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 […]
In Euclidean geometry, the sum of two sides of any triangle is greater than the third side. We introduce this idea to labeling of graphs. A (p,q)-graph G=(V,E) is said to […]
Title: Biquandle Brackets and Knotoids Abstract: Biquandle brackets are a type of quantum enhancement of the biquandle counting invariant for oriented knots and links, defined by a set of skein […]
Cells make fate decisions in response to dynamic environmental and pathological stimuli as well as cell-to-cell communications. Recent technological breakthroughs have enabled to gather data in previously unthinkable quantities at […]
An “Adinkra” is a graphical tool to describe a branch of particle physics known as supersymmetry. Understanding the mathematics of Adinkras shines a light on the underlying physics, as well […]
Single-cell genomics is a catch phrase for numerous new technologies and methods that allow for probing cells at genome scale. I will explain what this means and describe some examples […]
The classical, one-boundary, and two-boundary Temperley-Lieb algebras arise in mathematical physics related to solving certain rectangular lattice models.They also have beautiful presentations as "diagram algebras", meaning that they have basis […]
Title: Understanding Structure in the Single Variable Knot Polynomials Abstract: We examine the dimensionality and internal structure of the aggregated data produced by the Alexander, Jones, and Z0 polynomials using topological data analysis and dimensional reduction […]
The beauty of mathematics is often encountered when one discovers that two apparently very different phenomena actually share a common origin. I will discuss such a surprising connection between two […]
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 […]
TOPIC: Symmetry Symmetry seems to be an important idea in mathematics, but how do mathematicians think about symmetry? In this workshop, we’ll talk about mathematical objects called groups, see how […]
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 develop mathematical models from single-cell data. Particularly for high-dimensional single-cell gene sequencing data, dimension reduction techniques are applied to find the trajectories of cell states […]
