Mathematics & Statisticshttp://hdl.handle.net/10211.3/1224902017-11-23T14:27:29Z2017-11-23T14:27:29ZAssessing Blinding in Randomized Clinical TrialsWaite, Jesse C.http://hdl.handle.net/10211.3/1966992017-10-04T19:37:40Z2017-10-04T00:00:00ZAssessing Blinding in Randomized Clinical Trials
Waite, Jesse C.
In the realm of randomized clinical trials, protocols intended to protect the knowledge pertaining to which treatment assignment each participant actually receives are usually employed. These protocols promote what is known as \textit{blinding}. When these protocols are meant to obscure the assignment from the clinicians as well as the participant, this is known as a double blind study. It is widely held that successfully employing protocols to insure blinding will help to insure the results of the study are not subject to bias. This thesis will discuss some of the methods commonly included in the protocols regarding blinding and the assessment of its success as it pertains to randomized clinical trials. Three methods which have been and could be used to assess the success of blinding protocols will be analyzed. A simulation study comparing the three methods for assessing blinding using R will show the differences between these methods, and their strengths and weaknesses will be discussed. Finally the development and employment of a method for determining when unblinding occurs because appropriate protocols are not enacted or followed is discussed.
2017-10-04T00:00:00ZTridiagonal Stochastic MatricesNguyen, Uyenhttp://hdl.handle.net/10211.3/1963472017-09-26T19:56:02Z2017-09-25T00:00:00ZTridiagonal Stochastic Matrices
Nguyen, Uyen
A birth-death chain with one-step transition probability matrix P often has a dual birth-death chain with one-step transition probability matrix P^*. The same holds for birth-death processes. From Professor Kouachi's work, we are able to determine the eigenvalues of suitable matrices P and P^*. We describe the exact diagonalization of P and P^* in Chapter 1. Chapter 2 summarizes Professor Kouachi's work in determining the exact formulas for eigenvalues and eigenvectors of certain tridiagonal matrices having arbitrary large dimension.
In Chapter 3, we apply Professor Kouachi's results to diagonalize a certain class of birth-death chains and processes. We obtain exact expressions for P^n, (P^*)^n and P(t). Generalizations of our results to non-tridiagonal stochastic matrices are presented in Chapter 4. Final conclusions and plans for future work are given in Chapter 5. Computer programs written by collaborators by Luis Cervantes, Mark Dela and Dave Luk to calculate P^n, (P^*)^n and P(t) are gratefully acknowledged and used in this thesis to obtain results in higher dimensions.
2017-09-25T00:00:00ZFractional-order Controllers for an Unmanned Aerial VehicleNavarro, Jesushttp://hdl.handle.net/10211.3/1960722017-09-18T18:55:39Z2017-09-18T00:00:00ZFractional-order Controllers for an Unmanned Aerial Vehicle
Navarro, Jesus
Fractional calculus is a new field of study where the main focus is on differentiation and integration of non-integer order. We then expand upon this idea into linear fractional-order differential equations and apply those techniques into fractional order PID, PI, and PD controllers where lambda and mu are arbitrary real numbers. The way we accomplish this is by implementing methods that have been proposed in "Fractional-order Systems and Controls". There are two different models that we look into, the longitudinal model which deals with the pitch angle of the aircraft, and the lateral model which deals with the roll angle of the aircraft. In order to obtain an ideal controller, we optimize the performance index and obtain the best parameters for the system. Then, looking at the step information of the controller, we want to ensure that we get a reasonable overshoot, rise time, and settling time. In one of the examples, we notice a significant difference where the fractional-order controller's rise time was 27.7 seconds faster, the settling time was 24.5 seconds faster, and our performance index gave us 4 more decimal places of accuracy compared to that of a regular controller. With these new techniques, we now have the opportunity to achieve better results than by using regular PID, PI, and PD controllers.
2017-09-18T00:00:00ZEpidemic Modeling: From Zombies to EbolaTomlinson, Chalmerhttp://hdl.handle.net/10211.3/1950242017-08-23T15:59:43Z2017-08-23T00:00:00ZEpidemic Modeling: From Zombies to Ebola
Tomlinson, Chalmer
2014 saw by far the largest Ebola outbreak in history. In this thesis, we explain the basics of epidemic modeling. The classic SI, SIR, and SEIR models are detailed with a hypothetical zombie apocalypse. The importance of the basic reproduction number, R_0, is shown. For Ebola, data is obtained from the World Health Organization on Guinea, Liberia, and Sierra Leone of West Africa (the most affected regions), and the Ebola outbreak is fit to the SEIR disease model. R_0 is calculated as a function of time for all three countries. To introduce a hypothetical cure, the infected group of the SEIR model is split up into a modified S-E-I1-I2-R model to differentiate between patients whose disease is advanced versus those whose is not. More complicated models make calculating R_0 increasingly difficult. The next-generation matrix (NGM) is introduced to show an effective way of obtaining R_0.
2017-08-23T00:00:00Z