Frontiers in mathematics and computer science
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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!. t oday we will experiment with some code l earn a bit about graph theory and genetic algorithm

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Frontiers in mathematics and computer science

Frontiers in Mathematics and Computer Science

Salt Lake City Public Library, SLC, Utah

NazmusSaquib

Scientific Computing and Imaging Institute


Welcome back

welcome back!

  • today we will

    • experiment with some code

    • learn a bit about graph theory and genetic algorithm

    • discuss the implications of mathematics research


I nstalling python and pygame

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


A genda day 2

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

agenda – day 2

  • computer science

    • machine learning

      • big data

      • genetic algorithms

    • data mining

      • sentiment analysis

      • digital humanities


Graph theory

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

jargon

  • node and edge

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


C ulture hubs

culture hubs

  • degree of a node

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


Very primary types of analysis

(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

(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 analysis1

(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


E xample 15 th century florence

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

that finishes our math portion


Artificial intelligence

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

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

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

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

simple genetic algorithm

  • start with “;wql* opqlq”

  • end goal: “hello world”


Genetic algorithm1

genetic algorithm

  • treat these characters as genes!

  • genes can mutate, right?


Genetic algorithm2

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 algorithm3

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 algorithm4

genetic algorithm

  • text evolution example (textevolve.py)

  • music evolution example (music_evolve.py)


Research in mathematics

research in mathematics

  • discussion


End of day 2

end of day 2

  • resources can be found at

    • nsaquib.com/presentations

    • code examples

    • things to try out

  • thanks for attending! 


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