Download Frontiers in Mathematics and Computing

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
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suitable for beginning and learning programming

we will play with some python examples today
agenda – day 2

mathematics
◦ chaos theory
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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
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can we predict the behavior of a group of
people? (given some information)
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group dynamics
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graph network
jargon
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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
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power
◦ (who’s The Guy?!)
◦ related to the degree of a graph
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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
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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
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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
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Medici family was less powerful than others
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they ended up dominating
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why is that so?
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betweeness score
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Medici: 0.52
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second largest: 0.25
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moral: networking is important!
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Medici held the network together
that finishes our math portion

artificial intelligence

machine learning is the development of
algorithms from which programs can
learn
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what can they learn?
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what can they do with the training?
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training datasets
invitation to big data
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we deal with exabytes of data nowadays
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1 exabyte = 1 099 511 627 776 megabytes
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2147483 hard disks (that are each 500 GB) !!
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how do we make sense of such a huge amount of information?
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opportunities in supercomputing and machine learning
flavor of artificial intelligence

Terminator 2 was not quite right, robots
haven’t taken over yet
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but we can use AI in other ways
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evolutionary algorithms
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set a goal, evolve your given information
towards the goal
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genetic algorithm
genetic algorithm
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say, you would like to break someone’s
password
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you can try all random combinations
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or you can do some intelligent guesses
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how can we simulate this process for a
computer?
simple genetic algorithm
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start with “;wql* opqlq”
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end goal: “hello world”
;
w
q
l
*
o
p
q
l
q
h
e
l
l
o
w
o
r
l
d
genetic algorithm
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treat these characters as genes!
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genes can mutate, right?
;
w
q
l
*
o
p
q
l
q
;
w
q
l
*
o
o
q
l
q
genetic algorithm
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but wait, the program should not accept
every mutation
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how does it know it is closer to the goal?
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how can we find the difference between
two sets?
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Euclidean distance
genetic algorithm
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fitness test: is a gene fit to pass?
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If the difference between source and target is
lower, we accept the mutation.
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intermediate results are important too!
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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
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text evolution example (textevolve.py)
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music evolution example
(music_evolve.py)
research in mathematics

discussion
end of day 2
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resources can be found at
◦ nsaquib.com/presentations
◦ code examples
◦ things to try out

thanks for attending! 