I am a fifth year graduate student from the UNL Mathematics department advised by Professor Petronela Radu. My research is in nonlocal models and applied partial differential equations. Currently, we are studying the convergence of nonlocal conservation laws to the classical model as the horizon vanish.
Research Interest (click on each tab to expand)
I worked with Dr. Ekpenyong to develop a robust fractional viscoelastic model of cells using fractional calculus. We used Matlab to fit cell data and to verify good of fitness of cells in each model.
a)The average creep compliance of macrophages are fitted using four integer models. b)Instances where the four models failed to fit and produce meaningful parameters. c)Fractional calculus KV model quantifies drug-induced changes in cell viscoelasticproperties. d) The average creep compliance of macrophages are fitted using four fractional calculus models.
Application of Fractional Calculus in Modeling Cell Viscoelasticity Mathfest in Chicago 2017Contributed talk
PublicationsFractional calculus modeling of cell viscoelasticity quantifies drug response and maturation more robustly than integer order models (preprinted)
Nonlocal models utilize integral operators that mimic differential operators to capture material and phenomenon behavior. These operators capture long-range interaction and often have a finite horizon which is measured through the support of the kernel. Nonlocal models allow discontinuities in solutions thus offering more flexibility and under specific assumptions, it can be shown that nonlocal solutions converge to their classical counterparts. In my research with Dr. Radu, we study nonlocal nonlinear conservation laws whose operators and solutions are shown to converge to their classical counterparts under different sets of requirements on the flux densities.
Convergence of solution of nonlocal conservation law to local conservation laws SIDIM
Nonlocality in nonlinear conservation models CAMS at ISU
Nonlocal Advection-Convection Equation KUMUNU-ISO
Nonlocal nonlinear conservation laws BANFF
Nonlinear nonlocal conservation laws: convergence of operators and solutions SES2022
Convergence of solutions in nonlinear nonlocal conservation laws Prairie Seminar
In the course "Introduction to Deep Learning", I and a group of graduate students Nate Thach, Richard Mwaba, Junxiao Zhang created a machine learning model to detect lane marking on highway. Our problem of interest is to train a deep learning model for lane marker detection. In particular, we perform multiclass segmentation on the lanes, where each lane corresponds to one class. Inspired by the idea of neural ODE network, which introduces the novel neural ordinary differential equation (NODE) architecture for image segmentation in medical fields, we attempt to innovate the well-studied U-Net architecture, by replacing all convolutional layers with ODE blocks, in order to convert it into U-NODE. Here we trained both U-Net and U-NODE architectures on TuSimple dataset for a more comprehensive study.
Using our own custom quantitative evaluation method, our best U-NODE model returns accuracy values of 96.22\% and 84.01\% in the positive and negative tests, respectively, which are both higher than the result from our best U-Net model, having respective 93.29\% and 70.91\% accuracy instead. Our work has shown that (1) the newly proposed U-NODE architecture is reasonably robust in lane marker detection applications and (2) it can replace conventional U-Net architectures in this particular area.
Instructor of Record
College Algebra and TrigonometryF2020, F2021, F2022
Calculus IIF2018, S2019
Differential EquationS2021, S2022