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variables. Unlike real landscapes, the classification of
saddles by index is trivial. Instead, the spectrum of fluctuations at stationary points determines their
topological stability under analytic continuation of the
- theory. Topological changes, which occur at so-called Stokes points, proliferate when the
- saddles have marginal (flat) directions and are suppressed
+ theory. Topological changes, which occur at so-called Stokes points, proliferate among
+ saddles with marginal (flat) directions and are suppressed
otherwise. This gives a direct interpretation of the gap or `threshold' energy---which
in the real case separates saddles from minima---as the level where the spectrum of
the hessian matrix of stationary points develops a gap. This leads to different consequences