  Motivated by a range of applications in engineering and genomics, we consider
in this paper detection of very short signal segments in three settings:
signals with known shape, arbitrary signals, and smooth signals. Optimal rates
of detection are established for the three cases and rate-optimal detectors are
constructed. The detectors are easily implementable and are based on scanning
with linear and quadratic statistics. Our analysis reveals both similarities
and differences in the strategy and fundamental difficulty of detection among
these three settings.
