For two genus $g$ handlebody-knots $H_{1}$ and $H_{2}$, we denote $H_{1} \geq H_{2}$ if there exists an epimorphism from the fundamental group of the handlebody-knot complement of $H_{1}$ onto the […]
We study the problems of clustering covariance stationary ergodic processes and locally asymptotically self-similar stochastic processes, when the true number of clusters is priorly known. A new covariance-based dissimilarity measure is introduced, […]
In 1897, Indiana physician Edwin J. Goodwin believed he had discovered a way to square the circle, and proposed a bill to Indiana Representative Taylor I. Record which would secure […]
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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
