  We numerically investigate the conical emission (CE) from ultrashort laser
filaments, both considering and disregarding the higher-order Kerr effect
(HOKE). While the consideration of HOKE has almost no influence on the
predicted CE from collimated beams, differences arise for tightly focused
beams. This difference is attributed to the different relative contributions of
the non-linear focus and of the modulational instability over the whole
filament length.
