, establishing new state-of-the-art benchmarks for many of them, and even approaching estimated theoretical limits of performance.
However, there is still space and need for improvement, particularly in highly specialized domains. The purpose of this thesis will be to improve upon these prior patch-based image processing methods by developing a computationally efficient way to model the underlying set of patches as arising from a low-dimensional manifold. In contrast to other works that have attempted to use a manifold model for patches, ours will rely on the machinery of kernel methods to efficiently approximate the solution. This will make our approach much more suitable for practical use than those of our predecessors. We will show experimental results paralleling or exceeding those of modern state-of-the-art image processing algorithms for several inverse problems. Additionally, near the end of the thesis, we will revisit the problem of learning a representation for the manifold from its samples and develop an improved approach for it. In contrast to prior methods for manifold learning, our kernel-based strategy will be robust to issues of learning from very few or noisy samples, and it will readily allow for interpolation along or projection onto the manifold.
Advisors/Committee Members: Shannon M. Hughes, Youjian Liu, Lijun Chen, Jem Corcoran, Elizabeth Bradley.
Subjects/Keywords: Image processing; Inverse problems; Kernel methods; Machine learning; Manifold models; Computer Sciences; Electrical and Computer Engineering
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Matviychuk, Y. (2016). Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/ecen_gradetds/124
Chicago Manual of Style (16th Edition):
Matviychuk, Yevgen. “Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing.” 2016. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/ecen_gradetds/124.
MLA Handbook (7th Edition):
Matviychuk, Yevgen. “Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing.” 2016. Web. 25 Jan 2021.
Vancouver:
Matviychuk Y. Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/ecen_gradetds/124.
Council of Science Editors:
Matviychuk Y. Learning and Mapping onto Manifolds with Applications to Patch-based Image Processing. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/ecen_gradetds/124
University of Colorado
21.
Broido, Anna.
Characterizing the tails of degree distributions in real-world networks.
Degree: PhD, Applied Mathematics, 2019, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/143
► This is a thesis about how to characterize the statistical structure of the tails of degree distributions of real-world networks. The primary contribution is…
(more)
▼ This is a thesis about how to characterize the statistical structure of the tails of degree distributions of real-world networks. The primary contribution is a statistical test of the prevalence of scale-free structure in real-world networks. A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree k follows a power law, decaying like k
-a, often with 2 < a< 3. However, empirical evidence for this belief derives from a relatively small number of real-world networks. In the first section, we test the universality of scale-free structure by applying state-of-the-art statistical tools to a large corpus of nearly 1000 network data sets drawn from social, biological, technological, and informational sources. We fit the power-law model to each degree distribution, test its statistical plausibility, and compare it via a likelihood ratio test to alternative, non-scale-free models, e.g., the log-normal. Across domains, we find that scale-free networks are rare, with only 4% exhibiting the strongest-possible evidence of scale-free structure and 52% exhibiting the weakest-possible evidence. Furthermore, evidence of scale-free structure is not uniformly distributed across sources: social networks are at best weakly scale free, while a handful of technological and biological networks can be called strongly scale free. These results undermine the universality of scale-free networks and reveal that real-world networks exhibit a rich structural diversity that will likely require new ideas and mechanisms to explain. A core methodological component of addressing the ubiquity of scale-free structure in real-world networks is an ability to fit a power law to the degree distribution. In the second section, we numerically evaluate and compare, using both synthetic data with known structure and real-world data with unknown structure, two statistically principled methods for estimating the tail parameters for power-law distributions, showing that in practice, a method based on extreme value theory and a sophisticated bootstrap and the more commonly used method based an empirical minimization approach exhibit similar accuracy.
Advisors/Committee Members: Aaron Clauset, Jem Corcoran, Daniel Larremore, Manuel Lladser, Juan Restrepo.
Subjects/Keywords: networks; power law; scale free; Applied Statistics; Other Applied Mathematics; Probability; Statistical Methodology; Statistical Models
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Broido, A. (2019). Characterizing the tails of degree distributions in real-world networks. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/143
Chicago Manual of Style (16th Edition):
Broido, Anna. “Characterizing the tails of degree distributions in real-world networks.” 2019. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/143.
MLA Handbook (7th Edition):
Broido, Anna. “Characterizing the tails of degree distributions in real-world networks.” 2019. Web. 25 Jan 2021.
Vancouver:
Broido A. Characterizing the tails of degree distributions in real-world networks. [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/143.
Council of Science Editors:
Broido A. Characterizing the tails of degree distributions in real-world networks. [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/appm_gradetds/143
University of Colorado
22.
Kightley, Eric P.
Stokes, Gauss, and Bayes walk into a bar...
Degree: PhD, Applied Mathematics, 2019, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/144
► This thesis consists of three distinct projects. The first is a study of microbial aggregate fragmentation, in which we develop a dynamical model of…
(more)
▼ This thesis consists of three distinct projects. The first is a study of microbial aggregate fragmentation, in which we develop a dynamical model of aggregate deformation and breakage and use it to obtain a post-fragmentation density function. The second and third projects deal with dimensionality reduction in machine learning problems. In the second project, we derive a one-pass sparsified Gaussian mixture model to perform clustering analysis on high-dimensional streaming data. The model estimates parameters in dense space while storing and performing computations in a compressed space. In the final project, we build an expert system classifier with a Bayesian network for use on high-volume streaming data. Our approach is specialized to reduce the number of observations while obtaining sufficient labeled training data in a regime of extreme class-imbalance and expensive oracle queries.
Advisors/Committee Members: Stephen Becker, Jem Corcoran, Manuel Lladser, David Bortz, Farhad Pourkamali Anaraki.
Subjects/Keywords: Gaussian mixture models; clustering; Bayesian networks; probabilistic graphical models; anomaly detection; classification; Artificial Intelligence and Robotics; Information Security; Numerical Analysis and Computation; Other Applied Mathematics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kightley, E. P. (2019). Stokes, Gauss, and Bayes walk into a bar... (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/144
Chicago Manual of Style (16th Edition):
Kightley, Eric P. “Stokes, Gauss, and Bayes walk into a bar...” 2019. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/144.
MLA Handbook (7th Edition):
Kightley, Eric P. “Stokes, Gauss, and Bayes walk into a bar...” 2019. Web. 25 Jan 2021.
Vancouver:
Kightley EP. Stokes, Gauss, and Bayes walk into a bar... [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/144.
Council of Science Editors:
Kightley EP. Stokes, Gauss, and Bayes walk into a bar... [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/appm_gradetds/144
University of Colorado
23.
Kightley, Eric Paul.
Stokes, Gauss, and Bayes Walk into a Bar...
Degree: PhD, 2019, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/152
► This thesis consists of three distinct projects. The first is a study of microbial aggregate fragmentation, in which we develop a dynamical model of aggregate…
(more)
▼ This thesis consists of three distinct projects. The first is a study of microbial aggregate fragmentation, in which we develop a dynamical model of aggregate deformation and breakage and use it to obtain a post-fragmentation density function. The second and third projects deal with dimensionality reduction in machine learning problems. In the second project, we derive a one-pass sparsified Gaussian mixture model to perform clustering analysis on high-dimensional streaming data. The model estimates parameters in dense space while storing and performing computations in a compressed space. In the final project, we build an expert system classifier with a Bayesian network for use on high-volume streaming data. Our approach is specialized to reduce the number of observations while obtaining sufficient labeled training data in a regime of extreme class-imbalance and expensive oracle queries.
Advisors/Committee Members: Stephen Becker, David Bortz, Manuel Lladser, Jem Corcoran, Farhad Pourkamali Anaraki.
Subjects/Keywords: classification; clustering; dimensionality reduction; probabilistic graphical models; random projections; Applied Mathematics; Artificial Intelligence and Robotics; Statistical Models
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kightley, E. P. (2019). Stokes, Gauss, and Bayes Walk into a Bar... (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/152
Chicago Manual of Style (16th Edition):
Kightley, Eric Paul. “Stokes, Gauss, and Bayes Walk into a Bar...” 2019. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/152.
MLA Handbook (7th Edition):
Kightley, Eric Paul. “Stokes, Gauss, and Bayes Walk into a Bar...” 2019. Web. 25 Jan 2021.
Vancouver:
Kightley EP. Stokes, Gauss, and Bayes Walk into a Bar... [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/152.
Council of Science Editors:
Kightley EP. Stokes, Gauss, and Bayes Walk into a Bar... [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/appm_gradetds/152
University of Colorado
24.
Broido, Anna D.
Characterizing the Tails of Degree Distributions in Real-World Networks.
Degree: PhD, 2019, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/153
► This is a thesis about how to characterize the statistical structure of the tails of degree distributions of real-world networks. The primary contribution is a…
(more)
▼ This is a thesis about how to characterize the statistical structure of the tails of degree distributions of real-world networks. The primary contribution is a statistical test of the prevalence of scale-free structure in real-world networks. A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree k follows a power law, decaying like k^-a, often with 2 < a < 3. However, empirical evidence for this belief derives from a relatively small number of real-world networks. In the first section, we test the universality of scale-free structure by applying state-of-the-art statistical tools to a large corpus of nearly 1000 network data sets drawn from social, biological, technological, and informational sources. We fit the power-law model to each degree distribution, test its statistical plausibility, and compare it via a likelihood ratio test to alternative, non-scale-free models, e.g., the log-normal. Across domains, we find that scale-free networks are rare, with only 4% exhibiting the strongest-possible evidence of scale-free structure and 52% exhibiting the weakest-possible evidence. Furthermore, evidence of scale-free structure is not uniformly distributed across sources: social networks are at best weakly scale free, while a handful of technological and biological networks can be called strongly scale free. These results undermine the universality of scale-free networks and reveal that real-world networks exhibit a rich structural diversity that will likely require new ideas and mechanisms to explain. A core methodological component of addressing the ubiquity of scale-free structure in real-world networks is an ability to fit a power law to the degree distribution. In the second section, we numerically evaluate and compare, using both synthetic data with known structure and real-world data with unknown structure, two statistically principled methods for estimating the tail parameters for power-law distributions, showing that in practice, a method based on extreme value theory and a sophisticated bootstrap and the more commonly used method based an empirical minimization approach exhibit similar accuracy.
Advisors/Committee Members: Aaron Clauset, Jem Corcoran, Daniel Larremore, Manuel Lladser, Juan Restrepo.
Subjects/Keywords: networks; power law; scale free; Applied Mathematics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Broido, A. D. (2019). Characterizing the Tails of Degree Distributions in Real-World Networks. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/153
Chicago Manual of Style (16th Edition):
Broido, Anna D. “Characterizing the Tails of Degree Distributions in Real-World Networks.” 2019. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/153.
MLA Handbook (7th Edition):
Broido, Anna D. “Characterizing the Tails of Degree Distributions in Real-World Networks.” 2019. Web. 25 Jan 2021.
Vancouver:
Broido AD. Characterizing the Tails of Degree Distributions in Real-World Networks. [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/153.
Council of Science Editors:
Broido AD. Characterizing the Tails of Degree Distributions in Real-World Networks. [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/appm_gradetds/153
University of Colorado
25.
Ali, Ashar Fawad.
ULF Waves and Diffusive Radial Transport of Charged Particles.
Degree: PhD, Applied Mathematics, 2016, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/71
► The Van Allen radiation belts contain highly energetic particles which interact with a variety of plasma and magnetohydrodynamic (MHD) waves. Waves in the ultra…
(more)
▼ The Van Allen radiation belts contain highly energetic particles which interact with a variety of plasma and magnetohydrodynamic (MHD) waves. Waves in the ultra low-frequency (ULF) range play an important role in the loss and acceleration of energetic particles. Considering the geometry of the geomagnetic field, charged particles trapped in the inner magnetosphere undergo three distinct types of periodic motions; an adiabatic invariant is associated with each type of motion. The evolution of the phase space density of charged particles in the magnetosphere in the coordinate space of the three adiabatic invariants is modeled by the Fokker-Planck equation. If we assume that the first two adiabatic invariants are conserved while the third invariant is violated, then the general Fokker-Planck equation reduces to a radial diffusion equation with the radial diffusion coefficient quantifying the rate of the radial diffusion of charged particles, including contributions from perturbations in both the magnetic and the electric fields.
This thesis investigates two unanswered questions about ULF wave-driven radial transport of charged particles. First, how important are the ULF fluctuations in the magnetic field compared with the ULF fluctuations in the electric field in driving the radial diffusion of charged particles in the Earth's inner magnetosphere? It has generally been accepted that magnetic field perturbations dominate over electric field perturbations, but several recently published studies suggest otherwise. Second, what is the distribution of ULF wave power in azimuth, and how does ULF wave power depend upon radial distance and the level of geomagnetic activity? Analytic treatments of the diffusion coefficients generally assume uniform distribution of power in azimuth, but in situ measurements suggest that this may not be the case. We used the magnetic field data from the Combined Release and Radiation Effects Satellite (CRRES) and the electric and the magnetic field data from the Radiation Belt Storm Probes (RBSP) to compute the electric and the magnetic component of the radial diffusion coefficient using the Fei et al. [2006] formulation. We conclude that contrary to prior notions, the electric component is dominant in driving radial diffusion of charged particles in the Earth's inner magnetosphere instead of the magnetic component. The electric component can be up to two orders of magnitude larger than the magnetic component. In addition, we see that ULF wave power in both the electric and the magnetic fields has a clear dependence on
Kp with wave power decreasing as radial distance decreases. For both fields, the noon sectors generally contain more ULF wave power than the dawn, dusk, and the midnight magnetic local time (MLT) sectors. There is no significant difference between ULF wave power in the dawn, dusk, and the midnight sectors.
Advisors/Committee Members: Scot R. Elkington, Jem Corcoran, Howard Singer, Juan Restrepo, William Kleiber.
Subjects/Keywords: CRRES; Magnetospheric Physics; Radial Diffusion; RBSP; ULF Waves; Van Allen Radiation Belts; Applied Mathematics; Plasma and Beam Physics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Ali, A. F. (2016). ULF Waves and Diffusive Radial Transport of Charged Particles. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/71
Chicago Manual of Style (16th Edition):
Ali, Ashar Fawad. “ULF Waves and Diffusive Radial Transport of Charged Particles.” 2016. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/71.
MLA Handbook (7th Edition):
Ali, Ashar Fawad. “ULF Waves and Diffusive Radial Transport of Charged Particles.” 2016. Web. 25 Jan 2021.
Vancouver:
Ali AF. ULF Waves and Diffusive Radial Transport of Charged Particles. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/71.
Council of Science Editors:
Ali AF. ULF Waves and Diffusive Radial Transport of Charged Particles. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/appm_gradetds/71
University of Colorado
26.
Wong, Tony E.
The Impact of Stable Water Isotopic Information on Parameter Calibration in a Land Surface Model.
Degree: PhD, Applied Mathematics, 2016, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/72
► The single largest uncertainty in climate model energy balance is the surface latent heating over tropical land. Furthermore, the partitioning of the total latent…
(more)
▼ The single largest uncertainty in climate model energy balance is the surface latent heating over tropical land. Furthermore, the partitioning of the total latent heat flux into contributions from surface evaporation and plant transpiration offers acute insight into the hydrological and biogeochemical behaviors of an ecosystem, but is notoriously difficult to establish directly. Evapotranspiration (ET) partitioning relies heavily on knowledge of the relative pathways by which water moves from the soil to the atmosphere. These pathways are parameterized by ecosystem resistances, which may not be known with great certainty in practical situations. Resolving these issues requires the development of statistical methods to maximize the use of limited information to best improve models. First, we introduce a commonly-used land surface model, the Community Land Model version 4 (CLM4). We describe an approach to calibrating select model parameters to observational data in a Bayesian estimation framework, requiring Markov chain Monte Carlo sampling of the posterior distribution. We demonstrate the ability of this Bayesian framework to constrain land-atmosphere exchanges of moisture and heat in CLM4, and yield an estimate of ET partitioning which is informed by data. Next, an isotopically-enabled version of CLM4 (iCLM4) is described in detail and validated using site-level and global observations. By leveraging the unique signatures of evaporation and transpiration on the ratios of stable water isotopes, additional constraint on the ET partitioning may be obtained. Finally, an extensive set of isotopic, meteorological and hydrological data from Erie,
Colorado, USA is assimilated to calibrate land-atmosphere fluxes and state variables in iCLM4. It is demonstrated that the inclusion of water isotopic data in the assimilation step provides additional constraint on the estimated ET partitioning, and the benefits of these water isotopic datasets relative to common, non-isotopic datasets is quantified.
Advisors/Committee Members: William Kleiber, David C. Noone, Keith Julien, Jem Corcoran, David Lawrence.
Subjects/Keywords: Bayesian; calibration; isotope; Markov; model; uncertainty; Applied Mathematics; Hydrology
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Wong, T. E. (2016). The Impact of Stable Water Isotopic Information on Parameter Calibration in a Land Surface Model. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/72
Chicago Manual of Style (16th Edition):
Wong, Tony E. “The Impact of Stable Water Isotopic Information on Parameter Calibration in a Land Surface Model.” 2016. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/72.
MLA Handbook (7th Edition):
Wong, Tony E. “The Impact of Stable Water Isotopic Information on Parameter Calibration in a Land Surface Model.” 2016. Web. 25 Jan 2021.
Vancouver:
Wong TE. The Impact of Stable Water Isotopic Information on Parameter Calibration in a Land Surface Model. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/72.
Council of Science Editors:
Wong TE. The Impact of Stable Water Isotopic Information on Parameter Calibration in a Land Surface Model. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/appm_gradetds/72
University of Colorado
27.
Mullen, Zachary.
Theory and Methods for Large Spatial Data.
Degree: PhD, 2018, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/105
► Correlated Gaussian processes are of central importance to the study of time series, spatial statistics, computer experiments, and many machine learning models. Large spatially…
(more)
▼ Correlated Gaussian processes are of central importance to the study of time series, spatial statistics, computer experiments, and many machine learning models. Large spatially or temporally indexed datasets bring with them a host of computational and mathematical challenges. Parameter estimation of these processes often relies on maximum likelihood, which for Gaussian processes involves manipulations of the covariance matrix including solving systems of equations and determinant calculations. The score function, on the other hand, avoids direct calculation of the determinant, but still requires solving a large number of linear equations. We propose an equivalent kernel approximation to the score function of a stationary Gaussian process. A nugget effect is required for the approximation. We suggest two approximations, and for large sample sizes, our proposals are fast, accurate, and compare well against existing approaches. We then present a method for simulating time series of high frequency wind data calibrated by real data. The method provides and fits a parametric model for local wind directions by embedding them into the angular projection of a bivariate normal. Incorporating a temporal autocorrelation structure in that normal induces a continuous angular correlation over time in the simulated wind directions. The final joint model for speed and direction can be decomposed into the simulation of a single multivariate normal and a series of transformations thereof, allowing for fast and easy repeated generations of long time series. This is compared to a state of the art approach for simulating angular time series of swapping between discrete regimes of wind direction, a method that does not fully translate to high frequency data.
Advisors/Committee Members: William Kleiber, Eric Vance, Balaji Rajagopalan, Jem Corcoran, James Curry.
Subjects/Keywords: circular data; equivalent kernel; gaussian processes; spatial statistics; stochastic weather generators; wind modeling; Applied Mathematics; Statistical Theory
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Mullen, Z. (2018). Theory and Methods for Large Spatial Data. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/105
Chicago Manual of Style (16th Edition):
Mullen, Zachary. “Theory and Methods for Large Spatial Data.” 2018. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/105.
MLA Handbook (7th Edition):
Mullen, Zachary. “Theory and Methods for Large Spatial Data.” 2018. Web. 25 Jan 2021.
Vancouver:
Mullen Z. Theory and Methods for Large Spatial Data. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/105.
Council of Science Editors:
Mullen Z. Theory and Methods for Large Spatial Data. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/appm_gradetds/105
University of Colorado
28.
Saraiva, Paulo Quinderé.
GMM Estimation of Spatial Autoregressive Models in a System of Simultaneous Equations.
Degree: PhD, Economics, 2015, University of Colorado
URL: https://scholar.colorado.edu/econ_gradetds/63
► This dissertation proposes a generalized method of moments (GMM) estimation framework for the spatial autorregressive (SAR) model in a system of simultaneous equations with…
(more)
▼ This dissertation proposes a generalized method of moments (GMM) estimation framework for the spatial autorregressive (SAR) model in a system of simultaneous equations with homoskedastic and heteroskedastic disturbances. It includes two chapters based on joint work with Prof. Xiaodong Liu.
The first chapter extends the GMM estimator in Lee (2007) to estimate SAR models with endogenous regressors and homoskedastic disturbances. We propose a new set of quadratic moment equations exploring the correlation of the spatially lagged dependent variable with the disturbance term of the main regression equation and with the endogenous regressor. The proposed GMM estimator is more efficient than the IV-based linear estimators in the literature, and computationally simpler than the ML estimator. With carefully constructed quadratic moment equations, the GMM estimator can be asymptotically as efficient as the full information ML estimator. Monte Carlo experiment shows that the proposed GMM estimator performs well in finite samples.
The second chapter proposes a GMM estimator for the SAR model in a system of simultaneous equations with heteroskedastic disturbances. Besides linear moment conditions, the GMM estimator also utilizes quadratic moment conditions based on the covariance structure of model disturbances within and across equations. Compared with the QML approach considered in Yang and Lee (2014), the GMM estimator is easier to implement and robust under heteroskedasticity of an unknown form. We also derive a heteroskedasticity-robust estimator for the asymptotic covariance of the GMM estimator. Monte Carlo experiments show that the proposed GMM estimator performs well in finite samples.
Advisors/Committee Members: Xiaodong Liu, Jem Corcoran, Robert McNown, Scott Savage, Donald Waldman.
Subjects/Keywords: GMM; Heterosgedasticity; IV; Robust; SAR; System of Equations; Economics; Statistical Models
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Saraiva, P. Q. (2015). GMM Estimation of Spatial Autoregressive Models in a System of Simultaneous Equations. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/econ_gradetds/63
Chicago Manual of Style (16th Edition):
Saraiva, Paulo Quinderé. “GMM Estimation of Spatial Autoregressive Models in a System of Simultaneous Equations.” 2015. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/econ_gradetds/63.
MLA Handbook (7th Edition):
Saraiva, Paulo Quinderé. “GMM Estimation of Spatial Autoregressive Models in a System of Simultaneous Equations.” 2015. Web. 25 Jan 2021.
Vancouver:
Saraiva PQ. GMM Estimation of Spatial Autoregressive Models in a System of Simultaneous Equations. [Internet] [Doctoral dissertation]. University of Colorado; 2015. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/econ_gradetds/63.
Council of Science Editors:
Saraiva PQ. GMM Estimation of Spatial Autoregressive Models in a System of Simultaneous Equations. [Doctoral Dissertation]. University of Colorado; 2015. Available from: https://scholar.colorado.edu/econ_gradetds/63
University of Colorado
29.
Dunlap, Colton Ray.
Reverberation Chamber Characterization Using Enhanced Backscatter Coefficient Measurements.
Degree: PhD, Electrical, Computer & Energy Engineering, 2013, University of Colorado
URL: https://scholar.colorado.edu/ecen_gradetds/74
► The primary focus of this thesis is to evaluate the use of the enhanced backscatter coefficient as a quantity for characterizing the spatial uniformity…
(more)
▼ The primary focus of this thesis is to evaluate the use of the enhanced backscatter coefficient as a quantity for characterizing the spatial uniformity of the reverberation chamber (RC). An RC is a statistical measurement facility constructed from a large metallic hallow cavity containing an irregularly shaped paddle stirrer for mixing electromagnetic fields to obtain many statistically independent samples. The average power, measured from antennas placed inside of the RC, is ideally uniform over any chosen antenna position and orientation within the RCs working volume. Spatial uniformity is a fundamental assumption to all RC theoretical analysis, and thus the spatial dependence of the RC is directly related to the uncertainty of the measurements. Comparisons are made with standard multiple-configuration measurements (different antenna positions) to show that comparable values of standard deviation caused by spatial non-uniformity are obtained using the transfer function (as typically used) and the enhanced backscatter coefficient. Additionally, it is shown that the enhanced backscatter coefficient for an ideal RC is theoretically a constant value of 2, but has variation over frequency when measured. This variation over frequency is used in a single-configuration measurement to obtain values of standard deviation that are nearly the same as those found using multiple-configuration measurements. This is possible because the statistical variation of the reverberation chamber is similar over frequency and over different measurement positions. Furthermore, data is presented from various tests showing that the value of the enhanced backscatter coefficient is sensitive to calibration issues, and the improper use of frequency stirring. This helps to justify that the enhanced backscatter coefficient can be used as a benchmark quantity for determining if computations from the RC measured data are useful and can be trusted. One- and two-dimensional Greens function models are also used to explore the enhanced backscatter coefficient value for different types of stirring mechanisms. Lastly, application of the enhanced backscatter coefficient for determining the total efficiency of an antenna measured in the reverberation chamber is presented. Along with the estimates of total efficiency, the confidence interval of the results is computed from the frequency variation of the enhanced backscatter coefficient.
Advisors/Committee Members: Edward Kuester, Christopher Holloway, Scott E. Palo, David A. Hill, Jem Corcoran.
Subjects/Keywords: antenna efficiency; enhanced backscatter; Green's function model; power delay profile; reverberation chamber; statistical measurement; Electromagnetics and Photonics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Dunlap, C. R. (2013). Reverberation Chamber Characterization Using Enhanced Backscatter Coefficient Measurements. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/ecen_gradetds/74
Chicago Manual of Style (16th Edition):
Dunlap, Colton Ray. “Reverberation Chamber Characterization Using Enhanced Backscatter Coefficient Measurements.” 2013. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/ecen_gradetds/74.
MLA Handbook (7th Edition):
Dunlap, Colton Ray. “Reverberation Chamber Characterization Using Enhanced Backscatter Coefficient Measurements.” 2013. Web. 25 Jan 2021.
Vancouver:
Dunlap CR. Reverberation Chamber Characterization Using Enhanced Backscatter Coefficient Measurements. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/ecen_gradetds/74.
Council of Science Editors:
Dunlap CR. Reverberation Chamber Characterization Using Enhanced Backscatter Coefficient Measurements. [Doctoral Dissertation]. University of Colorado; 2013. Available from: https://scholar.colorado.edu/ecen_gradetds/74
. 
Open Access Theses and Dissertations