Music - original and synthetic

around_the_world-atc-midi.wav

One `holy grail' of automatic sound analysis is music transcription, which could be defined as trying to convert a real recording of music into an equivalent MIDI representation.

Notes on sources

The track selection and MIDI file processing was done by Rob Turetsky. The manual transcriptions were created by Angel Umpierre during an internship in Summer 2003. Thanks to them both.

Acknowledgment

This material is based in part upon work supported by the National Science Foundation under Grant No. IIS-0238301. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).

http://www.ee.columbia.edu/~dpwe/sounds/music/

Lifting operators for 0-1 integer programming (Daniel Bienstock)

This research extends the work of Lovasz and Schrijver, Sherali-Adams, and Lasserre, on the idea of lifting an n-dimensional polyhedron to a space whose coordinates are indexed by members of a subset-lattice of an n-element set. 

Instead, in work to appear in the PhD dissertation of Mark Zuckerberg, we have devised operators that lift to a space whose coordinates are indexed by the much larger subset algebra of an n-element set. 

This leads to provably stronger operators. As an example of our results, we have obtained a polynomial-time algorithm that solves a relaxation of set-covering problems that is stronger than that provided by the set of all valid inequalities with coefficients 0,1,2, ..., k (for any fixed k). 

Our current research centers on extending these operators with the goal of making them computationally practicable. 

http://www.corc.ieor.columbia.edu/projects/algebra/algebra.html