Colloquium

Convolutional sparse representation is an efficient tool for computing sparse representations for entire signals in terms of sums of a set of convolutions with dictionary filters. Unlike representations that are […]

Abstract: The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size. This problem […]

Abstract: Augusta Ada, Countess of Lovelace, is today viewed as the rst person to recognize the power of algorithmic machines and a pioneer in computer programming. Her biographers have often […]

From the view of a pure mathematician, those working in pure mathematics produce pure knowledge. Whether used or not, it has a great elegance and value in and of itself. Those in applied mathematics simply pick up what has been done and use it in designing or building things. Number theory is often used to […]

In the 1970s, James O’Keefe and his team observed that certain neurons in the brain, called place cells, spike in their firing rates when the animal is in a particular physical location within its arena. If a place cell is thought of as either “active” or “silent,” then one may represent the co-firing patterns of […]

Understanding how fluid flows through heterogeneous materials, and how it can make these materials fail, are among the hardest challenges in materials science.  Experiments and simulations show that flow through subsurface rock is mostly limited to a small subnetwork, or backbone, of fractures.  Identifying this backbone would allow for a large speedup in flow and […]

Abstract:  A great deal of my research journey has involved the study of m-ary partitions.  These are integer partitions wherein each part must be a power of a fixed integer m > 1.  Beginning in the late 1960s, numerous mathematicians (including Churchhouse, Andrews, Gupta, and Rodseth) studied divisibility properties of m-ary partitions.  In this talk, I will discuss work I completed […]

Abstract: Whether enjoying the lucid prose of a favorite author or slogging through some other writer's cumbersome, heavy-set prattle (full of parentheses, em-dashes, compound adjectives, and Oxford commas), readers will notice stylistic signatures not only in word choice and grammar, but also in punctuation itself. Indeed, visual sequences of punctuation from different authors produce marvelously […]

Abstract:  Growing up, I always loved learning about world-changing scientific breakthroughs that were discovered by accident.  Penicillin, artificial sweeteners, X-rays, and synthetic dyes are just a few of the discoveries that were stumbled upon by scientists who had other goals in mind.  More recently, I have come to wonder why anecdotes about accidental discoveries in […]

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 […]