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The Antarctic Impulsive Transient Antenna (ANITA) is a NASA long-duration balloon experiment with the primary goal of detecting ultra-high-energy (\(> 10^{18}\)eV) neutrinos via the Askaryan Effect. In the fourth ANITA mission, the Tunable Universal Filter Frontend (TUFF) boards were deployed for mitigation of narrow-band, anthropogenic noise with tunable, switchable notch filters. They contributed to a factor of 2.8 higher total instrument livetime in ANITA-4 compared to ANITA-3. A search for a diffuse flux of ultra-high-energy neutrinos was conducted using the data collected during the ANITA-3 flight with a new approach where the Antarctic ice area is sectioned off into bins and a search is performed with different thresholds in different bins. The binned analysis methods were extended to the development of a search for neutrinos from Gamma Ray Bursts, implementing constraints in time, and for the first time, in direction. Lower analysis thresholds were achieved in a feasibility search even when extending the search to include longer afterglow periods. Authored with osudiss-2.cls (v0.9.1)