226IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCE,VOL.31,NO.2,FEBRUARY2009
thankProfessorHarmDerksenandProf.MichaelWakinoftheUniversityofMichigan,ProfessorRobertFossumandYoavSharonoftheUniversityofIllinoisfortheadviceanddiscussionsonpolytopegeometryandsparserepre-sentation.ThisworkwaspartiallysupportedbytheGrantsAROMURIW911NF-06-1-0076,USNationalScienceFoundation(NSF)CAREERIIS-0347456,NSFCRS-EHS-0509151,NSFCCF-TF-0514955,ONRYIPN00014-05-1-0633,NSFECCS07-01676,andNSFIIS07-03756.
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