GAZA CITY, Gaza Strip (AP) — Terrified residents ran for cover Tuesday in a densely populated neighborhood of Gaza City as Israeli troops backed by tanks thrust deeper into the city and sought Hamas fighters in alleyways and cellars. On the diplomatic front, Egyptian mediators pushed Hamas to accept a truce proposal and, in a hopeful sign, Israel sent its lead negotiator to Cairo for “decisive” talks on a cease-fire. U.N. Secretary-General Ban Ki-moon also headed for the region to join diplomatic efforts. Israeli military officials say that depending on what happens with what they described as “decisive” talks in Cairo, Israel will move closer to a cease-fire or widen its offensive.