Aromaticity of 1,1'-bi(cycloprop-2-en-1-ylidene) and 1,4-dioxine
Antiaromaticity is a fictional state with real consequences,  that any molecule will distort to avoid.

In the case of molecule 1, the primary state will be a triplet (unpaired pi-electrons), with the central bond lengthening to decrease the pairing of the pi-electrons.  This will lead to 3 electrons in each pi-system, and hence preventing antiaromaticity, because there are no longer 4n electrons in the rings.  A fictional molecule, with the constituency shown for molecule 1 that is in a singlet state would be antiaromatic.

In the case of molecule 2, the molecule will distort itself to make the at least one of the oxygens non-coplanaer with the pi-system, and no longer being co-planar, the system will not be antiaormatic.  A fictional molecule with the constituency shown for molecule 2 that is co-planar, would be antiaromatic.

It is unclear what you are asking about for pyrene.