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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)
A 19-year-old male military recruit developed erythema multiforme 20 days after receiving a triad of vaccinations: smallpox (vaccinia virus), anthrax, and tetanus. Over the course of a few days, the erythema multiforme evolved into Stevens-Johnson syndrome, associated with widespread bullae, stomatitis, conjunctivitis, and fever. After 7 days of(More)
Given a polynomial system f : C N → C n , the methods of numerical algebraic geometry produce numerical approximations of the isolated solutions of f (z) = 0, as well as points on any positive-dimensional components of the solution set, V(f). One of the most recent advances in this field is regeneration, an equation-by-equation solver that is often more(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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