Computer Systems Lab TJHSST Current Projects 2004-2005 Third Period

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Computer Systems LabTJHSSTCurrent Projects
2004-2005Third Period
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Current Projects, 3rd Period

• Robert Brady A Naive Treatment of Digital
  Sentience in a Stochastic Game
• Blake Bryce Bredehoft Robot World A Evolution
  Simulation
• Michael Feinberg Computer Vision Edge
  DetectionsVertical diff., Roberts, Sobels

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Current Projects, 3rd Period

• Scott Hyndman Agent Modeling and Optimization of
  a Traffic Signal
• Greg Maslov Machine Intelligence Walking Robot
• Eugene Mesh
• Thomas Mildorf A Self-Propagating Continuous
  Differential System as Limiting Discrete
  Numerical Construct and Device of Sorting

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Current Projects, 3rd Period

• Carey Russell Graphical Modeling of Atmospheric
  Change
• Matthew Thompson Genetic Algorithms and Music
• Justin Winkler Modeling a Saturnian Moon

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Developing a Learning AgentThe goal of this
project was to create a learning agent for the
game of bridge. I think my current agent, which
knows the rules, plays legally, and finds some
basic good plays, is a step in the right
direction. This agent could and will be improved
upon over the course of the year and will become
smarter and learn faster throughout the year
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A Naive Treatment of Digital Sentience in a
Stochastic GameRobert Brady

• Abstract
• My techlab project deals with the field of
  Artificial Intelligence or more specifically,
  Machine Learning. I am designing an
  agent/environment for the card game of bridge.
  After it learns the rules, I will run simulations
  where it decides on its own what the best play
  is. The level of play for the agent will increase
  as the year continues because it will look up
  past decisions in its history to determine what
  the best bid or play is in a current state of the
  environment.

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A Naive Treatment of Digital Sentience in a
Stochastic GameRobert Brady

• Background
• Machine learning has been researched in the past
  and has dealt with bridge before. This area is
  new, though, and anything from intelligent agents
  for games to the traveling salesman problem count
  as part of it. An algorithm used for one problem
  can be applied in a similar manner to another
  such as the minimax algorithm or the backtracking
  search. To build on current work, there would
  have to be some sort of improvement on current
  bridge-playing agents such as Bridge Baron or
  GIB. Both of these programs play at a moderate
  level, but none of them can compare to an expert
  player. The reason why an intelligent
  bridge-playing agent has been hard to program in
  the past is that bridge is a partially observable
  environment.

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A Naive Treatment of Digital Sentience in a
Stochastic GameRobert Brady

• In games such as chess, or checkers, the agent
  could conceivably come up with the best solution
  (given enough time to think about it) because it
  knows where everything is. In bridge, there are
  certain cards that haven't been played yet and
  although you may be able to guess where they are,
  you can not determine this with 100 certainty.
  This makes programming a learning agent for a
  partially observable environment much harder.
  Progress For the first semester, I worked on this
  program with regards to finishing programming in
  the rules to the game and some simple AI
  commands.

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A Naive Treatment of Digital Sentience in a
Stochastic GameRobert Brady

• When this was completed about a week before the
  semester was over, I began researching different
  AI algorithms that could be implemented for
  searching. This research halted once I realized
  the tree that would be searched was difficult to
  construct. I consulted my professional contact
  Fred Gitleman and he had also encountered this
  problem when programming a similar search
  algorithm. He talked me through the problems I
  had and gave some advice on where to find
  information that would help me with those
  problems. During the third quarter, I worked
  solely on running an algorithm (the minimax
  algorithm) through a depth-first search with
  pruning of bad nodes.

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A Naive Treatment of Digital Sentience in a
Stochastic GameRobert Brady

• The algorithm still has a few problems and will
  hopefully be finished soon. Another portion of
  the code that I added this quarter deals with the
  machine learning part of my pro ject. This part
  of the pro ject stores information from the hand
  that the computer just played in a file that is
  essentially the computer's "brain." The brain
  stores information about how many tricks were
  taken with the combined hands in a trump suit or
  in no-trump. It uses this information for the
  bidding stage of the following hands. If the
  numbers it reads from the file are much lower
  than what it believes the current state of the
  environment is, it will bid higher and if the
  numbers are higher, it will try to refrain from
  bidding.

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A Naive Treatment of Digital Sentience in a
Stochastic GameRobert Brady

• My future plans include testing of the program
  against other players at the school. I will use
  students from my tech-lab class for a preliminary
  test and then after the program has established a
  competitive nature with these kids, it will play
  against the bridge club on Fridays during school.
  I hope it will be able to compete with the
  students of the club at some point in the next
  quarter, but if this is an unrealistic goal, I
  will just try and improve upon it's algorithm as
  much as I possibly can before the end of the
  year. As it is currently, the program needs a
  little more work on the algorithm to make it
  fully operational before I open it up to tests
  from fellow students. Co de This section is
  pretty much self explanatory. Some important
  sections are in bold and commented while the less
  important parts have been left out.

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A Naive Treatment of Digital Sentience in a
Stochastic GameRobert Brady

• References
• 1. Fred Gitelman (fred_at_bridgebase.com) A
  programmer who also is an expert bridge player.
  He advised me on how to look through a tree to
  find the solution comparable to a minimax search.
  
• 2. Russell, S. and Norvig, P. Artificial
  Intelligence A Modern Approach Seco Prentice
  Hall, NJ. 2003.

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Robot SwarmsMy project is an agent based
simulation, posing robots in a game of life,
with each new generation of robot comes new genes
using a random number selection process creating
the mutations and evolutions that in real life we
experience for DNAcross over and such.
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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• Abstract
• My project is an agent based simulation, posing
  robots in a "game of life", with each new
  generation of robot comes new genes using a
  random number selection process creating the
  mutations and evolutions that in real life we
  experience for DNA cross over and such. There are
  two versions of my program a Simulation and a
  Game.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• The Simulation As stated in my abstract.
• The Process The base of my program was not the
  genetics, but the graphics itself. First one
  robot, then a random Artificial Intelligence for
  it. I then modified the world to sustain several
  robots, with dying a breeding. After introducing
  two more Artificial Intelligences a "group"
  Artificial Intelligence and a "battery"
  Artificial Intelligence promoting grouping and
  collecting batteries selectively. I then tweaked
  the environment and code until it could sustain
  life. I then programed in several possible places
  for environmental interaction, like viruses and
  the batteries. I added the graphical output for
  easier analysis. Finally I created the random
  number selection process to splice the genes of
  the parents and create a child. The heart of the
  program.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• The Game
• There is the above stated "simulation" version of
  my program, and a later created "game" version.
  The game version includes all the same components
  as the simulation but also has a user controlled
  robot with "laser eyes" and "grenade launchers"
  use to kill the other robots. It also includes
  "Bosses".The Process Taking the simulation
  version and modifying it was easy, first removing
  the natural deaths and graph. Then I introduced
  and tweaked the user controls and the user
  controlled robot. Then adding lasers and grenades
  and all the necessary coding, i finally added a
  status display embedded window in the top left
  corner. I continually add new pieces of flare to
  the program, such as bosses.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• 1 Introduction
• My project has several basic components 3D
  modeling, Artificial Intelligence, The selection
  process, and then basic game theory. All these
  components form the amalgam that makes up my
  project. Both the simulation and the game use all
  these components except the simulation doesn't
  have any game theory.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• 2 Background 2.1 Monte Carlo Simulation
• Since Monte Carlo is a Simulation technique,
  let's first define exactly what we mean by
  Simulation. A true Simulation will merely
  describe a system, not optimize it! (However, it
  should be noted that a true simulation may be
  modified in a manner such that it can be used to
  significantly enhance the efficiency of a
  system.) Therefore, our primary goal in
  Simulation is to build an experimental model that
  will accurately and precisely describe the real
  system. However, the breadth and extent of
  Simulation models is extensive!

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• This can be illustrated by considering the three
  general "classifications" of Simulation Models,
  below. And in each of these "classifications", I
  have defined two possible "characteristics".
• 1. Functional Classification Deterministic
  Characteristic - These are "exact" models that
  will produce the same outcome each time they are
  run. Stochastic Characteristic - These models
  include some "randomness" that may produce a
  different outcome each time it is run. This
  randomness forces us to make a large number of
  runs to develop a "trend" in our "collection" of
  outcomes. Further, the exact number of how many
  "runs" you must make to obtain the "right trend"
  is simply a matter of statistics.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• 2. Time Dependence Static Characteristic - These
  models are not time-dependent. This even includes
  the calculation of a specific variable after a
  fixed period of time. Dynamic Characteristic -
  These models depict the change in a system over
  many time intervals during the calculation
  process.
• 3. Input Data Discrete Characteristic - The input
  data form a discrete frequency distribution.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• Discrete frequency distributions are
  characterized by the random variable X taking on
  an enumerable number of values xi that each have
  a corresponding frequency, or count, pi.
  Continuous Characteristic - The input data can be
  described by a continuous frequency distribution.
  Continuous frequency distributions are
  characterized by a continuous analytical function
  of the form y (x) where y is defined as the
  frequency of x. This definition is valid for all
  possible values of x (over the domain of the
  function).

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• We can now say that Monte Carlo Simulations are
  "True Stochastic Simulations" in that they
  describe the "final state" of a model by just
  knowing the frequency distributions of the
  parameters describing the "beginning state" and
  the appropriate metric that maps, or transforms,
  the beginning state to the final state. They can
  also be either static (easy) or dynamic (more
  difficult). If a prediction were required, then
  "every possible" option would have to be
  considered and this is where the well-known
  "Variance Reduction Methods" (antithetic
  variables, correlated sampling, geometry
  splitting, source biasing, etc.) would be used to
  reduce the number of iterations required in the
  simulation.
• Definition courtesy of JAMES F. WRIGHT, Ph.D Ltd.
  Co. at http//www.drjfwright.com/

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• 3 Theory
• 3.1 3D Modeling My graphics are done using
  OpenGL. In the simulation version there are three
  different aspects to the graphical output the
  agents (the robots), the environment (the floor
  and batteries), and the events (explosions) and
  the population graph. The game version has all
  these same component except the agents include a
  user controlled robot and bosses, the events
  include grenades, lasers and grenade explosions,
  there is no graph, and there is a stat indicator,
  and a mini map. There is also the interface of my
  program from where you launch the simulations and
  games.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• The environment consist of a floor and background
  and small cubes representing batteries. Simple
  enough (below right). The robots consist of
  prisms and spheres to form arms, legs, torso,
  head and facial features (below left). The
  explosions are tori spinning on the y-axis that
  get more transparent as the grow in size (below
  center). The is also a program that is able to
  output numbers for the counters in the game
  version.
• See appendix A.1 for example code.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• There is also a graph out put that is fairly
  simple. Every iteration it plots a new point on
  the grid, and never erases, therefore creating a
  line graph for the populations of each artificial
  intelligence type (below left). The game mode
  utilizes a mini map and a status bar, the bar
  includes life, number of grenades, and number of
  kills (bottom right).

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• 3.2 Artificial Intelligence There are three
  different main artificial intelligences in the
  program and one that uses a combination of the
  others. The first is a random artificial
  intelligence that is the most basic, second is
  the group artificial intelligence that condones
  forming groups for reproduction, and the last is
  the battery or food artificial intelligence that
  promotes eating. The fourth is one that is
  advanced, and has the agent use the battery
  artificial intelligence when it requires energy,
  and uses the group artificial intelligence when
  he doesn't require energy. The random artificial
  intelligence first randomly decides whether to
  turn left, right, or go forward.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• It has a preference to turn if it turned the
  iteration before. This done over time produces
  interesting behavior. The fact that offspring
  spawn close to parents and that parents have to
  be close to produce offspring means that after a
  while these will group, and any robot that
  randomly strays from the group will die off,
  where as those in the group re spawn as fast as
  they die.
• Code is located in Appendix A.2.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• The group artificial intelligence goes through
  the list of robots and first recognizes all the
  robots that are of a color suitable for
  reproduction for the given robot. Then from this
  list the closest robot is chosen, the robot then
  turns towards this robot and walks. This
  obviously forms groups that are more efficient
  than the groups produced by the random artificial
  intelligence, because robots will not stray off.
• Code is located in Appendix A.2.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• The battery artificial intelligence goes through
  the list of batteries and finds the one closest
  to the robot and then turns the robot towards it
  and walks. Robots will end up heading after the
  same battery and form groups, these groups may or
  may not be able to reproduce though, but when a
  pair find each other these groups produce to be
  fairly strong.
• Code is located in Appendix A.2.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• The group that is the strongest is an
  amalgamation of both group artificial intelligent
  robots and battery artificial intelligent robots.
  These groups stay together due to the number of
  group robots and will search for food due to the
  battery robots. Proving to be extremely effective
  in keeping alive. Sooner or later however one of
  the artificial intelligences ends up getting bred
  out. There is a fourth artificial intelligence
  that is an amalgamation of the group artificial
  intelligence and the battery artificial
  intelligence. When the agent is low on energy it
  uses the battery artificial intelligence, until
  it has a decent amount then it uses the group
  artificial intelligence.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• 3.3 Selection Process
• The selection process doesn't start with
  selecting but instead starts at the beginning of
  every iteration. The process is began by
  inventorying the population, tallying the number
  of robots and their characteristics, this then
  produces a few tables stored as a "genome" (code
  for class in Appendix A.3). This tables are
  formed to make graphs of the frequency of the
  specific gene settings. When the selection is
  called, it goes thorough and finds the optimal
  gene, in the parents gene pool, using a random
  number process, and the fore mentioned graphs.
  This is done for each gene. There is also a level
  of randomness calculated in the allows for
  mutations. These mutations give a new status to
  the gene, not in the gene pool.
• Code can be seen in Appendix A.3.

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Robot World A Evolution SimulationBlake Bryce
Bredehoft

• While the theory behind this selection process
  may seem somewhat simple the code on the other
  hand is not.
• 3.4 Game Theory
• There are lasers and grenades. Your tools for
  destroying the surrounding robot population.
  Combine their power by shooting the grenade as it
  falls with your laser and produce a powerful
  explosion. After every 50 kills boss robots
  appear. One will appear the first 50, two the
  second 50 and so on. The bosses use a boss
  artificial intelligence of their own. The boss
  artificial intelligence will find the user
  controlled robot a turn it toward it and walk.

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Computer Vision Edge DetectionsVertical diff.,
Roberts, Sobels
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Computer Vision Edge DetectionsVertical diff.,
Roberts, SobelsMichael Feinberg

• Abstract and paper needed

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Optimization of a Traffic SignalThe purpose of
this project is to produce an intelligent
transport system (ITS) that controls a traffic
signal in order to achieve maximum traffic
throughput at the intersection. To produce an
accurate model of the traffic flow, it is
necessary to have each car be an autonomous agent
with its own driving behavior. A learning agent
will be used to optimize a traffic signal for the
traffic of the autonomous cars.
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Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• Abstract
• Traffic in the Washington, D.C. area is known to
  be some of the worst traffic in the nation.
  Optimizing traffic signal changes at
  intersections would help traffic on our roads
  flow better. This pro ject is to produces an
  intelligent transport system (ITS) that controls
  a traffic signal in order to achieve maximum
  traffic throughput at the intersection. In order
  to produce an accurate model of the traffic flow
  through an intersection, it is necessary to have
  each car be an autonomous agent with its own
  driving behavior.

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Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• The cars cannot all drive the same because all
  the drivers on our roads do not drive the same. A
  learning agent is used to optimize a traffic
  signal for the traffic of the autonomous cars.
  Note The results and conclusion pieces of the
  abstract are not included yet because the pro
  ject is not finished.

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Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• Introduction
• Traffic in the Washington, D.C. area is known to
  be some of the worst traffic in the nation.
  optimizing traffic signal changes at
  intersections would help traffic on our roads
  flow better. the purpose of this pro ject is to
  produce an intelligent transport system (its)
  that controls a traffic signal in order to
  achieve maximum traffic throughput at the
  intersection. in order to produce an accurate
  model of the traffic flow through an
  intersection, it is necessary to have each car be
  an autonomous agent with its own driving
  behavior. the cars cannot all drive the same
  because all the drivers on our roads do not drive
  the same. a learning agent will be used to
  optimize a traffic signal for the traffic of the
  autonomous cars .

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Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• Background
• 1.1 Traffic Signal Control Strategies
• There are three main traffic signal control
  strategies pretimed control, actuated control,
  and adaptive control.
• 1.1.2 Pretimed Control
• Pretimed control is the most basic of the three
  strategies. In the pretimed control strategy, the
  lights changed based on fixed time values. The
  values are chosen based on data concerning
  previous traffic flow through the intersection.
  This control strategy operates the same no matter
  what the traffic volume is.

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Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• 1.1.3 Actuated Control
• The actuated control strategy utilizes sensors to
  tell where cars are at the intersection. It then
  uses what it learns from the sensors to figure
  out how long it should wait before changing the
  light colors. For example, if the signal picks up
  a car coming just before the green light is
  scheuled to change, the length of the green light
  can be extended for the car to go through.

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Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• 1.1.4 Adaptive Control
• The adaptive control strategy is similar to the
  actuated control strategy. It differs in that it
  can change more parameters than just the light
  interval length. Adaptive control estimates what
  the intersection will be like based on data from
  a long way up the road. For example, if the
  signal notices that there is a lot of traffic
  building up down the road during rush hour, it
  might lengthen the green light intervals on the
  main road and shorten them on the smaller road.

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Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• 1.2 Driver Behavior
• None at this time.
• 1.3 Machine Learning
• This piece of the pro ject has not been started.

43
Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• Development 2.1 Model
• I am using MASON software to do my traffic
  simulation. MASON is a Javabased modeling package
  that is distributed by George Mason University.
  My simulation is based on the MAV simulation
  included with the MASON download. In MASON,
  everything runs from the Schedule class. The
  Schedule keeps track of time and moves the
  simulation along one step at a time. Ob jects
  that move implement the Steppable interface.
  Thus, each has its own Step method that the
  Schedule calls at each step in time. There is
  also a Stoppable interface that takes ob jects
  off the Schedule.

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Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• In this program, the visible simulation is made
  by the CarUI Car User Interface class. The CarUI
  starts the CarRun class running. The CarRun class
  is what starts the Schedule and creates
  everything in the simulation. CarUI takes
  information from CarRun to display on the screen.
  CarRun creates Continuous2D's, one for each of
  the ob ject types used in CarRun - Car, Region,
  Signal, and eventController. Continuous2D's store
  ob jects in a continuous 2D environment. They
  make it easier keep track of the ob jects in the
  simulation. The Continuous2D breaks the space of
  the simulation into "buckets."

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Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• If you want to find an ob ject in a certain area
  of the simulation, you can check in the bucket
  there. For example, if you want to see if a car
  has another car near its front, you can look in
  the bucket that that car is in and check to see
  where the other cars in that bucket are. The Car
  class contains the information for how each
  autonomous car runs. It implements both the
  Steppable and Stoppable interfaces. Regions are
  what goes on the background of the visual output.
  Examples of Region ob jects are the roads and
  medians. The Signal class is almost identical to
  the Region class. However, the signals are
  redrawn at every time iteration while the Regions
  are only redrawn if they change loaction or size.

46
Agent Modeling and Optimization of a Traffic
SignalScott Hyndman

• Lastly, because there is no way in MASON to
  control when actions happen in the Schedule, I
  made the eventController class to tell actions
  when to happen. The eventController class uses
  functions defined in other classes to control the
  ob jects of those classes.
• 2.2 Driver Behavior
• None at this time.
• 2.3 Optimization
• This piece of the pro ject has not been started.

47
Greg MaslovMachine IntelligenceWalking Robot
47
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Machine IntelligenceWalking RobotGreg Maslov

• Paper ?

49
Eugene MeshProject?
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Eugene MeshProject?

• Research paper?

51
Sorting Parts of Variable WidthProblem
Statement. To analyze the efficacy of sort parts
by using slots and utilizing the variable angular
velocities that result when parts of distinct
physical dimensions move off of a relatively flat
inclined surface. Purpose. The final goal is to
assess the feasibility of quality control based
on taking advantage of the different orientations
at various time after release that are caused by
deviations from the original product.
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A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Abstract
• Apology.
• In a manufacturing environment, it is crucial to
  establish a high standard of quality control
  while at the same time maintaining a balanced
  budget. Robustness of production as well as the
  minimization of risk are also of concern. Ergo,
  simple, automated techniques for weeding out
  defective pieces are desirable. It is the
  intention of this pro ject to analyze the
  effectiveness of one such technique.

53
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Purpose.
• It is not uncommon for constructs to be delivered
  by conveyor belts as they are processed in a
  factory. Their continuous motion, when directed
  over the end of such a surface, induces a certain
  rotation that accompanies each item during the
  pursuant fall. Proposed is to sort these items by
  exploiting variance in this rotation via the
  precise positioning of one or more slots. It is
  hoped that this motion will be sufficiently
  sensitive to deformation as for this procedure to
  be feasible.

54
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Scope and Procedure.
• The scope of this pro ject is exploratory in
  nature there is no sense in attempting to
  develop a general method. Thus, we will work with
  a rather simple subset of possible pieces.
  Moreover, due to logistic constraints,
  experimentation will be conducted primarily
  within a digitally rendered environment. The
  model will be coded from scratch so as to give me
  total control of the physics involved, and
  repeated trials with dependent variance will be
  employed to discern the efficacy of this sorting
  technique.

55
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• 2 Model Synthesis
• Derivation of Theoretical Equations. We will work
  under admittedly simplistic circumstances,
  assuming that the ob jects being sorted are
  approximated by a rectangular block of length,
  height, and depth l, h, and d respectively. We
  call the generic block B . We suppose furthermore
  that there exists a uniform density within B ,
  so that its mass M , generally given by V M dV
  is instead given by M hld . In a real
  environment, products are typically delivered by
  conveyor belt. Due to aforementioned logistic
  constraints, we use the approximation of an
  inclined plane, which we call P . B will be
  released from the top of P .

56
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• We write for the angle beween P and the
  gravitational equipotential contour. Let µs and
  µk denote the static and kinetic coefficients of
  friction, respectively, between B and P . Under
  our assumptions of uniform density, the relevant
  calculations are straightforward. If µs tan(),
  then no motion results du, to static friction,
  otherwise B moves under the force of gravity and
  friction. he If gt - tan-1 l then the block
  tumbles down the incline we assert that this is
  not the case. 2 The normal component of the
  contact force, Fn , is given by Fn MB g
  cos(), and the frictional component, Fk , by Fk
  MB g µk cos(). B then slides down P along
  path C until enough of it hangs over the edge of
  P for it to begin to rotate.

57
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Let us call this phase of sliding initiation.
  Initiation is governed by Newton's 2nd Law
  applied in the direction x, with the positive
  direction pointing straight down P F
• x
• MB g sin() - MB g µk cos() MB ax
• Fgx - Fk MB ax
• ax g (sin() - µk cos())

58
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• 1 If the plane has length D in the x
  direction, B slides a distance of D - 2 (l h
  tan()) straight down the plane, after which it
  begins to pivot about the edge of the plane. Let
  us call this edge e. Calculation of its velocity
  v at this time can be simplified via conservation
  of energy C 1 F dr -P Eg - WF MB v2 K E
  k 2 D 1 MB g H - MB g µk - (l cos() h
  sin()) 2 2 T D 1 v g - (l cos() h sin()) H -
  µk 2

59
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Thus far, our equations have dealt with
  constants. In this phase (angular velocity) is
  determined. Accordingly, we call it
  glide-rotation. During glide-rotation, critical
  variables that govern the movement of B , such as
  Ie and Te , the moment of interia and torque
  about e respectively, are functions of the
  position of B itself. Let eo denote the axis
  parallel to e that passes through the 3-D center
  of B . The calculation of the moment of intertia
  of B about eo is straightforward Ieo V r dm
• 2
• 2 -l 2

60
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• h2 l2 h2 l2 MB 12 12 , h2 2 l 2 The
  parallel axis theorem yields Ie MB where r is
  the distance between e and 12 r eo . Torque is
  given by Te MB g x , where x is the horizontal
  displacement of the center of the block past e.
  The torque equation then gives us e T Te Ie
  dhl MB g x MB d dt Where x cos( ) r 2 l
  -h 2 h2 0 d x2 y2 dz dy dx

61
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• g x
• h2 l 2 12 h2 l2 r2 12
• d dt r2 .
• A central calculation of determines the - h2 4
  sin( ) h and 2 3

62
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• torque due to the contact force between B and P ,
  which in turn yields Fn e T TF TFn Ieo k
  o Fn µ kh 2 r h2 2- 4
• MB h2 l2 12 g x h2 l 2 12 T
• Fn r2 MB g x - h2 4 µ h k2 r 2 1 12r 2
  h2 l 2
• This set of implicit differential equations is
  much too difficult to resolve by elementary
  methods, and thus requires a computational model.
  he observant reader will surely notice that the
  theoretical T
• h µ2 1
• k equation for Fn is asymptotic as r . This
  anomaly is the result of a

63
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• theoretical Newtonian 2 decomposition that is
  invalid as the direction of the combined contact
  force approaches that of r. A graph of the normal
  force reveals that the interval of gravely
  affected r is rather slim hence, it will be
  reasonable patch this anomaly by assuming a
  constant force until our equation is valid again.
  Furthermore, we assume that contact between B and
  any slots is by nature a rigid-body collision in
  which the slots are fixed and infinitely massive.
  Moreover, we assume a constant elasticity E 0,
  1 for all of the collisions. Let r, po , p, i ,
  and vi denote the vector pointing from the center
  of B to the parcel of B in the collision, a unit
  vector in the direction of the impulse delivered,
  the impulse delivered, the initial angular
  rotation and velocity of B .

64
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• By our hypotheses, 1 1 1 2 2 2 E 2 MB vf 2
  1 Io f . Now, 2 MB vi 2 Io i 2 r po d
  signedmagnitude Io f i pd v v 2 2 1 p
  1 p 1 1 2 2 E pox iy poy MB vi Io i
  MB Io (i pd )2 ix 2 2 2 MB MB 2 1 122 1 1
  p2 2 0 p (vi po ) Io i d p Io d
  p (1 - E ) MB vi 2 Io i 2 MB 2 2 2 ( (
  1 -(vi po Io i d ) vi po Io i d )2 - 2
  MB Io d2 1 - E )Ei p 1 2 MB Io d

65
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• 1 2 where Ei is the initial energy 2 MB vi 2
  1 Io i and vi po vix pox viy poy . We
  choose 2 because as E 1- , the
  expression with - tends to 0. (Recall, for
  instance, that vi po is always negative.) Of
  course, the fixed elasticity opens the
  possibility that p is computed to be imaginary.
  For such instances, we adopt the convention of
  perfect elasticity, which is uniquely determined
  by computing p with E 1. The crux of my pro
  ject is to create and refine this model to the
  degree that I can predict the that will result
  when B is released from the top of P . Hopefully,
  there will be a high enough degree of sensitivity
  to the dimensions of B that I will be able to
  sort good and bad pieces based on the variation
  in .

66
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Computational Mo deling In order to separate the
  model itself from the input and graphics
  implementation, the source has been partitioned
  into three files
• 1. PhysModel.cpp - The body that contains most of
  the physics equations and graphics routines to
  render the set up.
• 2. Parse.cpp - The file which takes the command
  line input, defaulting unassigned variables to
  the previous run via an intermediary storage
  file.
• 3. Polygon.cpp - The source that defines general
  graphics functions, the structs Polygon and
  Vertex, and several polygonal intersection
  routines.

67
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• The fundamental hypothesis of this pro ject is
  the assumption that the complicated motion of the
  block can be modeled as a discrete set of
  equations repeatedly propagated through a small
  time step. The goal, then, is to apply such
  modeling techniques to a system that is hopefully
  sufficiently complicated as to exhibit a high
  degree of sensitivity to independent variables
  such as height and length. Implementation begins
  with calls to several initialization routines.
  The first call interprets the command line input.

68
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• From the command line, independent variables can
  be assigned by appending the word
  "VariableNameValue" to the end of the command
  line call. Graphics and a number of debugging
  flags can be assigned via the word "-flags".
  (Graphics, for example, is the flag "g", which
  then propagates as GFX1.) Then the Sine, Cosine,
  Tangent, and Sqrt look-up tables are calculated.
  By precomputing the values of sine, cosine,
  tangent, and square root at millions of points,
  we can effectively negate the cost-expensiveness
  of computationally expense Taylor series
  calculations without intolerable loss of
  precision. Indeed, a brief scan of direct
  comparison indicates accuracy to roughly 6
  correct decimal places.

69
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Implementation continues with a call to display,
  which serves to manage thousands of repeated
  calls to Model, in which the independent
  variables of length, height, and the position of
  the rightmost slot-block are minimally altered.
  The values returned are tabulated in the file
  specified by the ofstream DAT. The variable
  ANOMALOUS is a global that keeps track of the
  validity of the computed outcome the block being
  either or rejected by the slot. The potential
  loss of validity is a function of the theoretical
  assumptions that we have made which are not
  necessarily valid.

70
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Some potential errors and mitigating devices I
  have used to address them include Error induced
  by Eulerian time discretization. Because of the
  complex nature of the system, it is difficult to
  determine precisely how this affects accuracy.
  The runs I have conducted on a typical PC use
  what appears to be a small time step between one
  and three hundredths of a second. Perfectly
  rigid collision. As we shall see, there is a
  small tolerance built into impulse function which
  governs this collision. Look-up table error as
  mentioned, calculated sufficiently many times,
  this error can be reduced to on the order of 1
  part in 1,000,000. Implementation continues to
  the model itself.

71
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• A few qualitative comparisons are conducted.
  Static friction must meet or exceed kinetic
  friction, but must not be so great as to prevent
  any motion at all. Moreover, the assumption that
  block-plane contact remains face-to-face
  throughout initiation asserts a simple
  trigonometric relation. Finally, if the block is
  simply too large to fit through the slot, the
  rejection is categorically recorded as a
  rejection with zero anomaly. After the said
  preconditioning, the model simulates the
  triphasic experiment in three consecutive loops.
  checking its center with a set of horizontal and
  vertical thresholds. Model returns 0 for a
  rejection and a 1 for acceptance.

72
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• The variable IPS is employed in conjunction with
  SDL DELAY to add sufficient artificial delay so
  as to obtain the desired number of iterations per
  second. The delay function itself takes only
  integer arguments thus, all values of IPS in
  excess of 1000 are equivalent. Otherwise, the
  loops are governed by a discrete version of the
  physics described in detail above. The Collision
  function returns whether or not the block
  overlaps with any of the slot polygons, assigning
  to every edge of each shape the number of other
  edges it intersects with.

73
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Upon return to the base loop making the call, the
  program calls impulse to handle the relevant
  impulse transfer. impulse runs time forwards and
  backwards with progressively smaller time steps
  until it has precisely determined when the said
  collision occurred. Again, we have employed a
  calculational technique to lower the number of
  computations necessary while maintaining high
  precision. The function then computes under the
  standard two-dimensional Newtonian dichotomy
• 1. Either a corner of the block has protruded
  over an edge of a slot-block, or
• 2. A corner of a slot-block has protruded over an
  edge of the block.

74
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• That is, it assumes that we do not have the
  scenario where two corners mutually protrude over
  one another. The above physics equations are then
  applied. The direction of the frictional
  component is determined via a sequence of vector
  calculations. The normal component is then scaled
  according to COLFRICOF, the fixed coefficient of
  friction for these impacts, and impulse is
  delivered. The potential error is of the block
  rotating partially into the slot-block due to its
  rigidity. A small fraction of the collisions
  result in this anomalous motion hence, the
  resultant motion is checked by another loop
  governed by the Collision function. If at least
  one iteration is spent with such positioning, the
  current iteration is flagged with an anomaly
  value of 2. If too many such iterations occur, a
  value of 4 is used instead.

75
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• Finally, the acceptance / rejection of the block
  is determined by checking its center with a set
  of horizontal and vertical thresholds. Model
  returns 0 for a rejection and a 1 for acceptance.
• Conclusion
• In converting the records of the trials into
  images for a cursory and qualitative analysis, it
  becomes clear that the sensitivity obeys a
  semi-chaotic decay. Green pixels are plotted for
  trials resulting in acceptance and black is
  plotted for rejection. Anomalous cases are those
  appearing in red. Here we refer to the parameters
  of the subsequent image.

76
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• For this particular image, the horizontal scale
  is one pixel equal to one millimeter in block
  variance, with the base value being plotted in
  the leftmost column and increased with each pixel
  to right. Vertically, one pixel is a half of a
  centimeter in slotwidth flux, with the initial
  value at the top and increases in slotwidth with
  each pixel down. The base block is one meter long
  and half a meter in height. The image itself
  actually consists of two sensitivity tests - the
  top half corresponds to flux in length, with the
  bottom depicting sensitivity to increases in
  height. Small, discrete regions of acceptance are
  visible.

77
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• This exploratory experiment seems to indicate
  that the setup can be manipulated to exact
  sensitivities of at least one part in one
  hundred. Moreover, there is nothing to confine
  the application of this methodology to simply one
  slot. Though we do not review a precise analytic
  treatment here, it is readily apparent that an
  additional venue of selection would be the use
  several ramps and slots.

78
A Case Study A Self-Propagating Continuous
Differential System as Limiting Discrete
Numerical Construct and Device of SortingThomas
Mildorf.

• In conclusion, further refinement in this method
  of sorting appears to be possible.
• Appendix A - Code
• For completeness, the three source files
  PhysModel.cpp, Parse.cpp, and Polygon.cpp are
  reproduced here. PhysMo del.cpp include include
  include include include include include
  include ltstdlib.hgt ltSDL/SDL.hgt ltGL/glut.hgt
  ltiostreamgt ltmath.hgt ltfstreamgt "Polygon.cpp"
  "Parse.cpp"

79
Modeling Atmosperic ChangeMy goal is to create
a model of the atmosphere over time, predicting
its strength given the increasing amount of
pollution as well as the controversial but
effective Montreal Protocol. Many projects are in
place to save the ozone, and this model will
assist in assessing the impact of anti-pollution
movements and determine the longterm possible
outcome given many parameters. This model
features usercontrolled variables, allowing the
user to manipulate the year, solar flux, and
existence of anti-pollution projects.
79
80
Graphical Modeling of Atmospheric ChangeCarey
Russell

• 1. Abstract The goal is to create a model of the
  atmosphere over time, predicting it's strength
  given the increasing (and in this case, user
  controlled) amount of pollutants like greenhouse
  gases. Many projects are in place to save the
  ozone, and this model will assist in assessing
  the impact of antipollution movements and
  determine the long-term possible outcome giving
  the many and flexing parameters.
• 2. Background
• 2.1 The Ozone
• Ozone, a feared word in the media, is essential
  to life on Earth. Averaging about three molecules
  per ten million, O3 is very rare, representing a
  minute fraction of atmospheric composition.
  Nearly 90 of all ozone is found in the
  stratosphere, the atmospheric layer between 10
  and 40 km above the Earth's surface, where it
  shields the surface from ultra-violet radiation
  (UV-B).

81
Graphical Modeling of Atmospheric ChangeCarey
Russell

• Ozone filters out the high energy radiation below
  0.29 mircrometers, allowing only a small amount
  to reach the Earth's surface. Strongest at about
  25 km altitude, this layer is known as the ozone
  layer damages to this layer result in subsequent
  increases in UV-B radiation and risks of eye
  damage, skin cancer, and adverse effects on
  marine and plant life. 2.2 The Hole In the
  1980's, scientists noticed a noticeable and
  dramatic increase in the amount of UV-B reaching
  the surface. At first, they began to suspect and
  then detect a steady thinning of the ozone layer.
  Scientific concern morphed into public alarm when
  the British Antarctic Survey announced the
  detection of the first Antarctic 'hole' in 1985.

82
Graphical Modeling of Atmospheric ChangeCarey
Russell

• In truth, this ozone 'hole' is not a gap in the
  ozone layer at all merely, it is a sharp decline
  in the stratospheric ozone concentrations over
  most of Antarctica for several months during the
  southern hemisphere spring. Continued research
  revealed and satellite data recorded depleting
  ozone levels over Antarctica growing worse with
  each passing year.

83
Graphical Modeling of Atmospheric ChangeCarey
Russell

• 1985 Antarctic Hole 2003 Antarctic Hole
• http//www.ucar.edu/communications/atmosphere-time
  line.html http//www.noaanews.noaa.gov/stories/s20
  99.htm
• Research now shows that the ozone layer over
  Antarctica thins to 55-44 of its pre-1980s
  level. The result is up to a 70 deficiency for
  short time periods, and at some altitudes, ozone
  destruction is practically total. The picture
  above to the right shows the current satellite
  images of the ozone hole, now more than two and a
  half times the size of Europe.

84
Graphical Modeling of Atmospheric ChangeCarey
Russell

• possibility that CFCs could lead to serious ozone
  decomposition, policy makers worldwide signed the
  Montreal Protocol treaty in 1987. In brief, this
  protocol limits CFC production and usage. By
  1992, ozone loss was continuing to increase
  exponentially. These evidence prompted leaders to
  strengthen the Montreal Protocol. The revision
  called for a complete phase out of CFC production
  in industrialized countries by 1996.
• http//www.eohandbook.com/ceos/part2e.html

85
Graphical Modeling of Atmospheric ChangeCarey
Russell

• 3.3 The Result
• As a result, most CFC concentrations are
  decreasing around the globe. Production in
  developed countries has fallen by 95. Current
  research suggest that the Montreal Protocol is
  working relatively effectively. The abundance of
  CFCs and other ozone-depleting substances in the
  lower atmosphere peaked in 1994 and has now begun
  to decline. There is a key distinction, however
  the rate of atmospheric destruction is now
  decreasing. Many people translate this to mean
  that the atmosphere is repairing itself, but
  unfortunately, merely the rate of decomposition
  is decreasing not the amount of decomposition
  itself. On the positive, resulting from the
  Montreal Protocol, the ozone layer is expected to
  recover gradually over the next 50 years.

86
Graphical Modeling of Atmospheric ChangeCarey
Russell

• 4. Materials and Apparatus 4.1 The Software
  (NetLogo)
• NetLogo began with StarLogo. It's the next in the
  generation of multi-agent model languages,
  building "off the functionality of the major
  product StarLogoT, and adds significant new
  features and a redesigned language and user
  interface." So in summary, NetLogo is a modeling
  environment for simulations. It very well suited
  for modeling complex system such as natural or
  social phenomena. Because NetLogo is
  programmable, modelers can give instructions to
  hundreds or thousands of independent agents
  operating simultaneously. This makes it possible
  to discover the connection between individual
  behavior and group patterns. Additionally, it
  lets users open simulation and "play" with them,
  exploring various conditions.
• See References for citation information.

87
Graphical Modeling of Atmospheric ChangeCarey
Russell

• 4.2 NetLogo Details
• The "Net" in NetLogo is "meant to evoke the
  decentralized, interconnected nature of the
  phenomena you can model with NetLogo. It also
  refers to HubNet, the networked participatory
  simulation environment included in NetLogo. The
  'Logo' part is because NetLogo is a dialect of
  the Logo language.

88
Graphical Modeling of Atmospheric ChangeCarey
Russell

• 5. Results/Discussion
• So far, the program has modeled successfully the
  modern day deterioration of the atmosphere. The
  user is able to "switch" on or off the Montreal
  Protocol and see the difference the mere
  existence of the program. Additionally, the user
  can watch the absorption rate and watch as the
  radiation reaches earth. The user is alerted when
  (or if) the radiation reaches dangerous levels.
  The solar flux is considered a constant,
  especially because on such a short time scale
  (through 3500) and the small fluctuations make a
  mediocre difference in the overall radiation to
  earth. Next on the to-do list is continued
  research into the inter-workings of the
  atmosphere. I plan to expand on the time scale,
  and allow for atmospheric regeneration, which is
  expected (although not currently observable).

89
Graphical Modeling of Atmospheric ChangeCarey
Russell

• Also, so far the user cannot change the amount of
  incoming radiation because (as stated above) the
  solar flux has been defined as constant. However,
  soon the ability to manipulate the IR flux will
  be added. A necessary complexity in the coding is
  allowing for the release of radiation emitted
  back from earth, which as of current is left
  unattended.
• 6. References/Appendixes Much credit goes to
  Netlogo, and the National Wildlife Association
  for posting so many articles concerning the
  future of the ozone. The Montreal Protocol is my
  guide for regeneration programs.

90
Genetic Algorithms and MusicGenetic algorithms
use feedback resulting from evaluating data sets
to optimize these data sets for the best
performance as defined by the user. The main
dataprocessing is done in LISP. The creation of
audio files is done using Csound.
90
91
An Investigation of Genetic Algorithms Using
Audio OutputMatthew Thompson

• Abstract
• This paper documents my work of researching and
  testing genetic algorithms.
• 1 Introduction
• Genetic algorithms use feedback resulting from
  evaluating data sets to optimize these data sets
  for optimum performance, where optimum
  performance is defined by the user. The main data
  processing is done in LISP. The program has a
  simple shell script as its frontend. CSound is
  used to convert the data sets to audio files,
  which are heard and evaluated by the user.

92
An Investigation of Genetic Algorithms Using
Audio OutputMatthew Thompson

• 2 Research
• The first area of research was into various forms
  of genetic algorithms1. Topics covered included
  different methods of storing data, such as in a
  tree, list, or array. In a tree, mutation
  operators include subtree destructive, node swap,
  and subtree swap, and a single point subtree
  exchange as a crossover method. In a list,
  mutations can be generative, destructive, element
  flip, node swap, or sequence swap, and crossover
  can be single point or order based. In an array,
  mutations can be destructive, element flips, or
  element swaps, and crossovers can be single point
  or variable length.

93
An Investigation of Genetic Algorithms Using
Audio OutputMatthew Thompson

• The second area of research was into music
  theory, to ensure that the program would, even
  with random data, produce something that sounded
  decent. To do this, I wrote the program such that
  a melody will stay on key, and used a hash table
  of notes and frequencies2 to accomplish this.

94
An Investigation of Genetic Algorithms Using
Audio OutputMatthew Thompson

• 3 Program Development
• The initial program was made to store data in
  lists, mutate using element flips, and crossover
  being single point. I used this type of genetic
  algorithm because at the time of starting the pro
  ject, it was the type of genetic algorithm with
  which I was most familiar. After finishing a
  simple score processing function that would turn
  a list of numbers into a usable audio file, I
  integrated this with the genetic algorithm code
  so that the algorithm's evaluation function was
  user input telling what the user thought of the
  melody a specific population member created.
  Melodies were rated on a scale of 1 to 9, with
  higher numbers indicating a stronger like of the
  melody. A shell script was written to serve as a
  frontend for the algorithm.

95
An Investigation of Genetic Algorithms Using
Audio OutputMatthew Thompson

• 4 Program Testing
• Testing of the program involved running it over
  repeated trials, using different data storage,
  mutation, and crossover methods, and observing
  trends in the improvement of the melodies created
  by the program.

96
An Investigation of Genetic Algorithms Using
Audio OutputMatthew Thompson

• References
• 1 Intro to Genetic Algorithms
  http//lancet.mit.edu/ mbwall/presentations/IntroT
  oGAs/index.html
• 2 Frequencies of Musical Notes
  http//www.phy.mtu.edu/ suits/notefreqs.html

97
Modeling a Saturnian MoonThis project hopes to
add to our understanding of space systems by
providing a comprehensive simulation of the
Saturnian moon system. By doing this, this
project attempts to expose what phenomena can't
be explained with modern models and perhaps
suggest theories to explain the unexplained.
97
98
Space System Modeling Saturnian Moons Justin
Winkler

• Abstract
• The Saturnian moon system is home to many
  fascinating and unusual astronomical phenomena.
  For example, Epimetheus and Janus share orbits
  and exchange momentum every four years. Hyperion
  has chaotic rotation. Our understanding of these
  phenomena, however, is unfortunately limited.
  This project hopes to add to our understanding of
  space systems by providing a comprehensive
  simulation of the Saturnian moon system. By doing
  this, this project attempts to expose what
  phenomena can't be explained with modern models
  and perhaps suggest theories to explain the
  unexplained.

99
Space System Modeling Saturnian Moons Justin
Winkler

• Introduction
• This project focuses on the modeling of complex
  space systems. A problem with the realm of
  modeling is that there are nearly always
  discrepancies in our explanations of certain
  phenomena. The purpose of this project is to
  create a simulation of the Saturnian moon system
  in hopes of better understanding unexplained
  occurrences within the system. This project
  therefore aims to reveal phenomena which current
  models do not explain, and possibly offer
  explanations of such phenomena. The scope of this
  project is limited only by time and computer
  resources.

100
Space System Modeling Saturnian Moons Justin
Winkler

• By adding more para