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Frontiers in Mathematics and Computer Science

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Frontiers in Mathematics and Computer Science

Salt Lake City Public Library, SLC, Utah

NazmusSaquib

Scientific Computing and Imaging Institute

- today we will
- experiment with some code
- learn a bit about graph theory and genetic algorithm
- discuss the implications of mathematics research

- 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

- mathematics
- chaos theory
- butterfly effect
- weather forecast
- fractal music
- L-systems
- social interactions (in facebook)

- graph theory
- social interactions example (continued)

- chaos theory

- computer science
- machine learning
- big data
- genetic algorithms

- data mining
- sentiment analysis
- digital humanities

- machine learning

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

- node and edge

http://pc57724.uni-regensburg.de/morgan/teaching/CS104-Social_Networking.pdf

- degree of a node

http://en.wikipedia.org/wiki/File:Scale-free_network_sample.png

- 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

- 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

- betweeness

(only equation in the slides, I promise!)

this is to show you how easy it is to calculate such metrics

- 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

- 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

- 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

- 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

- 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?

- start with “;wql* opqlq”
- end goal: “hello world”

- treat these characters as genes!
- genes can mutate, right?

- 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

- 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!

- text evolution example (textevolve.py)
- music evolution example (music_evolve.py)

- discussion

- resources can be found at
- nsaquib.com/presentations
- code examples
- things to try out

- thanks for attending!