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View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Estudo Geral AppliedIntelligence16,101–118,2002 (cid:2)c 2002KluwerAcademicPublishers.ManufacturedinTheNetherlands. ∗ All the Truth About NEvAr PENOUSALMACHADOANDAM´ILCARCARDOSO CentrodeInforma´ticaeSistemasdaUniversidadedeCoimbra(CISUC),PinhaldeMarrocos, 3030Coimbra,Portugal [email protected] [email protected] Abstract. TheuseofEvolutionaryComputationapproachestogenerateimageshasreachedagreatpopularity. This led to the emergence of a new art form—Evolutionary Art—and to the proliferation of Evolutionary Art Tools.Inthispaper,wepresentanEvolutionaryArtTool,NEvAr,theexperimentalresultsachieved,andthework methodologyusedtogenerateimages.InNEvAr,usefulindividualsarestoredinadatabaseinordertoallowtheir reuse. This database is playing an increasingly important role in the creation of new images, which led us to the developmentofautomaticseedingprocedures,alsodescribed.Theautomationoffitnessassignmentisoneofour presentresearchinterests.Wewill,therefore,describesomepreliminaryresultsachievedwithourcurrentapproach toautomaticevaluation. Keywords: evolutionaryart,geneticprogramming,computationalcreativity 1. Introduction development of an incredible amount and variety of solutions,species,toaspecificproblem,survival.Itis, Creativityisoftenregardedasoneofthemostimpres- therefore,unquestionablethatthisprocesscangiverise sive features of the human mind, which may explain toinnovativesolutions[5]. the current interest of the Artificial Intelligence com- InthepastfewyearstwoEvolutionaryComputation munityinthestudyofcomputationalcreativity.Several (EC)techniques,namelyGeneticAlgorithms[6](GA) otherfactors,however,contributetothisrisinginterest: andGeneticProgramming[7](GP),havebeenusedas artificialcreativesystemsmayproveusefulinawide meanstoimplementcomputationalcreativity,resulting rangeofartistic,architecturalandengineeringdomains inthedevelopmentofseveralapplicationsinfieldssuch where conventional problem solving techniques have asmusicandimagegeneration,architectureanddesign. failed; its study may bring insight to the overall un- GAarethemostcommonECapproachinthemusi- derstandingofhumancreativity;thestudyofartificial calfield(e.g.[8–11]).However,accordingto[12],and creativitycanbeviewedasthelogicalnextstepinAI inspiteofthenumerousapplications,GAarenotideal research,i.e.ifwecanalreadybuildsystemscapableof forthesimulationofhumanmusicalthought. performing tasks requiring intelligence, can we build In the image generation field, GP is the most used systemsabletoperformtasksrequiringcreativity? EC approach, some examples being [13–16], which The development of artificial creative systems is evolve images, and [17], where GP is used to evolve often inspired in models of the human creative pro- humanfaces.GPhasalsobeensuccessfullyappliedin cess (e.g. [1–4]). There are, however, other possible thefieldsofdesign[18,19]andanimation[14,16,20]. sourcesofinspiration.Evolutionisresponsibleforthe The main difficulty in the application of EC ap- proachestofieldssuchasimageandmusicgenerationis ∗This work was partially funded by the Portuguese Ministry of thedevelopmentofanappropriatefitnessfunction.Asa ScienceandTechnology,underProgramPRAXISXXI. result,mostsystemsrelyonInteractiveEvolution(IE), 102 MachadoandCardoso i.e. the user evaluates the individuals and thus guides to succeed, i.e. produce appealing images, it would evolution.Thereareseveralsystemsinthemusicalfield havetodoitinfewevolutionarystepsandwithalow thatperformautomaticevaluation(e.g.[21–25]).Inthe numberofindividuals’evaluations.Ontheotherhand, fieldofimagegeneration,however,therewasonlyone askilledusercanguidetheevolutionaryprocessinan attempttofullyautomatefitnessassignment[26]. extremelyefficientway.She/hecanpredictwhichim- The use of IE for image generation has achieved a agesarecompatible,detectwhentheevolutionarypro- great popularity. The roots of these applications can cess is stuck in a local optimum, etc. In other words, befoundinRichardDawkinsbook“TheBlindWatch- theusercanchangeitsevaluationcriteriaaccordingto maker” [13], in which the author suggests the use of the specific context in which the evaluation is taking a GA to evolve the morphology of virtual organisms, place. biomorphs. This work was, apparently, the source of It is crucial to consider these idiosyncrasies in the inspirationforthesystemsdevelopedbyK.Sims[14] developmentofanEvolutionaryArtTool.InFig.1we and W. Latham [27], which can be considered as the showtheevolutionarymodelofNEvAr.Fromnowon, first applications of IE in the field of the visual arts, wewilldesignatebyexperimentthesetofallpopula- andwhichareusuallyconsideredasthemostinfluen- tionsofaparticularGPrun. tialworksinthisarea.Thesuccessoftheseapproaches NEvAr implements a parallel evolutionary algo- hasledtotheemergenceofanewartform,“Evolution- rithm, in the sense that we can have several different aryArt”,andalsototheproliferationofIEapplications andindependentexperimentsrunningatthesametime. inthisfield,usuallycalledEvolutionaryArtTools. It is also asynchronous, meaning that one experiment Inthispaperwewillmakeanin-depthdescriptionof can be in its first population, while another can be in anEvolutionaryArtTool,NEvAr(NeuroEvolutionary itshundredth.Additionally,wecantransferindividuals Art).Ourobjectiveistwofold:provideusefulinforma- betweenexperiments(migration). tiononthedevelopmentofanEvolutionaryArtTool; Theuseofmigrationallowstheconstructionofim- presentourcurrentresearchideas,whichweconsider agedatabases.Wecan,forinstance,createanemptyex- thatcanenrichnowadayssystems. perimentandtransfertoitindividualsthatwefindinter- Thepaperisstructuredasfollows:inSection2we estingoruseful.Theimagesbelongingtothisdatabase makeanoverviewofthesystem,whichcomprisesthe canbeusedtoinitialisenewexperiments,oraddedto descriptionofNEvAr’sevolutionarymodel,usedrep- thecurrentpopulationofanexperimentwhentheuser resentation(2.1),andgeneticoperators(2.2);wepro- finds that this addition may improve the evolutionary ceedbypresentingexperimentalresults(Section3)and process. the process used to produce them (3.2); in Section 4 NEvAr also allows the migration within the same wedescribeourcurrentresearchefforts,whicharere- experiment. This feature is important due to the lim- latedwiththedevelopmentofseedingprocedures(4.1) itedsizeofthepopulations,allowingtherevivalofim- andautomaticevaluation(4.2),andpresentsomepre- agesfrompreviousones.Itisalsopossibletogotoa liminary experimental results; finally, we draw some previous population and change the evaluation of the conclusionsandpointdirectionsforfutureresearch. individuals, which is extremely useful since it allows theexplorationofdifferentevolutionarypaths. 2. OverviewoftheSystem Throughtime,wehaveconstructedalargedatabase of individuals. Nowadays, the extensive use of this FitnessassignmentplaysakeyroleonECalgorithms databaseplaysakeyroleinNEvAr,aswillbeshownin sinceitguidestheevolutionaryprocess.Consequently, Section3.Throughtheuseofthedatabasesandmigra- thequalityoftheresultsisdeeplyconnectedwiththe tion,wetrytoovercomeoneofthemainweaknessesof quality of the evaluation. In its present form, NEvAr ECapproaches:thelackoflongtermmemorymecha- ismainlyanIEsystem,therefore,theuserplaysakey nisms(althoughmultiploidycanbeviewedasalimited roleintheprocess. memory mechanism). Although the use of migration The interaction between human and computer has anddatabasesisnotparticulartoNEvAr(e.g.systems someadvantages,butalsoposessomeproblems.Itis, like[14,15]alsopossessthesefeatures),theemphasis forinstance,virtuallyimpossibletouselargepopula- we give to its use is. Additionally, we have also de- tionsizesortoperformextendedruns.Itwasclearfrom velopedautomaticseedingmechanisms,whichwillbe the beginning of its development that if NEvAr were explainedinSection4.1. AlltheTruthAboutNEvAr 103 Figure1. EvolutionarymodelofNEvAr.Theactiveexperimentisdepictedingrey. Afinalwordgoestooureffortstoautomatefitness lexiconoffunctionsandterminals.Theinternalnodes assignment.AutomaticEvaluationisstillunderdevel- are functions and the leafs terminals. We use a func- opment; in Section 3 we will present our current ap- tion set composed, mainly, by simple functions such proach and the experimental results achieved so far. asarithmetic,trigonometricandlogicoperations.The The filtering module is linked with the idea of auto- terminalsetiscomposedbythevariablesx andy,and maticevaluationandwillbeexplainedinSection4.2. byconstantswhichcanbescalarvaluesor3d-vectors.1 Theinterpretationofagenotype(anindividual)re- 2.1. Representation sults on a phenotype, which in NEvAr’s case is an image. To generate an image, we evaluate the corre- In NEvAr, like in most GP applications, the individ- spondingexpressionforeachpixelcoordinateandthe uals are represented by trees. Thus, the genotype of outputisinterpretedasthegreyscalevalueofthepixel. an individual is a symbolic expression, which can be InFig.2wepresentsomeexamplesofgenotypesand representedbyatree.Thetreesareconstructedfroma theircorrespondingphenotypes. Figure2. Somesimplefunctionsandthecorrespondingimages. 104 MachadoandCardoso NEvAr allows the evolution of true-colour images, standardGPcrossoveroperator[7],whichexchanges whichisachievedbytheuseofthe3d-vectorterminals. sub-treesbetweenindividuals.InGPmutationis,usu- Eachofthecomponentsofthesevectorscorrespondto ally,consideredlessimportantthanrecombination[7]. a different colour channel (Red, Green and Blue or, InNEvAr,however,thepictureisquitedifferent.Con- alternatively, Hue, Saturation and Value). We will re- ventionalGPsystemsuseasmallfunctionsetandlarge sorttoanexampleinordertoexplainhowthecalcula- population sizes. In NEvAr this situation is inverted. tions are performed. Consider the following expres- Therefore,mutationbecomesnecessary,inordertoal- sion: sin(([0,1,0.5]×([1,0.5,0.5])+X). The first low the reintroduction of genetic material that would operationtoexecuteisthemultiplicationofthetwovec- beotherwiselost. tors;themultiplicationisnotperformedinthestandard Weresorttofivemutationoperators(seeFig.3): way.Instead,eachofthecomponentsofthefirstvector is multiplied by the corresponding component of the • Sub-tree swap—randomly select two mutation second,i.e.[0×1,1×0.5,0.5×0.5]=[0,0.5,0.25]. pointsandexchangethecorrespondingsub-trees. NextweaddthevariableX tothisvector,whichyields • Sub-tree replacement—randomly select a mutation [0+ X,0.5+ X,0.25+ X].Finally,weapplythesin point and replace the corresponding sub-tree by a operator to each of the components, thus obtaining: randomlycreatedone. [sin(0+X),sin(0.5+X),sin(0.25 + X)]. By using • Nodeinsertion—randomlyselectaninsertionpoint thisapproach,weavoidhavingtodevelopspecialop- foranew,randomlychosen,node.Ifnecessary,cre- erators designed to manipulate vectors; instead each atetherequiredargumentsrandomly. operator is applied to a scalar value that represents a • Nodedeletion—thedualofnodeinsertion. colourcomponentoftheimage.2 • Nodemutation—randomlyselectanodeandchange itsvalue. 2.2. GeneticOperators Thegeneticoperatorsinducechangesatthepheno- type level. In Fig. 4, we show examples of the appli- We use two kinds of genetic operators: recombina- cation of the crossover operator. As can be seen, the tion and mutation. For the recombination, we use the crossoverbetweentwoimagescanproduceinteresting Figure3. Examplesoftheapplicationofthemutationoperatorsonindividual A.Theindividual A(cid:7)wasgeneratedbysub-treeswap,B(cid:7)by sub-treereplacement,C(cid:7)bynodeinsertion,D(cid:7)bynodedeletionandE(cid:7)bynodemutation. AlltheTruthAboutNEvAr 105 Figure4. Ontheleft,thetwoprogenitorimages.Ontheright,someimagesresultingfromtheircrossover. Figure5. Ontheleft,theoriginalimage.Ontheright,severalmutationsofthisimage.Imagea wasgeneratedthroughnodemutation,b throughnodeinsertion,cthroughnodedeletion,dthroughsub-treeswapandebysub-treereplacement. andunexpectedresults.Additionally,therearecasesin artistusingthetool.Inotherwords,theartistmustbe whichtheimagesseemtobeincompatible,i.e.images abletoexpressher/himselfthroughtheuseofthetool. that,whencombined,resultin“bad”images. TheimagesgeneratedwithNEvArduringtheearly In Fig. 5 we give examples of images generated stagesofexperimentationwereclearlydisappointing. through mutation. Once again, the results of this op- Thisfailuredidn’tresultfromthelackofpowerofthe erationcangivequiteunexpectedresults. tool, but from our lack of expertise in its use. Like any other tool, NEvAr requires a learning period. To exploreallthepotentialofatool,theusermustknow 3. ExperimentalResults it in detail and develop or learn an appropriate work methodology.Theresults,andusersatisfaction,depend AsanEvolutionaryArtTool,themaingoalofNEvAr notonlyonthetoolbutalsoonitsmastering.Inother istheproductionofartworks.Itsanalysismustbeper- words,theevaluationofapianoasatoolcanonlybe formedwiththisinmind.Astrictlyobjectiveanalysis madebysomeonethatknowshowtoplayitwell.This oftheresultsachievedwithNEvArisimpossible,due rises a problem: unfortunately few people know how tothenatureoftheresults(images).Themostobvious toplayNEvAr. waytoassesstheperformanceofthesystemistoask Due to these factors, instead of presenting charts to a set of people to rate the images generated by the evaluatingtheperformanceofNEvAr,wewillpresent system.Thistypeofanalysishasacertainappealand someresults,i.e.images.Ourintentionistoshowthe appearstobeavalidwaytoevaluatethesystem’sre- type of artwork that can be produced by the system. sults. However, this idea encompasses a fundamental Additionally,wewilldescribetheworkmethodology error. thatwecurrentlyusetogenerateimageswithNEvAr. NEvArisguidedbyauser.Therefore,itsgoalisto produce images compatible with the aesthetic and/or artistic principles of the user. As such, the evaluation 3.1. TheResults bythirdpartiesissecondary.Thus,thereallyimportant issueisthelevelofusersatisfaction. Nextwewillpresentseveralexamplesofimagesgen- Itisimportanttonoticethatthefactthatatoolcan eratedwithNEvAr.TheimagespresentedinFig.6are generate “interesting” images is irrelevant from the asubsetoftheonespresentedatthe“ArtandAesthetics artistic point of view. What is really important is that ofArtificialLife”exhibit,thattookplaceattheCentre theproducedartworksconveytheartisticideasofthe fortheDigitalArtsoftheUCLA,during1998. 106 MachadoandCardoso Figure6. Someoftheimagespresentedatthe“ArtandAestheticsofArtificialLife”exhibit,curator:NicholasGesseler,1998.Furtherimages canbefoundintheCD-ROMaccompanying[19]. Fromthepresentedexamples,itisclearthattheim- ingevolutionarypath,which,typically,correspondsto ages generated with NEvAr are typically of abstract evolvingapromisingsetofimagesfromaninitialran- nature.Fromthetheoretical3 pointofview,itispossi- dompopulation(generationoftheideas);inthesecond bletoconstructpictorialimages,butinpracticethatis stage, Exploration, the “ideas” evolved on the previ- hardtoachieve. ousstageareusedtogenerateimagesofhighaesthetic value (exploration of the ideas); the Selection stage 3.2. TheProcess involves choosing the best produced images; the se- lectedimages,whennecessary,willbesubjectedtoa Thecreationofanartworkencompassesseveralstages, processofRefinement,whosegoalisthealterationof such as: genesis of the idea, elaboration of sketches, smalldetails(i.e.itcorrespondstothefinalexecution exploration of the idea, refinement, and artwork exe- oftheartwork). cution.Themethodologythatweproposecanbecon- Next,wewilldescribehowweuseNEvArineach sidered, in some way, analogous. It is composed by ofthementionedstages,referringthemostimportant four main stages: Discovery, Exploration, Selection issuestotakeintoaccountineachofthemandtheskills andRefinement. involved. In this description we will consider that we Thesestagescanbedescribed,concisely,asfollows: startwitharandomlygeneratedpopulation.Theuseof the stage of Discovery consists on finding a promis- theimagedatabasewillbedescribedafterwards. AlltheTruthAboutNEvAr 107 3.2.1.Discovery. Ourempiricalexperienceallowsus In which concerns fitness assignment, the images to classify the Discovery stage as the most crucial of havebydefaultafitnessvalueof0,andweusuallygive the process, and, together with the Exploration stage, a classification greater than 0 to a very restrict set of the one in which the faculties of the user are more images(typically1to3).Thenextpopulationwillbe, important. therefore, composed by the combination of these im- Discovery corresponds to the genesis of the idea, ages.Weuseroulettewheelinsteadoftournamentse- and is therefore inappropriate to approach this stage lection.Althoughtournamentselectionisusuallypre- withpre-conceivedideasregardingthefinalaspectof ferredinGPsystems,inouropinionrouletteselection theartwork.Inotherwords,itisimpossibleinpractice ismoreadequatetoIEsystems,sinceitismoreintuitive (yettempting)tothinkonanimageanduseNEvArto andallowsagreaterdegreeofcontrolbytheuser. evolve it. This is probably the most important aspect Duringtheexplorationstage,weusehighcrossover toretain,becauseitcontrastswithwhatisusuallyex- and mutation rates (e.g. 90% crossover and 20% mu- pectedinatool,i.e.thatitallowstheimplementation tationprobabilities).Theobjectiveistoincreasepop- of an idea. This aspect can be viewed as a weakness, ulation diversity, thus avoiding the loss of interest by butitisalsothedistinguishingfeatureandstrengthof the user. In Fig. 8, we present the best images from NEvAr (and other evolutionary art tools). A conven- population7to30.Colourwasintroducedinthe10th tional tool only plays an important role in the artistic population. By the 21st population, the images were processinstagesposteriortothegenerationoftheidea. sufficientlyinterestingtoallowatransitiontotheEx- NEvAr,however,playsakeyroleinthegenerationof plorationstage. the idea itself. Its influence is noticeable throughout all the artistic process and in its main creative stage. 3.2.2.Exploration. Thegoalofthisstageistoexplore The artist is no longer responsible for the creation of theideaspresentinthecurrentpopulationinorderto the idea; instead, she/he is responsible for the recog- producesomethingclosetoanartwork.Whenwereach nitionofpromisingconcepts.Moreprecisely,theidea thisstage,wearealreadydealingwithimagesofhigh results from an evolutionary process, and is created aesthetic value. Through the recombination of these by the artist and the tool, in a (hopefully) symbiotic images,weexploreaspaceofformssmallerthanthe interaction. oneexploredinthediscoverystage,andwhichmaybe, The most important principle that we have identi- therefore,morethoroughlysearched. fied is the prevalence of the form in relation to the Ideally,thequalityofthepopulationsshouldincrease colour.Thus,duringtheinitialstagesoftheevolution- steadily. In practice this is unachievable. The Explo- aryprocesstheusershouldconcentrateintheevolved rationstagecanprolongitselfconductingtheartistto forms and “forget”, for the time being, hers/his chro- apointthat,atleastapparently,hasnothingtodowith matic preferences. One way to achieve independence the original one. Sometimes, the path to this point is from colour is to use, exclusively, greyscale images relativelydirect.Therearecases,however,inwhicha duringthefirstpopulations,untilappropriateformsare dead end is reached. In these cases, it is necessary to found,andonlyallowthegenerationoffullcolourim- descendthehill,whichusuallyimpliesadeliberateac- ages afterwards. This methodology proved to be ex- tionbytheuser.Thisdescentmaycauseareturntothe tremely efficient, allowing a greater systematisation Discoverystage. of the evolutionary process. The way NEvAr handles Apparently,thediscoveryofnewinterestingimages, colourisadequatetothisformofoperation,sinceittyp- evenwhentheyhaveacompletelydifferentaspectfrom icallyallowsthealterationandincorporationofcolour thepreviouslygeneratedones,isusuallyfasterthanthe withoutsignificantlychangingtheimages’form. first discovery process. This may indicate that some Theimagesbelongingtothefirstpopulationsusually type of learning occurs during the evolutionary pro- fallinoneoftwoextremes,beingeithertoosimpleor cess, i.e. that, during evolution, useful combinations too complex. The discovery stage is characterised by ofprimitivesarebuilt,andthatthesesub-treescanbe thecombinationofsimpleimages,inordertogradually recombinedallowingthegenerationofinterestingim- increaseimagecomplexityuntilreachinganappropri- agesinfewpopulations. atelevel.Itisadvisabletoavoid“noisy”images,since Additionally,thehighplasticityinherenttotheused the removal of noise is usually difficult. In Fig. 7 we representationmethodallowstheevolutionofradically presentthefirstpopulationsofanexperiment. differentphenotypesfromresemblinggenotypes. 108 MachadoandCardoso Figure7. Populations0,1and6ofanexperiment.Thenumbersbellowtheimagescorrespondtothefitnessgivenbytheuser.Theincreasein thecomplexityoftheimagesisevident.Fromthe6thpopulationontheusergavepreferencetoorganicandfluidformsindetrimentofgeometric ones. Figure8. Thebestimages,accordingtothefitnessassignment,ofpopulations7to30(fromlefttorightandtoptobottom). It is important to notice that an individual is more wherealreadyabandonedbytheevolutionaryprocess thanitsphenotype.Duringevolutionthereisanaccu- (e.g. the reappearance in population 30 of an image mulationofgeneticmaterialthatisnotexpressedinthe frompopulation5). phenotype.Thisgeneticmaterialcanbecomeactiveat Like in the Discovery stage, the expertise of the anytimeduetocrossoverormutation.Astrikingev- user is determinant to the success of the Exploration idence of this fact is the reappearance of images that stage. With the accumulation of experience, the user AlltheTruthAboutNEvAr 109 learnshowtodistinguishbetweenpromisingpathsand 3.2.3.Selection. TheSelectionstagecanbedivided theonesthatleadnowhere,topredictwhichcombina- in two different ones: one that is concurrent with the tionsofimagesproducebestresults,howtomanipulate evolutionaryprocess,andonethatisposterior.During crossover and mutation rates in order to produce best thestageofExplorationthebestimages(accordingto results,etc. the user criteria) are added to a different experiment, InFigs.9to11wepresentsomepopulationsbelong- which works as a gallery. As stated before, NEvAr ingtothisstage. storesallpopulations,whichallowsthereviewofthe Figure9. TheuserisexploringimagesgeneratedduringDiscovery.Theconnectionbetweentheimagesofpopulation32andthebestimages ofpopulations29and30isevident(seeFig.8) Figure10. Atthisstagetheuserchoosestoabandontheideathatshe/hewasexploring.Thecircularimagesthatdominatedpreviouspopulations whereneglected,withtheobjectiveofintroducingachangeofpath. Figure11. Ascanbeseentherewasasignificantincreaseinpopulationdiversity.Populationsizewasincreaseinordertoallowagreater searchwidth.Theusercontinuestoforceachangeofevolutionarypaththroughhers/hischoices,whichwillresultinadecreaseoftheaverage qualityoftheimages,andatransitiontotheDiscoverystage.Therewhereseveralothertransitionsbetweenthisstages,andtheexploration stagewasendedinthe57thpopulation. 110 MachadoandCardoso evolutionaryprocessandtheadditiontothegalleryof • Discard—Imagesthatareconsideredirrelevant. imagesthatwerepreviouslyneglected.Thisrevisionis • Useful—Images that, at least apparently, represent highlyrecommended,andasubstantialamountoftime goodideasandthatshouldbestoredinthedatabases shouldseparatethegenerationoftheimagesanditsre- ofNEvAr. viewinordertoallowthenecessarydistancebetween • Refine—Imagesthatstillneedsomeworktoachieve generationandcriticism.InFig.12,weshowtheim- thestatusofartworks. agegalleryresultingfromtheexperimentthatwehave • Artworks—Composed,ideally,byimagesthatfully beenusingtoillustrateourdescription. satisfytheaestheticand/orartisticcriteriaoftheuser. Theimagesbelongingtothegallerywillbesubjected toaprocessofanalysis,whichwillleadtotheirdivision InFig.13wepresenttheresultsoftheclassification infourgroups: oftheimagesofFig.12intheabovementionedgroups. Figure12. Imagegallery. Figure13. TheUseful,RefineandArtworkgroups.Animagecanbelongtoseveralgroups.

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All the Truth About NEvAr. Authors; Authors and affiliations. Penousal Machado; Amílcar Cardoso. Article. DOI : 10.1023/A:1013662402341. Cite this
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