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On The Riesz Representation For Optimal Stopping Problems, Markus Schuster
On The Riesz Representation For Optimal Stopping Problems, Markus Schuster
Theses and Dissertations
In this thesis we summarize results about optimal stopping problems analyzed with
the Riesz representation theorem. Furthermore we consider two examples: Firstly
the optimal investment problem with an underlying d-dimensional geometric Brow-
nian motion. We derive formulas for the optimal stopping boundaries for the one-
and two-dimensional cases and we find a numerical approximation for the boundary
in the two-dimensional problem. After this we change the focus to a space-time
one-dimensional geometric Brownian motion with finite time horizon. We use the
Riesz representation theorem to approximate the optimal stopping boundaries for
three financial options: the American Put option, American Cash-or-Nothing …
Associated Hypotheses In Linear Models For Unbalanced Data, Carlos J. Soto
Associated Hypotheses In Linear Models For Unbalanced Data, Carlos J. Soto
Theses and Dissertations
When looking at factorial experiments there are several natural hypotheses that can be tested. In a two-factor or a by b design, the three null hypotheses of greatest interest are the absence of each main effect and the absence of interaction. There are two ways to construct the numerator sum of squares for testing these, namely either adjusted or sequential sums of squares (also known as type I and type III in SAS). Searle has pointed out that, for unbalanced data, a sequential sum of squares for one of these hypotheses is equal (with probability 1) to an adjusted sum …
Semiparametric Estimation Of The Survival Function In The Presence Of Covariates, Madlen Gebauer
Semiparametric Estimation Of The Survival Function In The Presence Of Covariates, Madlen Gebauer
Theses and Dissertations
The main interest of survival analysis is to estimate the distribution function of the survival time based on observations of a random sample. In this thesis, a semiparametric estimator is used not only to estimate the survival probability, but also to consider the influence of explanatory variables within the estimation. Therefore, the weighted maximum likelihood estimator of the conditional survival function is derived and a corresponding pointwise likelihood ratio confidence band is developed. Subsequently, the established estimator is compared to a similar estimator which was proposed by Iglesias-Pérez and de Ũna-Álvarez (2008). Since the idea of this paper arose in …
Recent Advances In Compressed Sensing: Discrete Uncertainty Principles And Fast Hyperspectral Imaging, Megan E. Lewis
Recent Advances In Compressed Sensing: Discrete Uncertainty Principles And Fast Hyperspectral Imaging, Megan E. Lewis
Theses and Dissertations
Compressed sensing is an important field with continuing advances in theory and applications. This thesis provides contributions to both theory and application. Much of the theory behind compressed sensing is based on uncertainty principles, which state that a signal cannot be concentrated in both time and frequency. We develop a new discrete uncertainty principle and use it to demonstrate a fundamental limitation of the demixing problem, and to provide a fast method of detecting sparse signals. The second half of this thesis focuses on a specific application of compressed sensing: hyperspectral imaging. Conventional hyperspectral platforms require long exposure times, which …
The Steiner Problem On Closed Surfaces Of Constant Curvature, Andrew Logan
The Steiner Problem On Closed Surfaces Of Constant Curvature, Andrew Logan
Theses and Dissertations
The n-point Steiner problem in the Euclidean plane is to find a least length path network connecting n points. In this thesis we will demonstrate how to find a least length path network T connecting n points on a closed 2-dimensional Riemannian surface of constant curvature by determining a region in the covering space that is guaranteed to contain T. We will then provide an algorithm for solving the n-point Steiner problem on such a surface.
A Mathematical Model Of Amoeboid Cell Motion As A Continuous-Time Markov Process, Lynnae Despain
A Mathematical Model Of Amoeboid Cell Motion As A Continuous-Time Markov Process, Lynnae Despain
Theses and Dissertations
Understanding cell motion facilitates the understanding of many biological processes such as wound healing and cancer growth. Constructing mathematical models that replicate amoeboid cell motion can help us understand and make predictions about real-world cell movement. We review a force-based model of cell motion that considers a cell as a nucleus and several adhesion sites connected to the nucleus by springs. In this model, the cell moves as the adhesion sites attach to and detach from a substrate. This model is then reformulated as a random process that tracks the attachment characteristic (attached or detached) of each adhesion site, the …
Commutator Studies In Pursuit Of Finite Basis Results, Nathan E. Faulkner
Commutator Studies In Pursuit Of Finite Basis Results, Nathan E. Faulkner
Theses and Dissertations
Several new results of a general algebraic scope are developed in an effort to build tools for use in finite basis proofs. Many recent finite basis theorems have involved assumption of a finite residual bound, with the broadest result concerning varieties with a difference term (Kearnes, Szendrei, and Willard (2013+)). However, in varieties with a difference term, the finite residual bound hypothesis is known to strongly limit the degree of nilpotence observable in a variety, while, on the other hand, there is another, older series of results in which nilpotence plays a key role (beginning with those of Lyndon (1952) …
Domination Numbers Of Semi-Strong Products Of Graphs, Stephen R. Cheney
Domination Numbers Of Semi-Strong Products Of Graphs, Stephen R. Cheney
Theses and Dissertations
This thesis examines the domination number of the semi-strong product of two graphs G and H where both G and H are simple and connected graphs. The product has an edge set that is the union of the edge set of the direct product of G and H together with the cardinality of V(H), copies of G. Unlike the other more common products (Cartesian, direct and strong), the semi-strong product is neither commutative nor associative.
The semi-strong product is not supermultiplicative, so it does not satisfy a Vizing like conjecture. It is also not submultiplicative so it shares these two …
Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan
Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan
Theses and Dissertations
We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of folding - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.
We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation …
Coloring The Square Of Planar Graphs Without 4-Cycles Or 5-Cycles, Robert Jaeger
Coloring The Square Of Planar Graphs Without 4-Cycles Or 5-Cycles, Robert Jaeger
Theses and Dissertations
The famous Four Color Theorem states that any planar graph can be properly colored using at most four colors. However, if we want to properly color the square of a planar graph (or alternatively, color the graph using distinct colors on vertices at distance up to two from each other), we will always require at least \Delta + 1 colors, where \Delta is the maximum degree in the graph. For all \Delta, Wegner constructed planar graphs (even without 3-cycles) that require about \frac{3}{2} \Delta colors for such a coloring.
To prove a stronger upper bound, we consider only planar graphs …
Trees, Partitions, And Other Combinatorial Structures, Heather Christina Smith
Trees, Partitions, And Other Combinatorial Structures, Heather Christina Smith
Theses and Dissertations
This dissertation contains work on three main topics.
Chapters 1 through 4 provide complexity results for the single cut-or-join model for genome rearrangement. Genomes will be represented by binary strings. Let S be a finite collection of binary strings, each of the same length. Define M to be the collection of medians – binary strings μ which minimize Sigma v belongs to S H(μ,v) where H is the Hamming distance. For any non-negative function f(x), define Z(f(x), S) to be (Sigma μ belongs to M) (Pi v belongs to S)f(H(μ,v)). We study the complexity of calculating Z(f(x), S), with respect …
Modeling And Computations Of Cellular Dynamics Using Complex-Fluid Models, Jia Zhao
Modeling And Computations Of Cellular Dynamics Using Complex-Fluid Models, Jia Zhao
Theses and Dissertations
Cells are fundamental units in all living organisms as all living organisms are made up of cells of different varieties. The study of cells is therefore an essential part of research in life science. Cells can be classified into two basic types: prokaryotic cells and eukaryotic cells. One typical organisms of prokaryotes is bacterium. And eukaryotes mainly consist of animal cells. In this thesis, we focus on developing predictive models mathematically to study bacteria colonies and animal cell mitotic dynamics.
Instead of living alone, bacteria usually survive in a biofilm, which is a microorganism where bacteria stick together by extracellular …
Toward The Combinatorial Limit Theory Of Free Words, Danny Rorabaugh
Toward The Combinatorial Limit Theory Of Free Words, Danny Rorabaugh
Theses and Dissertations
Free words are elements of a free monoid, generated over an alphabet via the binary operation of concatenation. Casually speaking, a free word is a finite string of letters. Henceforth, we simply refer to them as words. Motivated by recent advances in the combinatorial limit theory of graphs–notably those involving flag algebras, graph homomorphisms, and graphons–we investigate the extremal and asymptotic theory of pattern containment and avoidance in words.
Word V is a factor of word W provided V occurs as consecutive letters within W. W is an instance of V provided there exists a nonerasing monoid homomorphsism phi with …
Avoiding Doubled Words In Strings Of Symbols, Michael Lane
Avoiding Doubled Words In Strings Of Symbols, Michael Lane
Theses and Dissertations
A word on the n-letter alphabet is a finite length string of symbols formed from a set of n letters. A word is doubled if every letter that appears in the word appears at least twice. A word w avoids a word u if there is no non-erasing homomorphism h (a map that respects concatenation) such that h (u) is a subword of w. Finally, a word w is n-avoidable if there is an infinite list of words on the n-letter alphabet that avoid w. In 1906, Thue showed that the simplest doubled word, namely xx, is 3-avoidable. In 1984, …
The Packing Chromatic Number Of Random D-Regular Graphs, Ann Wells Clifton
The Packing Chromatic Number Of Random D-Regular Graphs, Ann Wells Clifton
Theses and Dissertations
Let G = (V (G),E(G)) be a simple graph of order n and let i be a positive integer. Xi superset V (G) is called an i-packing if vertices in Xi are pairwise distance more than i apart. A packing coloring of G is a partition X = {X1,X2,X3, . . . ,Xk} of V (G) such that each color class Xi is an i-packing. The minimum order k of a packing coloring is called the packing chromatic number of G, denoted by Xp(G). Let Gn,d …