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Many data sets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a data set. A useful representation of this homological(More)
The snow surface is very dynamic, and the roughness of the snowpack surface varies spatially and temporally. The snow surface roughness influences the movement of air across the snow surface as well as the resulting transfers of energy, and is used to estimate the sensible and latent heat fluxes to and/or from the snow surface to the atmosphere. In the(More)
When the surface of a nominally flat binary material is bombarded with a broad, normally incident ion beam, disordered hexagonal arrays of nanodots can form. Shipman and Bradley have derived equations of motion that govern the coupled dynamics of the height and composition of such a surface [Shipman and Bradley, Phys. Rev. B 84, 085420 (2011)]. We(More)
For positive integers k, n, a de Bruijn sequence B(k, n) is a finite sequence of elements drawn from k characters whose subwords of length n are exactly the k n words of length n on k characters. This paper introduces the unoriented de Bruijn sequence uB(k, n), an analog to de Bruijn sequences, but for which the sequence is read both forwards and backwards(More)
1 Abstract Persistent homology is a relatively new tool from topo-logical data analysis that has transformed, for many, the way data sets (and the information contained in those sets) are viewed. It is derived directly from techniques in computational homology but has the added feature that it is able to capture structure at multiple scales. One way that(More)
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