Other Applied Mathematics Commons^™

Liutex - A Fluid Vortex, Oscar Alvarez

Mathematics Dissertations

Fluid vortices are found everywhere in our universe. A vortex can take the form of almost anything - from the classical spiral vortex to chaotic plumes. Defining a vortex physically and mathematically is absolutely necessary if we desire to study vortices and their interactions with each other as well as our physical world. Fluid vortices are incredibly important in the study of turbulent flows. From determining wear, optimizing design for better flow, efficiency, etc., to even predicting the weather on Earth or other planets, having the ability to measure vortices in fluid flow is invaluable. In this study, I investigate …

Using Provided Guided Notes In Coordinated Introductory First-Year Mathematics Courses, Jennifer L. Huber

Mathematics Dissertations

The goal of this study is to investigate how standardized guided notes shape instructional practices and student engagement in coordinated introductory first-year college mathematics courses at a large public university. The researcher explored three multi-section introductory mathematics courses with overlapping learning objectives. Each course required students to purchase a student workbook as part of the instructional materials for the class. The instructors taught primarily from the workbook containing guided notes created by a former coordinator of the course. The researcher used a mixed-methods approach. Instructors and students participated in surveys, class observations and provided class meeting notes. Instructors shared additional …

A Bayesian Late-Fusion Supportability Framework For Rare-Disease Severity Prediction In Glut1 Deficiency Syndrome, Jordan M. Rodriguez

Mathematics Dissertations

Glucose transporter type 1 deficiency syndrome (GLUT1-DS) is a rare neurometabolic disorder with heterogeneous neurological and developmental severity. Because patient-level severity is not observed as a single validated outcome, this dissertation develops a Bayesian late-fusion supportability framework for constructing and predicting an ordered latent severity phenotype from clinical, genetic, and EEG-derived evidence. The primary target was constructed in a larger clinical cohort using age-5 symptom burden and learning cognition, then assigned to an aligned multimodal prediction cohort. Target-defining variables were excluded from supervised predictors, and models were evaluated using patient-exclusive cross-validation with training-fold preprocessing and fold-wise EEG PCA.

The primary …

Discrete Time Risk Processes With Stochastic Premiums And Dividends, Enoch J. Dangbe

Mathematics Dissertations - Archive

Risk processes typically emerge in insurance and finance and are concerned with stochastic representation of uncertainties of real-world events. Main objective amounts to quantifying the chances of both desirable and undesirable events and balancing their mutual impact for the purpose of developing models that in some sense optimize the outcome from the business perspective. Our research is concerned with studying the evolution of the surplus process in which time and assets are integer-valued. Initial capital, random premiums, random claims, dividend payments based on assets’ performance constitute the components of our model. Our findings established recursive formulas for the total expected …

Estimating Per-Infection Cost And Burden For Dengue And Zika As A Function Of Antibody-Dependent Enhancement, Christopher M. Kribs

Mathematics Faculty Publications - Archive

The complex immune interactions produced by the tetravalent dengue vaccine Dengvaxia have foregrounded the important role of antibody-dependent enhancement (ADE) in dengue infection. Some evidence exists that ADE may extend beyond the four dengue serotypes to Zika, a closely related flavivirus transmitted by the same mosquito species as dengue, and may also account for the increased severity of some cases. Estimates of the public health impact of dengue vaccination may then need to include its effects on the transmission of Zika in addition to dengue. This study gathers primary references to build estimates of per-case economic cost and disease burden …

New Methods In Electrical Source Imaging Based On Eeg And Post-Mortem Pathology Data, Julio Cesar Enciso Alva

Mathematics Dissertations - Archive

A central task for Neuroscience is to determine the location of electrical activity of neural origin inside the brain. Electrical signals can be recorded at a high resolution in time but low resolution in space, thus making it difficult to locate their source unambiguously. Electrical Source Imaging (ESI) is a particular framework for neural electrical source location; it is possible by modeling any additional information we may have about the electrical sources. For instance, minimal-norm estimators assume that the most plausible estimation is that with a lower norm. However, these estimators possess a low resolution in space.

In this work, …