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\section{Preamble}
Complex landscapes are basically functions of many variables having many minima and, inevitably,
-many saddles of all indices, i.e. the number of unstable directions. Optimization problems
+many saddles of all `indices' (their number of unstable directions). Optimization problems
require us to find the deepest minima, often a difficult task.
For example, particles with a repulsive mutual potential enclosed in a box will have many stable
configurations, and we are asked to find the one with lowest energy.