Modeling and Simulation in Python

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Software
CHAPTER 1: Introduction
CHAPTER 2: Random Values
	2.1. DEFINING RANDOM
	2.2. REPLICATING RANDOM SEQUENCES
	2.3. BIAS AND OFFSET
	2.4. OTHER TYPES OF RANDOM VALUES
	2.5. ALTERNATE DISTRIBUTIONS
	2.6. CONFIRMING RANDOMNESS
	2.7. SUMMARY
CHAPTER 3: Application of Random Values
	3.1. THE CARD GAME NAMED WAR
	3.2. PYTHON IMPLEMENTATION
	3.3. ALTERATIONS
		3.3.1. One Ace
		3.3.2. Four Aces
	3.4. SUMMARY
CHAPTER 4: The Monte Carlo Method
	4.1. RANDOM VECTORS
	4.2. ROLLING DICE
	4.3. THE MONTE CARLO METHOD
		4.3.1. Horizontal Barrier
		4.3.2. Slanted Barrier
		4.3.3. Integration
		4.3.4. Square
		4.3.5. Estimation of ˇ
	4.4. HYPER-DIMENSIONAL BALL
	4.5. PROPER SAMPLING
	4.6. ESTIMATING THE AREA OF A STAR
		4.6.1. Geometric Properties
		4.6.2. Theoretic Ratio
		4.6.3. Monte Carlo Estimate of the Star Area Ratio
			4.6.3.1. Determining Side of Line
			4.6.3.2. Python Script for Side of Line
	4.7. UNEQUAL DISTRIBUTIONS
	4.8. SUMMARY
CHAPTER 5: Modeling Self-Organization
	5.1. SCHELLING’S MODEL
	5.2. MODELING IN PYTHON
	5.3. TRIALS
	5.4. ALTERATIONS TO THE ALGORITHM
	5.5. SUMMARY
CHAPTER 6: Hidden Markov Models
	6.1. AN EMISSION HMM
	6.2. A TRANSITION HMM
		6.2.1. Data Structures for the Transition HMM
		6.2.2. Constructing a Transition HMM
	6.3. A RECURRENT HMM
	6.4. CONSIDERATIONS
		6.4.1. Assuming Data
		6.4.2. Spurious Strings
		6.4.3. Recurrent Probabilities
	6.5. SUMMARY
CHAPTER 7: Identification of Start Codons
	7.1. BRIEF BIOLOGICAL BACKGROUND
	7.2. IMPLEMENTATION INTO PYTHON
		7.2.1. Data
		7.2.2. Probabilities and Log Odds
		7.2.3. Building the Matrices
		7.2.4. A Query
		7.2.5. Testing Queries
	7.3. SUMMARY
CHAPTER 8: HMM Application in Baseball
	8.1. JUST ENOUGH BASEBALL
	8.2. BASEBALL HMM
	8.3. GATHERING DATA
	8.4. COUNTING EVENTS
	8.5. CREATING THE TRANSITION HMM
	8.6. ANALYSIS
		8.6.1. The User-Selected Inning
		8.6.2. Rarest Transition
		8.6.3. Unusual Inning
	8.7. SUMMARY
CHAPTER 9: Hidden Shakespeare Model
	9.1. BUILDING THE HMM
	9.2. CREATING NEW STRINGS
	9.3. DISCOVERING A NEW SHAKESPEARE
	9.4. STRUCTURE
	9.5. MIDSUMMER MADNESS
	9.6. SUMMARY
CHAPTER 10: Connected Data
	10.1. MOVIES DATABASE
	10.2. PYTHON QUERIES
	10.3. CONNECTIONS
	10.4. FLOYD-WARSHALL ALGORITHM
		10.4.1. The B and P Matrices
		10.4.2. Creating the G and P Matrices
		10.4.3. Creating the Matrices in Python
		10.4.4. Finding the Shortest Path
	10.5. APPLICATION OF FLOYD-WARSHALL TO ACTORS
	10.6. BEYOND CONNECTIONS
	10.7. SUMMARY
CHAPTER 11: Gene Expression Arrays
	11.1. THE DATA
	11.2. READING THE SPREADSHEET
	11.3. PROTOCOL
		11.3.1. Background Subtraction
		11.3.2. Ratios and Intensities
		11.3.3. M and A
		11.3.4. LOWESS
	11.4. MULTIPLE FILES
	11.5. SIMPLE ANALYSIS
	11.6. SUMMARY
CHAPTER 12: Simultaneous Equations
	12.1. A LINEAR ALGEBRA APPROACH
	12.2. IMPLEMENTATION INTO PYTHON
	12.3. LIMITS OF COMPUTATION
		12.3.1. Matrix Inversion Precision
		12.3.2. Singularity
	12.4. WORD PROBLEMS
		12.4.1. Amusement Park Fees
		12.4.2. Traffic Flow
	12.5. APPLICATION TO KIRCHHOFF’S LAWS
		12.5.1. The Junction Rule
		12.5.2. The Loop Rule
		12.5.3. Creating the Equations
		12.5.4. Computing the Currents
	12.6. SUMMARY
CHAPTER 13: Simulations of Motion
	13.1. LINEAR MOTION
	13.2. CAR CRASH
	13.3. ACCELERATED MOTION
	13.4. VERTICAL MOTION
		13.4.1. Going Up
		13.4.2. Going Down
		13.4.3. Going Up and Down
	13.5. PROJECTILE MOTION
	13.6. ENERGIES
		13.6.1. Example 1
		13.6.2. Example 2
	13.7. AIM POINT FOR A FALLING OBJECT
		13.7.1. Define the Variables
		13.7.2. Point the Gun
		13.7.3. Paintball Velocity
		13.7.4. Time of Flight
		13.7.5. Heights of Objects
	13.8. ROCKET TEST
		13.8.1. Creating the Simulation
		13.8.2. Finding Correct Parameters
	13.9. SUMMARY
CHAPTER 14: Oscillations
	14.1. SPRING THEORY
	14.2. SPRING SIMULATION
	14.3. CORRECTED SIMULATION
		14.3.1. Average Acceleration
		14.3.2. The Leapfrog Method
	14.4. THE PENDULUM
	14.5. SUMMARY
CHAPTER 15: Coupled Differential Equations
	15.1. SIMPLE EXAMPLE
	15.2. TWO VARIABLES DEPENDENT ON TIME
	15.3. DEPENDENT EQUATIONS
	15.4. COUPLED EQUATIONS
	15.5. HIV SIMULATION
	15.6. THE SPRING MODEL
		15.6.1. The Spring Model without Friction
		15.6.2. The Spring Model with Friction
		15.6.3. A Forced System
	15.7. COUPLED SPRINGS
	15.8. SUMMARY
CHAPTER 16: Extraordinary Number of Solutions
	16.1. THE GAME
	16.2. BUILDING A SOLUTION
		16.2.1. Cell Identities
		16.2.2. Cell Representation
		16.2.3. Puzzle Architecture
		16.2.4. Creating a Puzzle
		16.2.5. Presenting a Puzzle
		16.2.6. Rule 1
		16.2.7. Rule 2
	16.3. ALTERNATE PUZZLE ARCHITECTURES
		16.3.1. Larger Puzzles
		16.3.2. Jigsaw Sudoku Puzzles
		16.3.3. Rule 3
	16.4. CREATING GAMES
		16.4.1. Creating a Solved Puzzle
		16.4.2. The Trivial Solution
		16.4.3. Modifications to the Trivial Solution
		16.4.4. Paring the Puzzle
	16.5. SUMMARY
CHAPTER 17: Agent Based Modeling − Virus Spread
	17.1. THE ABM MODEL
		17.1.1. Movement
		17.1.2. Agent Collision
		17.1.3. An Example
		17.1.4. Alternate Computation
	17.2. IMPLEMENTATION IN PYTHON
		17.2.1. Agents as Objects
		17.2.2. Iterations
		17.2.3. Altering the Simulation
	17.3. SPEED OF COMPUTATION
	17.4. SUMMARY
CHAPTER 18: Chess
	18.1. THEORY
	18.2. IMPLEMENTATION
		18.2.1. Piece Values
		18.2.2. Creating the Board
		18.2.3. Moving
		18.2.4. Individual Pieces
		18.2.5. Assigning a Score to the State of the Game
			18.2.5.1. Piece Values
			18.2.5.2. Board Control
			18.2.5.3. Pieces in Peril
			18.2.5.4. Combining Scores
	18.3. PLAYING THE GAME
		18.3.1. Move Selection
		18.3.2. Improving the Performance
	18.4. SUMMARY
Bibliography
Index