You searched for +publisher:"University of Colorado" +contributor:("Francois Meyer").
Showing records 1 – 8 of
8 total matches.
No search limiters apply to these results.
University of Colorado
1.
Bertrand, Nicholas.
Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations.
Degree: MS, Applied Mathematics, 2012, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/55 
► We investigate the problem of finding a parameterization of a smooth, low-dimensional manifold based on noisy observations from a high-dimensional ambient space. The formulation…
(more)
▼ We investigate the problem of finding a parameterization of a smooth, low-dimensional manifold based on noisy observations from a high-dimensional ambient space. The formulation of such parameterizations sees applications in a variety of areas such as data denoising and image segmentation.
We introduce algorithms inspired by the existing k-svd algorithm for training dictionaries for sparse data representation, and the local best-fit at algorithm for hybrid linear modeling. The output of our algorithm is an assignment of input data points to locally linear models. To demonstrate the applicability of our algorithm, we discuss experiments performed on synthetic datasets.
Advisors/Committee Members: Francois Meyer, James Curry, Shannon Hughes.
Subjects/Keywords: k-svd algorithm; MLBF; 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):
Bertrand, N. (2012). Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations. (Masters Thesis). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/55
Chicago Manual of Style (16th Edition):
Bertrand, Nicholas. “Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations.” 2012. Masters Thesis, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/55.
MLA Handbook (7th Edition):
Bertrand, Nicholas. “Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations.” 2012. Web. 25 Jan 2021.
Vancouver:
Bertrand N. Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations. [Internet] [Masters thesis]. University of Colorado; 2012. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/55.
Council of Science Editors:
Bertrand N. Sparse Encoding of Observations from a Smooth Manifold via Locally Linear Approximations. [Masters Thesis]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/appm_gradetds/55
University of Colorado
2.
Feeney, Daniel Francis.
The Coordination of Movement from Motor Units to Muscle Synergies.
Degree: PhD, 2018, University of Colorado
URL: https://scholar.colorado.edu/iphy_gradetds/80
► This dissertation comprises computational and experimental studies that examined the neuromuscular factors underlying differences in manual dexterity and mobility in health and disease. The…
(more)
▼ This dissertation comprises computational and experimental studies that examined the neuromuscular factors underlying differences in manual dexterity and mobility in health and disease. The first two studies developed models of motor unit force production. The first model used a Proportional-Integral-Derivative (PID) control algorithm to activate a pool of motor units to simulate the force trajectory during force-matching tasks. The second model comprised a probabilistic state-space model to estimate the common synaptic input to motor neurons based on the discharge times of action potentials by activated motor units. The state-space model demonstrated superior sensitivity compared with previous models. The next three studies examined manual dexterity and begin with the use of the state-space model to quantify variability in common synaptic input for young and older adults during isometric contractions, and how this variability related to performance on a pegboard test of manual dexterity. Variability in common synaptic input was significantly associated with the coefficient of variation for force during steady contractions (force steadiness) and with pegboard times in older adults. The source of the force fluctuations was evaluated by comparing force steadiness during voluntary and electrically evoked contractions. Force steadiness was worse for old adults than young adults during voluntary contractions, but there was no difference between age groups during the electrically evoked contractions. Thus, differences in force steadiness must arise from signal transduction in the central nervous system and not the periphery. The plasticity of pegboard performance was examined by comparing peg-manipulation characteristics of persons with multiple sclerosis to healthy controls. Grooved pegboard time for individuals with MS was most associated with the time to select a peg, whereas times for healthy controls were most related to peg transportation and selection. The last two studies examine the influence of an orthopedic problem (sacroiliac joint dysfunction) on movement patterns. These individuals exhibited a compromised muscle synergy when walking and greater movement asymmetries during a sit-to-stand task. This dissertation explored how common synaptic input influences force steadiness and manual dexterity, how multiple sclerosis alters manual dexterity, and how individuals with sacroiliac joint dysfunction differ from healthy controls during walking and sit-to-stand tasks.
Advisors/Committee Members: Roger M. Enoka, Francois Meyer, Alaa Ahmed, Rodger Kram, Alena Grabowski.
Subjects/Keywords: computational model; motor unit; pid controller; synergies; muscle synergy; Biomedical Engineering and Bioengineering; Neurosciences; Physiology
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):
Feeney, D. F. (2018). The Coordination of Movement from Motor Units to Muscle Synergies. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/iphy_gradetds/80
Chicago Manual of Style (16th Edition):
Feeney, Daniel Francis. “The Coordination of Movement from Motor Units to Muscle Synergies.” 2018. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/iphy_gradetds/80.
MLA Handbook (7th Edition):
Feeney, Daniel Francis. “The Coordination of Movement from Motor Units to Muscle Synergies.” 2018. Web. 25 Jan 2021.
Vancouver:
Feeney DF. The Coordination of Movement from Motor Units to Muscle Synergies. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/iphy_gradetds/80.
Council of Science Editors:
Feeney DF. The Coordination of Movement from Motor Units to Muscle Synergies. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/iphy_gradetds/80
University of Colorado
3.
Qi, Hanchao.
Low-Dimensional Signal Models in Compressive Sensing.
Degree: PhD, Electrical, Computer & Energy Engineering, 2013, University of Colorado
URL: https://scholar.colorado.edu/ecen_gradetds/68
► In today's world, we often face an explosion of data that can be difficult to handle. Signal models help make this data tractable, and…
(more)
▼ In today's world, we often face an explosion of data that can be difficult to handle. Signal models help make this data tractable, and thus play an important role in designing efficient algorithms for acquiring, storing, and analyzing signals. However, choosing the right model is critical. Poorly chosen models may fail to capture the underlying structure of signals, making it hard to achieve satisfactory results in signal processing tasks. Thus, the most accurate and concise signal models must be used.
Many signals can be expressed as a linear combination of a few elements of some dictionary, and this is the motivation behind the emerging field of compressive sensing. Compressive sensing leverages this signal model to enable us to perform signal processing tasks without full knowledge of the data.
However, this is only one possible model for signals, and many signals could in fact be more accurately and concisely described by other models. In particular, in this thesis, we will look at two such models, and show how these other two models can be used to allow signal reconstruction and analysis from partial knowledge of the data.
First, we consider signals that belong to low-dimensional nonlinear manifolds, i.e. that can be represented as a continuous nonlinear function of few parameters. We show how to apply the kernel trick, popular in machine learning, to adapt compressive sensing to this type of sparsity. Our approach provides computationally-efficient, improved signal reconstruction from partial measurements when the signal is accurately described by such a manifold model.
We then consider collections of signals that together have strong principal components, so that each individual signal may be modeled as a linear combination of these few shared principal components. We focus on the problem of finding the center and principal components of these high-dimensional signals using only their measurements. We show experimentally and theoretically that our approach will generally return the correct center and principal components for a large enough collection of signals. The recovered principal components also allow performance gains in other signal processing tasks.
Advisors/Committee Members: Shannon M. Hughes, Youjian Liu, Francois Meyer, Lijun Chen, Alireza Doostan.
Subjects/Keywords: algorithms; compressive sensing; nonlinear manifolds; high-dimensional signals; 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):
Qi, H. (2013). Low-Dimensional Signal Models in Compressive Sensing. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/ecen_gradetds/68
Chicago Manual of Style (16th Edition):
Qi, Hanchao. “Low-Dimensional Signal Models in Compressive Sensing.” 2013. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/ecen_gradetds/68.
MLA Handbook (7th Edition):
Qi, Hanchao. “Low-Dimensional Signal Models in Compressive Sensing.” 2013. Web. 25 Jan 2021.
Vancouver:
Qi H. Low-Dimensional Signal Models in Compressive Sensing. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/ecen_gradetds/68.
Council of Science Editors:
Qi H. Low-Dimensional Signal Models in Compressive Sensing. [Doctoral Dissertation]. University of Colorado; 2013. Available from: https://scholar.colorado.edu/ecen_gradetds/68
University of Colorado
4.
Reynolds, Matthew Jason.
Nonlinear approximations in tomography, quadrature construction, and multivariate reductions.
Degree: PhD, Applied Mathematics, 2012, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/37
► This thesis consists of contributions to three topics: algorithms for computing generalized Gaussian quadratures, tomographic imaging algorithms, and reduction algorithms. Our approach is based…
(more)
▼ This thesis consists of contributions to three topics: algorithms for computing generalized Gaussian quadratures, tomographic imaging algorithms, and reduction algorithms. Our approach is based on using non-linear approximations of functions. We develop a new algorithm for constructing generalized Gaussian quadratures for exponentials inte- grated against a non-sign-definite weight function. These quadratures integrate band-limited exponentials to a user-defined accuracy. We also introduce a method of computing quadrature weights via l∞ minimization. Second, we develop a new imaging algorithm for X-ray tomography. This algorithm, Polar Quadrature Inversion, uses rational approximations to approximate tomographic projections with a near optimal number of terms for a given accuracy. This rational signal model allows us to augment the measured data by extending the tomographic projection's domain in Fourier space. As the extended data from all the projections fill a disk in the Fourier domain, we use polar quadratures for band-limited exponentials and the Unequally Spaced Fast Fourier Transform to obtain our image. We demonstrate that the resulting images have significantly improved resolution without additional artifacts near sharp transitions. Finally, we develop an extension of existing reduction algorithms for functions of one variable to functions of many variables. By reduction, we understand an approximation (to a user-supplied accuracy) of a linear combination of decaying exponentials by a representation of the same form but with a minimal number of terms. While for functions of one variable there is an underlying theory based on the analysis of functions of one complex variable, no such theory is available for the multivariate case. Our approach is a first step in the development of such theory. We demonstrate our algorithm on two examples of multivariate functions, a suboptimal linear combination of real-valued, decaying exponentials, and that of complex-valued, decaying exponentials.
Advisors/Committee Members: Gregory Beylkin, Gunnar Martinsson, Keith Julien, Francois Meyer, Rafael Peistun.
Subjects/Keywords: 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):
Reynolds, M. J. (2012). Nonlinear approximations in tomography, quadrature construction, and multivariate reductions. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/37
Chicago Manual of Style (16th Edition):
Reynolds, Matthew Jason. “Nonlinear approximations in tomography, quadrature construction, and multivariate reductions.” 2012. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/37.
MLA Handbook (7th Edition):
Reynolds, Matthew Jason. “Nonlinear approximations in tomography, quadrature construction, and multivariate reductions.” 2012. Web. 25 Jan 2021.
Vancouver:
Reynolds MJ. Nonlinear approximations in tomography, quadrature construction, and multivariate reductions. [Internet] [Doctoral dissertation]. University of Colorado; 2012. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/37.
Council of Science Editors:
Reynolds MJ. Nonlinear approximations in tomography, quadrature construction, and multivariate reductions. [Doctoral Dissertation]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/appm_gradetds/37
University of Colorado
5.
Martin, Bradley Pifer.
Application of Rbf-Fd to Wave and Heat Transport Problems in Domains with Interfaces.
Degree: PhD, Applied Mathematics, 2016, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/79
► Traditional finite difference methods for solving the partial differential equations (PDEs) associated with wave and heat transport often perform poorly when used in domains…
(more)
▼ Traditional finite difference methods for solving the partial differential equations (PDEs) associated with wave and heat transport often perform poorly when used in domains that feature jump discontinuities in model parameter values (interfaces). We present a radial basis function-derived finite difference (RBF-FD) approach that solves these types of problems to a high order of accuracy, even when curved interfaces and variable model parameters are present. The method generalizes easily to a variety of different problem types, and requires only the inversion of small, well-conditioned matrices to determine stencil weights that are applied directly to data that crosses an interface. These weights contain all necessary information about the interface (its curvature; the contrast in model parameters from one side to the other; variability of model parameter value on either side), and no further consideration of the interface is necessary during time integration of the numerical solution.
Advisors/Committee Members: Bengt Fornberg, Natasha Flyer, Keith Julien, Gunnar Martinsson, Francois Meyer.
Subjects/Keywords: finite differences; heat equation; interfaces; mesh free; RBF; wave equation; 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):
Martin, B. P. (2016). Application of Rbf-Fd to Wave and Heat Transport Problems in Domains with Interfaces. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/79
Chicago Manual of Style (16th Edition):
Martin, Bradley Pifer. “Application of Rbf-Fd to Wave and Heat Transport Problems in Domains with Interfaces.” 2016. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/79.
MLA Handbook (7th Edition):
Martin, Bradley Pifer. “Application of Rbf-Fd to Wave and Heat Transport Problems in Domains with Interfaces.” 2016. Web. 25 Jan 2021.
Vancouver:
Martin BP. Application of Rbf-Fd to Wave and Heat Transport Problems in Domains with Interfaces. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/79.
Council of Science Editors:
Martin BP. Application of Rbf-Fd to Wave and Heat Transport Problems in Domains with Interfaces. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/appm_gradetds/79
University of Colorado
6.
Fox, Alyson Lindsey.
Algebraic Multigrid(amg) for Graph Laplacian Linear Systems: Extensions of Amg for Signed, Undirected and Unsigned, Directed Graphs.
Degree: PhD, Applied Mathematics, 2017, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/96
► Relational datasets are often modeled as an unsigned, undirected graph due the nice properties of the resulting graph Laplacian, but information is lost if…
(more)
▼ Relational datasets are often modeled as an unsigned, undirected graph due the nice properties of the resulting graph Laplacian, but information is lost if certain attributes of the graph are not represented. This thesis presents two generalizations of Algebraic Multigrid (AMG) solvers with graph Laplacian systems for different graph types: applying Gremban’s expansion to extend unsigned graph Laplacian solvers to signed graph Laplacian systems and generalizing techniques in Lean Algebraic Multigrid (LAMG) to a new multigrid solver for unsigned, directed graph Laplacian systems. Signed graphs extend the traditional notion of connections and disconnections to in- clude both favorable and adverse relationships, such as friend-enemy social networks or social networks with “likes” and “dislikes.” Gremban’s expansion is used to transform the signed graph Laplacian into an unsigned graph Laplacian with twice the number of unknowns. By using Gremban’s expansion, we extend current unsigned graph Laplacian solvers’ to signed graph Laplacians. This thesis analyzes the numerical stability and applicability of Grem- ban’s expansion and proves that the error of the solution of the original linear system can be tightly bounded by the error of the expanded system. In directed graphs, some subset of relationships are not reciprocal, such as hyperlink graphs, biological neural networks, and electrical power grids. A new algebraic multigrid algorithm, Nonsymmetric Lean Algebraic Multigrid (NS-LAMG), is proposed, which uses ideas from Lean Algebraic Multigrid, nonsymmetric Smoothed Aggregation, and multigrid solvers for Markov chain stationary distribution systems. Low-degree elimination, intro- duced in Lean Algebraic Multigrid for undirected graphs, is redefined for directed graphs. A semi-adaptive multigrid solver, inspired by low-degree elimination, is instrumented in the setup phase, which can be adapted for Markov chain stationary distributions systems. Nu- merical results shows that NS-LAMG out performs GMRES(k) for real-world, directed graph Laplacian linear systems. Both generalizations enable more choices in modeling decisions for graph Laplacian systems. Due the successfulness of NS-LAMG and other various nonsymmetric AMG (NS-AMG) solvers, a further study of theoretical convergence properties are discussed in this thesis. In particular, a necessary condition known as “weak approximation property”, and a sufficient one, referred to as “strong approximation property” as well as the “super strong approx- imation property” are generalized to nonsymmetric matrices and the various relationships between the approximation properties are proved for the nonsymmetric case. In NS-AMG, if P ̸= R the two-grid error propagation operator for the coarse-grid correction is an oblique projection with respect to any reasonable norm, which can cause the error to increase. A main focal point of this paper is a discussion on the conditions in which the error propagation operator is bounded, as the stability of the error…
Advisors/Committee Members: Tom Manteuffel, Geoff Sanders, John Ruge, Christian Ketelsen, Francois Meyer.
Subjects/Keywords: Algebraic Multigrid; Directed graphs; Graph Laplacians; Gremban's expansion; Signed graphs; Applied Mechanics
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):
Fox, A. L. (2017). Algebraic Multigrid(amg) for Graph Laplacian Linear Systems: Extensions of Amg for Signed, Undirected and Unsigned, Directed Graphs. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/96
Chicago Manual of Style (16th Edition):
Fox, Alyson Lindsey. “Algebraic Multigrid(amg) for Graph Laplacian Linear Systems: Extensions of Amg for Signed, Undirected and Unsigned, Directed Graphs.” 2017. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/96.
MLA Handbook (7th Edition):
Fox, Alyson Lindsey. “Algebraic Multigrid(amg) for Graph Laplacian Linear Systems: Extensions of Amg for Signed, Undirected and Unsigned, Directed Graphs.” 2017. Web. 25 Jan 2021.
Vancouver:
Fox AL. Algebraic Multigrid(amg) for Graph Laplacian Linear Systems: Extensions of Amg for Signed, Undirected and Unsigned, Directed Graphs. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/96.
Council of Science Editors:
Fox AL. Algebraic Multigrid(amg) for Graph Laplacian Linear Systems: Extensions of Amg for Signed, Undirected and Unsigned, Directed Graphs. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/appm_gradetds/96
University of Colorado
7.
Brutz, Michael Joseph.
Mathematical Modelling and Analysis of Several Diffusive Processes.
Degree: PhD, Applied Mathematics, 2014, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/60
► The underlying theme of this research is using numerical methods to develop computationally efficient algorithms for three separate problems driven by diffusive processes. The…
(more)
▼ The underlying theme of this research is using numerical methods to develop computationally efficient algorithms for three separate problems driven by diffusive processes. The problems under consideration are: contaminant dispersal through fracture networks, modelling the flow of glacial ice, and community detection on networks.
A common feature of containment facilities for nuclear waste is to use expansive geological formations as an added barrier to contaminant dispersal in the event of a leak. Although these formations are generally comprised of dense rock that is difficult to penetrate, fractures within them provide a potential means for contaminants to rapidly transport across the barrier. The typical width of such fractures is only on the order of millimeters whereas the typical scale of interest for contaminant transport is on the order of kilometers. When particle tracking methods are used to simulate the contaminant dispersal in fracture networks, this disparity of scales severely restricts maximum time step sizes because features at the millimeter scale need to be resolved. Our contribution to this problem is developing a coarse scale particle tracking method that allows for substantially larger time steps when particles are navigating straight fractures.
With global warming comes concerns as to how the changing temperature will impact glacial systems and their contribution to sea level rise. On glacial scales, ice behaves as a very slowly moving non-Newtonian fluid, and the primary problem for numerically simulating the evolution of ice masses comes with Glen's flow law for the effective viscosity. The flow law is empirically based, and its simple form has proven useful for analytical calculations. However, its simple form also allows for the effective viscosity to become unbounded in regions of low strain rate, and has proven to be very problematic for numerical simulations. Our contribution to this problem is re-examining the datasets the flow law was originally based on to develop an alternative model that fits the data with comparable accuracy, but without the problematic singularity.
When working with networks that represent real world systems, a common feature of interest is to find collections of vertices that form communities. Because the word "community" is an ambiguous term, our interpretation is that it is necessary to quantify what it means to be a community at a minimum of three scales for any given problem. These scales are at the level of: individual nodes, individual communities, and the network as a whole. Although our work focuses on detecting overlapping communities in the context of social networks, our primary contribution is developing a methodology that is highly modular and can easily be adapted to target other problem-specific notions of community.
Advisors/Committee Members: Francois Meyer, Tom Manteuffel, Harihar Rajaram, John Ruge, Juan Restrepo.
Subjects/Keywords: community; glacier; multiscale; network; flow; particle tracking; 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):
Brutz, M. J. (2014). Mathematical Modelling and Analysis of Several Diffusive Processes. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/60
Chicago Manual of Style (16th Edition):
Brutz, Michael Joseph. “Mathematical Modelling and Analysis of Several Diffusive Processes.” 2014. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/60.
MLA Handbook (7th Edition):
Brutz, Michael Joseph. “Mathematical Modelling and Analysis of Several Diffusive Processes.” 2014. Web. 25 Jan 2021.
Vancouver:
Brutz MJ. Mathematical Modelling and Analysis of Several Diffusive Processes. [Internet] [Doctoral dissertation]. University of Colorado; 2014. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/60.
Council of Science Editors:
Brutz MJ. Mathematical Modelling and Analysis of Several Diffusive Processes. [Doctoral Dissertation]. University of Colorado; 2014. Available from: https://scholar.colorado.edu/appm_gradetds/60
University of Colorado
8.
Jennings, Dale Kurtis.
Advances in MCMC Methods with Applications to Particle Filtering, DSMC, and Bayesian Networks.
Degree: PhD, Applied Mathematics, 2016, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/81
► Markov Chain Monte Carlo (MCMC) methods are a class of algorithms for sampling from a desired probability distribution. While there exist many algorithms that attempt…
(more)
▼ Markov Chain Monte Carlo (MCMC) methods are a class of algorithms for sampling from a desired probability distribution. While there exist many algorithms that attempt to be somewhat universal, these algorithms can struggle for tractability in specific applications. The work in this dissertation is focused on improving MCMC methods in three application areas: Particle Filtering, Direct Simulation Monte Carlo, and Bayesian Networks. In particle filtering, the dimension of the target distribution grows as more data is obtained. As such, sequential sampling methods are necessary in order to have an efficient algorithm. In this thesis, we develop a "windowed" rejection sampling procedure to get more accurate algorithms while still preserving the necessary sequential structure. Direct Simulation Monte Carlo is a Monte Carlo algorithm for simulating rarefied gas flows. In this dissertation, we review the derivation of the Kac master equation model for 1-dimensional flows. From this, we show how the Poisson process can be exploited to construct a more accurate algorithm for simulating the Kac model. We then develop an epsilon-perfect proof of concept algorithm for the limiting velocity distribution as time goes to infinity. Bayesian Networks (BNs) are graphical models used to represent high dimensional probability distributions. There has been a great deal of interest in learning the structure of a BN from observed data. Here, we do so by walking through the space of graphs by modeling the appearance and disappearance of edges as a birth and death process. We give empirical evidence that this novel jump process approach exhibits better mixing properties than the commonly used Metropolis-Hastings algorithm.
Advisors/Committee Members: Jem N. Corcoran, Manuel Lladser, James H. Curry, William Kleiber, Francois Meyer.
Subjects/Keywords: Applied Probability; Bayesian Networks; Birth and Death Process; Kac Model; MCMC; Particle Filtering; 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):
Jennings, D. K. (2016). Advances in MCMC Methods with Applications to Particle Filtering, DSMC, and Bayesian Networks. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/81
Chicago Manual of Style (16th Edition):
Jennings, Dale Kurtis. “Advances in MCMC Methods with Applications to Particle Filtering, DSMC, and Bayesian Networks.” 2016. Doctoral Dissertation, University of Colorado. Accessed January 25, 2021.
https://scholar.colorado.edu/appm_gradetds/81.
MLA Handbook (7th Edition):
Jennings, Dale Kurtis. “Advances in MCMC Methods with Applications to Particle Filtering, DSMC, and Bayesian Networks.” 2016. Web. 25 Jan 2021.
Vancouver:
Jennings DK. Advances in MCMC Methods with Applications to Particle Filtering, DSMC, and Bayesian Networks. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Jan 25].
Available from: https://scholar.colorado.edu/appm_gradetds/81.
Council of Science Editors:
Jennings DK. Advances in MCMC Methods with Applications to Particle Filtering, DSMC, and Bayesian Networks. [Doctoral Dissertation]. University of Colorado; 2016. Available from: https://scholar.colorado.edu/appm_gradetds/81
. 
Open Access Theses and Dissertations