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Geena Ildefonso

Undergraduate Major: Mathematics

Future Plans: PhD. in Mathematics

Geena Ildefonso

Geena Ildefonso was born and raised in Cooper City, Florida. While growing up in South Florida, she became interested in mathematics after exploring the concept of a derivative. Geena is the President of the Collegiate Mathematical Society, as well as Vice President of the Society for Advancement of Hispanics/Chicanos and Native Americans in Science (SACNAS) chapter here at UCF. Geena is pursuing her Bachelor's degree in Mathematics. Her research interests are in Biomathematics with a focus in math modeling of dysregulations in cancers . Last summer she conducted research in math modeling of cancer lineages and radiotherapy at the University of California, Irvine. Geena is currently researching the Hall Effect in the Magnetic Reconnection Process here at UCF, as well as various applications of Hilbert Spaces used in Quantum Mechanics, Signal Processing, and Harmonic Analysis. This summer she is researching the NFkB signal transduction pathway and its role in inflammation, cancer, and improper immune development. Her future educational plan is to obtain a PhD in Mathematics and open a Cancer Research Institute. After her time in the McNair program she hopes to be able to advance underprivileged youth into higher education.
Conducted at University of Central Florida as part of the ICubed National Science Foundation funded research project.

Mathematical Modeling of the NFkB Signaling Pathway using PySB

Conducted at Vanderbilt University, as part of the Leadership Alliance Program in the Vanderbilt Summer Science Academy

Mentor: Carlos Lopez, Ph.D., Department of Cancer Biology, Vanderbilt University

Abstract: Nuclear Factor-KappaB (NF-κB) is a signal transduction pathway centering around transcription factors that regulate gene expression in response to environmental stimuli. Aberrant activation of NF-κB has been linked to inflammation, autoimmune diseases, and improper immune development. In addition, NF-κB has a pivotal role in the initiation and progression of several cancers. The importance of NF-κB to these pathologies has led to the development of many mathematical models over the past decade, motivated by the need to gain a detailed quantitative—and ideally predictive—understanding of biological systems. In particular, Tay et al.'s model [Nature, 466, 7303 (2010)] successfully recapitulates key aspects of NF-κB signaling, and in turn has yielded insights into the pathway's structure, dynamics, and function. Recently, modeling frameworks such as PySB have emerged, which construct mathematical rule-based models of biochemical systems as computer programs. PySB facilitates reusable shareable, and transparently developed biological models. Here, we implement Tay et al.'s model of NF-κB signaling in PySB, and examine the pathway's ability to control programmed cell death through regulation of anti-apoptotic signals. We also intend to link the model with other models of apoptosis and necrosis to better understand cell fate outcomes in cancers.

Hilbert Spaces- Applications

Conducted at The University of Central Florida as part of the Career Advancement Mentoring Program for Young Entrepreneur Scholars (CAMP-YES) and the McNair Scholars Program

Mentor: Zhe Liu, Ph.D., Department of Mathematics, University of Central Florida
Abstract: A Hilbert space is an abstract vector space that possesses the structure of an inner product allowing length and angle to be measured, generalizing the notion of Euclidean space. Hilbert spaces are widely used in mathematics, but also have many applications in physics. Here we explore some applications of Hilbert spaces in Classical Mechanics, and Quantum Mechanics.

Cancer Lineages and Radiotherapy

Conducted at The University of California, Irvine as part of the Summer Undergraduate Research Fellowship Program and the McNair Scholars Program

Mentor: Dr. John Lowengrub, Professor – Department of Mathematics, University of California, Irvine.

Abstract: The traditional view of cancer states that the unregulated division and growth of cells is the cause of tumor formation and growth. In recent years, studies have shown that only small subpopulations of tumor cells are responsible for the relentless growth of tumors. These cells are called cancer stem cells (CSC) and this new point of view is known as the CSC hypothesis. Here, we propose to investigate the use of radiotherapy in cancer treatment of heterogeneous tumors containing stem and non-stem cells. A feature of our approach is that we incorporate feedback processes that regulate cell behavior. In addition, we account for radiation-induced reprogramming of differentiated cells into stem cells, which has been observed experimentally. We develop a mathematical model of the cell dynamics using differential equations and the linear-quadratic model to estimate the survival of cells to radiation exposure. To simulate spatial effects, we also plan to use the Cellular-Potts model in which individual cells are represented as a collection of pixels and the dynamics are governed through a probabilistic algorithm that is based on an energy that also takes into account adhesion, motility, and cell stiffness. To parameterize the models, we will use data from brain tumors provided by the laboratory of F. Pajonk (UCLA). The goal is to develop tumor-specific therapy schedules and dosages to optimize response of tumors to radiation treatment. This is an important step towards developing individualized therapy protocols where therapy is designed to optimize response for patient-specific tumor cells. 

Hall Magnetohydrodynamic Reconnection: Parker Problem 

Conducted at University of Central Florida as part of the ICubed National Science Foundation funded research project.

Mentor: Bhimsen Shivamoggi, Ph.D., Department of Mathematics, University of Central Florida

Abstract:The Hall Magnetohydrodynamic (MHD) model has successfully described a fast magnetic reconnection process in laboratories. This process has also effectively described space plasmas that release tremendous magnetic energy. Here, we consider the role of the Hall Effect in magnetic flux pile-up driven anti-parallel magnetic field merging. In this process, there is a magnetic field building upstream of a Sweet-Parker current sheet. We propose to give analytical and numerical solutions of the Hall-resistive MHD equations describing stagnation-point flows in a thin current sheet-Parker problem. We will then compare these results with the previous results of Shivamoggi [1] given by a different mathematical procedure