Knotting in proteins was once considered exceedingly rare. However, systematic analyses of solved protein structures over the last two decades have demonstrated the existence of many deeply knotted proteins, and […]
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 […]
