Software prototyping of educational games Geometry Tetris Robotic Poet Witty Go ( 围棋 )

1. Professor S.-Y. Robert Lihttp://www.ie.cuhk.edu.hk/bobli • Software prototyping of educational games • Geometry Tetris • Robotic Poet • Witty Go(围棋) • Each FYP project is to create a modern prototype of one of these unique games in the world:

2. Professor S.-Y. Robert Lihttp://www.ie.cuhk.edu.hk/bobli Network codingtheory research & appl Stochastic processes theory research & appl Switching/routingtheory research & appl Each FYP group will be matched with a specific topic.

3. Demo Project SYL1: Geometry Tetris Project SYL2: Robotic Poet

4. This software project is revolutionary in two aspects: • The variation of the game board dilutes the advantage of professionals over beginners. • With computerization, we have a set of natural rules that completely replaces human referees. Project SYL3: Witty GO(圍棋)

5. Project SYL4: Network coding x = 0 or 1 y = 0 or 1 Every channels transmits one bit. xy = Store-and-forward 0 if x = y 1 if x  y Either x or y Figure adapted from Scientific American, Chinese 7/2007 edition

6. Treating information like parcel Traffic jam Figure adapted from Scientific American, Chinese 7/2007 edition

7. But, information can be processed. xy = 0 if x = y 1 if x  y Figure adapted from Scientific American, Chinese 7/2007 edition

8. But, information can be processed. xy = 0 if x = y 1 if x  y Decode x Decode y Figure adapted from Scientific American, Chinese 7/2007 edition

9. Wireless application Wireless communications in the air is multicasting, NC applies naturally. 4 steps by store-and-forward y x 3 steps by NC y x x+y xy 50% saving in downlink capacity M.I.T. prototype  standard of wireless LAN (802.11 Wi-Fi).

10. Redundancy of Data Storage (Redundant Array of Independent Disks) Disk A B Backup A B

11. Backup “by NC” (Redundant Array of Independent Disks) Single backup Disks A B AB

12. NC over an imaginary network Data Disks A B AB A’

13. NC over an imaginary network Data Disks A B AB AB B’ A’ So far, all applications are equivalent to the Butterfly Network.

14. P2P on NC Avalanche Microsoft’s version of BitTorrent UUSee.com (悠視網)

15. Computing by symmetry Martingales of patterns … Project SYL5: Stochastic process

17. Casino blackjack Sequential random variables = card points received by gambler Given the value of dealer’s up-card, let K (resp. KS) = min hard (resp. soft) points not known to be sure hit = threshold for stopping time Payoffat a hand upon stopping = receipt averaged over all dealer possibilities Figure reproduced from: Dynamic programming by exchangeability, SIAM J. Comput., 6/1989

18. William Feller on coin-tossing Project 5b: Stochastic process • H = head, T = tail, P{H} = P{T} = ½ • Average waiting time for HHHHHH = 64? • Average waiting time for HHTTHH = 70 • Feller found these results counter-intuitive. 126

19. Race between 2 patterns nothing like 10 : 9,but rather … • On fair coin-toss, • Average waiting for HTHH = 18// A slightly faster pattern • Average waiting for THTH = 20// A slightlyslower pattern • In a race between HTHH vs. THTH, the odds are • the landslide 5 :9.

20. On fair coin-toss, Average waiting for HTHH = 18// A slightly faster pattern Average waiting for THTH = 20// A slightlyslower pattern In a race between HTHH vs. THTH, the odds are the landslide 5 :9 in favor of THTH. The Sting The fairy-tale race HareTortoise Scientific truth and fairy tales happilyagree with each other, while ordinary intuition is left out.

21. The process HTHH a new species of deadly virus The process THTH a benign one Applications to bio informatics • Basic model 1. Patterns over the DNA alphabet {A, T, G, C} or the amino acid alphabet. • Basic model 2.Let H & T = two environmental/genetic changes. • Since the appearance of [Li '80], the ensuing literature kept claiming the impact on genetics. In 2000, the ensuing literature started to include biology papers on such topics of as • Superiority of Spaced Seeds for Homology Search • Probabilistic and Statistical Properties of Words

22. Basicmodel. Let outcomes of a repeated experiment be a = , b = , c = 0, d = , e = , … Track a large number of patterns in the past record in order to catch gambler behavior, short covering panic, fund redemption crunch, governmental behavior before an election, surplus retirement pension due to population aging Application to financial engineering a, b, c, d, e d, c, d, c, d, c, a, a, a, a, c b, b, b, c, d, d, d c, c, a c, a, c, c

23. Applications to communications • In ad hoc networks ofwireless communications, some protocols use binary patterns (H = listen, T = talk) for node discovery. • The correlation operator  of patterns is useful in signal design toward particular purposes.

24. Project 6: Switching/routing • Types of switches/routers: • Crossbar (or equivalent) • Shared buffer memory switch • Algebraic switching fabric Component complexity = O(n2)

25. B D B C A D A C B • Crossbar (or equivalent) • Shared buffer memoryswitch • Algebraic switching fabric Types of switches/routers Limited capacity

26. Crossbar (or equivalent) • Shared buffer memory switch • Algebraic switching fabric Types of switches/routers

27. 32-lined version of the 44 banyan network

28. A 32-lined version of a 44 network consisting of Boolean multicast switching cells 2014/9/17 數學與工程的對話4: Unified algebraic theory for … networks 28

29. Algebraic switching theoryemphasized on the algebra on I/O addresses. 1st-gen technology: Chip set used in Metro Switch Project of ITRI (Taiwan) 2nd-gen technology: Developed during the last 10 years.

30. Thank you