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 based on overlapping image patches, the convolutional representation optimizes over the entire image, yielding representations that are very sparse both spatially and across the filters. […]

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 > […]

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 […]

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 […]

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 […]