Emek Köse’s research while affiliated with St. Mary's College of Maryland and other places

The stem cell hypothesis suggests that there is a small group of malignant cells, the cancer stem cells, that initiate the development of tumors, encourage its growth, and may even be the cause of metastases. Traditional treatments, such as chemotherapy and radiation, primarily target the tumor cells leaving the stem cells to potentially cause a recurrence. Chimeric antigen receptor (CAR) T-cell therapy is a form of immunotherapy where the immune cells are genetically modified to fight the tumor cells. Traditionally, the CAR T-cell therapy has been used to treat blood cancers and only recently has shown promising results against solid tumors. We create an ordinary differential equations model which allows for the infusion of trained CAR-T cells to specifically attack the cancer stem cells that are present in the solid tumor microenvironment. Additionally, we incorporate the influence of TGF-[Formula: see text] which inhibits the CAR-T cells and thus promotes the growth of the tumor. We verify the model by comparing it to available data and then examine combinations of CAR-T cell treatment targeting both non-stem and stem cancer cells and a treatment that reduces the effectiveness of TGF-[Formula: see text] to determine the scenarios that eliminate the tumor.

Ideally, students of mathematics gain much from their coursework and undergraduate careers. If we (teachers and professors) do our jobs right, then math majors and minors should, among other achievements, gain the ability to apply their mathematical knowledge to other disciplines and real-world problems. Project-based learning offers one way to achieve this goal, as it encourages students to solve interdisciplinary problems that arise outside of the traditional classroom. Project-based learning can be implemented as part of a class or as an enrichment program, and it typically features problems arising from a variety of sources (including social concerns of different communities, demands from business and industry, and non-profit or government organizations). In this special issue on Project-Based Curricula, we present six papers that address different aspects of project-based learning, including how it can be facilitated, ideas for projects, and evidence of its effectiveness.

Therapeutic vaccines play a large role in the cast of immunotherapies that are now an essential component in most cancer treatment regimes. The complexity of the immune response and the ability of the tumour to mount a counter-offensive to this response have made it difficult to predict who will respond to what treatments, and for clinicians to optimise treatment strategies for individual patients. In this paper, we present a mathematical model that captures the dynamics of the adaptive response to an autologous whole-cell cancer vaccine, without some of the complexities of previous models that incorporate delays. Model simulations are compared to published experimental and clinical data, and used to discuss possible improvements to vaccine design.

In this article, we present a case study of a course called Women in Mathematics. Students in the course studied the lives and the mathematical contributions of women mathematicians throughout history, as well as current gender equity issues in the study of mathematics and in mathematical careers. They also mentored 20 middle school girls throughout the semester. This nested strategy (with the professor providing an environment where the college students could appreciate math, and they, in turn, creating the same for middle school girls) resulted in improvements in both the college students’ and middle school girls’ attitudes towards mathematics.

Mirror surfaces used in catadioptric sensors are often designed so as to minimize one particular kind of image distortion. In this article we explore some finer properties of equi-areal mirrors, those that feature no area distortion, and we propose novel ways to measure compound forms of distortion. Specifically, we develop new mirror surfaces with large fields of view that simultaneously minimize angular and areal distortion with respect to different cost functions.

We compute a family of double-mirror catadioptric sensors with ultrawide field of view and no distortion. The two concentric mirrors are rotationally symmetric, and the inside mirror is a revolved conic section. The mapping between the object and the image planes was linear, hence the lack of distortion. The equations describing the outer mirror were determined by the projection induced by the inside mirror and the rectifying property of the sensor. Solving the resulting nonlinear ordinary differential equations yielded the cross section of the secondary mirror. The sensors we present require no further digital processing.

Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of discrete curves in mathematics and science. There are conflicting definitions of even basic concepts such as discrete curvature {\kappa}, discrete torsion {\tau}, or discrete Frenet frame.

Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth’s climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a research project for students interested in environmental studies and mathematics.