An Optimal Threshold Strategy In The Two-Envelope Problem With Partial Information, 2015 Universidad de la Republica Oriental del Uruguay

#### An Optimal Threshold Strategy In The Two-Envelope Problem With Partial Information, Martin Egozcue, Luis Fuentes García

*Martin Egozcue*

No abstract provided.

Chaotic Behavior In Monetary Systems: Comparison Among Different Types Of Taylor Rule, 2015 Auckland University of Technology

#### Chaotic Behavior In Monetary Systems: Comparison Among Different Types Of Taylor Rule, Reza Moosavi Mohseni Dr., Wenjun Zhang Dr., Jiling Cao Prof.

*Reza Moosavi Mohseni*

The aim of the present study is to detect the chaotic behavior in the monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase the complexity of the system and leads to more chaotic behavior.

Using Community Structure Networks To Model Heterogeneous Mixing In Epidemics, And A Potential Application To Hiv In Washington, D.C., 2015 Bates College

#### Using Community Structure Networks To Model Heterogeneous Mixing In Epidemics, And A Potential Application To Hiv In Washington, D.C., Katherine Ragland Paulson

*Honors Theses*

Using models, mathematicians can better understand and analyze the factors that influence the dynamic spread of infectious disease through a population. The most fundamental epidemiological model is the SIR model, originally proposed by Kermack and McKendrick. In this model individuals in a population are categorized as Susceptible (S), Infected (I), or Removed (R), and differential equations are used to analyze the flow of people from one compartment to another. Many epidemiological models use the SIR model as a foundation, building complexities into it. Modeling HIV, for example, is complex because not all people in a population are at equal risk ...

Spatially Random Processes In One-Dimensional Maps: The Logistic Map And The Arnold Circle Map, 2015 University of Colorado Boulder

#### Spatially Random Processes In One-Dimensional Maps: The Logistic Map And The Arnold Circle Map, An T. Le

*Applied Mathematics Graduate Theses & Dissertations*

One way to model in-situ remediation of contaminated groundwater is to consider spatially random processes in nonlinear systems. Groundwater remediation often requires injecting an aquifer with treatment solution, where degradation reactions break down the toxins. As the treatment solution and contaminated water flow through the aquifer, their movement is limited by the types of sediment found in the aquifer, which act as spatial barriers to mixing. The onset of chaos in this system implies the two solutions are well mixed, and thus the contaminants are rendered inert. The spatially random processes explored in this thesis are meant to mimic the ...

A Hierarchical Graph For Nucleotide Binding Domain 2, 2015 East Tennessee State University

#### A Hierarchical Graph For Nucleotide Binding Domain 2, Samuel Kakraba

*Electronic Theses and Dissertations*

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2 ...

Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, 2015 Western Kentucky University

#### Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik

*Masters Theses & Specialist Projects*

This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental ...

Application Of A Numerical Method And Optimal Control Theory To A Partial Differential Equation Model For A Bacterial Infection In A Chronic Wound, 2015 Western Kentucky University

#### Application Of A Numerical Method And Optimal Control Theory To A Partial Differential Equation Model For A Bacterial Infection In A Chronic Wound, Stephen Guffey

*Masters Theses & Specialist Projects*

In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange Multipliers. Both of these techniques have seen prevalent use in the modern theories of Physics, Economics, as well as in the study of Partial Differential Equations. The numerical method we consider is the method of lines, a prominent method for solving partial differential equations. This method uses finite difference schemes to discretize the ...

Bioinformatic Game Theory And Its Application To Cluster Multi-Domain Proteins, 2015 University of Nebraska-Lincoln

#### Bioinformatic Game Theory And Its Application To Cluster Multi-Domain Proteins, Brittney Keel

*Dissertations, Theses, and Student Research Papers in Mathematics*

The exact evolutionary history of any set of biological sequences is unknown, and all phylogenetic reconstructions are approximations. The problem becomes harder when one must consider a mix of vertical and lateral phylogenetic signals. In this dissertation we propose a game-theoretic approach to clustering biological sequences and analyzing their evolutionary histories. In this context we use the term evolution as a broad descriptor for the entire set of mechanisms driving the inherited characteristics of a population. The key assumption in our development is that evolution tries to accommodate the competing forces of selection, of which the conservation force seeks to ...

Boundary Problems For One And Two Dimensional Random Walks, 2015 Western Kentucky University

#### Boundary Problems For One And Two Dimensional Random Walks, Miky Wright

*Masters Theses & Specialist Projects*

This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with ...

On Mikhailov's Reduction Group, 2015 Dublin Institute of Technology

#### On Mikhailov's Reduction Group, Tihomir I. Valchev

*Articles*

We present a generalization of the notion of reduction group which allows one to study in a uniform way certain classes of nonlocal $S$-integrable equations like Ablowitz-Musslimani's nonlocal Schr\"odinger equation. Another aspect of the proposed generalization is the possibility to derive in a systematic way solutions to S-integrable equations with prescribed symmetries.

An Experimental Analysis Of Adaptive Learning In A Multi-Subject Economy, 2015 Ursinus College

#### An Experimental Analysis Of Adaptive Learning In A Multi-Subject Economy, David Martin

*Business and Economics Honors Papers*

The rational expectations hypothesis (REH) has long served as a foundation in macroeconomic laws of motion. However, the assumptions of REH are likely too powerful to be representative of economic actors. This research evaluates adaptive learning, a developing alternative to rational expectations, using a multi-agent macroeconomic prediction “game.” Data was gathered from a group of students, each predicting the outcome of a single economy over time. Each agent was asked to forecast output (GDP) and inflation in each period based on historic levels of output, inflation, and interest rates. These data were then analyzed under various theoretical models of adaptive ...

Modeling Traffic At An Intersection, 2015 Kennesaw State University

#### Modeling Traffic At An Intersection, Kaleigh L. Mulkey, Saniita K. Fasenntao

*Symposium of Student Scholars*

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program ...

A Seasonal Analysis Of Extreme Precipitation Trends In The Contiguous United States, 2015 Boise State University

#### A Seasonal Analysis Of Extreme Precipitation Trends In The Contiguous United States, Rachael Balstad, Jaechoul Lee

*College of Arts and Sciences Presentations*

The purpose of this paper is to examine extreme precipitation trends in the United States. The National Climate Assessment estimated that average precipitation in the United States has increased in the last 100 years, with variation occurring regionally. Some regions have experienced larger increases in average precipitation, while others have experienced decreases. However, this aggregate increase in average precipitation does not necessarily indicate an analogous trend in extreme precipitation. Statistically, average and extreme values are nearly independent. In this paper, a changepoint technique and extreme value statistical models will be used for estimation of trend and its uncertainty. A changepoint ...

Extensions Of The Cross-Entropy Method With Applications To Diffusion Processes And Portfolio Losses, 2015 The University of Western Ontario

#### Extensions Of The Cross-Entropy Method With Applications To Diffusion Processes And Portfolio Losses, Alexandre Scott

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

Rare event simulation is a crucial part of simulations. In financial mathematics, the study of rare events appear naturally when we consider risk measures such as the conditional value at risk. This thesis is composed of three related papers treating the rare event simulations subject: the first paper addresses rare event simulations using for diffusion processes, the second paper addresses rare event simulations for the normal and the Student t-copula model while the last paper addresses rare event simulations for a portfolio model where there is a correlation structure between the loss-given-default and the probability of default.

Helping A Microfinance Institution Select Its Clients: A Risk Analysis Using Social Networks, 2015 College of Wooster

#### Helping A Microfinance Institution Select Its Clients: A Risk Analysis Using Social Networks, Sayantan Mitra, Varunavi Newar

*Black & Gold*

This paper formulates an objective mathematical model for a Microfinance Institution (MFI) to measure the credit worthiness associated with a potential client. We use concepts from network theory to determine the credit worthiness of an individual in relation to other households in the community. We use the concept of eigenvector centrality to evaluate the relative credit worthiness in the network. The latter part of the model focuses on the absolute measures of credit worthiness such as income, ownership of assets and risk of the proposed investment. This model would help MFIs reduce the risk of borrowing by ensuring that there ...

Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, 2015 Liberty University

#### Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate

*Senior Honors Theses*

Differential equations have bearing on practically every scientific field. Though they are prevalent in nature, they can be challenging to solve. Most of the work done in differential equations is dependent on the use of many methods to solve particular types of equations. Sophus Lie proposed a modern method of solving ordinary differential equations in the 19th century along with a coordinate free variation of finding the infinitesimal generator by combining the influential work of Élie Cartan among others in the field of differential geometry. The driving idea behind using symmetries to solve differential equations is that there exists a ...

Complementary Effect Of Electrical And Inhibitory Coupling In Bursting Synchronization, 2015 Georgia State University

#### Complementary Effect Of Electrical And Inhibitory Coupling In Bursting Synchronization, Kevin Daley

*Georgia State Undergraduate Research Conference*

gsurc 2015

Quantitative And Qualitative Stability Analysis Of Polyrhythmic Circuits, 2015 Georgia State University

#### Quantitative And Qualitative Stability Analysis Of Polyrhythmic Circuits, Drake Knapper

*Georgia State Undergraduate Research Conference*

No abstract provided.

Determination Of Lie Superalgebras Of Supersymmetries Of Super Differential Equations, 2015 The University of Western Ontario

#### Determination Of Lie Superalgebras Of Supersymmetries Of Super Differential Equations, Xuan Liu

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

Superspaces are an extension of classical spaces that include certain (non-commutative) supervariables. Super differential equations are differential equations defined on superspaces, which arise in certain popular mathematical physics models. Supersymmetries of such models are superspace transformations which leave their sets of solutions invariant. They are important generalization of classical Lie symmetry groups of differential equations.

In this thesis, we consider finite-dimensional Lie supersymmetry groups of super differential equations. Such supergroups are locally uniquely determined by their associated Lie superalgebras, and in particular by the structure constants of those algebras. The main work of this thesis is providing an algorithmic method ...

Mathematical Analysis Of Uniform Polyhedron (Trapezohedron) Having 2n Congruent Right Kite Faces, 4n Edges & 2n+2 Vertices Lying On A Spherical Surface By H.C. Rajpoot), 2015 M.M.M. University of Technology, Gorakhpur-273010 (UP) India

#### Mathematical Analysis Of Uniform Polyhedron (Trapezohedron) Having 2n Congruent Right Kite Faces, 4n Edges & 2n+2 Vertices Lying On A Spherical Surface By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot Hcr

*Harish Chandra Rajpoot H.C. Rajpoot*

The generalized formula are applicable on any uniform polyhedron having 2n congruent right kite faces, 4n edges & 2n+2 vertices lying on a spherical surface with a certain radius. These formula have been derived by the author Mr H.C. Rajpoot to analyse infinite no. of the uniform polyhedrons having congruent right kite faces simply by setting n=3,4,5,6,7,………………upto infinity, to calculate all the important parameters such as ratio of unequal edges, outer radius, inner radius, mean radius, surface area, volume, solid angles subtended by the polyhedron at its vertices, dihedral angles between the adjacent ...