Contents - Max-Planck-Institut für Physik komplexer Systeme
Contents - Max-Planck-Institut für Physik komplexer Systeme
Contents - Max-Planck-Institut für Physik komplexer Systeme
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oftherapidlymaturingtheoryoffixeddelayequations,andgiverisetochallengingproblemsinboth<br />
themathematicalanalysisoftheequationsandthenumericalcomputationandanalysisofsolutions.<br />
Althoughprogresshasbeenmadeinrecentyearsonsomemodelstate-dependentproblems,inparticular<br />
monotoneproblemswithpositiveornegativefeedback,thebehaviorofmoregeneralandrealisticsystems<br />
remainspoorlyunderstood.<br />
Theworkshopbroughttogetherresearchersfromdifferentfieldsincludingphysics,engineering,physiology<br />
andmathematicstoexchangerecentresults, ideas, techniquesandproblems, andtodiscussfuture<br />
directionsinthefield.Manyoftheparticipantsweremeetingeachotherforthefirsttime,aclearsign<br />
thatweweresucceedinginthebringingpractitionersfromdifferentfieldstogether,asevidencedbydirect<br />
feedbackandthearticleathttp://www.dynamicalsystems.org/ma/ma/display?item=315<br />
Eventhebasictheoryofstate-dependentdelaysstillraisesmanyopenquestions,andtheanalysisand<br />
numericalanalysisoftheseproblemsconstitutedthemainthemesoftheworkshop,andwerethecommonpointthatunitedtheparticipantsfromdisparatefields.<br />
InhiscolloquiumtalkHans-OttoWalther<br />
presentedthemathematicalframeworkforconsideringstate-dependentdelayequationsasdynamical<br />
systemswithsemi-flowsonaninfinite-dimensionalfunctionalspace,andtheresultsandopenproblems<br />
ofthisapproach.<br />
Fourtalks,deliveredbyGernotBauer,DirkDeckertandC.K.RajuandSavioRodrigues,consideredthe<br />
equationsofmotionofchargedparticlesintheaction-at-a-distanceelectrodynamics,whichareaneutral<br />
mixed-typeimplicitlystate-dependentdifferentialequation,andtheirformulationandnumericalsolution<br />
as(well-posed)initialvalueorboundaryvalueproblems.Thesewereperhapsthemostchallengingequationsconsideredduringtheworkshop,butcombinationsofthedifferentdifficultiestheypose(including<br />
neutrality,advancedandretardedarguments,implicitstate-dependencyandnumericalsolution)arosein<br />
otherequationspresentedthroughouttheweek.<br />
MikeMackeyshowedhowdelaysariseinBacterialoperondynamics,andothertalksconsidereddelays<br />
inmicrovascularbloodflow,neuraldynamics,epidemiologyandpopulationdynamics. Statedependent<br />
equations(includingimplicitlystate-dependent)wereshowntoarisenaturallyinaseriesofinteresting<br />
engineeringproblems,includingregenerativecuttingandhybridsystemstesting.<br />
AnalysisandnumericalanalysiswereshowntoworkinconsortinthetalkofAlfredoBellenconcerning<br />
terminationandregularizationofsolutionsofstatedependentneutraldelayequations.Othernumerical<br />
analysistalkstackledproblemsincludingcomputationofLyapunovexponents,boundaryvalueproblems,<br />
spectralmethodsanddelaydependentstabilityofnumericalmethods,thelastofwhichresonatedwith<br />
theanalysistalkofFerencHartungconsideringlinearizedstabilityinstate-dependentDDEs. Other<br />
analysistalksconsideredsingularperturbedproblemsandslowlyoscillatingperiodicsolutions,computer<br />
assistedproofs,smoothnessofmanifoldsandco-existenceofperiodicsolutions. Ifdelayproblemsare<br />
hardbecauseoftheinfinitedimensionality,asarePDEs,partialdifferentialdelayequationsaredoubly<br />
hardandWolfgangRuessclosedthemeetingbypresentingthetheoryandopenproblemsofPDDEs.<br />
Aparticularaimoftheworkshopwastogiveyoungscientistsaforumtopresenttheirwork,andinteract<br />
withestablishedresearchersinthefield,andofthe48participants,11weregraduatestudents,and<br />
another11postdoctoralresearchers. Thesejuniorscientistsparticipatedfullyintheworkshopwith12<br />
presentingpostersinthepostersession,and9givingtalks. Someofthemwilllikelybeworkinginthis<br />
fieldforalongtimetocome.<br />
Thiswastothebestofourknowledgethefirstworkshopdedicatedtostate-dependentdelayequations,<br />
and it brought together all manner of scientists that had not interacted before. Many interesting<br />
discussionsensued,anumberofparticipantsindicatedthattheyareintheearlystagesofexploring<br />
completelynewcollaborationsasaresultoftheworkshop.Nodoubtthefruitionsofthesecollaborations<br />
willberevealedatfutureSDDEworkshops,butthefirstsuchworkshopwasatthe mpipksinDresden,<br />
anditwasagreatsuccess.<br />
Physicalprinciplesofproteinbehaviorinthecell,Workshop<br />
Scientificcoordinators:M.Porto,H.E.Roman,M.Vendruscolo<br />
Theworkshop,whichtookplaceon26-30October2009,wasconcernedwiththeproblemofunderstandingthephysicalprinciplesthatgovernthebehaviorofproteinsinthecell.<br />
Thisthemeisrelevant<br />
sinceproteinsareinvolvedinessentiallyallofthebiochemicalreactionsthattakeplaceinlivingorganisms,includingthoserequiredforthecontrolofgeneexpression,metabolism,transport,andenzymatic<br />
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