Introduction to Computer Science

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??????? Introduction to Computer Science
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Simulation and Modeling (?????)
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Objectives

• In this class, you will learn about
• Computational modeling
• Running the model and visualizing results

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Introduction

• Simulation and modeling
• Probably the single most important scientific use
  of computing today
• Having an impact on quantitative fields, such as
  chemistry, biology, medicine, meteorology,
  ecology, geography, economics, and so on

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Computational Modeling Introduction to Systems
and Models

• The scientific method
• Observe the behavior of a system
• Formulate a hypothesis about system behavior
• Design and carry out experiments to prove or
  disprove the validity of the hypothesis
• Often a model of the system is used

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Introduction to Systems and Models (continued)

• A model
• An abstraction of the system being studied that
  we claim behaves much like the original
• Computer simulation
• A physical system is modeled as a set of
  mathematical equations and/or algorithmic
  procedures

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Introduction to Systems and Models (continued)

• Computer simulation (continued)
• Model is translated into a high-level language
  and executed on the Von Neumann computer
• Computational models
• Also called simulation models
• Used to
• Design new systems
• Study and improve the behavior of existing systems

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Introduction to Systems and Models (continued)

• Computational models (continued)
• Allow the use of an interactive design
  methodology (sometimes called computational
  steering)
• Used in most branches of science and engineering

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Figure 12.1 Using a Simulation in an Interactive
Design Environment
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Computational Models, Accuracy, and Errors

• Proper balance between accuracy and complexity
  must be achieved
• A model must be both
• An accurate representation of the physical system
• Simple enough to implement as a program and solve
  on a computer in a reasonable amount of time

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Computational Models, Accuracy, and Errors
(continued)

• To build a model
• Include important factors that act on the system
• Omit unimportant factors that only make the model
  harder to build, understand, and solve

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Computational Models, Accuracy, and Errors
(continued)

• Continuous model
• A set of equations that describe the behavior of
  a system as a continuous function of time t
• Models that use statistical approximations
• Needed for systems that cannot be modeled using
  precise mathematical equations

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An Example of Model Building

• Discrete event simulation
• One of the most popular and widely used
  techniques for building computer models
• The behavior of a system is modeled only at an
  explicit and finite set of times
• Only the times when an event takes place are
  modeled
• Event An activity that changes the state of the
  system

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An Example of Model Building (continued)

• To process an event
• Change the state of the simulated system in the
  same way that the actual system would change if
  the event had occurred in real life
• Once finished, move to the next event
• When simulation is complete, the program displays
  results that characterize the systems behavior

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Example Models

• Coin Flipping Example
• Conways Game of Life Example
• Opening a restaurant Example

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Conways Game of Life

• Von Neumann wondered if it was possible for a
  machine to build copies of itself
• Conway created a simple zero-person game that is
  a complete von-neumann machine.
• Game is played on a grid

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Conways Game of Life
Any live cell with lt 2 live Neighbors dies
(loneliness) Any live cell with gt 3
live Neighbors dies (overcrowding) Any live
cell with 2 or 3 live Neighbors continues
living Any empty cell with exactly 3 live
neighbors comes alive (birth)















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Is it Possible?

• Create an initial condition that does not change
  from generation to generation?
• Create an initial condition that oscillates from
  generation to generation?
• Create an initial condition that moves through
  space from generation to generation?

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What additional Hypotheses?

• Will all initial conditions eventually
• All die out?
• Reach some stable state (no changes)?
• Reach some state of oscillation?
• Is it possible to make an initial state that will
  grow indefinitely?
• Is it possible to make an initial state that will
  create copies of itself?

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An Example of Model Building (Restaurant)

• Problem
• You are the owner of a new take-out restaurant,
  McBurgers, currently under construction
• You want to determine the proper number of
  checkout stations needed
• You decide to build a model of McBurgers to
  determine the optimal number of servers

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• Figure 12.3
• System to Be Modeled

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An Example of Model Building (continued)

• First Identify the events that can change the
  system
• A new customer arriving
• An existing customer departing after receiving
  food and paying
• Next Develop an algorithm for each event
• Should describe exactly what happens to the
  system when this event occurs

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• Figure 12.4
• Algorithm for New Customer Arrival

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An Example of Model Building (continued)

• The algorithm for the new customer arrival event
  uses a statistical distribution (Figure 12.5) to
  determine the time required to service the
  customer
• Can model the statistical distribution of
  customer service time using the algorithm in
  Figure 12.6

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• Statistical Distribution of Customer Service Time

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• Figure 12.6
• Algorithm for Generating Random Numbers That
  Follow the Distribution Given in Figure 12.5

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• Figure 12.7
• Algorithm for Customer Departure Event

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An Example of Model Building (continued)

• Must initialize parameters to the model
• Model must collect data that accurately measures
  performance of the McBurgers restaurant

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An Example of Model Building (continued)

• When simulation is ready, the computer will
• Run the simulation
• Process all M customers
• Print out the results

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• Figure 12.8
• The Main Algorithm of Our Simulation Model

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Running the Model and Visualizing Results

• Scientific visualization
• Visualizing data in a way that highlights its
  important characteristics and simplifies its
  interpretation
• An important part of computational modeling
• Different from computer graphics

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Running the Model and Visualizing Results
(continued)

• Scientific visualization is concerned with
• Data extraction Determine which data values are
  important to display and which are not
• Data manipulation Convert the data to other
  forms or to different units to enhance display

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Running the Model and Visualizing Results
(continued)

• Output of a computer model can be represented
  visually using
• A two-dimensional graph
• A three-dimensional image
• Visual representation of data helps identify
  important features of the models output

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• Figure 12.9
• Using a Two-Dimensional Graph to Display Output

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• Figure 12.10 Using a Two-Dimensional Graph to
  Display and Compare Two Data Values

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• Figure 12.11
• Three-Dimensional Image of a Region of the
  Earths Surface

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• Figure 12.12
• Three-Dimensional Model of a Methyl Nitrite
  Molecule

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• Figure 12.13
• Visualization of Gas Dispersion

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Running the Model and Visualizing Results
(continued)

• Image animation
• One of the most powerful and useful forms of
  visualization
• Shows how models output changes over time
• Created using many images, each showing system
  state at a slightly later point in time

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• Figure 12.14
• Use of Animation to Model Ozone Layers in the
  Atmosphere

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Summary

• A model is an abstraction of a system that
  behaves much like the original
• Computer simulation
• Physical system is modeled using mathematical
  equations and/or algorithmic procedures
• Model is translated into a high-level language
  program and executed

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Summary (continued)

• Computational models allow the use of an
  interactive design methodology
• Scientific visualization Visualizing data to
  highlight its important characteristics and
  simplify its interpretation