PhD, University of Cincinnati, 2024, Arts and Sciences: Mathematical Sciences

The generalized Hastings-McLeod solutions to the inhomogeneous Painleve-II equation arise in multi-critical unitary random matrix ensembles, the chiral two-matrix model for rectangular matrices, non-intersecting squared Bessel paths, and non-intersecting Brownian motions on the circle. We establish the leading-order asymptotic behavior of the generalized Hastings-McLeod solutions as the inhomogeneous parameter approaches infinity using the Deift-Zhou nonlinear steepest-descent method for Riemann-Hilbert problems. This analysis is done in both the pole-free region and pole region. The asymptotic formulae show excellent agreement with numerically solutions in both regions.

Committee: Robert Buckingham Ph.D. (Committee Chair); Deniz Bilman Ph.D. (Committee Member); Bingyu Zhang Ph.D. (Committee Member); Yizao Wang Ph.D. (Committee Member) Subjects: Materials Science

Specialist in Education (Ed.S.), University of Dayton, 2021, School Psychology

The field of school psychology is currently facing a shortage that has impacted states across the nation. This study examined data gathered from individual interviews of currently licensed school psychologists within the state of Ohio who have worked with an educator on special assignment due to the shortage of trained school psychologists within the state. The study aimed to gather more information regarding school psychologists' perceptions of this practice including any benefits or drawbacks that they had experienced or anticipated. Analysis of the interviews resulted in four broad themes, variation in the role of an educator on special assignment, need, concerns, benefits/opportunities, and solutions. Interviewees indicated a clear need for support based upon the shortage and clerical demands, while also revealing concerns surrounding potential misuse of the position, a lack of opportunity to work with students, and inconsistent background/training for the role. Some of the benefits noted included reduced burnout and additional time to engage in consultation and other practice. While the use of educators on special assignment is one potential solution being utilized within the state of Ohio, additional proposals for solutions such as clerical support/paperwork reductions, more trained school psychologists/graduate programs, more flexible training opportunities, and pay commensurate with education were also revealed. Recommendations for future discussions to provide clarification of this role and explore other potential solutions to the shortage both within Ohio and nationally are provided.

Committee: Sawyer Hunley Dr. (Committee Chair); Susan Davies Dr. (Committee Member); David Dolph Dr. (Committee Member) Subjects: Education; Psychology; School Counseling

Master of Arts (M.A.), University of Dayton, 2014, Psychology, Clinical

Behaviors exhibited while online differ radically from behaviors exhibited while offline (Suler, 2004a). Research suggests that this difference in behaviors results from online disinhibition (OD) while engaging in computer-mediated communication (Suler, 2004a). An example of the effects of OD can be seen when a person flirts outside of his or her dyadic relationship while online when he or she would not normally in person. Flirting can cause harm to a romantic relationship when it is directed towards someone outside of the romantic relationship (Glass, 2003). Due to the immense use of the internet among college students, and the negative impact that extradyadic flirting can have on a romantic relationship, the first goal of this research was to provide a basis of information on the amount of online flirting, how online flirting occurs, and the impact of online flirting among college-age students. The second goal of this study is to assess participants' perception of how detrimental the impact of online flirting would be on their romantic relationship compared to offline flirting. Malt (2007) found that there is a general view in society that flirting online is less detrimental to a romantic relationship than flirting offline. Given this finding, along with the possibility that participants are aware of OD, I predicted that online flirting would be perceived as less detrimental to a romantic relationship than offline flirting as a result of an informal understanding of OD from personal internet use. The third goal of this study was to understand the perceived impact of public versus private extradyadic online flirting on a romantic relationship. Pittman (1990) found that infidelity that occurs in private has more of a detrimental impact on a romantic relationship than infidelity that occurs in public. Therefore, I predicted that private online flirting, such as through a Facebook message, would be perceived as more detrimental to a relationship than public online fli (open full item for complete abstract)

Committee: Lee Dixon (Advisor); Melissa Layman-Guadalupe (Committee Member); Erin O'Mara (Committee Member); Keri Kirschman (Committee Chair) Subjects: Psychology; Social Psychology; Sociology; Technology

Doctor of Philosophy (PhD), Ohio University, 2014, Mathematics (Arts and Sciences)

Mathematical models are used to study two biological systems: pulmonary innate immunity and autonomous oscillation in yeast. In order to better understand the dynamics of an early infection of the lungs, we construct a predator-prey ODE model of pulmonary innate immunity which describes several observed properties of the pulmonary innate immune system. Under reasonable biological assumptions, the model predicts a single nontrivial equilibrium point with a stable and unstable manifold. Trajectories to one side of the stable manifold are asymptotic to the disease-free equilibrium and on the other side are unbounded in the size of the infection. The model also reproduces a phenomenon observed by Ben-David et al whereby the innate response to an infectious challenge reduces the ability of further infections to take hold. The model may be useful in analyzing and understanding time series data obtained by new methods in pathogen detection in ventilated patients. We also examine several models of autonomous oscillation in yeast (YAO), called the Immediate, Gap, and Mediated models. These models are based on a new concept of Response / Signaling (RS) coupled oscillator models, where feedback signaling and response are phase-dependent. In all three models, clustering of the type seen in YAO is a robust and generic phenomenon. The Gap and Mediated models add a dynamical delay, the latter by modeling a signaling agent present in the culture. For dense populations the Mediated model approximates the Immediate model, but the Mediated model includes dynamical quorum sensing where clustered solutions become stable through density-dependent bifurcations. A partial differential equations model is also examined, and we demonstrate existence and uniqueness of solutions for most parameter values.

Committee: Todd Young (Advisor); Winfried Just (Committee Member); Alexander Neiman (Committee Member); Tatiana Savin (Committee Member) Subjects: Applied Mathematics; Cellular Biology; Immunology

DMA, University of Cincinnati, 2010, College-Conservatory of Music : Conducting, Wind Emphasis

The repertoire of the modern wind band has experienced a dramatic metamorphosis throughout the past one hundred years. With firm beginnings in the British band movement at the turn of the century with noted composers such as Ralph Vaughan Williams, Gustav Holst, and Percy Grainger, this unique literature has continued to expand with other composers including Darius Milhaud, Paul Hindemith, Igor Stravinsky, Arnold Schoenberg, and others. Among the current pioneers of notable wind music composers stands David Werner Amram (b. 1930). Spanning the past fifty years, Amram's musical output rivals that of many of his contemporaries. This composer has etched a distinctive position in the American musical culture. As the first composer-in-residence in the history of the New York Philharmonic, Amram secured his stature as one of the world's leading composers, but his background and life experiences have produced a style that is uniquely his own. Amram's professional career includes an eclectic diversity, which encompasses working with jazz legends such as Charlie Parker and Dizzy Gillespie. He has also achieved fame for his collaborations with Joseph Papp and his Shakespearean performances in New York City. In addition, he has traversed the globe as a major advocate of world music. As a composer of opera, symphonies, concertos, chamber music, and film and television scores, David Amram has developed a style that is purely his own. His compositions are essentially tonal, occasionally dissonant, at times neo-Elizabethan, but very often infused with a distinct jazz element and other folk tendencies. This thesis will trace these elements through an investigation of three compositions for wind band, comparing and contrasting specific traits that are unique to Amram. The titles include King Lear Variations, Andante and Variations on a Theme for Macbeth and Ode to Lord Buckley. As one source for this paper, in addition to the Sources Consulted and personal analysis, David Amram spok (open full item for complete abstract)

Committee: Rodney Winther MMus (Committee Chair); Terence Milligan DMA (Committee Member); James Vanmatre MM (Committee Member) Subjects: Music

MS, University of Cincinnati, 2009, Engineering : Electrical Engineering

A biological pathway represents a network of complex reactions at the molecular level of living cells. Pathways model how biological molecules interact to carry out a biological function and how they respond to external stimuli. The pathway models are derived through scientific experimentation and data analysis. Modeling biochemical reactions is a component in studying and analyzing biological pathways. The modeling and control of biological pathways is extremely important in understanding various biological phenomena. Biological pathways can be controlled in the laboratory and this process has applications in medicine and also in the invention of certain biologically based components for computer circuits or bio-circuits. However, direct experimental study of the pathways is expensive and also time consuming. Mathematical modeling and stochastic simulation techniques provide an affordable and easy to use experimental platform. Mathematical modeling and stochastic simulations, based on biochemical rate equations, provide us with rigorous tools to understand the intricacies involved in biological pathways. In this thesis we model the Phage Lambda system, which functions as a biological switch, and the Bioluminescence system, which provides a model of communication. We use the stochastic simulation techniques based on Gibson and Bruck's Next Reaction Method. We compare our results with the results of simulations using Gillespie's Algorithm and with the results from an agent-based model. We also provide easy-to-use templates for the simulations to support future research in this area.

Committee: Carla Purdy, C PhD (Committee Chair); Wen-Ben Jone PhD (Committee Member); George Purdy PhD (Committee Member) Subjects: Electrical Engineering

Master of Science, The Ohio State University, 2008, Mechanical Engineering

The goal of this master's project is to develop and test a numerical tool to simulate the fluid physics and chemical reactions inside of a shock tube. The one-dimensional Euler equations for chemically reacting flow are employed to model the fluid flows and detailed finite-rate chemistry models are used to simulate chemical reactions. The CESE method is used to solve the Euler equation. The implicit trapezoidal method with sub-time steps is used to solve the stiff ODEs for chemical reactions. The newly developed code has been validated by (i) zero-dimensional calculations for testing the chemistry solver (ii) Calculation of the ignition delay in a shock tube. The results were compared with the ignition time from shock tube experiments. The new shock-tube tool will be used (i) to study the lean-blow-out in scramjet engines and (ii) to assess the required mesh and time resolution for 2/3-dimensional simulation of chemically reacting flows.

Committee: Prof. Sheng-Tao Yu (Advisor); Dr. Douglas Davis (Other); Prof. Jeffrey Sutton (Other) Subjects: