Bramble Portrait

The Bramble-hilbert Lemma *

In numerical analysis, the Bramble-Hilbert lemma bounds the error of an approximation of a function u by a polynomial of order at most m− 1 in terms of derivatives of u of order m. Both the error of the approximation and the derivatives of u are measured by L norms on a bounded domain in R. This is similar to classical numerical analysis, where, for example, the error of interpolation u on an i...

Portrait

Born in 1944, I grew up in a world in which polio was both a gripping fear and real threat. Then in a matter of a few years-polio was eradicated by a vaccine developed by Jonas Salk. Later I learned that Salk's efforts were built on pioneering work of many others, including John Enders, Thomas Weller and Frederick Robbins (Nobelists, 1954), and David Bodian, who pioneered studies of polio patho...

BraMBLe: A Bayesian Multiple-Blob Tracker

Blob trackers have become increasingly powerful in recent years largely due to the adoption of statistical appearance models which allow effective background subtraction and robust tracking of deforming foreground objects. It has been standard, however, to treat background and foreground modelling as separate processes — background subtraction is followed by blob detection and tracking — which ...

On tree width, bramble size, and expansion

A bramble in a graph G is a family of connected subgraphs of G such that any two of these subgraphs have a nonempty intersection or are joined by an edge. The order of a bramble is the least number of vertices required to cover every subgraph in the bramble. Seymour and Thomas [8] proved that the maximum order of a bramble in a graph is precisely the tree width of the graph plus one. We prove t...

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