Mathematical modeling

Progression from a ductal carcinoma in situ (DCIS) to an invasive tumor is a major step initiating a devastating and often lethal metastatic cascade. One sentinel event that initiates this process is the development of ductal microinvasions, i.e., small cohorts of tumor cells capable of invading the surrounding the extracellular matrix (ECM) leading to irreversible changes in tumor and stromal architecture.

The heterogeneous nature of cancer observed across different regions of the primary tumor, across metastatic sites, across time, and across patients makes designing efficacious yet tolerable therapies a challenge. Both standard of care and personalized treatment protocols run the risk of not exhibiting a robust anti-tumor response in the face of these uncertainties. Here we introduce a platform for exploring this robustness question.

Prion proteins cause a variety of fatal neurodegenerative diseases in mammals but are harmless to yeast, making it an ideal model organism for these diseases. My research focuses on stochastic and deterministic models of both prion protein dynamics within individual yeast cells as well as how those yeast cells grow and divide to create a heterogeneous colony of cells. Determining kinetic parameters of prion replication in yeast are complicated because experiments reflect both the disease and yeast population dynamics.

As graduate students or postdoctoral researchers, we are taught to focus
on learning the research that is most closely related to our project so
that we can find the edge of what is known and expand the boundary. This
is, of course, necessary to complete our research project. However, we
often forget to seek out opportunities to develop skills and experience in
other areas of our work that are transferrable to a wider set of projects.
I will discuss some of these opportunities and specific dispositions that

Joint work with
Matthias Ruth¹, Ning Zeng¹,
Safa Motesharrei¹, and Jorge Rivas².

The intertwined processes of platelet deposition and coagulation can
lead to the development of blood clots inside a blood vessel or on an
implanted medical device. Their disregulation is responsible for
immense morbidity and mortality, particularly in the western world.

The development of a blood clot involves complex interactions of diverse
type (e.g., biochemistry, cell signaling and adhesion, fluid dynamics)
on diverse spatial and temporal scales. Exploring how these

An ideally polarizable cation-selective solid particle is suspended in an
electrolyte solution and is exposed to a uniformly applied ambient electric
field. The electrokinetic transport processes are described in a closed
mathematical model, consisting of differential equations, representing the
physical balance laws, as well as boundary conditions and integral constraints,
representing the physicochemical condition on the particle boundary and at
large
distances away from it. Solving this model would in principle provide the

The study of the interaction between (large) molecules and inorganic (metal) surfaces is a typical multiscale problem. In fact while the specific chemistry emerges
at the quantum scale with the interaction of the electrons of the surface with the valence
electrons of the molecule, the molecular conformations are instead the expression of a large scale statistical behavior. The delicate interplay
between these two aspects, intimately linked during the adsorption process, gives rise to

In this talk I will describe some of the ways in which Math is used and IBM. I will cover project in research, consulting,product design and manufacturing.

BIO:

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