on the size of memory : human memory modeling by simulation (hum2s)

On The Size of MemoryOn The Size of Memory::Human Memory Modeling by Human Memory Modeling by Simulation (HuM2S)Simulation (HuM2S)

Haluk BingHaluk BingoollComplex Systems LabComplex Systems LabDept. of Computer EngineeringDept. of Computer EngineeringBogazici UniversityBogazici University

Ulusal Grid ÇalıştayıUlusal Grid Çalıştayı 200 20077MarMar 0101, 200, 20077

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OutlineOutline• MotivationMotivation• Memory RepresentationMemory Representation• RecommendationRecommendation• Simple Recommendation ModelSimple Recommendation Model• Effect of Small Memory SizeEffect of Small Memory Size• ConclusionsConclusions

[Bingol, [Bingol, LNCS 3733 pp.294-303LNCS 3733 pp.294-303 (2005)] (2005)][Bingol, arXiv nlin.AO/0609033, 2006 ][Bingol, arXiv nlin.AO/0609033, 2006 ]

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MotivationMotivation

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Motivation Motivation

If you need somebodyIf you need somebody

If you need a plumber, how do you find If you need a plumber, how do you find one?one?

• know one?know one?– You ?You ?– Your friends ?Your friends ?– Google ?Google ?

• FamousFamous plumber! plumber!

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Motivation Motivation

Key conceptsKey concepts• My My memorymemory• My friends memoryMy friends memory

My My networknetwork of friends of friendsLocalLocal memory memory

• Google’s memoryGoogle’s memoryAccessibleAccessible memory of the memory of the populationpopulationGlobalGlobal memory memory

• FameFameBeing Being knownknown to the general public to the general public

• RecommendationRecommendation

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RepresentationRepresentation(Static View)(Static View)

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22

Memory Memory Representation Representation

Who-knows-who GraphWho-knows-who Graph• Digraph Digraph G G ((PP, , AA))• Vertices Vertices PP ={1, 2, ..., ={1, 2, ..., nn}}

• Arc from Arc from ppii to to ppjj – if if ppii knows knows ppjj

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33

55

44

44 22 55 3311

44 3322

44

4455

--

44 11 5533

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• MemoryMemory of of ppii

– MMii = {= {ppjj | | ppii knows knows ppjj } ⊆ } ⊆ PP

• mm : memory size of an individual : memory size of an individual– ||MMi i || = = mm

• nn : population size : population size– mn mn : memory capacity of the : memory capacity of the populationpopulation

......1 2 ... 1 2 ... mm

......

......

......

: : ... :: : ... :

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::

nn

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mm

......

abstractionabstraction

......1 2 ... 1 2 ... mm

......

......

......

: : ... :: : ... :

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::

nn

......1 2 ... 1 2 ... mm

......

......

......

: : ... :: : ... :

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nn


MemoryMemory

• RemarksRemarks– out-degree: out-degree: mm

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• Knownness Knownness – kki i == ||{{ppi i | | ppi i knows knows ppjj}}||

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mm

...... ......


DefinitionsDefinitions

......1 2 ... 1 2 ... mm

......

......

......

: : ... :: : ... :

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::

nn

......1 2 ... 1 2 ... mm

......

......

......

: : ... :: : ... :

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::

nn

......1 2 ... 1 2 ... mm

......

......

......

: : ... :: : ... :

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::

nn

• RemarksRemarks– out-degree: out-degree: mm – in-degree: 0 ≤ in-degree: 0 ≤ kkii ≤ ≤ nn

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Interacting Agents:Interacting Agents: RecommendationRecommendation

->->

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RecommendationRecommendation

Recommendation ProcessRecommendation ProcessPerson (from)Person (from)

• RememberRemember• RecommendRecommend• LearnLearn

Person (to)Person (to)

timetime

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fromfrom

• Select a person Select a person ppff

– Select Select ff in {1, 2, ... , in {1, 2, ... , nn}}

• ppf f remembersremembers a known person a known person– Select Select rr in {1, 2, ... , in {1, 2, ... , mm}}

• Find person Find person ppr r

......1 2 ... 1 2 ... mm

......

......

......: : ... :: : ... :

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::

nn

pprrff

rr

• f f : : ffromrom• rr : : rrecommendedecommended

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......1 2 ... 1 2 ... mm

......

......

......: : ... :: : ... :

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::

nn


toto

• Select a person Select a person pptt

– Select Select tt in {1, 2, ... , in {1, 2, ... , nn}}

• Recommend Recommend ppr r to to pptt

ff pprr

rr

tt

• t t : : ttoo

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......1 2 ... 1 2 ... mm

......

......

......: : ... :: : ... :

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::

nn


toto

• LearnLearn recommended person recommended person pprr

– ppt t remembersremembers a known person a known person• Select Select ee in {1, 2, ... , in {1, 2, ... , mm}}

– Person Person ppee

ff pprr

rr

tt

ee

ppee

• e e : slot to be : slot to be eemptiedmptied

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......1 2 ... 1 2 ... mm

......

......

......: : ... :: : ... :

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::

nn


toto• LearnLearn recommended person recommended person pprr

– ppt t remembersremembers a known person a known person• Select Select ee in {1, 2, ... , in {1, 2, ... , mm}}

– Person Person ppee

– Forget a personForget a person• Obtain an empty memory locationObtain an empty memory location

– Put Put ppr r to locationto location t-bt-bff pprr

rr

tt

ee

pprr

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Simple Simple RecommendationRecommendation ModelModel

->->

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Simple Recommendation Simple Recommendation ModelModel• Random selections Random selections

– f, tf, t ∊∊ {1, 2, ... , {1, 2, ... , nn}}– r, r, ee ∊∊ {1, 2, ... , {1, 2, ... , mm} }

• Initial memory contentInitial memory content– Every person knows next Every person knows next mm personspersons

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Effect of Small Memory SizeEffect of Small Memory Size

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DefinitionsDefinitions• Memory ratioMemory ratio

– ρ ρ = = m m / / nn– 0 < ρ 0 < ρ ≪ 1≪ 1

• FameFame– ffii = = kki i //nn

PopulatioPopulationn

nn mm ρρ

NDCOSNDCOS 7070 55 7 x 107 x 10--

11

IstanbulIstanbul 15 M15 M 1 k1 k 6 x 106 x 10--

55

TurkeyTurkey 73 M73 M 2 k2 k 3 x 103 x 10--

55

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Effect of Effect of ρρAs ρAs ρ→0→0

• ffminmin ↘ ↘– Some completely Some completely forgottenforgotten

• ffmaxmax ↗ ↗– A few gets more A few gets more knownknown

nn = 100 = 100

ffminmin

ffmaxmax

Completely Completely forgottenforgotten

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Minimum Fame Minimum Fame As As ρρ→→00

• ffminmin ↘ ↘

• LinearLinear

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Completely Forgotten Completely Forgotten AgentsAgentsc c : the number of : the number of

completely completely fforgotten agents orgotten agents

u u = = cc / / nn

As As ρρ→→00• uu ↗↗• LinearLinear

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Maximum FameMaximum FameAs As ρρ→→00

• ffmmaxax ↘↗↘↗

• LinearLinear

• Emergence of fameEmergence of fame

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Top 5% FameTop 5% FameAs As ρρ→→00

• ff5%5% : : Top 5% fame Top 5% fame

• ff5%5% ↘↘

• LinearLinear

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ConclusionsConclusions

• A new modelA new model–““too little memory, too little memory, too many items” casestoo many items” cases–Information Information disseminationdissemination–Building consensusBuilding consensus–AdvertisementAdvertisement

• Linear patternLinear patternss–ffminmin ↘ ↘–uu ↗↗–ffmaxmax ↘↗ ↘↗

• Emergence of Emergence of “fame” “fame” • Population Population PP could could be anythingbe anything

–PapersPapers–BooksBooks–MoviesMovies–Movie StarsMovie Stars–PaintersPainters–PoetsPoets–......

http://www.cmpe.boun.edu.tr/soslabhttp://www.cmpe.boun.edu.tr/soslab

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Human Memory Modeling by Human Memory Modeling by Simulation (HuM2S) ProjectSimulation (HuM2S) Project

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Project DescriptionProject Description

• An agent-based Complex Systems An agent-based Complex Systems modeling and simulation projectmodeling and simulation project

• Human population is studiedHuman population is studied– Human memory is modeled Human memory is modeled – Interaction of humans are simulatedInteraction of humans are simulated– Effect of memory size is investigatedEffect of memory size is investigated

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Potential OutcomesPotential Outcomes

•Understanding Understanding dynamics of human dynamics of human populationpopulation

–FameFame–Cultural islandsCultural islands–Integration of culturesIntegration of cultures–Dissemination of Dissemination of informationinformation–Building consensusBuilding consensus–Building public opinionBuilding public opinion–CooperationCooperation–Effects of Effects of advertisementadvertisement

• A new A new agent-based agent-based modelmodel for complex for complex sytemssytems

–““too little memory, too too little memory, too many items” casesmany items” cases–SynchronizationSynchronization

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Need for GridNeed for Grid

• Currently a single simulation takes Currently a single simulation takes months on a single machinemonths on a single machine

• Parametric parallelization possibleParametric parallelization possible– Number of persons currently 1.000Number of persons currently 1.000

• need for 1.000.000need for 1.000.000

– Memory sizes of currently 200Memory sizes of currently 200• need 1.000need 1.000

– Number of interactions currently 10Number of interactions currently 1088 • need 10need 101010

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BudgetBudget

• Research Assistant Research Assistant – 12 man-months12 man-months

• Notebook ?Notebook ?– 2.500 Euro2.500 Euro

• Conference/Travel ?Conference/Travel ?– 2.000 Euro2.000 Euro

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HuM2S ProjectHuM2S Project

• Just startedJust started– Feb 1, 2007Feb 1, 2007

• 25 000 Euro25 000 Euro– AssistantAssistant

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ReferencesReferences

• Bingol, Fame as an Effect of the Memory Size, Bingol, Fame as an Effect of the Memory Size, LNCS LNCS 37333733,, 294 (2005)294 (2005)

• Bingol, Fame as an Effect of the Memory Size, Bingol, Fame as an Effect of the Memory Size, ECCS’05 (presented), (2005)ECCS’05 (presented), (2005)

• Bingol, Bingol, On The Size of MemoryOn The Size of Memory, NDCOS , NDCOS (presented), (2006)(presented), (2006)

• Bingol, Emergence of Fame, PRE (submitted)Bingol, Emergence of Fame, PRE (submitted)preprint arXiv nlin.AO/0609033, 2006 preprint arXiv nlin.AO/0609033, 2006

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Thank YouThank You

http://www.cmpe.boun.edu.tr/http://www.cmpe.boun.edu.tr/soslabsoslab

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Future workFuture work

• Larger populationLarger population and memory and memory– Currently Currently nn=1 000 & =1 000 & mm=900=900

• Interaction of societiesInteraction of societies– Population size vs memoryPopulation size vs memory

• Effect of advertisementEffect of advertisement– Recommendation prefers someRecommendation prefers some

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RepresentationRepresentation Memory ContentMemory Content

jj thth memory content of person memory content of person ppii

ppkk ∈∈MMii

......1 2 ... 1 2 ... mm

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nn

......1 2 ... 1 2 ... mm

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......1 2 ... 1 2 ... mm

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......ppkkii

jj

on the size of memory : human memory modeling by simulation (hum2s)

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