We prove the existence of a poly(n,m)-time computable pseudorandom generator which “1/poly(n,m)-fools” DNFs with n variables and m terms, and has seed length O(log nm · log log nm). Previously, the best pseudorandom generator for depth-2 circuits had seed length O(log nm), and was due to Bazzi (FOCS 2007). It follows from our proof that a 1/m-biased distribution 1/poly(nm)-fools DNFs with m ter...

A semiparametric accelerated failure time (AFT) model is proposed to evaluate the effects of risk factors on the unbiased failure times for the target population given the observed length-biased data. The analysis of length-biased data is complicated by informative right censoring due to the biased sampling mechanism, and consequently the techniques for conventional survival analysis are not ap...

To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and as a result, the sample is length biased. The selection bias model can be demonstrated through Buffon's Needle Problem, which was extended to general curves that more realistically repre...