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Articles 121 - 150 of 255
Full-Text Articles in Mathematics
Modelling Infertility With Markov Chains, Rebecca Dorff
Modelling Infertility With Markov Chains, Rebecca Dorff
Theses and Dissertations
Infertility affects approximately 15% of couples. Testing and interventions are costly, in time, money, and emotional energy. This paper will discuss using Markov decision and multi-armed bandit processes to identify a systematic approach of interventions that will lead to the desired baby while minimizing costs.
Investment-Consumption With A Randomly Terminating Income, James Benjamin Taylor Jr.
Investment-Consumption With A Randomly Terminating Income, James Benjamin Taylor Jr.
Theses and Dissertations
We develop a stochastic control model for an investor's optimal investment and consumption over an uncertain planning horizon when the investor is endowed with a defaultable income stream. The distributions of the random time of default and the random terminal time are prescribed by deterministic hazard rates, and the investor makes investments in a standard financial market with a bond and a stock, modeled by geometric Brownian motion. In addition, the investor purchases insurance against both default and the terminal date, the default insurance serving as a proxy for the investor's disutility for default. We approximate the original continuous-time problem …
Quadratic Fields With 2-Skylow Class Group Isomorphic To C2kc2, Adele Lopez, Dr. Paul Jenkins
Quadratic Fields With 2-Skylow Class Group Isomorphic To C2kc2, Adele Lopez, Dr. Paul Jenkins
Journal of Undergraduate Research
We prove that there are infinitely many imaginary quadratic fields with 2-class group isomorphic to C2kC2 for any given positive integer k. This work is based on a related result for cyclic 2-class groups by Dominguez, Miller and Wong, and our proof proceeds similarly. However, we make some improvements in some of the techniques used. In particular, we provide a more general way of introducing congruence conditions into Perelli’s version of the Goldbach conjecture for polynomials.
Moral Hazard In Hedge Funds: An Approach Using Stochastic Differential Games, Jeremiah Bejarano, Dr. Jeffrey Humpherys
Moral Hazard In Hedge Funds: An Approach Using Stochastic Differential Games, Jeremiah Bejarano, Dr. Jeffrey Humpherys
Journal of Undergraduate Research
This project is a continuation of a line of research that I have been working on over the last two years, with the object of analyzing the relationship incentive structure present in the hedge fund industry and identifying any potential for moral hazard. In economics theory, “moral hazard” is a situation in which one party is more willing to take on a risk due to the fact that he or she knows that the potential costs or burden of that risk will be borne, in part or in whole, by others. In this project, my goal was to develop a …
The Planar Equitent Conjecture: Combining Isoperimetry And Minimal Surfaces, Abraham Frandsen, Dr. Michael Dorff
The Planar Equitent Conjecture: Combining Isoperimetry And Minimal Surfaces, Abraham Frandsen, Dr. Michael Dorff
Journal of Undergraduate Research
The goal of this project was to explore a new problem in geometric optimization: isoperimetric surfaces with both boundary and volume constraints. The idea behind the problem is the following: what is the optimal way to enclose a given volume with a surface that must also span a given boundary? In this case, optimal means least possible surface area. If we were to consider only the volume constraint, we would have the classical isoperimetric problem—and by now it is well-known and mathematically proven that the best way to enclose a given volume is with a sphere. On the other hand, …
An Explanation Of Strange Duality In Terms Of Landau-Ginzburg Mirror Symmetry, Rachel Suggs, Dr. Tyler Jarvis
An Explanation Of Strange Duality In Terms Of Landau-Ginzburg Mirror Symmetry, Rachel Suggs, Dr. Tyler Jarvis
Journal of Undergraduate Research
Suppose you have a physical system that can jump suddenly between two stable states. Then a function modeling the system will have a singularity at the jump. Our singularities will all be defined by polynomials, such as x3y + y5 + z2. Mathematician V.I. Arnol’d studied such singularities in an abstract setting, and he noticed that a certain 14 singularities came in pairs: numbers describing two di erent aspects of these singularities matched each singularity with its \dual” partner, which had the same numbers but with reversed roles (see Table 1). Arnol’d found no mathematical or physical reason why these …
Poincaré Polynomial Of Fjrw Rings And The Group-Weights Conjecture, Julian Boon Kai Tay
Poincaré Polynomial Of Fjrw Rings And The Group-Weights Conjecture, Julian Boon Kai Tay
Theses and Dissertations
FJRW-theory is a recent advancement in singularity theory arising from physics. The FJRW-theory is a graded vector space constructed from a quasihomogeneous weighted polynomial and symmetry group, but it has been conjectured that the theory only depends on the weights of the polynomial and the group. In this thesis, I prove this conjecture using Poincaré polynomials and Koszul complexes. By constructing the Koszul complex of the state space, we have found an expression for the Poincaré polynomial of the state space for a given polynomial and associated group. This Poincaré polynomial is defined over the representation ring of a group …
American Spread Option Models And Valuation, Yu Hu
American Spread Option Models And Valuation, Yu Hu
Theses and Dissertations
Spread options are derivative securities, which are written on the difference between the values of two underlying market variables. They are very important tools to hedge the correlation risk. American style spread options allow the holder to exercise the option at any time up to and including maturity. Although they are widely used to hedge and speculate in financial market, the valuation of the American spread option is very challenging. Because even under the classic assumptions that the underlying assets follow the log-normal distribution, the resulting spread doesn't have a distribution with a simple closed formula. In this dissertation, we …
Byu Computational Number Theory Research Group, Dr. Paul Jenkins
Byu Computational Number Theory Research Group, Dr. Paul Jenkins
Journal of Undergraduate Research
The computational number theory group has clearly been a success, with students writing papers, giving conference presentations, winning prestigious national fellowships, and going off to strong PhD programs in mathematics. The weekly seminar has helped students learn presentation skills and learn more mathematics, and has provided a convenient entry point for new students interested in research. It is anticipated that the group will continue into the foreseeable future, and that students will continue to benefit from the allocated resources.
Inverse Spectral Problems For Graphs, Dr. Wayne Barrett
Inverse Spectral Problems For Graphs, Dr. Wayne Barrett
Journal of Undergraduate Research
This MEG grant made it possible to support several student research activ- ities from Spring 2009 through Winter 2010.
Character Tables Of Metacyclic Groups, Dane Christian Skabelund
Character Tables Of Metacyclic Groups, Dane Christian Skabelund
Theses and Dissertations
We show that any two split metacyclic groups with the same character tables are isomorphic. We then use this to show that among metacyclic groups that are either 2-groups or are of odd order divisible by at most two primes, that the dihedral and generalized quaternion groups of order 2^n, n = 3, are the only pairs that have the same character tables.
A Classification Tool For Predictive Data Analysis In Healthcare, Mason Lemoyne Victors
A Classification Tool For Predictive Data Analysis In Healthcare, Mason Lemoyne Victors
Theses and Dissertations
Hidden Markov Models (HMMs) have seen widespread use in a variety of applications ranging from speech recognition to gene prediction. While developed over forty years ago, they remain a standard tool for sequential data analysis. More recently, Latent Dirichlet Allocation (LDA) was developed and soon gained widespread popularity as a powerful topic analysis tool for text corpora. We thoroughly develop LDA and a generalization of HMMs and demonstrate the conjunctive use of both methods in predictive data analysis for health care problems. While these two tools (LDA and HMM) have been used in conjunction previously, we use LDA in a …
Cell Speed Is Independent Of Force In A Mathematical Model Of Amoeboidal Cell Motion With Random Switching Terms., J. C. Dallon, Emily J. Evans, Christopher Grant, William V. Smith
Cell Speed Is Independent Of Force In A Mathematical Model Of Amoeboidal Cell Motion With Random Switching Terms., J. C. Dallon, Emily J. Evans, Christopher Grant, William V. Smith
Faculty Publications
In this paper the motion of a single cell is modeled as a nucleus and multiple integrin based adhesion sites. Numerical simulations and analysis of the model indicate that when the stochastic nature of the adhesion sites is a memoryless and force independent random process, the cell speed is independent of the force these adhesion sites exert on the cell. Furthermore, understanding the dynamics of the attachment and detachment of the adhesion sites is key to predicting cell speed. We introduce a differential equation describing the cell motion and then introduce a conjecture about the expected drift of the cell, …
A Force Based Model Of Individual Cell Migration With Discrete Attachment Sites And Random Switching Terms, J. C. Dallon, Matthew Scott, William V. Smith
A Force Based Model Of Individual Cell Migration With Discrete Attachment Sites And Random Switching Terms, J. C. Dallon, Matthew Scott, William V. Smith
Faculty Publications
A force based model of cell migration is presented which gives new insight into the importance of the dynamics of cell binding to the substrate. The main features of the model are the focus on discrete attachment dynamics, the treatment of the cellular forces as springs, and an incorporation of the stochastic nature of the attachment sites. One goal of the model is to capture the effect of the random binding and unbinding of cell attachments on global cell motion. Simulations reveal one of the most important factor influencing cell speed is the duration of the attachment to the substrate. …
Methods Of Music Classification And Transcription, Jonathan Peter Baker
Methods Of Music Classification And Transcription, Jonathan Peter Baker
Theses and Dissertations
We begin with an overview of some signal processing terms and topics relevant to music analysis including facts about human sound perception. We then discuss common objectives of music analysis and existing methods for accomplishing them. We conclude with an introduction to a new method of automatically transcribing a piece of music from a digital audio signal.
A Maple Program For Computing Landau-Ginzburg A- And B-Models And An Exploration Of Mirror Symmetry, Evan D. Merrell
A Maple Program For Computing Landau-Ginzburg A- And B-Models And An Exploration Of Mirror Symmetry, Evan D. Merrell
Theses and Dissertations
Mirror symmetry has been a significant area of research for geometry and physics for over two decades. Berglund and Hubsch proposed that for a certain family of singularities W, the so called "transposed" singularity WT should be the mirror partner of W. cite{BH} The techniques for constructing the orbifold LG models to test this conjecture were developed by FJR in cite{FJR} with a cohomological field theory generalized from the study of r-spin curves. The duality of LG A- and B-models became more elaborate when Krawitz cite{Krawitz} generalized the Intriligator-Vafa orbifold B-model to include contributions from more than one sector.This thesis …
Total Character Groups, Chelsea Lorraine Kennedy
Total Character Groups, Chelsea Lorraine Kennedy
Theses and Dissertations
The total character of a finite group G is the sum of the irreducible characters of G. When the total character of a finite group can be written as a monic polynomial with integer coefficients in an irreducible character of G, we say that G is a total character group. In this thesis we examine the total character of the dicyclic group of order 4n, the non-abelian groups of order p^3, and the symmetric group on n elements for all n ≥ 1. The dicyclic group of order 4n is a total character group precisely when n is congruent to …
Unknotting Tunnels Of Hyperbolic Tunnel Number N Manifolds, Stephan Daniel Burton
Unknotting Tunnels Of Hyperbolic Tunnel Number N Manifolds, Stephan Daniel Burton
Theses and Dissertations
Adams conjectured that unknotting tunnels of tunnel number 1 manifolds are always isotopic to a geodesic. We generalize this question to tunnel number n manifolds. We find that there exist complete hyperbolic structures and a choice of spine of a compression body with genus 1 negative boundary and genus n ≥ 3 outer boundary for which (n−2) edges of the spine self-intersect. We use this to show that there exist finite volume one-cusped hyperbolic manifolds with a system of n tunnels for which (n−1) of the tunnels are homotopic to geodesics arbitrarily close to self-intersecting. This gives evidence that the …
K-S-Rings, Emma Louise Turner
K-S-Rings, Emma Louise Turner
Theses and Dissertations
For a finite group G we study certain rings called k-S-rings, one for each non-negative integer k, where the 1-S-ring is the centralizer ring of G. These rings have the property that the (k+1)-S-ring determines the k-S-ring. We show that the 4-S-ring determines G when G is any group with finite classes. We show that the 3-S-ring determines G for any finite group G, thus giving an answer to a question of Brauer. We show the 2-characters defined by Frobenius and the extended 2-characters of Ken Johnson are characters of representations of the 2-S-ring of G. We find the character …
Spread Option Pricing With Stochastic Interest Rate, Yi Luo
Spread Option Pricing With Stochastic Interest Rate, Yi Luo
Theses and Dissertations
In this dissertation, we investigate the spread option pricing problem with stochastic interest rate. First, we will review the basic concept and theories of stochastic calculus, give an introduction of spread options and provide some examples of spread options in different markets. We will also review the market efficiency theory, arbitrage and assumptions that are commonly used in mathematical finance. In Chapter 3, we will review existing spread pricing models and term-structure models such as Vasicek Mode, and the Heath-Jarrow-Morton framework. In Chapter 4, we will use the martingale approach to derive a partial differential equation for the price of …
New Computational Techniques In Fjrw Theory With Applications To Landau Ginzburg Mirror Symmetry, Amanda Francis
New Computational Techniques In Fjrw Theory With Applications To Landau Ginzburg Mirror Symmetry, Amanda Francis
Theses and Dissertations
Mirror symmetry is a phenomenon from physics that has inspired a lot of interesting mathematics. In the Landau-Ginzburg setting, we have two constructions, the A and B models, which are created based on a choice of an affine singularity with a group of symmetries. Both models are vector spaces equipped with multiplication and a pairing (making them Frobenius algebras), and they are also Frobenius manifolds. We give a result relating stabilization of singularities in classical singularity to its counterpart in the Landau-Ginzburg setting. The A model comes from so-called FJRW theory and can be de fined up to a full …
Persistence And Foliation Theory And Their Application To Geometric Singular Perturbation, Ji Li
Persistence And Foliation Theory And Their Application To Geometric Singular Perturbation, Ji Li
Theses and Dissertations
Persistence problem of compact invariant manifold under random perturbation is considered in this dissertation. Under uniformly small random perturbation and the condition of normal hyperbolicity, the original invariant manifold persists and becomes a random invariant manifold. The random counterpart has random local stable and unstable manifolds. They could be invariantly foliated thanks to the normal hyperbolicity. Those underlie an extension of the geometric singular perturbation theory to the random case which means the slow manifold persists and becomes a random manifold so that the local global structure near the slow manifold persists under singular perturbation. A normal form for a …
Diagonal Entry Restrictions In Minimum Rank Matrices, And The Inverse Inertia And Eigenvalue Problems For Graphs, Curtis G. Nelson
Diagonal Entry Restrictions In Minimum Rank Matrices, And The Inverse Inertia And Eigenvalue Problems For Graphs, Curtis G. Nelson
Theses and Dissertations
Let F be a field, let G be an undirected graph on n vertices, and let SF(G) be the set of all F-valued symmetric n x n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let MRF(G) be defined as the set of matrices in SF(G) whose rank achieves the minimum of the ranks of matrices in SF(G). We develop techniques involving Z-hat, a process termed nil forcing, and induced subgraphs, that can determine when diagonal entries corresponding to specific vertices of G must be zero or nonzero for all matrices in …
Weak Cayley Table Isomorphisms, Long Pham Bao Nguyen
Weak Cayley Table Isomorphisms, Long Pham Bao Nguyen
Theses and Dissertations
We investigate weak Cayley table isomorphisms, a generalization of group isomorphisms. Suppose G and H are groups. A bijective map phi : G to H is a weak Cayley table isomorphism if it satisfies two conditions:(1) If x is conjugate to y, then phi(x) is conjugate to phi(y); (2) For all x, y in G, phi(xy) is conjugate to phi(x)phi(y).If there exists a weak Cayley table isomorphism between two groups, then we say that the two groups have the same weak Cayley table.This dissertation has two main goals. First, we wish to find sufficient conditions under which two groups have …
Quadratic Spline Approximation Of The Newsvendor Problem Optimal Cost Function, Christina Marie Burton
Quadratic Spline Approximation Of The Newsvendor Problem Optimal Cost Function, Christina Marie Burton
Theses and Dissertations
We consider a single-product dynamic inventory problem where the demand distributions in each period are known and independent but with density. We assume the lead time and the fixed cost for ordering are zero and that there are no capacity constraints. There is a holding cost and a backorder cost for unfulfilled demand, which is backlogged until it is filled by another order. The problem may be nonstationary, and in fact our approximation of the optimal cost function using splines is most advantageous when demand falls suddenly. In this case the myopic policy, which is most often used in practice …
Metacalibration In Geometric Optimization, Donald C. Sampson
Metacalibration In Geometric Optimization, Donald C. Sampson
Theses and Dissertations
A introduction to metacalibration methods and their application. This includes a new proof of the double bubble conjecture, new results in the area of equitent problems (isoperimetric problems with boundary), and comments on a mapping conjecture.
Subdivision Rules, 3-Manifolds, And Circle Packings, Brian Craig Rushton
Subdivision Rules, 3-Manifolds, And Circle Packings, Brian Craig Rushton
Theses and Dissertations
We study the relationship between subdivision rules, 3-dimensional manifolds, and circle packings. We find explicit subdivision rules for closed right-angled hyperbolic manifolds, a large family of hyperbolic manifolds with boundary, and all 3-manifolds of the E^3,H^2 x R, S^2 x R, SL_2(R), and S^3 geometries (up to finite covers). We define subdivision rules in all dimensions and find explicit subdivision rules for the n-dimensional torus as an example in each dimension. We define a graph and space at infinity for all subdivision rules, and use that to show that all subdivision rules for non-hyperbolic manifolds have mesh not going to …
Dynamic Appointment Scheduling In Healthcare, Mckay N. Heasley
Dynamic Appointment Scheduling In Healthcare, Mckay N. Heasley
Theses and Dissertations
In recent years, healthcare management has become fertile ground for the scheduling theory community. In addition to an extensive academic literature on this subject, there has also been a proliferation of healthcare scheduling software companies in the marketplace. Typical scheduling systems use rule-based analytics that give schedulers advisory information from programmable heuristics such as the Bailey-Welch rule cite{B,BW}, which recommends overbooking early in the day to fill-in potential no-shows later on. We propose a dynamic programming problem formulation to the scheduling problem that maximizes revenue. We formulate the problem and discuss the effectiveness of 3 different algorithms that solve the …
Topological Properties Of Invariant Sets For Anosov Maps With Holes, Skyler C. Simmons
Topological Properties Of Invariant Sets For Anosov Maps With Holes, Skyler C. Simmons
Theses and Dissertations
We begin by studying various topological properties of invariant sets of hyperbolic toral automorphisms in the linear case. Results related to cardinality, local maximality, entropy, and dimension are presented. Where possible, we extend the results to the case of hyperbolic toral automorphisms in higher dimensions, and further to general Anosov maps.
Crouzeix's Conjecture And The Gmres Algorithm, Sarah Mcbride Luo
Crouzeix's Conjecture And The Gmres Algorithm, Sarah Mcbride Luo
Theses and Dissertations
This thesis explores the connection between Crouzeix's conjecture and the convergence of the GMRES algorithm. GMRES is a popular iterative method for solving linear systems and is one of the many Krylov methods. Despite its popularity, the convergence of GMRES is not completely understood. While the spectrum can in some cases be a good indicator of convergence, it has been shown that in general, the spectrum does not provide sufficient information to fully explain the behavior of GMRES iterations. Other sets associated with a matrix that can also help predict convergence are the pseudospectrum and the numerical range. This …