Summary
2011 International Symposium on Nonlinear Theory and Its Applications
2011
Session Number:A3L-C
Session:
Number:A3L-C2
Unimodal Category and Topological Statistics
Yuliy Baryshnikov, Robert Ghrist,
pp.196-199
Publication Date:2011/9/4
Online ISSN:2188-5079
Summary:
We consider the problem of decomposing a compactly supported distribution f : Rn → [0,∞) into a minimal number of unimodal components by means of some convex operation (e.g., sum or sup). The resulting "unimodal category" of f is a topological invariant of the distribution which shares a number of properties with the Lusternik-Schnirelmann category of a topological space. This work introduces the concept of a unimodal category, provides fundamental examples (l p unimodal category), and computes various unimodal categories for distributions on Rn with n small