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University of Colorado
1.
Aguiar, Izabel Pirimai.
Dynamic Active Subspaces: a Data-Driven Approach to Computing Time-Dependent Active Subspaces in Dynamical Systems.
Degree: MS, 2018, University of Colorado
URL: https://scholar.colorado.edu/csci_gradetds/169 
► Computational models are aiding in the advancement of science – from biological, to engineering, to social systems. To trust the predictions of computational models, however,…
(more)
▼ Computational models are aiding in the advancement of science – from biological, to engineering, to social systems. To trust the predictions of computational models, however, we must understand how the errors in the models’ inputs (i.e., through measurement error) affect the output of the systems: we must quantify the uncertainty that results from these input errors. Uncertainty quantification (UQ) becomes computationally complex when there are many parameters in the model. In such cases it is useful to reduce the dimension of the problem by identifying unimportant parameters and disregarding them for UQ studies. This makes an otherwise intractable UQ problem tractable. <i>Active subspaces</i> extend this idea by identifying important linear combinations of parameters, enabling more powerful and effective dimension reduction. Although active subspaces give model insight and computational tractability for scalar-valued functions, it is not enough. This analysis does not extend to time-dependent systems. In this thesis we discuss time-dependent, dynamic active subspaces. We develop a methodology by which to compute and approximate dynamic active subspaces, and introduce the analytical form of dynamic active subspaces for two cases. To highlight these methods we find dynamic active subspaces for a linear harmonic oscillator and a nonlinear enzyme kinetics system.
Advisors/Committee Members: Paul G. Constantine, Elizabeth Bradley, James Curry, Gianluca Iaccarino.
Subjects/Keywords: active subspaces; dimension reduction; dynamical systems; mathematical biology; sensitivity analysis; uncertainty quantification; Applied Mathematics; Computer Sciences
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APA (6th Edition):
Aguiar, I. P. (2018). Dynamic Active Subspaces: a Data-Driven Approach to Computing Time-Dependent Active Subspaces in Dynamical Systems. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/169
Chicago Manual of Style (16th Edition):
Aguiar, Izabel Pirimai. “Dynamic Active Subspaces: a Data-Driven Approach to Computing Time-Dependent Active Subspaces in Dynamical Systems.” 2018. Masters Thesis, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/csci_gradetds/169.
MLA Handbook (7th Edition):
Aguiar, Izabel Pirimai. “Dynamic Active Subspaces: a Data-Driven Approach to Computing Time-Dependent Active Subspaces in Dynamical Systems.” 2018. Web. 23 Jan 2021.
Vancouver:
Aguiar IP. Dynamic Active Subspaces: a Data-Driven Approach to Computing Time-Dependent Active Subspaces in Dynamical Systems. [Internet] [Masters thesis]. University of Colorado; 2018. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/csci_gradetds/169.
Council of Science Editors:
Aguiar IP. Dynamic Active Subspaces: a Data-Driven Approach to Computing Time-Dependent Active Subspaces in Dynamical Systems. [Masters Thesis]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/csci_gradetds/169
University of Colorado
2.
Azofeifa, Joseph Gaspare.
Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity.
Degree: PhD, 2017, University of Colorado
URL: https://scholar.colorado.edu/csci_gradetds/193
► Seventy-six percent of disease associated variants occur in non-genic sites of open chromatin suggesting that the regulation of gene expression plays a crucial role…
(more)
▼ Seventy-six percent of disease associated variants occur in non-genic sites of open chromatin suggesting that the regulation of gene expression plays a crucial role in human health. Nucleosome- free with flanking chromatin modifications, these regulatory loci are optimal platforms for tran- scription binding and, in fact, recruit RNA Polymerase. The subsequent transcription of these sites is an unintuitive discovery as these regulatory loci do not harbor an open reading frame. The role these enhancer RNAs (eRNA) play in downstream gene regulation remains an open and exciting question. However, fast RNA degradation rates challenge eRNA identification, requiring non-traditional sequencing technologies. Global Run-on followed by sequencing (GRO- seq) detects non-genic transcription and thus, in theory, eRNA presence. Yet GRO-seq is not without noise and bias, predictive modeling of both the sequencing error and the stochastic nature of RNA polymerase itself is required to discover enhancer RNA transcripts. In short, this thesis asks: what regulates eRNA transcription? To answer this question, I first develop two novel probabilistic models to unbiasedly determine eRNA location. A regression method was constructed to quickly identify all transcribed regions in GRO-seq. Based on the known enzymatic stages of RNA polymerase, a subsequent latent variable model was built to infer the precise location of eRNA initiation. With the relevant technology developed, I undertake a massive data integration project and show strong contextual relationships between TF-binding events, epigenetics and eRNA transcription. I conclude by showing that enhancer RNAs can unbiasedly quantify transcription factor activity and predict cell type.
Advisors/Committee Members: Robin Dowell, Aaron Clauset, Elizabeth Bradley, Michael Mozer.
Subjects/Keywords: genetics; gro-seq; hidden markov models; high throughput sequencing; machine learning; mixture models; Bioinformatics; Computer Sciences
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APA (6th Edition):
Azofeifa, J. G. (2017). Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/193
Chicago Manual of Style (16th Edition):
Azofeifa, Joseph Gaspare. “Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity.” 2017. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/csci_gradetds/193.
MLA Handbook (7th Edition):
Azofeifa, Joseph Gaspare. “Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity.” 2017. Web. 23 Jan 2021.
Vancouver:
Azofeifa JG. Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/csci_gradetds/193.
Council of Science Editors:
Azofeifa JG. Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/csci_gradetds/193
University of Colorado
3.
Nelson, Thomas Harrison.
Genetic Algorithms with Chaotic Population Dynamics.
Degree: MS, Computer Science, 2010, University of Colorado
URL: https://scholar.colorado.edu/csci_gradetds/18
► In this thesis I demonstrate a novel application of chaotic dynamics to evolutionary algorithms, specifically in population size management. Typical evolutionary algorithms require a…
(more)
▼ In this thesis I demonstrate a novel application of chaotic dynamics to evolutionary algorithms, specifically in population size management. Typical evolutionary algorithms require a population size to be set as a parameter, which remains constant throughout execution. I created a new algorithm that can vary the population size chaotically or periodically, and do a series of performance tests comparing static, periodic, and chaotic population control. The problems targeted in these tests are chosen from both continuous and discrete multi-dimensional domains. I find that both chaotic and static population control perform well in certain situations; my evidence suggests that periodic population control is rarely a good choice. I also present additional analysis on the effects of the population dynamics and how they relate to mean population size and variance in the performance results.
Advisors/Committee Members: Elizabeth Bradley, Robin Dowell, Richard Byrd.
Subjects/Keywords: algorithms; population size management; Theory and Algorithms
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APA (6th Edition):
Nelson, T. H. (2010). Genetic Algorithms with Chaotic Population Dynamics. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/18
Chicago Manual of Style (16th Edition):
Nelson, Thomas Harrison. “Genetic Algorithms with Chaotic Population Dynamics.” 2010. Masters Thesis, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/csci_gradetds/18.
MLA Handbook (7th Edition):
Nelson, Thomas Harrison. “Genetic Algorithms with Chaotic Population Dynamics.” 2010. Web. 23 Jan 2021.
Vancouver:
Nelson TH. Genetic Algorithms with Chaotic Population Dynamics. [Internet] [Masters thesis]. University of Colorado; 2010. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/csci_gradetds/18.
Council of Science Editors:
Nelson TH. Genetic Algorithms with Chaotic Population Dynamics. [Masters Thesis]. University of Colorado; 2010. Available from: https://scholar.colorado.edu/csci_gradetds/18
University of Colorado
4.
Garland, Joshua T.
Prediction in Projection: Computer Performance Forecasting, a Dynamical Systems Approach.
Degree: MS, Applied Mathematics, 2011, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/13
► Recent work in the field of dynamical systems provides evidence that computer systems are nonlinear-deterministic dynamical systems. This implies the existence of a deterministic…
(more)
▼ Recent work in the field of dynamical systems provides evidence that computer systems are nonlinear-deterministic dynamical systems. This implies the existence of a deterministic update rule, which, in turn, implies the existence of a deterministic forecasting rule for the state variables of a running computer. Even a short-term prediction of these quantities, if accurate, could be effective in tailoring system resources on-the-fly to the dynamics of a computing application. For example, a good prediction of processor load could allow a computer to increase its energy efficiency by dynamically turning off unused CPUs, and then turning them back on based on the programs predicted needs. To explore this, I use a custom measurement infrastructure, delay-coordinate embedding and nonlinear time-series analysis to forecast processor load and cache performance of a set of simple C programs running on an Intel Core2 Duo. This proved to be quite effective. However, the use of traditional embedding techniques `on the fly' is impractical due to the time required to correctly perform the processing and post-processing of the data. My alternative to this is to use arbitrary low-dimensional projections. While this is not consistent with the requirements in the current literature, recent work by Mischaikow suggests that this alternative might work. I verified this conjecture, showing that forecasts based on two-dimensional projections are largely as effective as strategies that use the full embedded dynamics. This is in contrast to the current view in the nonlinear dynamics community that a one-to-one delay map is sufficient for successful prediction using delay coordinate embedding. My results suggest that this may not be a necessary condition. The success of the projection-based forecasting schemes brings into questions the need for full topological conjugacy in forecasting schema. The results presented here suggest ways of improving computer design at a systems level; they also provide evidence to support the use of semi-conjugacies in forecasting schemes.
Advisors/Committee Members: Elizabeth Bradley, James Meiss, Bob Easton.
Subjects/Keywords: Applied Mathematics; Numerical Analysis and Computation
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APA (6th Edition):
Garland, J. T. (2011). Prediction in Projection: Computer Performance Forecasting, a Dynamical Systems Approach. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/13
Chicago Manual of Style (16th Edition):
Garland, Joshua T. “Prediction in Projection: Computer Performance Forecasting, a Dynamical Systems Approach.” 2011. Masters Thesis, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/appm_gradetds/13.
MLA Handbook (7th Edition):
Garland, Joshua T. “Prediction in Projection: Computer Performance Forecasting, a Dynamical Systems Approach.” 2011. Web. 23 Jan 2021.
Vancouver:
Garland JT. Prediction in Projection: Computer Performance Forecasting, a Dynamical Systems Approach. [Internet] [Masters thesis]. University of Colorado; 2011. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/appm_gradetds/13.
Council of Science Editors:
Garland JT. Prediction in Projection: Computer Performance Forecasting, a Dynamical Systems Approach. [Masters Thesis]. University of Colorado; 2011. Available from: https://scholar.colorado.edu/appm_gradetds/13
University of Colorado
5.
Alexander, Zachary.
A Topology-Based Approach for Nonlinear Time Series with Applications in Computer Performance Analysis.
Degree: PhD, Applied Mathematics, 2012, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/24
► We present a topology-based methodology for the analysis of experimental data generated by a discrete-time, nonlinear dynamical system. This methodology has significant applications in…
(more)
▼ We present a topology-based methodology for the analysis of experimental data generated by a discrete-time, nonlinear dynamical system. This methodology has significant applications in the field of computer performance analysis. Our approach consists of two parts. In the first part, we propose a novel signal separation algorithm that exploits the continuity of the dynamical system being studied. We use established tools from computational topology to test the connectedness of various regions of state space. In particular, a connected region of space that has a disconnected image under the experimental dynamics suggests the presence of multiple signals in the data. Using this as a guideline, we are able to model experimental data as an Iterated Function System (IFS). We demonstrate the success of our algorithm on several synthetic examples – including a Henon-like IFS. Additionally, we successfully model experimental computer performance data as an IFS. In the second part of the analysis, we represent an experimental dynamical system with an algebraic structure that allows for the computation of algebraic topological invariants. Previous work has shown that a cubical grid and the associated cubical complex are effective tools that can be used to identify isolating neighborhoods and compute the corresponding Conley Index – thereby rigorously verifying the existence of periodic orbits and/or chaotic dynamics. Our contribution is to adapt this technique by altering the underlying data structure – improving flexibility and efficiency. We represent the state space of the dynamical system with a simplicial complex and its induced simplicial multivalued map. This contains information about both geometry and dynamics, whereas the cubical complex is restricted by the geometry of the experimental data. This representation has several advantages; most notably, the complexity of the algorithm that generates the associated simplicial multivalued map is linear in the number of data points – as opposed to exponential in dimension for the cubical multivalued map. The synthesis of the two parts of our methodology results in a nonlinear time-series analysis framework that is particularly well suited for computer performance analysis. Complex computer programs naturally switch between `regimes' and are appropriately modeled as IFSs by part one of our program. Part two of our methodology provides the correct tools for analyzing each regime independently.
Advisors/Committee Members: Elizabeth Bradley, James D. Meiss, James Curry.
Subjects/Keywords: Applied Mathematics; Computer Sciences
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APA (6th Edition):
Alexander, Z. (2012). A Topology-Based Approach for Nonlinear Time Series with Applications in Computer Performance Analysis. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/24
Chicago Manual of Style (16th Edition):
Alexander, Zachary. “A Topology-Based Approach for Nonlinear Time Series with Applications in Computer Performance Analysis.” 2012. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/appm_gradetds/24.
MLA Handbook (7th Edition):
Alexander, Zachary. “A Topology-Based Approach for Nonlinear Time Series with Applications in Computer Performance Analysis.” 2012. Web. 23 Jan 2021.
Vancouver:
Alexander Z. A Topology-Based Approach for Nonlinear Time Series with Applications in Computer Performance Analysis. [Internet] [Doctoral dissertation]. University of Colorado; 2012. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/appm_gradetds/24.
Council of Science Editors:
Alexander Z. A Topology-Based Approach for Nonlinear Time Series with Applications in Computer Performance Analysis. [Doctoral Dissertation]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/appm_gradetds/24
University of Colorado
6.
Virkar, Yogesh.
Effects of Multilayer Network Interactions on Neural Network Dynamics.
Degree: PhD, Computer Science, 2017, University of Colorado
URL: https://scholar.colorado.edu/csci_gradetds/149
► Networks of excitable units are found in varied disciplines such as social science, neuroscience, genetics, epidemiology, etc. Previous studies have shown that some aspects of…
(more)
▼ Networks of excitable units are found in varied disciplines such as social science, neuroscience, genetics, epidemiology, etc. Previous studies have shown that some aspects of network function can be optimized when the network operates in the 'critical regime', i.e., at the boundary between order and disorder where the statistics of node excitations correspond to those of a classical branching process. In this thesis, we introduce and study a mathematical model of a neural network with the goal of understanding the long-standing problem of determining the mechanisms by which a neural network regulates its activity so as to operate in the critical regime. In particular, we study the dynamics of a two-layered network model consisting of an excitable node network and a complementary network that supplies resources required for node firing. More specifically, we study the dynamics of an excitable neural network consisting of neurons (nodes) connected via synapses (edges). Synaptic strengths are mediated by resources supplied by the complementary glial cell network. Resources from the bloodstream are supplied to the glial network at some fixed rate, resources transport diffusively within the glial cell network and ultimately to the synapses, and each time a presynaptic neuron fires the resources for all outgoing synapses get consumed at some fixed rate. We show that this natural and very compelling mechanism for feedback control can stabilize the critical state. Additionally, the neural network can learn, remember and recover the critical state after learning. The critical state is characterized by power-law distributed avalanche sizes that are robust to changes in the supply, consumption and diffusion rates. Finally, we show that our findings are fairly robust to heterogeneity in model parameters or network structure.
Advisors/Committee Members: Juan G. Restrepo, Elizabeth Bradley, Rafael Frongillo, Aaron Clauset.
Subjects/Keywords: criticality; glia; multilayer networks; network dynamics; neural networks; neuronal avalanches; Applied Mechanics; Computer Sciences; Neurosciences
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APA (6th Edition):
Virkar, Y. (2017). Effects of Multilayer Network Interactions on Neural Network Dynamics. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/149
Chicago Manual of Style (16th Edition):
Virkar, Yogesh. “Effects of Multilayer Network Interactions on Neural Network Dynamics.” 2017. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/csci_gradetds/149.
MLA Handbook (7th Edition):
Virkar, Yogesh. “Effects of Multilayer Network Interactions on Neural Network Dynamics.” 2017. Web. 23 Jan 2021.
Vancouver:
Virkar Y. Effects of Multilayer Network Interactions on Neural Network Dynamics. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/csci_gradetds/149.
Council of Science Editors:
Virkar Y. Effects of Multilayer Network Interactions on Neural Network Dynamics. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/csci_gradetds/149
University of Colorado
7.
Ikehara, Kansuke.
The Structure of Complex Networks Across Domains.
Degree: MS, Computer Science, 2016, University of Colorado
URL: https://scholar.colorado.edu/csci_gradetds/159
► The structure of complex networks has been of interest in many scientific and engineering disciplines over the decades. A number of studies in the field…
(more)
▼ The structure of complex networks has been of interest in many scientific and engineering disciplines over the decades. A number of studies in the field have been focused on finding the common properties among different kinds of networks such as heavy-tail degree distribution, small-worldness and modular structure and trying to establish a theory of structural universality in complex networks. However, there is no comprehensive study of network structure across a diverse set of domains in order to explain the structural diversity we observe in the real-world networks. In this paper, we study 986 real-world networks of diverse domains ranging from ecological food webs to online social networks along with 575 networks generated from four popular network models. Our study utilizes a number of machine learning techniques such as random forest and confusion matrix in order to show the relationships among network domains in terms of network structure. Our results indicate that there are some partitions of network categories in which networks are hard to distinguish based purely on network structure. We have found that these partitions of network categories tend to have similar underlying functions, constraints and/or generative mechanisms of networks even though networks in the same partition have different origins, e.g., biological processes, results of engineering by human being, etc. This suggests that the origin of a network, whether it's biological, technological or social, may not necessarily be a decisive factor of the formation of similar network structure. Our findings shed light on the possible direction along which we could uncover the hidden principles for the structural diversity of complex networks.
Advisors/Committee Members: Aaron Clauset, Elizabeth Bradley, Jordan Boyd-Graber.
Subjects/Keywords: complex networks; machine learning; network structure; social networks; engineering; Applied Statistics; Computer Sciences
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APA (6th Edition):
Ikehara, K. (2016). The Structure of Complex Networks Across Domains. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/159
Chicago Manual of Style (16th Edition):
Ikehara, Kansuke. “The Structure of Complex Networks Across Domains.” 2016. Masters Thesis, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/csci_gradetds/159.
MLA Handbook (7th Edition):
Ikehara, Kansuke. “The Structure of Complex Networks Across Domains.” 2016. Web. 23 Jan 2021.
Vancouver:
Ikehara K. The Structure of Complex Networks Across Domains. [Internet] [Masters thesis]. University of Colorado; 2016. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/csci_gradetds/159.
Council of Science Editors:
Ikehara K. The Structure of Complex Networks Across Domains. [Masters Thesis]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/csci_gradetds/159
University of Colorado
8.
Bennett, Trevor John.
On-Orbit 3-Dimensional Electrostatic Detumble for Generic Spacecraft Geometries.
Degree: PhD, 2017, University of Colorado
URL: https://scholar.colorado.edu/asen_gradetds/226
► In recent years, there is a growing interest in active debris removal and on-orbit servicing of Earth orbiting assets. The growing need for such…
(more)
▼ In recent years, there is a growing interest in active debris removal and on-orbit servicing of Earth orbiting assets. The growing need for such approaches is often exemplified by the Iridium-Kosmos collision in 2009 that generated thousands of debris fragments. There exists a variety of active debris removal and on-orbit servicing technologies in development. Conventional docking mechanisms and mechanical capture by actuated manipulators, exemplified by NASA's Restore-L mission, require slow target tumble rates or more aggressive circumnavigation rate matching. The tumble rate limitations can be overcome with flexible capture systems such nets, harpoons, or tethers yet these systems require complex deployment, towing, and/or interfacing strategies to avoid servicer and target damage. Alternatively, touchless methods overcome the tumble rate limitations by provide detumble control prior to a mechanical interface. This thesis explores electrostatic detumble technology to touchlessly reduce large target rotation rates of Geostationary satellites and debris. The technical challenges preceding flight implementation largely reside in the long-duration formation flying guidance, navigation, and control of a servicer spacecraft equipped with electrostatic charge transfer capability. Leveraging prior research into the electrostatic charging of spacecraft, electrostatic detumble control formulations are developed for both axisymmetric and generic target geometries. A novel relative position vector and associated relative orbit control approach is created to manage the long-duration proximity operations. Through detailed numerical simulations, the proposed detumble and relative motion control formulations demonstrate detumble of several thousand kilogram spacecraft tumbling at several degrees per second in only several days. The availability, either through modeling or sensing, of the relative attitude, relative position, and electrostatic potential are among key concerns with implementation of electrostatic detumble control on-orbit. Leveraging an extended Kalman filter scheme, the relative position information is readily obtained. In order to touchlessly acquire the target electrostatic potential, a nested two-time scale Kalman filter is employed to provide real-time estimates of both relative position and electrostatic potential while on-orbit. The culmination of the presented control formulations for generic spacecraft geometries, the proximity and formation flying control capability, and the availability of necessary state information provide significant contributions towards the viability of electrostatic detumble mission concepts.
Advisors/Committee Members: Hanspeter Schaub, Jay McMahon, Jeffrey Parker, Elizabeth Bradley, Zoltan Sternovsky.
Subjects/Keywords: contactless/touchless; electrostatic actuation; formation flying; orbital debris; relative navigation; Aerospace Engineering; Physics
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APA (6th Edition):
Bennett, T. J. (2017). On-Orbit 3-Dimensional Electrostatic Detumble for Generic Spacecraft Geometries. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/226
Chicago Manual of Style (16th Edition):
Bennett, Trevor John. “On-Orbit 3-Dimensional Electrostatic Detumble for Generic Spacecraft Geometries.” 2017. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/asen_gradetds/226.
MLA Handbook (7th Edition):
Bennett, Trevor John. “On-Orbit 3-Dimensional Electrostatic Detumble for Generic Spacecraft Geometries.” 2017. Web. 23 Jan 2021.
Vancouver:
Bennett TJ. On-Orbit 3-Dimensional Electrostatic Detumble for Generic Spacecraft Geometries. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/asen_gradetds/226.
Council of Science Editors:
Bennett TJ. On-Orbit 3-Dimensional Electrostatic Detumble for Generic Spacecraft Geometries. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/asen_gradetds/226
University of Colorado
9.
Azofeifa, Joseph Gaspare.
Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity.
Degree: PhD, 2017, University of Colorado
URL: https://scholar.colorado.edu/csci_gradetds/137
► Seventy-six percent of disease associated variants occur in non-genic sites of open chromatin suggesting that the regulation of gene expression plays a crucial role…
(more)
▼ Seventy-six percent of disease associated variants occur in non-genic sites of open chromatin suggesting that the regulation of gene expression plays a crucial role in human health. Nucleosome-free with flanking chromatin modifications, these regulatory loci are optimal platforms for transcription binding and, in fact, recruit RNA Polymerase. The subsequent transcription of these sites is an unintuitive discovery as these regulatory loci do not harbor an open reading frame.
The role these enhancer RNAs (eRNA) play in downstream gene regulation remains an open and exciting question. However, fast RNA degradation rates challenge eRNA identification, requiring non-traditional sequencing technologies. Global Run-on followed by sequencing (GRO- seq) detects non-genic transcription and thus, in theory, eRNA presence. Yet GRO-seq is not without noise and bias, predictive modeling of both the sequencing error and the stochastic nature of RNA polymerase itself is required to discover enhancer RNA transcripts.
In short, this thesis asks: what regulates eRNA transcription? To answer this question, I first develop two novel probabilistic models to unbiasedly determine eRNA location. A regression method was constructed to quickly identify all transcribed regions in GRO-seq. Based on the known enzymatic stages of RNA polymerase, a subsequent latent variable model was built to infer the precise location of eRNA initiation. With the relevant technology developed, I undertake a massive data integration project and show strong contextual relationships between TF-binding events, epigenetics and eRNA transcription. I conclude by showing that enhancer RNAs can unbiasedly quantify transcription factor activity and predict cell type.
Advisors/Committee Members: Robin Dowell, Aaron Clauset, Michael Mozer, Elizabeth Bradley, Katerina Kechris.
Subjects/Keywords: genetics; GRO-seq; hidden Markov models; high throughput sequencing; machine learning; mixture models; Bioinformatics; Molecular Genetics
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APA ·
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MLA ·
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APA (6th Edition):
Azofeifa, J. G. (2017). Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/137
Chicago Manual of Style (16th Edition):
Azofeifa, Joseph Gaspare. “Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity.” 2017. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/csci_gradetds/137.
MLA Handbook (7th Edition):
Azofeifa, Joseph Gaspare. “Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity.” 2017. Web. 23 Jan 2021.
Vancouver:
Azofeifa JG. Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/csci_gradetds/137.
Council of Science Editors:
Azofeifa JG. Stochastic Modeling of RNA Polymerase Predicts Transcription Factor Activity. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/csci_gradetds/137
University of Colorado
10.
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
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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 23, 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. 23 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 23].
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
11.
Sanderson, Nicole F.
Topological Data Analyses of Time Series Using Witness Complexes.
Degree: PhD, 2018, University of Colorado
URL: https://scholar.colorado.edu/math_gradetds/67
► Real-time regime shift detection between chaotic dynamical systems via time series analysis demands quick and correct, theoretically guaranteed methods. Often the best implemented techniques in…
(more)
▼ Real-time regime shift detection between chaotic dynamical systems via time series analysis demands quick and correct, theoretically guaranteed methods. Often the best implemented techniques in the field are well-motivated heuristics and even interpretable statistics are scarce. Topological data analysis can contribute to the canon of traditional methods for analyzing nonlinear time series but is not computationally cheap. We introduce a topological membership test for sliding windows of time series data that uses a sparse simplicial complex - the witness complex - to model the data and assess its performance across a range of model parameters affecting computational efficiency. We then explore how the topology of witness complexes changes across this range of model parameters. We next define a simplicial complex whose construction incorporates the temporal information available with time series data. We experimentally show that this construction results in filtrations with fewer simplices and improved topological signature. We apply our techniques to synthetic time series data including numerical solutions of classical low dimensional chaotic systems Lorenz and Rössler systems of ODEs as well as regimes of the higher dimensional Brunel neuronal network model and experimental live voltage recordings of musical instruments.
Advisors/Committee Members: Carla Farsi, James D. Meiss, Elizabeth Bradley, Markus Pflaum, Judith Packer.
Subjects/Keywords: topological data analyses; time series; witness complexes; filtrations; low dimensional chaotic systems; Applied Mathematics; Computer Sciences; Mathematics
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APA (6th Edition):
Sanderson, N. F. (2018). Topological Data Analyses of Time Series Using Witness Complexes. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/67
Chicago Manual of Style (16th Edition):
Sanderson, Nicole F. “Topological Data Analyses of Time Series Using Witness Complexes.” 2018. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/math_gradetds/67.
MLA Handbook (7th Edition):
Sanderson, Nicole F. “Topological Data Analyses of Time Series Using Witness Complexes.” 2018. Web. 23 Jan 2021.
Vancouver:
Sanderson NF. Topological Data Analyses of Time Series Using Witness Complexes. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/math_gradetds/67.
Council of Science Editors:
Sanderson NF. Topological Data Analyses of Time Series Using Witness Complexes. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/math_gradetds/67
University of Colorado
12.
Hoenigman, Rhonda.
Optimizing implicit plant interactions to conserve water on residential landscapes.
Degree: PhD, Computer Science, 2012, University of Colorado
URL: https://scholar.colorado.edu/csci_gradetds/45
► In drought-prone environments, interactions between plants can enable individuals to conserve water. The physical location of each individual not only influences its resource needs,…
(more)
▼ In drought-prone environments, interactions between plants can enable individuals to conserve water. The physical location of each individual not only influences its resource needs, but also affects the availability of resources on the landscape. This thesis seeks to model this observed behavior in natural systems and use that model to create a new optimization approach for water conservation in residential systems in drought-prone climates. In this research, the arrangement of plants on a landscape is treated as a location optimization problem where the objective is to find the best locations for a given set of plants on a landscape with a given set of resources.
The biological properties of the domain make this optimization problem novel. The search space is influenced by what I call it{neighbor effects}, which include heterogeneity, locality, and feedback. Plants are heterogeneous, both in their requirements for growth and in their effects on their surroundings. Interactions with other plants are primarily local, and can either increase or decrease growth depending on the types of plants involved and the resources on the landscape. These interactions also mean that distance is best treated it{implicitly} in modeling the effects of the interactions, rather than it{explicitly} as it is in most location problems. Both heterogeneity and locality generate feedback conditions, whereby the positioning of a plant on a landscape changes the resources available at that location. The placement of a tree, for example, changes the light available nearby, which then affects the growth of any plants located in those modified conditions.
The model presented here captures the domain-specific features of this problem using an agent-based strategy. In this model, each plant is an agent that ``lives'' on a simulated landscape. Agents have light and water requirements for growth, selected to match the requirements of real plants, and a growth curve that determines agent fitness in simulated light and water conditions. A multiobjective fitness function captures the trade-off between maximizing plant agent growth on the landscape and minimizing each agent's water use. The total water needed on the landscape is the emergent property of this individual behavior.
Two optimization strategies commonly used on location problems – simulated annealing and a genetic algorithm – are applied to find the locations on the landscape that maximize the fitness score. These strategies are compared to an agent-based optimization routine that is designed to capitalize on the novel features of this domain. In this approach, agents maximize their own individual fitness instead of the global fitness on the landscape. This distributed strategy produces solutions comparable to the genetic algorithm, but in a fraction of the time required for that algorithm.
his work also includes experiments with live plants to generate the data for the agent growth curves and to validate the performance of the optimized…
Advisors/Committee Members: Elizabeth Bradley, Nichole Barger, Nikolaus Correll, Richard Byrd, Manuel Laguna.
Subjects/Keywords: agent-based model; ecological modeling; facilitation; landscape design; location optimization; water conservation; Bioinformatics; Computer Sciences; Environmental Studies
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APA (6th Edition):
Hoenigman, R. (2012). Optimizing implicit plant interactions to conserve water on residential landscapes. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/45
Chicago Manual of Style (16th Edition):
Hoenigman, Rhonda. “Optimizing implicit plant interactions to conserve water on residential landscapes.” 2012. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/csci_gradetds/45.
MLA Handbook (7th Edition):
Hoenigman, Rhonda. “Optimizing implicit plant interactions to conserve water on residential landscapes.” 2012. Web. 23 Jan 2021.
Vancouver:
Hoenigman R. Optimizing implicit plant interactions to conserve water on residential landscapes. [Internet] [Doctoral dissertation]. University of Colorado; 2012. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/csci_gradetds/45.
Council of Science Editors:
Hoenigman R. Optimizing implicit plant interactions to conserve water on residential landscapes. [Doctoral Dissertation]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/csci_gradetds/45
University of Colorado
13.
Fox, Adam Merritt.
Destruction of Invariant Tori in Volume-Preserving Maps.
Degree: PhD, Applied Mathematics, 2013, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/36
► Invariant rotational tori play an important role in the dynamics of volume-preserving maps. When integrable, all orbits lie on these tori and KAM theory…
(more)
▼ Invariant rotational tori play an important role in the dynamics of volume-preserving maps. When integrable, all orbits lie on these tori and KAM theory guarantees the persistence of some tori upon perturbation. When these tori have codimension-one they act as boundaries to transport, and therefore play a prominent role in the global stability of the system. For the area-preserving case, Greene's residue criterion is often used to predict the destruction of tori from the properties of nearby periodic orbits. Even though KAM theory applies to the three-dimensional case, the robustness of tori in such systems is still poorly understood. This dissertation begins by extending Greene's residue criterion to three-dimensional, reversible, volume-preserving maps.
The application of Greene's residue criterion requires the repeated computation of periodic orbits, which is costly if the system is nonreversible. We describe a quasi-Newton, Fourier-based scheme to numerically compute the conjugacy of a torus and demonstrate how the growth of the Sobolev norm or singular values of this conjugacy can be used to predict criticality. We will then use this method to study both reversible and nonreversible volume-preserving maps in two and three dimensions. The near-critical conjugacies, and the gaps that form within them, will be explored in the context of Aubry-Mather and Anti-Integrability theory, when applicable. This dissertation will conclude by exploring the locally and globally most robust tori in area-preserving maps.
Advisors/Committee Members: James D. Meiss, Juan Restrepo, Keith Julien, Elizabeth Bradley, James Curry.
Subjects/Keywords: KAM theory; Greene's residue criterion; near-critical conjugacies; Applied Mathematics
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APA ·
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APA (6th Edition):
Fox, A. M. (2013). Destruction of Invariant Tori in Volume-Preserving Maps. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/36
Chicago Manual of Style (16th Edition):
Fox, Adam Merritt. “Destruction of Invariant Tori in Volume-Preserving Maps.” 2013. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/appm_gradetds/36.
MLA Handbook (7th Edition):
Fox, Adam Merritt. “Destruction of Invariant Tori in Volume-Preserving Maps.” 2013. Web. 23 Jan 2021.
Vancouver:
Fox AM. Destruction of Invariant Tori in Volume-Preserving Maps. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/appm_gradetds/36.
Council of Science Editors:
Fox AM. Destruction of Invariant Tori in Volume-Preserving Maps. [Doctoral Dissertation]. University of Colorado; 2013. Available from: https://scholar.colorado.edu/appm_gradetds/36
University of Colorado
14.
Bezrouk, Collin J.
Ballistic Capture into Lunar and Martian Distant Retrograde Orbits.
Degree: PhD, Aerospace Engineering Sciences, 2016, University of Colorado
URL: https://scholar.colorado.edu/asen_gradetds/147
► Distant retrograde orbits (DROs) are a neutrally stable class of three-body orbits. Because of their stability, DROs cannot be targeted with a low-energy transfer…
(more)
▼ Distant retrograde orbits (DROs) are a neutrally stable class of three-body orbits. Because of their stability, DROs cannot be targeted with a low-energy transfer along a stable manifold like unstable three-body orbits in the circular restricted three-body problem (CR3BP). However, in more complicated dynamical models, the effects of small perturbing forces can be exploited to build ballistic capture trajectories (BCTs) into DROs. We develop a method for building sets of BCTs for a particular reference DRO with recommendations for minimizing computational effort. Sets of BCTs are generated in the Earth-Moon system and the Mars-Phobos system due to their applicability to near-term missions and large difference in mass parameters. These BCT sets are stochastically analyzed to determine the range of conditions necessary for using a BCT, such as energy, solar system geometry, and origin. The nature of the DRO after the spacecraft is captured is studied, including minor body flyby altitudes and variations in the size and shape over time.
After a spacecraft has used a BCT, it can decrease its sensitivity to perturbations and extend its mission duration with a series of stabilizing maneuvers. Quasi-periodic orbits are constructed in the Earth-Moon CR3BP that lie on the boundary of stability, and closely resemble the DROs that result from using a BCT. Minimum cost transfers are then constructed between these quasi-periodic orbits and a target periodic DRO using a variety of methods for searching and optimizing. It is discovered that BCTs that target planar quasi-periodic DROs can be stabilized for about 15% of the cost of stabilizing a BCT with large out-of-plane motion.
Once a spacecraft is in a stable DRO, the long duration evolution of that orbit is of interest. Using a high fidelity dynamical model and numerical precision techniques, the evolution of several DROs in the Earth-Moon system is studied over a period of 30,000 years. The perturbing forces that cause a DRO to transition into an unstable orbit are identified and analyzed. DROs larger than 60,000~km grow in amplitude due to solar gravity until they depart the Moon after several centuries. DROs smaller than 45,000~km remain stable for 25,000 years or more, but decay in size due to the Moon's solid tide bulge, which eventually causes the DRO to depart the Moon. The DROs evolve chaotically and occasionally experience periods of relatively fast amplitude growth when the period of the DRO is in resonance with the frequency of particular perturbing forces.
Advisors/Committee Members: Jeffrey S. Parker, Daniel Scheeres, Daniel Kubitschek, Elizabeth Bradley, Daven Henze.
Subjects/Keywords: ballistic capture; distant retrograde orbit; low-energy; mission design; Phobos; weak stability boundary; Aerospace Engineering
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APA (6th Edition):
Bezrouk, C. J. (2016). Ballistic Capture into Lunar and Martian Distant Retrograde Orbits. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/147
Chicago Manual of Style (16th Edition):
Bezrouk, Collin J. “Ballistic Capture into Lunar and Martian Distant Retrograde Orbits.” 2016. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/asen_gradetds/147.
MLA Handbook (7th Edition):
Bezrouk, Collin J. “Ballistic Capture into Lunar and Martian Distant Retrograde Orbits.” 2016. Web. 23 Jan 2021.
Vancouver:
Bezrouk CJ. Ballistic Capture into Lunar and Martian Distant Retrograde Orbits. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/asen_gradetds/147.
Council of Science Editors:
Bezrouk CJ. Ballistic Capture into Lunar and Martian Distant Retrograde Orbits. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/asen_gradetds/147
University of Colorado
15.
Van wal, Stefaan.
High-Fidelity Simulation of Small-Body Lander/Rover Spacecraft.
Degree: PhD, 2018, University of Colorado
URL: https://scholar.colorado.edu/asen_gradetds/200
► The scientific return of spacecraft missions that explore solar system small bodies can be increased through the inclusion of surface exploration with deployed probes.…
(more)
▼ The scientific return of spacecraft missions that explore solar system small bodies can be increased through the inclusion of surface exploration with deployed probes. In this dissertation, a methodology is presented that allows for fast, parallel simulation of bouncing trajectories of arbitrary-shaped ballistic probes in the small-body environment. This enables planning of probe deployment and operation, and supports their inclusion on future missions. The coarse small-body shape is modeled using an implicit signed distance field (SDF) that allows for fast collision detection. Statistical features are included onto the SDF using procedural generation techniques. The small-body gravity field is captured using a voxelization of the classical constant-density polyhedron. Surface interactions between a probe and the surface are accounted for using a hard contact model that takes into account restitution and friction. These models are implemented in a GPU environment to allow for the parallel execution of multiple trajectories. The developed simulation framework is applied to perform parametric investigations of probe deployment, which quantify the effects of relevant properties of a probe and its target small body. The probe shape and internal mass distribution are found to strongly affect its deployment dynamics, with near-spherical probes dispersing over greater regions than more distorted shapes. The effect of the surface interactions coefficients on the different shapes variants is quantified. The presence of statistical surface features is also shown to further influence probe dynamics. Finally, the framework is applied to perform a pre-arrival deployment analysis of the MINERVA-II rovers onboard the Hayabusa-2 spacecraft. This analysis identified challenges in the rover deployment and was used to redesign aspects of the nominal rover release sequence. These models will be used to inform the target site selection and follow-on analysis for the Hayabusa-2 mission rover deployments.
Advisors/Committee Members: Daniel J. Scheeres, Hanspeter Schaub, Jay McMahon, Elizabeth Bradley, Simon Tardivel.
Subjects/Keywords: asteroid; comet; deployment; lander; rover; simulation; Aerospace Engineering; Models and Methods
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APA (6th Edition):
Van wal, S. (2018). High-Fidelity Simulation of Small-Body Lander/Rover Spacecraft. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/200
Chicago Manual of Style (16th Edition):
Van wal, Stefaan. “High-Fidelity Simulation of Small-Body Lander/Rover Spacecraft.” 2018. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/asen_gradetds/200.
MLA Handbook (7th Edition):
Van wal, Stefaan. “High-Fidelity Simulation of Small-Body Lander/Rover Spacecraft.” 2018. Web. 23 Jan 2021.
Vancouver:
Van wal S. High-Fidelity Simulation of Small-Body Lander/Rover Spacecraft. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/asen_gradetds/200.
Council of Science Editors:
Van wal S. High-Fidelity Simulation of Small-Body Lander/Rover Spacecraft. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/asen_gradetds/200
University of Colorado
16.
Fujimoto, Kohei.
New Methods in Optical Track Association and Uncertainty Mapping of Earth-Orbiting Objects.
Degree: PhD, Aerospace Engineering Sciences, 2013, University of Colorado
URL: https://scholar.colorado.edu/asen_gradetds/57
► As more and more sensing capabilities for space surveillance are introduced, we expect that both correlated and uncorrelated tracks of resident space objects will…
(more)
▼ As more and more sensing capabilities for space surveillance are introduced, we expect that both correlated and uncorrelated tracks of resident space objects will drastically increase. Existing observation association techniques rely on simplified dynamics, ad hoc association criteria, and linear propagation of Gaussian uncertainty. To maintain an accurate catalog of resident space objects now and into the future, however, a more consistent description of the uncertainty associated with said objects is desired. Two characteristics of the space situational awareness problem are applicable to this goal: that the type of observation significantly influences the geometry of the observational uncertainty, and that the dynamical system is amenable to analytic or semi-analytic solution techniques. In this dissertation, each of these characteristics are examined and ultimately applied to the problem of optical track association, often referred to as the too-short arc problem. First, an analytical method of non-linear uncertainty propagation is discussed. A special solution to the Fokker-Planck equations for deterministic systems and the state transition tensor concept are combined so that, given an analytical expression of both the initial probability distribution and the dynamics, the probability distribution may be expressed analytically for all time. Next, an observation association technique is proposed which involves admissible regions: probability density functions representing not only the measurement errors but also the limited knowledge in the unobserved variables. Bayes' rule is directly applied to associate multiple observations and subsequently obtain an orbit estimate. A quantitative argument on the effects of measurement errors on the admissible region, and consequently direct Bayesian track association, are also given. Finally, the proposed approach to short-arc association and initial orbit determination are applied to optical observations taken at the Astronomical Institute of the
University of Bern. In addition to matching over half of the objects detected by conventional techniques, the proposed method finds two additional objects at or near geostationary altitude, all without a priori information.
Advisors/Committee Members: Daniel J. Scheeres, George H. Born, Penina Axelrad, Elizabeth Bradley, David Vallado.
Subjects/Keywords: admissible region; astrodynamics; optical observations; propagation of uncertainty; space situational awareness; too-short arc; Aerospace Engineering
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APA (6th Edition):
Fujimoto, K. (2013). New Methods in Optical Track Association and Uncertainty Mapping of Earth-Orbiting Objects. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/57
Chicago Manual of Style (16th Edition):
Fujimoto, Kohei. “New Methods in Optical Track Association and Uncertainty Mapping of Earth-Orbiting Objects.” 2013. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/asen_gradetds/57.
MLA Handbook (7th Edition):
Fujimoto, Kohei. “New Methods in Optical Track Association and Uncertainty Mapping of Earth-Orbiting Objects.” 2013. Web. 23 Jan 2021.
Vancouver:
Fujimoto K. New Methods in Optical Track Association and Uncertainty Mapping of Earth-Orbiting Objects. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/asen_gradetds/57.
Council of Science Editors:
Fujimoto K. New Methods in Optical Track Association and Uncertainty Mapping of Earth-Orbiting Objects. [Doctoral Dissertation]. University of Colorado; 2013. Available from: https://scholar.colorado.edu/asen_gradetds/57
University of Colorado
17.
Garland, Joshua.
Prediction in Projection: A New Paradigm in Delay-Coordinate Reconstruction.
Degree: PhD, Computer Science, 2016, University of Colorado
URL: https://scholar.colorado.edu/csci_gradetds/115
► Delay-coordinate embedding is a powerful, time-tested mathematical framework for reconstructing the dynamics of a system from a series of scalar observations. Most of the…
(more)
▼ Delay-coordinate embedding is a powerful, time-tested mathematical framework for reconstructing the dynamics of a system from a series of scalar observations. Most of the associated theory and heuristics are overly stringent for real-world data, however, and real-time use is out of the question due to the expert human intuition needed to use these heuristics correctly. The approach outlined in this thesis represents a paradigm shift away from that traditional approach. I argue that perfect reconstructions are not only unnecessary for the purposes of delay-coordinate based forecasting, but that they can often be less effective than reduced-order versions of those same models. I demonstrate this using a range of low- and high-dimensional dynamical systems, showing that forecast models that employ
imperfect reconstructions of the dynamics –
i.e., models that are not necessarily true embeddings – can produce surprisingly accurate predictions of the future state of these systems. I develop a theoretical framework for understanding why this is so. This framework, which combines information theory and computational topology, also allows one to quantify the amount of predictive structure in a given time series, and even to choose which forecast method will be the most effective for those data.
Advisors/Committee Members: Elizabeth Bradley, James D. Meiss, Aaron Clauset, Sriram Sankaranarayanan, James P. Crutchfield.
Subjects/Keywords: computational topology; delay-coordinate embedding; forecasting; information theory; time-series analysis; Applied Mathematics; Theory and Algorithms
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APA (6th Edition):
Garland, J. (2016). Prediction in Projection: A New Paradigm in Delay-Coordinate Reconstruction. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/csci_gradetds/115
Chicago Manual of Style (16th Edition):
Garland, Joshua. “Prediction in Projection: A New Paradigm in Delay-Coordinate Reconstruction.” 2016. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/csci_gradetds/115.
MLA Handbook (7th Edition):
Garland, Joshua. “Prediction in Projection: A New Paradigm in Delay-Coordinate Reconstruction.” 2016. Web. 23 Jan 2021.
Vancouver:
Garland J. Prediction in Projection: A New Paradigm in Delay-Coordinate Reconstruction. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/csci_gradetds/115.
Council of Science Editors:
Garland J. Prediction in Projection: A New Paradigm in Delay-Coordinate Reconstruction. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/csci_gradetds/115
University of Colorado
18.
Surovik, David Allen.
Autonomous Mission Design in Extreme Orbit Environments.
Degree: PhD, Aerospace Engineering Sciences, 2016, University of Colorado
URL: https://scholar.colorado.edu/asen_gradetds/143
► An algorithm for autonomous online mission design at asteroids, comets, and small moons is developed to meet the novel challenges of their complex non-Keplerian…
(more)
▼ An algorithm for autonomous online mission design at asteroids, comets, and small moons is developed to meet the novel challenges of their complex non-Keplerian orbit environments, which render traditional methods inapplicable. The core concept of abstract reachability analysis, in which a set of impulsive maneuvering options is mapped onto a space of high-level mission outcomes, is applied to enable goal-oriented decision-making with robustness to uncertainty. These nuanced analyses are efficiently computed by utilizing a heuristic-based adaptive sampling scheme that either maximizes an objective function for autonomous planning or resolves details of interest for preliminary analysis and general study. Illustrative examples reveal the chaotic nature of small body systems through the structure of various families of reachable orbits, such as those that facilitate close-range observation of targeted surface locations or achieve soft impact upon them. In order to fulfill extensive sets of observation tasks, the single-maneuver design method is implemented in a receding-horizon framework such that a complete mission is constructed on-the-fly one piece at a time. Long-term performance and convergence are assured by augmenting the objective function with a prospect heuristic, which approximates the likelihood that a reachable end-state will benefit the subsequent planning horizon. When state and model uncertainty produce larger trajectory deviations than were anticipated, the next control horizon is advanced to allow for corrective action – a low-frequency form of feedback control. Through Monte Carlo analysis, the planning algorithm is ultimately demonstrated to produce mission profiles that vary drastically in their physical paths but nonetheless consistently complete all goals, suggesting a high degree of flexibility. It is further shown that the objective function can be tuned to preferentially minimize fuel cost or mission duration, as well as to optimize performance under different levels of uncertainty by appropriately balancing the mitigation paradigms of robust planning and reactive execution.
Advisors/Committee Members: Daniel J. Scheeres, Elizabeth Bradley, Eric W. Frew, Jay McMahon, Nisar Ahmed.
Subjects/Keywords: astrodynamics; autonomy; heuristic search; mission design; motion planning; receding horizon control; Aerospace Engineering; Artificial Intelligence and Robotics; Astrodynamics; Dynamics and Dynamical Systems; Robotics
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APA (6th Edition):
Surovik, D. A. (2016). Autonomous Mission Design in Extreme Orbit Environments. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/143
Chicago Manual of Style (16th Edition):
Surovik, David Allen. “Autonomous Mission Design in Extreme Orbit Environments.” 2016. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/asen_gradetds/143.
MLA Handbook (7th Edition):
Surovik, David Allen. “Autonomous Mission Design in Extreme Orbit Environments.” 2016. Web. 23 Jan 2021.
Vancouver:
Surovik DA. Autonomous Mission Design in Extreme Orbit Environments. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/asen_gradetds/143.
Council of Science Editors:
Surovik DA. Autonomous Mission Design in Extreme Orbit Environments. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/asen_gradetds/143
University of Colorado
19.
Olikara, Zubin Philip.
Computation of Quasi-Periodic Tori and Heteroclinic Connections in Astrodynamics Using Collocation Techniques.
Degree: PhD, Aerospace Engineering Sciences, 2016, University of Colorado
URL: https://scholar.colorado.edu/asen_gradetds/144
► Many astrodynamical systems exhibit both ordered and chaotic motion. The invariant manifold structure organizes these behaviors and is a valuable tool for the design of…
(more)
▼ Many astrodynamical systems exhibit both ordered and chaotic motion. The invariant manifold structure organizes these behaviors and is a valuable tool for the design of spacecraft trajectories. The study of a system's dynamics often begins with the computation of its invariant tori (equilibrium points, periodic orbits, quasi-periodic orbits) and associated stable and unstable manifolds. Periodic orbits, in particular, have been used effectively for the design of low-energy transfers in the circular restricted 3-body problem (CR3BP). Quasi-periodic orbits offer similar benefits and are often more prevalent in the phase space, but additional complexities are involved in their computation. The foundation of this work is the development of a numerical method for computing two-dimensional quasi-periodic tori. The approach is applicable to a general class of Hamiltonian systems. Using a Fourier discretization and Gauss-Legendre collocation, a continuous representation of the torus is obtained. Included in the scheme is the computation of the torus's stable and unstable manifolds. These manifolds can then be used for the design of natural transfers. Two methods are presented for locating and continuing families of heteroclinic connections between quasi-periodic orbits in the CR3BP. A collocation-based approach for transitioning trajectories to a higher-fidelity ephemeris model is also included.
Advisors/Committee Members: Daniel J. Scheeres, Elizabeth Bradley, James D. Meiss, Jeffrey S. Parker, Hanspeter Schaub.
Subjects/Keywords: Gauss-Legendre collocation; heteroclinic connections; invariant manifolds; quasi-periodic orbits; restricted 3-body problem; spacecraft trajectory design; Aerospace Engineering; Applied Mathematics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Olikara, Z. P. (2016). Computation of Quasi-Periodic Tori and Heteroclinic Connections in Astrodynamics Using Collocation Techniques. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/144
Chicago Manual of Style (16th Edition):
Olikara, Zubin Philip. “Computation of Quasi-Periodic Tori and Heteroclinic Connections in Astrodynamics Using Collocation Techniques.” 2016. Doctoral Dissertation, University of Colorado. Accessed January 23, 2021.
https://scholar.colorado.edu/asen_gradetds/144.
MLA Handbook (7th Edition):
Olikara, Zubin Philip. “Computation of Quasi-Periodic Tori and Heteroclinic Connections in Astrodynamics Using Collocation Techniques.” 2016. Web. 23 Jan 2021.
Vancouver:
Olikara ZP. Computation of Quasi-Periodic Tori and Heteroclinic Connections in Astrodynamics Using Collocation Techniques. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Jan 23].
Available from: https://scholar.colorado.edu/asen_gradetds/144.
Council of Science Editors:
Olikara ZP. Computation of Quasi-Periodic Tori and Heteroclinic Connections in Astrodynamics Using Collocation Techniques. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/asen_gradetds/144
. 
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