  We present the results of a search for transient radio bursts of between
0.125 and 32 millisecond duration in two archival pulsar surveys of
intermediate galactic latitudes with the Parkes multibeam receiver. Fourteen
new neutron stars have been discovered, seven of which belong to the recently
identified "rotating radio transients" (RRATs) class. Here we describe our
search methodology, and discuss the new detections in terms of how the RRAT
population relates to the general population of pulsars. The new detections
indicate (1) that the galactic z-distribution of RRATs in the surveys closely
resembles the distribution of pulsars, with objects up to 0.86 kpc from the
galactic plane; (2) where measurable, the RRAT pulse widths are similar to that
of individual pulses from pulsars of similar period, implying a similar beaming
fraction; and (3) our new detections span a variety of nulling fractions, and
thus we postulate that the RRATs may simply be nulling pulsars that are only
"on" for less than a pulse period. Finally, the newly discovered object PSR
J0941-39 may represent a link between pulsars and RRATs. This bizarre object
was discovered as an RRAT, but in follow-up observations often appeared as a
bright (~10 mJy) pulsar with a low nulling fraction. It is obvious therefore
that a neutron star can oscillate between being an RRAT and a pulsar.
Crucially, the sites of the RRAT pulses are coincident with the pulsar's
emission, implying that the two emission mechanisms are linked, and that RRATs
are not just pulsars observed from different orientations.
