简介：Classicalsortingbyreversalsusestheunit-costmodel,thatis,eachreversalconsumesanequalcost.Thismodellimitsthebiologicalmeaningofsortingbyreversal.Benderandhiscolleaguesextendeditbyassigningacostfunctionf(l)=lαforallα≥0,wherelisthelengthofthereversedsubsequence.Inthispaper,weextendtheirresultsbyconsideringamodelinwhichlongreversalsareprohibited.Usingthesamecostfunctionaboveforpermittedreversals,wepresenttightornearlytightboundsfortheworst-casecostofsortingbyreversals.Thenwedevelopalgorithmstoapproximatetheoptimalcosttosortagiven0/1sequenceaswellasagivenpermutation.OurproposedproblemsaremorebiologicallymeaningfulandmorealgorithmicallygeneralandchallengingthantheproblemconsideredbyBenderetal.Furthermore,ourboundsaretightandnearlytight,whereasouralgorithmsprovidegoodapproximationratioscomparedtotheoptimalcosttosort0/1sequencesorpermutationsbyreversals.

简介：Wedescribeanoveltechnique,lowsurfaceenergyGasExpansionMolding(GEM),tofabricatemicrobubblearraysinpolydimethylsiloxane(PDMS)whichareincorporatedintoparallelplateflowchambersandtestedincellsortingandmicrocellcultureapplications.Thisarchitectureconfersseveraloperationaladvantagesthatdistinguishthistechnologyapproachfromcurrentlyusedmethods.HereinwedescribetheGEMprocessandtheparametersthatareusedtocontrolmicrobubbleformationandaVacuum-AssistedCoating(VAC)processdevelopedtoselectivelyandspatiallyalterthePDMSsurfacechemistryinthewellsandonthemicrochannelsurface.WedescriberesultsfrommicroflowimagevisualizationstudiesconductedtoinvestigatefluidstreamsaboveandwithinmicrobubblewellsandconcludewithadiscussionofcellculturestudiesinPDMS.