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New methods for analysis of epidemiological data using capture-recapture methodsHuakau, John Tupou January 2002 (has links)
Capture-recapture methods take their origins from animal abundance estimation, where they were used to estimate the unknown size of the animal population under study. In the late 1940s and again in the late 1960s and early 1970s these same capture-recapture methods were modified and applied to epidemiological list data. Since then through their continued use, in particular in the 1990s, these methods have become popular for the estimation of the completeness of disease registries and for the estimation of the unknown total size of human disease populations. In this thesis we investigate new methods for the analysis of epidemiological list data using capture-recapture methods. In particular we compare two standard methods used to estimate the unknown total population size, and examine new methods which incorporate list mismatch errors and model-selection uncertainty into the process for the estimation of the unknown total population size and its associated confidence interval. We study the use of modified tag loss methods from animal abundance estimation to allow for list mismatch errors in the epidemio-logical list data. We also explore the use of a weighted average method, the use of Bootstrap methods, and the use of a Bayesian model averaging method for incorporating model-selection uncertainty into the estimate of the unknown total population size and its associated confidence interval. In addition we use two previously unanalysed Diabetes studies to illustrate the methods examined and a well-known Spina Bifida Study for simulation purposes. This thesis finds that ignoring list mismatch errors will lead to biased estimates of the unknown total population size and that the list mismatch methods considered here result in a useful adjustment. The adjustment also approximately agrees with the results obtained using a complex matching algorithm. As for the incorporation of model-selection uncertainty, we find that confidence intervals which incorporate model-selection uncertainty are wider and more appropriate than confidence intervals that do not. Hence we recommend the use of tag loss methods to adjust for list mismatch errors and the use of methods that incorporate model-selection uncertainty into both point and interval estimates of the unknown total population size. / Subscription resource available via Digital Dissertations only.
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New methods for analysis of epidemiological data using capture-recapture methodsHuakau, John Tupou January 2002 (has links)
Capture-recapture methods take their origins from animal abundance estimation, where they were used to estimate the unknown size of the animal population under study. In the late 1940s and again in the late 1960s and early 1970s these same capture-recapture methods were modified and applied to epidemiological list data. Since then through their continued use, in particular in the 1990s, these methods have become popular for the estimation of the completeness of disease registries and for the estimation of the unknown total size of human disease populations. In this thesis we investigate new methods for the analysis of epidemiological list data using capture-recapture methods. In particular we compare two standard methods used to estimate the unknown total population size, and examine new methods which incorporate list mismatch errors and model-selection uncertainty into the process for the estimation of the unknown total population size and its associated confidence interval. We study the use of modified tag loss methods from animal abundance estimation to allow for list mismatch errors in the epidemio-logical list data. We also explore the use of a weighted average method, the use of Bootstrap methods, and the use of a Bayesian model averaging method for incorporating model-selection uncertainty into the estimate of the unknown total population size and its associated confidence interval. In addition we use two previously unanalysed Diabetes studies to illustrate the methods examined and a well-known Spina Bifida Study for simulation purposes. This thesis finds that ignoring list mismatch errors will lead to biased estimates of the unknown total population size and that the list mismatch methods considered here result in a useful adjustment. The adjustment also approximately agrees with the results obtained using a complex matching algorithm. As for the incorporation of model-selection uncertainty, we find that confidence intervals which incorporate model-selection uncertainty are wider and more appropriate than confidence intervals that do not. Hence we recommend the use of tag loss methods to adjust for list mismatch errors and the use of methods that incorporate model-selection uncertainty into both point and interval estimates of the unknown total population size. / Subscription resource available via Digital Dissertations only.
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New methods for analysis of epidemiological data using capture-recapture methodsHuakau, John Tupou January 2002 (has links)
Capture-recapture methods take their origins from animal abundance estimation, where they were used to estimate the unknown size of the animal population under study. In the late 1940s and again in the late 1960s and early 1970s these same capture-recapture methods were modified and applied to epidemiological list data. Since then through their continued use, in particular in the 1990s, these methods have become popular for the estimation of the completeness of disease registries and for the estimation of the unknown total size of human disease populations. In this thesis we investigate new methods for the analysis of epidemiological list data using capture-recapture methods. In particular we compare two standard methods used to estimate the unknown total population size, and examine new methods which incorporate list mismatch errors and model-selection uncertainty into the process for the estimation of the unknown total population size and its associated confidence interval. We study the use of modified tag loss methods from animal abundance estimation to allow for list mismatch errors in the epidemio-logical list data. We also explore the use of a weighted average method, the use of Bootstrap methods, and the use of a Bayesian model averaging method for incorporating model-selection uncertainty into the estimate of the unknown total population size and its associated confidence interval. In addition we use two previously unanalysed Diabetes studies to illustrate the methods examined and a well-known Spina Bifida Study for simulation purposes. This thesis finds that ignoring list mismatch errors will lead to biased estimates of the unknown total population size and that the list mismatch methods considered here result in a useful adjustment. The adjustment also approximately agrees with the results obtained using a complex matching algorithm. As for the incorporation of model-selection uncertainty, we find that confidence intervals which incorporate model-selection uncertainty are wider and more appropriate than confidence intervals that do not. Hence we recommend the use of tag loss methods to adjust for list mismatch errors and the use of methods that incorporate model-selection uncertainty into both point and interval estimates of the unknown total population size. / Subscription resource available via Digital Dissertations only.
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New methods for analysis of epidemiological data using capture-recapture methodsHuakau, John Tupou January 2002 (has links)
Capture-recapture methods take their origins from animal abundance estimation, where they were used to estimate the unknown size of the animal population under study. In the late 1940s and again in the late 1960s and early 1970s these same capture-recapture methods were modified and applied to epidemiological list data. Since then through their continued use, in particular in the 1990s, these methods have become popular for the estimation of the completeness of disease registries and for the estimation of the unknown total size of human disease populations. In this thesis we investigate new methods for the analysis of epidemiological list data using capture-recapture methods. In particular we compare two standard methods used to estimate the unknown total population size, and examine new methods which incorporate list mismatch errors and model-selection uncertainty into the process for the estimation of the unknown total population size and its associated confidence interval. We study the use of modified tag loss methods from animal abundance estimation to allow for list mismatch errors in the epidemio-logical list data. We also explore the use of a weighted average method, the use of Bootstrap methods, and the use of a Bayesian model averaging method for incorporating model-selection uncertainty into the estimate of the unknown total population size and its associated confidence interval. In addition we use two previously unanalysed Diabetes studies to illustrate the methods examined and a well-known Spina Bifida Study for simulation purposes. This thesis finds that ignoring list mismatch errors will lead to biased estimates of the unknown total population size and that the list mismatch methods considered here result in a useful adjustment. The adjustment also approximately agrees with the results obtained using a complex matching algorithm. As for the incorporation of model-selection uncertainty, we find that confidence intervals which incorporate model-selection uncertainty are wider and more appropriate than confidence intervals that do not. Hence we recommend the use of tag loss methods to adjust for list mismatch errors and the use of methods that incorporate model-selection uncertainty into both point and interval estimates of the unknown total population size. / Subscription resource available via Digital Dissertations only.
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New methods for analysis of epidemiological data using capture-recapture methodsHuakau, John Tupou January 2002 (has links)
Capture-recapture methods take their origins from animal abundance estimation, where they were used to estimate the unknown size of the animal population under study. In the late 1940s and again in the late 1960s and early 1970s these same capture-recapture methods were modified and applied to epidemiological list data. Since then through their continued use, in particular in the 1990s, these methods have become popular for the estimation of the completeness of disease registries and for the estimation of the unknown total size of human disease populations. In this thesis we investigate new methods for the analysis of epidemiological list data using capture-recapture methods. In particular we compare two standard methods used to estimate the unknown total population size, and examine new methods which incorporate list mismatch errors and model-selection uncertainty into the process for the estimation of the unknown total population size and its associated confidence interval. We study the use of modified tag loss methods from animal abundance estimation to allow for list mismatch errors in the epidemio-logical list data. We also explore the use of a weighted average method, the use of Bootstrap methods, and the use of a Bayesian model averaging method for incorporating model-selection uncertainty into the estimate of the unknown total population size and its associated confidence interval. In addition we use two previously unanalysed Diabetes studies to illustrate the methods examined and a well-known Spina Bifida Study for simulation purposes. This thesis finds that ignoring list mismatch errors will lead to biased estimates of the unknown total population size and that the list mismatch methods considered here result in a useful adjustment. The adjustment also approximately agrees with the results obtained using a complex matching algorithm. As for the incorporation of model-selection uncertainty, we find that confidence intervals which incorporate model-selection uncertainty are wider and more appropriate than confidence intervals that do not. Hence we recommend the use of tag loss methods to adjust for list mismatch errors and the use of methods that incorporate model-selection uncertainty into both point and interval estimates of the unknown total population size. / Subscription resource available via Digital Dissertations only.
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The modulus and epidemic processes on graphsGoering, Max January 1900 (has links)
Master of Science / Department of Mathematics / Pietro Poggi-Corradini / This thesis contains three chapters split into two parts. In the first chapter, the discrete
p-modulus of families of walks is introduced and discussed from various perspectives.
Initially, we prove many properties by mimicking the theory from the continuous case and
use Arne Beurling's criterion for extremality to build insight and intuition regarding the
modulus. After building an intuitive understanding of the p-modulus, we proceed to switch
perspectives to that of convex analysis. From here, uniqueness and existence of extremal
densities is shown and a better understanding of Beurling's criterion is developed before
describing an algorithm that approximates the value of the p-modulus arbitrarily well.
In the second chapter, an exclusively edge-based approach to the discrete transboundary
modulus is described. Then an interesting application is discussed with some preliminary
numerical results.
The final chapter describes four different takes of the Susceptible-Infected (SI) epidemic
model on graphs and shows them to be equivalent. After developing a deep understanding
of the SI model, the epidemic hitting time is compared to a variety of different graph
centralities to indicate successful alternative methods in identifying important agents in
epidemic spreading. Numerical results from simulations on many real-world graphs are
presented. They indicate the effective resistance, which coincides with the 2-modulus for
connecting families, is the most closely correlated indicator of importance to that of the
epidemic hitting time. In large part, this is suspected to be due to the global nature of both
the effective resistance and the epidemic hitting time. Thanks to the equivalence between
the epidemic hitting time and the expected distance on an randomly exponentially weighted
graph, we uncover a deeper connection- the effective resistance is also a lower bound for the
epidemic hitting time, showing an even deeper connection.
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The cohomology of a finite matrix quotient groupPasko, Brian Brownell January 1900 (has links)
Doctor of Philosophy / Department of Mathematics / John S. Maginnis / In this work, we find the module structure of the cohomology of the group of four by four upper triangular matrices (with ones on the diagonal) with entries from the field on three elements modulo its center. Some of the relations amongst the generators for the cohomology ring are also given. This cohomology is found by considering a certain split extension. We show that the associated Lyndon-Hochschild-Serre spectral sequence collapses at the second page by illustrating a set of generators for the cohomology ring from generating elements of the second page. We also consider two other extensions using more traditional techniques.
In the first we introduce some new results giving degree four and five differentials in spectral sequences associated to extensions of a general class of groups and apply these to both the extensions.
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The obstacle problem for second order elliptic operators in nondivergence formTeka, Kubrom Hisho January 1900 (has links)
Doctor of Philosophy / Department of Mathematics / Ivan Blank / We study the obstacle problem with an elliptic operator in nondivergence form with principal coefficients in VMO. We develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results, in turn, allow us to begin the study of the regularity of the free boundary, and we show existence of blowup limits, a basic measure stability result, and a measure-theoretic version of the Caffarelli alternative proven in Caffarelli's 1977 paper ``The regularity of free boundaries in higher dimensions."
Finally, we show that blowup limits are in general not unique at free boundary points.
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Classification of certain genera of codes, lattices and vertex operator algebrasJunla, Nakorn January 1900 (has links)
Doctor of Philosophy / Department of Mathematics / Gerald H. Höhn / We classify the genera of doubly even binary codes, the genera of even lattices, and
the genera of rational vertex operator algebras (VOAs) arising from the modular tensor
categories (MTCs) of rank up to 4 and central charges up to 16. For the genera of even
lattices, there are two types of the genera: code type genera and non code type genera. The number of the code type genera is finite. The genera of the lattices of rank larger than or equal to 17 are non code type. We apply the idea of a vector valued modular form and the representation of the modular group SL[subscript]2(Z) in [Bantay2007] to classify the genera of the VOAs arising from the MTCs of ranks up to 4 and central charges up to 16.
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Graphs admitting (1, ≤ 2)-identifying codesLang, Julie January 1900 (has links)
Master of Science / Department of Mathematics / Sarah Reznikoff / A (1, ≤ 2)-identifying code is a subset of the vertex set C of a graph such that each
pair of vertices intersects C in a distinct way. This has useful applications in locating
errors in multiprocessor networks and threat monitoring. At the time of writing, there
is no simply-stated rule that will indicate if a graph is (1, ≤ 2)-identifiable. As such, we
discuss properties that must be satisfied by a valid (1, ≤ 2)-identifying code, characteristics of a graph which preclude the existence of a (1, ≤ 2)-identifying code, and relationships between the maximum degree and order of (1, ≤ 2)-identifiable graphs. Additionally, we show that (1, ≤ 2)-identifiable graphs have no forbidden induced subgraphs and provide a list of (1, ≤ 2)-identifiable graphs with minimum (1, ≤ 2)-identifying codes indicated.
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