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 in dimension three was the subject of a famous discussion between Isaac Newton and David Gregory in 1694. In three dimensions the problem was finally […]
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 […]
The Field Committee Meeting is our chance to socialize with our colleagues and coordinate our course offerings for the coming academic year (2019-2020). Please come to discuss course offerings and other synergistic items. Refreshments at 4:00, meeting at 4:15.
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. […]
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 […]
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 […]
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 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 present a few examples.
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 […]
