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Frontiers in Mathematics and Computer Science

Frontiers in Mathematics and Computer Science. Salt Lake City Public Library, SLC, Utah Nazmus Saquib Scientific Computing and Imaging Institute. welcome back!. t oday we will experiment with some code l earn a bit about graph theory and genetic algorithm

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Frontiers in Mathematics and Computer Science

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  1. Frontiers in Mathematics and Computer Science Salt Lake City Public Library, SLC, Utah NazmusSaquib Scientific Computing and Imaging Institute

  2. welcome back! • today we will • experiment with some code • learn a bit about graph theory and genetic algorithm • discuss the implications of mathematics research

  3. installing python and pygame • http://www.python.org/download/ • http://www.pygame.org/download.shtml • python is a programming language • suitable for beginning and learning programming • we will play with some python examples today

  4. agenda – day 2 • mathematics • chaos theory • butterfly effect • weather forecast • fractal music • L-systems • social interactions (in facebook) • graph theory • social interactions example (continued)

  5. agenda – day 2 • computer science • machine learning • big data • genetic algorithms • data mining • sentiment analysis • digital humanities

  6. graph theory • in the context of social interactions • can we predict the behavior of a group of people? (given some information) • group dynamics • graph network

  7. jargon • node and edge http://pc57724.uni-regensburg.de/morgan/teaching/CS104-Social_Networking.pdf

  8. culture hubs • degree of a node http://en.wikipedia.org/wiki/File:Scale-free_network_sample.png

  9. (very primary) types of analysis • power • (who’s The Guy?!) • related to the degree of a graph • closeness • how many people do I need to know to reach someone else asap? http://pc57724.uni-regensburg.de/morgan/teaching/CS104-Social_Networking.pdf

  10. (primary) types of analysis • betweeness • who can get me to the most important people asap? • asap:shortest path in the graph • number of times I need to go through someone to reach someone else

  11. (primary) types of analysis • betweeness (only equation in the slides, I promise!) this is to show you how easy it is to calculate such metrics

  12. example – 15th century Florence • Medici family was less powerful than others • they ended up dominating • why is that so? • betweeness score • Medici: 0.52 • second largest: 0.25 • moral: networking is important! • Medici held the network together

  13. that finishes our math portion

  14. artificial intelligence • machine learning is the development of algorithms from which programs can learn • what can they learn? • what can they do with the training? • training datasets

  15. invitation to big data • we deal with exabytes of data nowadays • 1 exabyte = 1 099 511 627 776 megabytes • 2147483 hard disks (that are each 500 GB) !! • how do we make sense of such a huge amount of information? • opportunities in supercomputing and machine learning

  16. flavor of artificial intelligence • Terminator 2 was not quite right, robots haven’t taken over yet • but we can use AI in other ways • evolutionary algorithms • set a goal, evolve your given information towards the goal • genetic algorithm

  17. genetic algorithm • say, you would like to break someone’s password • you can try all random combinations • or you can do some intelligent guesses • how can we simulate this process for a computer?

  18. simple genetic algorithm • start with “;wql* opqlq” • end goal: “hello world”

  19. genetic algorithm • treat these characters as genes! • genes can mutate, right?

  20. genetic algorithm • but wait, the program should not accept every mutation • how does it know it is closer to the goal? • how can we find the difference between two sets? • Euclidean distance

  21. genetic algorithm • fitness test: is a gene fit to pass? • If the difference between source and target is lower, we accept the mutation. • intermediate results are important too! • in reality, you would derive a good fitness function that would produce “intelligent” results • if you were writing a password breaker, you wouldn’t know the password to begin with!

  22. genetic algorithm • text evolution example (textevolve.py) • music evolution example (music_evolve.py)

  23. research in mathematics • discussion

  24. end of day 2 • resources can be found at • nsaquib.com/presentations • code examples • things to try out • thanks for attending! 

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