Frontiers in Mathematics and Computer Science
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Transcript of Frontiers in Mathematics and Computer Science
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Frontiers in Mathematics and Computer ScienceSalt Lake City Public Library, SLC, Utah
Nazmus SaquibScientific Computing and Imaging Institute
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welcome back!today we will
◦experiment with some code
◦learn a bit about graph theory and genetic algorithm
◦discuss the implications of mathematics research
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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
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agenda – day 2mathematics
◦chaos theory butterfly effect weather forecast fractal music L-systems social interactions (in facebook)
◦graph theory social interactions example (continued)
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agenda – day 2computer science
◦machine learning big data genetic algorithms
◦data mining sentiment analysis digital humanities
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graph theoryin the context of social
interactions
can we predict the behavior of a group of people? (given some information)
group dynamics
graph network
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jargonnode and edge
http://pc57724.uni-regensburg.de/morgan/teaching/CS104-Social_Networking.pdf
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culture hubsdegree of a node
http://en.wikipedia.org/wiki/File:Scale-free_network_sample.png
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(very primary) types of analysispower
◦ (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
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(primary) types of analysisbetweeness
◦ 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
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(primary) types of analysisbetweeness
(only equation in the slides, I promise!)
this is to show you how easy it is to calculate such metrics
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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
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that finishes our math portion
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artificial intelligencemachine learning is the
development of algorithms from which programs can learn
what can they learn?
what can they do with the training?
training datasets
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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
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flavor of artificial intelligenceTerminator 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
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genetic algorithmsay, 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?
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simple genetic algorithmstart 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
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genetic algorithmtreat these characters as genes!
genes can mutate, right?
; w q l * o p q l q
; w q l * o o q l q
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genetic algorithmbut 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
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genetic algorithmfitness 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!
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genetic algorithmtext evolution example
(textevolve.py)
music evolution example (music_evolve.py)
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research in mathematicsdiscussion
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end of day 2resources can be found at
◦nsaquib.com/presentations◦code examples◦things to try out
thanks for attending!