1Overview 1Overview MolecularCommunicationEuProkaryoticsystemsintercommunicate150Emissionreceptionofspecialmoleculestokens150IdenticaltokensAChglutamateepinephrineCaRutgersWINLABI ID: 299026
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1Overview MolecularCommunicationEu/ProkaryoticsystemsintercommunicateRutgersWINLABISIT2014C.Rose 1Overview MolecularCommunicationEu/Prokaryoticsystemsintercommunicate–Emission/receptionofspecialmolecules(tokens)–Identicaltokens(ACh,glutamate,epinephrine,Ca++...)RutgersWINLABISIT2014C.Rose 1Overview MolecularCommunicationEu/Prokaryoticsystemsintercommunicate–Emission/receptionofspecialmolecules(tokens)–Identicaltokens(ACh,glutamate,epinephrine,Ca++...)–Info-carryingtokens(DNA,mRNA,glycans,proteins...)NanosystemswillintercommunicateRutgersWINLABISIT2014C.Rose 1Overview MolecularCommunicationEu/Prokaryoticsystemsintercommunicate–Emission/receptionofspecialmolecules(tokens)–Identicaltokens(ACh,glutamate,epinephrine,Ca++...)–Info-carryingtokens(DNA,mRNA,glycans,proteins...)Nanosystemswillintercommunicate–RF/Optical/Acoustic–oftenantennamismatch/powerissues–TokenexchangecouldbemoreefcientRutgersWINLABISIT2014C.Rose 2Overview LOTSofrecentworkintheareaRutgersWINLABISIT2014C.Rose 3Overview ChrisIsGettingOld–andCRANKY!RutgersWINLABISIT2014C.Rose 3Overview ChrisIsGettingOld–andCRANKY!IsThereaUnifyingElephant?(framework)Whatcanacelltelltheworld?(fundamentallimits)RutgersWINLABISIT2014C.Rose 4Overview CartoonandDesiderataDiffusingMoleculesCartoon(httpfailsafe)WhatAreWelookingFor?RutgersWINLABISIT2014C.Rose 4Overview CartoonandDesiderataDiffusingMoleculesCartoon(httpfailsafe)WhatAreWelookingFor?Generalmultipurpose“outerbound”modelUseITboundstoavoidmodelingmorassRutgersWINLABISIT2014C.Rose 5Overview MyStabAtAUniedFrameworkTimingChannelIsFundamental!RutgersWINLABISIT2014C.Rose 5Overview MyStabAtAUniedFrameworkTimingChannelIsFundamental!Subsumestime-varyingconcentrationchannelProvidesmachineryfortokenswithinformationpayloadsRutgersWINLABISIT2014C.Rose 5Overview MyStabAtAUniedFrameworkTimingChannelIsFundamental!Subsumestime-varyingconcentrationchannelProvidesmachineryfortokenswithinformationpayloadsWhatI'llTalkAboutTodayChannelabstractionInformation-theoreticmodelingPastSuccessesandFrustrationsHelpFromAnOldReliableFriendGyrationsToAnUpperBoundCapacitySandwichRutgersWINLABISIT2014C.Rose 6Overview Abstractionof“WhatCanaCellTelltheWorld?” S=T+D~S=Sort[S]RutgersWINLABISIT2014C.Rose 7PREtails MutualInformationMtokensonaninterval (M)RutgersWINLABISIT2014C.Rose 7PREtails MutualInformationMtokensonaninterval (M)I(S;T)=h(S)�h(SjT)=h(S)�h(D)M(h(S)�h(D));(i.i.d.D)Easy,Right?RutgersWINLABISIT2014C.Rose 8PREtails HypersymmetriesRutgersWINLABISIT2014C.Rose 8PREtails Hypersymmetries9M!T !~T(permuatationoperatorP (),index )TandP (T)areindistinguishableatoutputWecanbalanceanygivenI()-maximizingfT()sothat:fT(T)=fT(P (T))8 RutgersWINLABISIT2014C.Rose 9PREtails MoreSymmetryfT()hypersymmetry!fS()hypersymmetryRutgersWINLABISIT2014C.Rose 9PREtails MoreSymmetryfT()hypersymmetry!fS()hypersymmetryfD()non-singular!Scontinuous)“EdgesandCorners”offS()havezeromeasureM!identical(permuted)patchesoffS()RutgersWINLABISIT2014C.Rose 10PREtails ChannelRedux S )~SRutgersWINLABISIT2014C.Rose 11PREtails AUsefulEquivalencef~S; g$SRutgersWINLABISIT2014C.Rose 11PREtails AUsefulEquivalencef~S; g$Sh(SjT)=h(~S; jT))=h(~SjT)+H( j~S;T)I(~S;T)=I(S;T)�logM!�H( j~S;T)RutgersWINLABISIT2014C.Rose 12PREtails TENSION!RutgersWINLABISIT2014C.Rose 12PREtails TENSION!EntropymaximizedbyindependentTh(S)Xmh(Sm)H( j~S;T)maximizedbycorrelatedTH( j~S;T)=logM!identicallaunchtimesT1=T2==TMRutgersWINLABISIT2014C.Rose 13PREtails MyPastPersonalStruggles 9closedformresultsforH( j~S;T)(exponentialD) maxfT()h(S)+H( j~S;T)?(LastYear'sTalk) maxfT()h(S)+H( j~S;T)=?RutgersWINLABISIT2014C.Rose 14PREtails ThisYear'sStruggle maxh(S)+H( j~S;T)?(obviousdataprocessingaside)RutgersWINLABISIT2014C.Rose 15Today'sMeat HelloJensenMyOldFriendH( j~S;~t)H"(~t)=M�1X`=1log(1+`)M�1Xm=`Xjxj=`mYj=1Gxj(~tm+1�~tj)G1�xj(~tm+1�~tj)G()CCDFofDandxabinaryvector:RutgersWINLABISIT2014C.Rose 16Today'sMeat Maximizeh(S)(Euler-Lagrange)argmaxffS();xed Sgh(S)=1 A()ePi;ji6=jQ(si�sj)where SES[Q(S1�S2)]RutgersWINLABISIT2014C.Rose 17Today'sMeat BoundingH( j~S;T)(forexponentialrstpassage)Theorem2.IftherstpassagedensityfD()isexponentialthenE[Q(S1�S2)]1 2E[Q(T1�T2)]RutgersWINLABISIT2014C.Rose 17Today'sMeat BoundingH( j~S;T)(forexponentialrstpassage)Theorem2.IftherstpassagedensityfD()isexponentialthenE[Q(S1�S2)]1 2E[Q(T1�T2)]So,xed S:xesmaximumh(S)upperbounds TRutgersWINLABISIT2014C.Rose 17Today'sMeat BoundingH( j~S;T)(forexponentialrstpassage)Theorem2.IftherstpassagedensityfD()isexponentialthenE[Q(S1�S2)]1 2E[Q(T1�T2)]So,xed S:xesmaximumh(S)upperbounds TupperboundsH"(T) Adaptabletootherrstpassagedensities(!)RutgersWINLABISIT2014C.Rose 18Today'sMeat OptimizemaxfT()hh(S)+H( j~S;T)imax24logA()�M(M�1) S()+Mlog(1+(M�1) S())35yields) S= S()=1� (M�1) Computationaldeadend(dimensionalitycurse):RutgersWINLABISIT2014C.Rose 19Today'sMeat FirstOrderApproximation S() S(0)+ 0S(0)RutgersWINLABISIT2014C.Rose 23TheEnd Summary+NextResults:RutgersWINLABISIT2014C.Rose 23TheEnd Summary+NextResults:–Molecularsignalingmodelingprinciple–Capacitybounds–Other(nitemean)rstpassagetimedensitiespossible–Large=)concentrationsignaling–ExtensiontotokenswithpayloadsCaveats:–DidNOTconsidertokenlossRutgersWINLABISIT2014C.Rose 23TheEnd Summary+NextResults:–Molecularsignalingmodelingprinciple–Capacitybounds–Other(nitemean)rstpassagetimedensitiespossible–Large=)concentrationsignaling–ExtensiontotokenswithpayloadsCaveats:–DidNOTconsidertokenloss–UpperboundprobablyNOTtightforlargeNewsFlash:Relationshiptonetworkcoding?(staytuned)RutgersWINLABISIT2014C.Rose