A lot of the mathematics done at NIST supports the research on and measurement of advanced materials and technology. In this rather applied context. surprising mathematics makes an appearance. We present a few examples.
I will talk about a few graph-theoretic metrics then introduce the concept of refinements on a class of functions that include all metrics. As a case study, we will construct various refinements on the shortest-path distance. Consequently, we obtain a few "better" versions of the Erdos number. In the course of our investigation, we realized various construction […]
Abstract: As intelligent agents assume larger role in our daily lives, reasoning by humans about liability of such agents as well as reasoning by the intelligent agents themselves about liability becomes more important. The existing laws, written with humans in mind, will eventually need to be re-interpreted in terms of their applicability in a hybrid […]
The traditional method of treating most human diseases is to direct a therapy against targets in the host patient, whereas conventional therapies against infectious diseases are directed against the pathogen. Unfortunately, the efficacy of pathogen-oriented therapies and their ability to combat emerging threats such as genetically engineered and non-traditional pathogens and toxins have been limited […]
A Fibonomial is what is obtained when you replace each term of the binomial coefficients $ {n \choose k}$ by the corresponding Fibonacci number. For example, the Fibonomial $${ 6\brace 3 } = \frac{F_6 \cdot F_5 \cdot \dots \cdot F_1}{(F_3\cdot F_2 \cdot F_1)(F_3\cdot F_2 \cdot F_1)} = \frac{8\cdot5\cdot3\cdot2\cdot1\cdot1}{(2\cdot1\cdot1)(2\cdot1\cdot1)} = 60$$ since the first six Fibonacci […]
Abstract: We overview some basic and striking facts concerning the theory of hypercyclic operators (considered to be born in 1982): 1. Hypercyclicity is a purely infinite-dimensional phenomenon: no finite dimensional space supports any hypercyclic operator; 2. It is not easy at all to determine whether a linear operator is hypercyclic. However, the set of hypercyclic […]
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 requires cations to move toward the macromolecules where they both screen and bind to the negatively-charged groups. An important class of mathematical models of species-flux […]
For centuries finding the determinant of a matrix was considered to be something that took $\Theta(n^3)$ steps. Only in 1969 did Strassen discover that there was a faster method. In this talk I'll discuss his finding, how the Master Theorem for divide-and-conquer plays into it, and how it was shown that finding determinants, inverting matrices, […]
Abstract: "We present a general Bayesian statistical model for discrete time, discrete state space stochastic processes. Applications include the modeling of recurrent and episodic disease processes, such as episodes of illicit drug use, as well as social processes such as educational enrollment and employment. We also present Markov chain Monte Carlo inference algorithms for our […]
An important question in classical representation theory is when the tensor product of two irreducible representations has another representation as a factor. In this talk, I will introduce a quantum generalization of this question and explain how we may relate this question to geometry of quotients of certain complex manifolds. This is joint work with […]
TOPIC: Graphs, matrices, and recurrences Abstract: In mathematics, we are often surprised to find that problems that look very different are actually the same problem in a different guise! In this seminar, we will build on the previous discussions about graph theory and describe how other areas of math are closely related to graphs. Specifically, […]
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 million cancer survivors living in the US as we speak. Over 50% of our society is overweight and/obese. Our society is aging and the age […]
