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

1. On The Size of Memory:Human Memory Modeling by Simulation (HuM2S) Haluk Bingol Complex Systems Lab Dept. of Computer Engineering Bogazici University Ulusal Grid Çalıştayı 2007 Mar01, 2007

2. Outline • Motivation • Memory Representation • Recommendation • Simple Recommendation Model • Effect of Small Memory Size • Conclusions • [Bingol, LNCS 3733 pp.294-303 (2005)] • [Bingol, arXiv nlin.AO/0609033, 2006 ]

3. Motivation

4. Motivation If you need somebody • If you need a plumber, how do you find one? • know one? • You ? • Your friends ? • Google ? • Famous plumber!

5. Motivation Key concepts • My memory • My friends memory My network of friends Local memory • Google’s memory Accessible memory of the population Global memory • Fame Being known to the general public • Recommendation

6. Representation(Static View)

7. Memory Representation Who-knows-who Graph • Digraph G (P, A) • Vertices P={1, 2, ..., n} • Arc from pi to pj • if pi knows pj 1 4 2 5 3 2 4 3 3 4 1 5 4 - 4 5 4 5 1 2 3

8. Memory of pi Mi= {pj| pi knows pj} ⊆ P m : memory size of an individual |Mi | = m n : population size mn : memory capacity of the population ... ... ... ... ... ... ... ... ... ... ... ... Memory Representation Memory abstraction 1 2 ... m 1 2 ... m 1 2 ... m 1 2 3 : n 1 2 3 : n 1 2 3 : n : : ... : : : ... : : : ... : 1 • Remarks • out-degree: m 2 ... m

9. Knownness ki =|{pi | pi knows pj}| ... ... ... ... ... ... ... ... ... ... ... ... Memory Representation Definitions 1 2 ... m 1 2 ... m 1 2 ... m 1 2 3 : n 1 2 3 : n 1 2 3 : n : : ... : : : ... : : : ... : 1 • Remarks • out-degree: m • in-degree: 0 ≤ ki ≤ n 2 ... ... m

10. Interacting Agents:Recommendation ->

11. Person (from) Remember Recommend Learn Person (to) RecommendationRecommendation Process time

12. 1 2 ... m ... ... ... ... 1 2 3 : n r : : ... : pr f Recommendationfrom • Select a person pf • Select f in {1, 2, ... , n} • pf remembers a known person • Select r in {1, 2, ... , m} • Find person pr • f : from • r : recommended

13. 1 2 ... m ... ... ... ... 1 2 3 : n : : ... : pr Recommendationto • Select a person pt • Select t in {1, 2, ... , n} • Recommend pr to pt r f t • t : to

14. 1 2 ... m ... ... ... ... 1 2 3 : n : : ... : pr pe Recommendationto • Learn recommended person pr • pt remembers a known person • Select e in {1, 2, ... , m} • Person pe r e f t • e : slot to be emptied

15. 1 2 ... m ... ... ... ... 1 2 3 : n : : ... : pr pr Recommendationto • Learn recommended person pr • pt remembers a known person • Select e in {1, 2, ... , m} • Person pe • Forget a person • Obtain an empty memory location • Put pr to locationt-b r e f t

16. Simple Recommendation Model ->

17. Simple Recommendation Model • Random selections • f, t∊ {1, 2, ... , n} • r, e∊ {1, 2, ... , m} • Initial memory content • Every person knows next mpersons

18. Effect of Small Memory Size

19. Effect of Small Memory SizeDefinitions • Memory ratio • ρ = m / n • 0 < ρ ≪ 1 • Fame • fi= ki /n

20. As ρ→0 fmin ↘ Some completely forgotten fmax ↗ A few gets more known Effect of Small Memory SizeEffect of ρ fmax fmin Completely forgotten n = 100

21. As ρ→0 fmin ↘ Linear Effect of Small Memory SizeMinimum Fame

22. c : the number of completely forgotten agents u = c / n As ρ→0 u↗ Linear Effect of Small Memory SizeCompletely Forgotten Agents

23. As ρ→0 fmax↘↗ Linear Emergence of fame Effect of Small Memory SizeMaximum Fame

24. As ρ→0 f5%: Top 5% fame f5%↘ Linear Effect of Small Memory SizeTop 5% Fame

25. A new model “too little memory, too many items” cases Information dissemination Building consensus Advertisement Linear patterns fmin ↘ u↗ fmax ↘↗ Emergence of “fame” Population P could be anything Papers Books Movies Movie Stars Painters Poets ... Conclusions http://www.cmpe.boun.edu.tr/soslab

26. Human Memory Modeling by Simulation (HuM2S) Project

27. Project Description • An agent-based Complex Systems modeling and simulation project • Human population is studied • Human memory is modeled • Interaction of humans are simulated • Effect of memory size is investigated

28. Understanding dynamics of human population Fame Cultural islands Integration of cultures Dissemination of information Building consensus Building public opinion Cooperation Effects of advertisement A new agent-based model for complex sytems “too little memory, too many items” cases Synchronization Potential Outcomes

29. Need for Grid • Currently a single simulation takes months on a single machine • Parametric parallelization possible • Number of persons currently 1.000 • need for 1.000.000 • Memory sizes of currently 200 • need 1.000 • Number of interactions currently 108 • need 1010

30. Budget • Research Assistant • 12 man-months • Notebook ? • 2.500 Euro • Conference/Travel ? • 2.000 Euro

31. HuM2S Project • Just started • Feb 1, 2007 • 25 000 Euro • Assistant

32. References • Bingol, Fame as an Effect of the Memory Size, LNCS 3733,294 (2005) • Bingol, Fame as an Effect of the Memory Size, ECCS’05 (presented), (2005) • Bingol, On The Size of Memory, NDCOS (presented), (2006) • Bingol, Emergence of Fame, PRE (submitted)preprint arXiv nlin.AO/0609033, 2006

33. Thank You http://www.cmpe.boun.edu.tr/soslab

34. Future work • Larger population and memory • Currently n=1 000 & m=900 • Interaction of societies • Population size vs memory • Effect of advertisement • Recommendation prefers some

35. jth memory content of person pi pk∈Mi ... ... ... ... ... ... ... ... ... ... ... ... ... RepresentationMemory Content j 1 2 ... m 1 2 ... m 1 2 ... m 1 2 3 : n 1 2 3 : n 1 2 3 : n : : ... : : : ... : : : ... : pk i