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Accepted by: Éva Czabarka, Director of Thesis
, 2012
"... This work is dedicated to my beautiful fiancé Amanda. Your support has helped make this thesis possible. You inherited much more than your fair share of the stress and pressure that came along with writing it. I truly could not have done this without you. I love you. iii Acknowledgments Firstly, I w ..."
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would like to thank my advisor Dr. Éva Czabarka for her guidance and advice. Your help during the writing of this thesis cannot be overstated. This thesis would not have been possible if not for you. I would also like to thank my committee members Dr. Anton Schep and Dr. Lincoln Lu for your thoughtful
References
, 2010
"... 6. / É. Czabarka, O. S´ykora, L.A. Székely, I. Vrˇto, Crossing numbers and biplanar crossing numbers. II. Comparing crossing numbers and biplanar crossing numbers using the probabilistic method. Random Structures and Algorithms 33 (4) (2008 Dec) 480–496 References 1. Joshua K.Lambert, Finding a bipl ..."
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6. / É. Czabarka, O. S´ykora, L.A. Székely, I. Vrˇto, Crossing numbers and biplanar crossing numbers. II. Comparing crossing numbers and biplanar crossing numbers using the probabilistic method. Random Structures and Algorithms 33 (4) (2008 Dec) 480–496 References 1. Joshua K.Lambert, Finding a
Accepted by:
, 2010
"... I would like to thank Dr. Eva Czabarka and Dr. Joshua Cooper for their helpful advice and patience. The problem of biological sequence comparison arises naturally in an attempt to explain many biological phenomena. Due to the combinatorial structure and pattern preserving properties of the sequences ..."
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I would like to thank Dr. Eva Czabarka and Dr. Joshua Cooper for their helpful advice and patience. The problem of biological sequence comparison arises naturally in an attempt to explain many biological phenomena. Due to the combinatorial structure and pattern preserving properties
External Examiner
, 2012
"... life. To Katharine, Patrick, Gregory, Aruno, and Simon: for the joy you bring into my iii Acknowledgments I would like to thank the community of people who have helped make this dissertation a reality, and the graduate experience a successful and enjoyable one. First and foremost, my deepest gratitu ..."
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gratitude to Dr. Éva Czabarka, whose patience, encouragement, good humor, and guidance have made this possible. Her guidance, not only with the research and dissertation, but with all aspects of academic life has been invaluable. Thank you Éva. My thanks also to Dr. László A. Székely who always made me feel
Inverting Random Functions II: Explicit Bounds for Discrete Maximum Likelihood Estimation, with Applications
 SIAM J. DISCR. MATH
, 2002
"... In this paper we study inverting random functions under the maximum likelihood estimation (MLE) criterion in the discrete setting. In particular, we consider how many independent evaluations of the random function at a particular element of the domain are needed for reliable reconstruction of that e ..."
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Cited by 22 (11 self)
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In this paper we study inverting random functions under the maximum likelihood estimation (MLE) criterion in the discrete setting. In particular, we consider how many independent evaluations of the random function at a particular element of the domain are needed for reliable reconstruction of that element. We provide explicit upper and lower bounds for MLE, both in the nonparametric and parametric setting, and give applications to cointossing and phylogenetic tree reconstruction.
Independent Sets and Eigenspaces
, 2004
"... Author’s declaration for electronic submission of a thesis I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public ..."
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Cited by 19 (4 self)
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Author’s declaration for electronic submission of a thesis I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii The problems we study in this thesis arise in computer science, extremal set theory and quantum computing. The first common feature of these problems is that each can be reduced to characterizing the independent sets of maximum size in a suitable graph. A second common feature is that the size of these independent sets meets an eigenvalue bound due to Delsarte and Hoffman. Thirdly, the graphs that arise belong to association schemes that have already been studied in other contexts. Our first problem involves covering arrays on graphs, which arises in computer science. The goal is to find a smallest covering array on a given graph G.
Genomewide molecular clock and horizontal gene transfer in bacterial evolution
 J. Bacteriol
, 2004
"... We describe a simple theoretical framework for identifying orthologous sets of genes that deviate from a clocklike model of evolution. The approach used is based on comparing the evolutionary distances within a set of orthologs to a standard intergenomic distance, which was defined as the median of ..."
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Cited by 18 (5 self)
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We describe a simple theoretical framework for identifying orthologous sets of genes that deviate from a clocklike model of evolution. The approach used is based on comparing the evolutionary distances within a set of orthologs to a standard intergenomic distance, which was defined as the median of the distribution of the distances between all onetoone orthologs. Under the clocklike model, the points on a plot of intergenic distances versus intergenomic distances are expected to fit a straight line. A statistical technique to identify significant deviations from the clocklike behavior is described. For several hundred analyzed orthologous sets representing three welldefined bacterial lineages, the �Proteobacteria, the �Proteobacteria, and the BacillusClostridium group, the clocklike null hypothesis could not be rejected for �70 % of the sets, whereas the rest showed substantial anomalies. Subsequent detailed phylogenetic analysis of the genes with the strongest deviations indicated that over onehalf of these genes probably underwent a distinct form of horizontal gene transfer, xenologous gene displacement, in which a gene is displaced by an ortholog from a different lineage. The remaining deviations from the clocklike model could be explained by lineagespecific acceleration of evolution. The results indicate that although xenologous gene displacement is a major force in bacterial evolution, a significant majority of orthologous gene sets in three major bacterial lineages evolved in accordance
A simple Havel–Hakimi type algorithm to realize graphical degree sequences of directed graphs
"... One of the simplest ways to decide whether a given finite sequence of positive integers can arise as the degree sequence of a simple graph is the greedy algorithm of Havel and Hakimi. This note extends their approach to directed graphs. It also studies cases of some simple forbidden edgesets. Final ..."
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Cited by 11 (0 self)
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One of the simplest ways to decide whether a given finite sequence of positive integers can arise as the degree sequence of a simple graph is the greedy algorithm of Havel and Hakimi. This note extends their approach to directed graphs. It also studies cases of some simple forbidden edgesets. Finally, it proves a result which is useful to design an MCMC algorithm to find random realizations of prescribed directed degree sequences.
THE INVERSE PROBLEM FOR CERTAIN TREE PARAMETERS
"... Abstract. Let p be a graph parameter that assigns a positive integer value to every graph. The inverse problem for p asks for a graph within a prescribed class (here, we will only be concerned with trees), given the value of p. In this context, it is of interest to know whether such a graph can be f ..."
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Cited by 3 (0 self)
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Abstract. Let p be a graph parameter that assigns a positive integer value to every graph. The inverse problem for p asks for a graph within a prescribed class (here, we will only be concerned with trees), given the value of p. In this context, it is of interest to know whether such a graph can be found for all or at least almost all integer values of p. We will provide a very general setting for this type of problem over the set of all trees, describe some simple examples and finally consider the interesting parameter “number of subtrees”, where the problem can be reduced to some numbertheoretic considerations. Specifically, we will prove that every positive integer, with only 34 exceptions, is the number of subtrees of some tree.
Results 1  10
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