In this presentation, some fundamentals of electrostatics in biology will be discussed with focus on the fact that most biological macromolecules including nucleic acids, carbohydrates, and proteins are negatively-charged. Electroneutrality […]
Abstract: Remember smoking? What’s the new public health problem? In the US, we are currently entangled within three converging and intertwined complex problems: Cancer, Obesity, Aging. There are over 16 […]
Linear evolution equations, such as the heat equation, are commonly studied on finite spatial domains via initial-boundary value problems. In place of the boundary conditions, we consider “multipoint conditions”, where one specifies some linear combination of the solution and its derivative evaluated at internal points of the spatial domain, and “nonlocal” specification of the integral […]
Data is exploding at a faster rate than computer architectures can handle. For that reason, mathematical techniques to analyze large-scale data need be developed. Stochastic iterative algorithms have gained interest due to their low memory footprint and adaptability for large-scale data. In this talk, we will study the Randomized Kaczmarz algorithm for solving extremely large […]
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 researchers now hypothesize that the knotting presents some functional or evolutionary advantage for those proteins. Unfortunately, there is very little known (whether experimentally, through […]
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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 stable reconstructions of the absorption coefficient of the fluorophores at the excitation frequency and the quantum efficiency coefficient simultaneously, provided that some background medium parameters […]
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 transitions from absolute (Rayleigh- Plateau) instability is useful in the design of heat and mass exchangers for applications that include cooling systems and desalination. We present a […]
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 of Markov chains, to developing distributed algorithms for programmable matter systems. Programmable matter is a material or substance that has the ability to change its […]
