Applied Math Seminar

As titled

We investigate a hybrid inverse problem in fluorescence ultrasound modulated optical tomography (fUMOT) in the diffusive regime. We prove that the boundary measurement of the photon currents allows unique and […]

Recent  experiments  of  thin  films  flowing  down  a  vertical  fiber  with  varying  nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. Determining  the  regime  […]

Recent advances in single-cell gene sequencing data and high-dimensional data analysis techniques are bringing in new opportunities in modeling biological systems. In this talk, I will discuss different approaches to […]

We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve […]

The hypothalamic-pituitary-adrenal (HPA) axis is a neuroendocrine system that regulates numerous physiological processes. Disruptions are correlated with stress-related diseases such as PTSD and major depression. We characterize "normal" and "diseased" […]

Markov chains are widely used throughout mathematics, statistics, and the sciences, often for modelling purposes or for generating random samples. In this talk I’ll discuss a different, more recent application […]

Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices, and an algorithm […]

Joan Ponce Purdue University Abstract: One of the main challenges of mathematical modeling is the balance between simplifying assumptions and incorporating sufficient complexity for the model to provide more accurate and […]

At the turn of the twentieth century, physicist Henri Bénard heated a shallow plate of fluid from below. For temperatures above a critical value, the fluid’s evenly heated state became unstable […]

Shannons sampling theorem provides a link between the continuous and thediscrete realms stating that bandlimited signals are uniquely determined by itsvalues on a discrete set. This theorem is realized in practice using so called analog to digital converters (ADCs). Unlike Shannons sampling theorem, the ADCs are limited in dynamic range. Whenever a signal exceeds some […]

Individuals may choose to create social groups where their individual fitness and success is influenced by those around them.  A group may increase an individual's success in finding food, shelter, and safety; however, if the group fails, so does the individual.  In this talk, we will explore how choices of individuals influence group dynamics using both agent-based modeling […]