The Beatles
If you don't know who the Beatles are, the very kind and ever polite people on this site recommend you go to youtube.
If you didn't know, the Beatles were an English rock band formed in Liverpool in 1960. They were extremely popular, becoming one of the most commercially successful and critically acclaimed acts in the history of music. The band consisted of John Lennon, Paul McCartney, George Harrison, and Ringo Starr. Getting their start in skiffle and 50s rock and roll, the Beatles later went on to add a wide range of genres to their music - ranging from pop ballads to psychedelic rock, incorporating classical and other elements in innovative ways.
On the iTunes LP for The Resistance, Matt stated that I Belong to You was influenced in part by Sgt. Pepper's Lonely Hearts Club Band. [1]
The main riff from "Falling Away With You" sounds distinctly like "Blackbird".
Also, Paul McCartney said that he saw Muse's performance at Glastonbury and thought Chris was one of the best bass players.[2]