Another way to approach the linear combination is to look at it geometrically. This is where the idea of barycentric coordinates can help. A barycentric coordinate system describes the location of a point as the weighted sum of the regular coordinates of the vertices forming a simplex. In other words, it describes a linear combination with respect to a set of points, where in -dimensional space.
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Anubis is a compromise. Anubis uses a Proof-of-Work scheme in the vein of Hashcash, a proposed proof-of-work scheme for reducing email spam. The idea is that at individual scales the additional load is ignorable, but at mass scraper levels it adds up and makes scraping much more expensive.