frontiers in mathematics and computer science

Frontiers in Mathematics and Computer ScienceSalt Lake City Public Library, SLC, Utah

Nazmus SaquibScientific 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 2mathematics

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

◦graph theory social interactions example (continued)

agenda – day 2computer science

◦machine learning big data genetic algorithms

◦data mining sentiment analysis digital humanities

graph theoryin the context of social

interactions

can we predict the behavior of a group of people? (given some information)

group dynamics

graph network

jargonnode and edge

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

culture hubsdegree of a node

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

(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

(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

(primary) types of analysisbetweeness

(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 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

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 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

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?

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

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

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

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!

genetic algorithmtext evolution example

(textevolve.py)

music evolution example (music_evolve.py)

research in mathematicsdiscussion

end of day 2resources can be found at

◦nsaquib.com/presentations◦code examples◦things to try out

thanks for attending!