34 research outputs found
Lipschitz Unimodal and Isotonic Regression on Paths and Trees
We describe algorithms for finding the regression of t, a sequence of values, to the closest sequence s by mean squared error, so that s is always increasing (isotonicity) and so the values of two consecutive points do not increase by too much (Lipschitz). The isotonicity constraint can be replaced with a unimodular constraint, where there is exactly one local maximum in s. These algorithm are generalized from sequences of values to trees of values. For each scenario we describe near-linear time algorithms.
Enhanced scattering efficiencies in spherical particles with weakly dissipating anisotropic materials
10.1007/s00339-008-4572-5Applied Physics A: Materials Science and Processing924773-776APAM