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In singularity theory the general phenomenon of points and sets of singularities is studied, as part of the concept that manifolds (spaces without singularities) may acquire special, singular points by a number of routes.
The triple helix model of innovation, as theorized by Etzkowitz and Leydesdorff, is based on the interactions between the three following elements and their associated 'initial role': [9] universities engaging in basic research, industries producing commercial goods and governments that are regulating markets. [2]
A wide range of supervised learning algorithms are available, each with its strengths and weaknesses. There is no single learning algorithm that works best on all supervised learning problems (see the No free lunch theorem).
A set C (blue) and its dual cone C * (red).. A duality in geometry is provided by the dual cone construction. Given a set of points in the plane (or more generally points in ), the dual cone is defined as the set consisting of those points (,) satisfying + for all points (,) in , as illustrated in the diagram.