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Frontiers in Mathematics and Computer Science Salt Lake City Public Library, SLC, Utah Nazmus Saquib Scientific Computing and Imaging Institute welcome back! today we will ◦ experiment with some code ◦ learn a bit about graph theory and genetic algorithm ◦ discuss the implications of mathematics research 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 agenda – day 2 mathematics ◦ chaos theory butterfly effect weather forecast fractal music L-systems social interactions (in facebook) ◦ graph theory social interactions example (continued) agenda – day 2 computer science ◦ machine learning big data genetic algorithms ◦ data mining sentiment analysis digital humanities 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 jargon node and edge http://pc57724.uni-regensburg.de/morgan/teaching/CS104-Social_Networking.pdf culture hubs degree of a node http://en.wikipedia.org/wiki/File:Scale-free_network_sample.png (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 (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 (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 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 that finishes our math portion 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 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 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 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? simple genetic algorithm start with “;wql* opqlq” end goal: “hello world” ; w q l * o p q l q h e l l o w o r l d genetic algorithm treat these characters as genes! genes can mutate, right? ; w q l * o p q l q ; w q l * o o q l q 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 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! genetic algorithm text evolution example (textevolve.py) music evolution example (music_evolve.py) research in mathematics discussion end of day 2 resources can be found at ◦ nsaquib.com/presentations ◦ code examples ◦ things to try out thanks for attending!