Now that you know you have to search for Security Bot Shutdown Panels that have these so-called signal relays on them, all you have to do is look at the map and head towards the areas with the panels. The nearest of these is in the theater area to the west of the foyer. Round the corner near the stairs and hack the Turret in the distance just as a rising curtain reveals the entrance to the theater.
Follow the walkway to the left and use the Rivet Gun to shoot the targets on the Plasmid demonstration machines. The first showcases the power of Incinerate!; the second electrocutes the water where the Splicer is standing; and the third demonstrates the wonders of Telekinesis and throws the distant Splicer high into the air (kind of how Cyclone Trap works). Gather up the First Aid Kits and ammo and continue through this demonstration area to the doors leading into the theater.
You’re now on the stage in the demonstration theater, and Gil Alexander’s special video bot is going to emcee the affair with you serving as the product demonstrator. Prepare for the audience participation segment by lining the two pedestals near the front of the stage with Trap Rivets and by placing a Mini-Turret in the center of the stage, near the microphone stand. If you have Cyclone Trap equipped, place a Cyclone Trap on each of the pedestals as well (charge them with Incinerate! or Electro Bolt if possible). You have a Telekinesis and Electro Bolt demonstrator to your right and an Incinerate! demonstration stand on the left—shoot the targets with the Rivet Gun to make them throw, shock, and burn the Splicers as they appear.
The first two participants attack individually, but then you’ll have to deal with multiple Houdini Splicers at once. A pair of Elite Security Bots can certainly help you get through this phase of the battle. Continue to use your Research Camera and blast the Houdini Splicers with Incinerate! and your Machine Gun.
An Alpha Series hops onto the stage and attacks next, but not before a brief intermission. Take this chance to lay down a couple Proximity Mines in preparation of the Alpha Series arrival and repair your Elite Security Bots with Handyman. Turn on the Research Camera and draw him in towards your mines before unloading on him with a Heat-Seeking Rocket and Incinerate! It won’t take long before you have the stage to yourself once again.
The second signal relay that must be destroyed is just behind the seats in the theater. Search the corpses in the chairs for a wealth of money and ammo, then destroy the signal relay and exit the area.