Preface |
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xiii | |
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Chapter 1 Dynamic-System Models And Simulation |
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1 | (30) |
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Simulation Is Experimentation With Models |
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1 | (1) |
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1-1 Simulation and Computer Programs |
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1 | (1) |
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1-2 Dynamic-System Models |
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2 | (1) |
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(a) Difference-Equation Models |
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2 | (1) |
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(b) Differential-Equation Models |
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2 | (1) |
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3 | (1) |
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1-3 Experiment Protocols Define Simulation Studies |
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3 | (1) |
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4 | (1) |
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1-5 Fast Simulation Program for Interactive Modeling |
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5 | (3) |
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Anatomy Of A Simulation Run |
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8 | (1) |
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1-6 Dynamic-System Time Histories Are Sampled Periodically |
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8 | (2) |
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1-7 Numerical Integration |
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10 | (1) |
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10 | (1) |
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(b) Improved Integration Rules |
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10 | (1) |
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1-8 Sampling Times and Integration Steps |
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11 | (1) |
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1-9 Sorting Defined-Variable Assignments |
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12 | (1) |
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Simple Application Programs |
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12 | (1) |
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1-10 Oscillators and Computer Displays |
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12 | (3) |
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12 | (2) |
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(b) Nonlinear Oscillator: Duffing's Differential Equation |
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14 | (1) |
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1-11 Space-Vehicle Orbit Simulation with Variable-Step Integration |
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15 | (2) |
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1-12 Population-Dynamics Model |
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17 | (1) |
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1-13 Splicing Multiple Simulation Runs: Billiard-Ball Simulation |
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17 | (4) |
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Inroduction To Control-System Simulation |
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21 | (1) |
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1-14 Electrical Servomechanism with Motor-Field Delay and Saturation |
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21 | (2) |
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1-15 Control-System Frequency Response |
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23 | (1) |
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1-16 Simulation of a Simple Guided Missile |
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24 | (4) |
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24 | (2) |
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(b) Complete Torpedo-Simulation Program |
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26 | (2) |
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28 | (1) |
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1-17 Simulation in the Real World: A Word of Caution |
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28 | (3) |
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29 | (2) |
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Chapter 2 Models With Difference Equations, Limiters, And Switches |
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31 | (26) |
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Sampled-Data Systems And Difference Equations |
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31 | (1) |
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2-1 Sampled-Data Difference-Equation Systems |
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31 | (1) |
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31 | (1) |
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31 | (1) |
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(c) A Minefield of Possible Errors |
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32 | (1) |
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2-2 Solving Systems of First-Order Difference Equations |
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32 | (3) |
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(a) General Difference-Equation Model |
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32 | (1) |
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(b) Simple Recurrence Relations |
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33 | (2) |
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2-3 Models Combining Differential Equations and Sampled-Data Operations |
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35 | (1) |
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35 | (1) |
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2-5 Initializing and Resetting Sampled-Data Variables |
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35 | (2) |
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Two Mixed Continuous/Sampled-Data Systems |
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37 | (1) |
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2-6 Guided Torpedo with Digital Control |
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37 | (1) |
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2-7 Simulation of a Plant with a Digital PID Controller |
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37 | (3) |
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Dynamic-System Models With Limiters And Switches |
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40 | (1) |
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2-8 Limiters, Switches, and Comparators |
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40 | (3) |
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40 | (2) |
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(b) Switching Functions and Comparators |
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42 | (1) |
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2-9 Integration of Switch and Limiter Outputs, Event Prediction, and Display Problems |
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43 | (1) |
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2-10 Using Sampled-Data Assignments |
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44 | (1) |
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2-11 Using the step Operator and Heuristic Integration-Step Control |
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44 | (1) |
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2-12 Example: Simulation of a Bang-Bang Servomechanism |
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45 | (1) |
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2-13 Limiters, Absolute Values, and Maximum/Minimum Selection |
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46 | (1) |
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2-14 Output-Limited Integration |
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47 | (1) |
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2-15 Modeling Signal Quantization |
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48 | (1) |
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Efficient Device Models Using Recursive Assignments |
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48 | (1) |
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2-16 Recursive Switching and Limiter Operations |
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48 | (1) |
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2-17 Track/Hold Simulation |
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49 | (1) |
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2-18 Maximum-Value and Minimum-Value Holding |
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50 | (1) |
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2-19 Simple Backlash and Hysteresis Models |
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51 | (1) |
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2-20 Comparator with Hysteresis (Schmitt Trigger) |
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52 | (1) |
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2-21 Signal Generators and Signal Modulation |
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53 | (4) |
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55 | (2) |
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Chapter 3 Fast Vector-Matrix Operations And Submodels |
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57 | (20) |
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Arrays, Vectors, And Matrices |
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57 | (1) |
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3-1 Arrays and Subscripted Variables |
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57 | (1) |
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57 | (1) |
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(b) Array Declarations, Vectors, and Matrices |
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57 | (1) |
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(c) State-Variable Declarations |
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58 | (1) |
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3-2 Vector and Matrices in Experiment Protocols |
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58 | (1) |
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58 | (1) |
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Vectors And Model Replication |
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59 | (1) |
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3-4 Vector Operations in DYNAMIC Program Segments: The Vectorizing Compiler |
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59 | (2) |
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(a) Vector Assignments and Vector Expressions |
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59 | (1) |
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(b) Vector Differential Equations |
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60 | (1) |
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(c) Vector Sampled-Data Assignments and Difference Equations |
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60 | (1) |
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3-5 Matrix-Vector Products in Vector Expressions |
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61 | (2) |
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61 | (1) |
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(b) Simple Example: Resonating Oscillators |
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61 | (2) |
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3-6 Index-Shift Operation |
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63 | (1) |
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63 | (1) |
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(b) Preview of Significant Applications |
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63 | (1) |
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3-7 Sorting Vector and Subscripted-Variable Assignments |
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64 | (1) |
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3-8 Replication of Dynamic-System Models |
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64 | (1) |
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65 | (1) |
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3-9 Sums, DOT Products, and Vector Norms |
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65 | (1) |
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(a) Sums and DOT Products |
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65 | (1) |
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(b) Euclidean, Taxicab, and Hamming Norms |
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65 | (1) |
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3-10 Maximum/Minimum Selection and Masking |
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66 | (1) |
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(a) Maximum/Minimum Selection |
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66 | (1) |
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(b) Masking Vector Expressions |
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66 | (1) |
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Vector Equivalence Declarations Simplify Models |
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67 | (1) |
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67 | (1) |
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3-12 Matrix-Vector Equivalence |
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67 | (1) |
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Matrix Operations In Dynamic-System Models |
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67 | (1) |
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3-13 Simple Matrix Assignments |
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67 | (1) |
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3-14 Two-Dimensional Model Replication |
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68 | (1) |
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(a) Matrix Expressions and DOT Products |
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68 | (1) |
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(b) Matrix Differential Equations |
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68 | (1) |
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(c) Matrix Difference Equations |
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69 | (1) |
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Vectors In Physics And Control-System Problems |
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69 | (1) |
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3-15 Vectors in Physics Problems |
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69 | (1) |
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3-16 Vector Model of a Nuclear Reactor |
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69 | (1) |
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3-17 Linear Transformations and Rotation Matrices |
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70 | (2) |
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3-18 State-Equation Models of Linear Control Systems |
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72 | (1) |
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User-Defined Functions And Submodels |
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72 | (1) |
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72 | (1) |
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3-20 User-Defined Functions |
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72 | (1) |
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3-21 Submodel Declaration and Invocation |
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73 | (2) |
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3-22 Dealing with Sampled-Data Assignments, Limiters, and Switches |
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75 | (2) |
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75 | (2) |
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Chapter 4 Efficient Parameter-Influence Studies And Statistics Computation |
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77 | (32) |
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Model Replication Simplifies Parameter-Influence Studies |
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77 | (1) |
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4-1 Exploring the Effects of Parameter Changes |
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77 | (1) |
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4-2 Repeated Simulation Runs Versus Model Replication |
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78 | (2) |
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(a) Simple Repeated-Run Study |
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78 | (1) |
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(b) Model Replication (Vectorization) |
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78 | (2) |
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4-3 Programming Parameter-Influence Studies |
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80 | (4) |
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(a) Measures of System Performance |
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80 | (1) |
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81 | (1) |
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(c) Two-Dimensional Model Replication |
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81 | (1) |
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(d) Cross-Plotting Results |
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82 | (1) |
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(e) Maximum/Minimum Selection |
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83 | (1) |
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(f) Iterative Parameter Optimization |
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83 | (1) |
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84 | (1) |
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4-4 Random Data and Statistics |
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84 | (1) |
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4-5 Sample Averages and Statistical Relative Frequencies |
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85 | (1) |
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Computing Statistics By Vector Averaging |
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85 | (1) |
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4-6 Fast Computation of Sample Averages |
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85 | (1) |
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4-7 Fast Probability Estimation |
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86 | (1) |
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4-8 Fast Probability-Density Estimation |
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86 | (4) |
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(a) Simple Probability-Density Estimate |
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86 | (1) |
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(b) Triangle and Parzen Windows |
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87 | (1) |
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(c) Computation and Display of Parzen-Window Estimates |
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88 | (2) |
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4-9 Sample-Range Estimation |
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90 | (1) |
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Replicated Averages Generate Sampling Distributions |
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91 | (1) |
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4-10 Computing Statistics by Time Averaging |
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91 | (1) |
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4-11 Sample Replication and Sampling-Distribution Statistics |
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91 | (4) |
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91 | (2) |
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(b) Demonstrations of Empirical Laws of Large Numbers |
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93 | (2) |
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(c) Counterexample: Fat-Tailed Distribution |
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95 | (1) |
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Random-Process Simulation |
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95 | (1) |
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4-12 Random Processes and Monte Carlo Simulation |
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95 | (2) |
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4-13 Modeling Random Parameters and Random Initial Values |
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97 | (1) |
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4-14 Sampled-Data Random Processes |
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97 | (1) |
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4-15 "Continuous" Random Processes |
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98 | (2) |
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(a) Modeling Continuous Noise |
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98 | (1) |
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(b) Continuous Time Averaging |
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99 | (1) |
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(c) Correlation Functions and Spectral Densities |
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100 | (1) |
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4-16 Problems with Simulated Noise |
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100 | (1) |
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Simple Monte Carlo Experiments |
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100 | (1) |
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100 | (1) |
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100 | (2) |
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4-19 Vectorized Monte Carlo Study of a Continuous Random Walk |
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102 | (7) |
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106 | (3) |
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Chapter 5 Monte Carlo Simulation Of Real Dynamic Systems |
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109 | (18) |
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109 | (1) |
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109 | (1) |
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Repeated-Run Monte Carlo Simulation |
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109 | (1) |
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5-2 End-of-Run Statistics for Repeated Simulation Runs |
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109 | (1) |
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5-3 Example: Effects of Gun-Elevation Errors on a 1776 Cannnonball Trajectory |
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110 | (3) |
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5-4 Sequential Monte Carlo Simulation |
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113 | (1) |
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Vectorized Monte Carlo Simulation |
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113 | (1) |
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5-5 Vectorized Monte Carlo Simulation of the 1776 Cannon Shot |
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113 | (2) |
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5-6 Combined Vectorized and Repeated-Run Monte Carlo Simulation |
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115 | (1) |
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5-7 Interactive Monte Carlo Simulation: Computing Runtime Histories of Statistics with DYNAMIC-Segment DOT Operations |
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115 | (2) |
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5-8 Example: Torpedo Trajectory Dispersion |
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117 | (2) |
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Simulation Of Noisy Control Systems |
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119 | (1) |
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5-9 Monte Carlo Simulation of a Nonlinear Servomechanism: A Noise-Input Test |
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119 | (2) |
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5-10 Monte Carlo Study of Control-System Errors Caused by Noise |
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121 | (2) |
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123 | (1) |
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5-11 Monte Carlo Optimization |
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123 | (1) |
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5-12 Convenient Heuristic Method for Testing Pseudorandom Noise |
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123 | (1) |
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5-13 Alternative to Monte Carlo Simulation |
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123 | (4) |
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123 | (1) |
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(b) Dynamic Systems with Random Perturbations |
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123 | (1) |
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(c) Mean-Square Errors in Linearized Systems |
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124 | (1) |
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125 | (2) |
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Chapter 6 Vector Models Of Neural Networks |
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127 | (50) |
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Artificial Neural Networks |
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127 | (1) |
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127 | (1) |
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6-2 Artificial Neural Networks |
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127 | (1) |
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6-3 Static Neural Networks: Training, Validation, and Applications |
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128 | (1) |
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6-4 Dynamic Neural Networks |
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129 | (1) |
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Simple Vector Assignments Model Neuron Layers |
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130 | (1) |
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6-5 Neuron-Layer Declarations and Neuron Operations |
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130 | (1) |
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6-6 Neuron-Layer Concatenation Simplifies Bias Inputs |
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130 | (1) |
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6-7 Normalizing and Contrast-Enhancing Layers |
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131 | (1) |
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(a) Pattern Normalization |
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131 | (1) |
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(b) Contrast Enhancement: Softmax and Thresholding |
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131 | (1) |
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132 | (1) |
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6-9 Exercising a Neural-Network Model |
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132 | (2) |
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(a) Computing Successive Neuron-Layer Outputs |
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132 | (1) |
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(b) Input from Pattern-Row Matrices |
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133 | (1) |
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(c) Input from Text Files and Spreadsheets |
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133 | (1) |
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SUPERVISED TRAINING FOR REGRESSION |
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134 | (1) |
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6-10 Mean-Square Regression |
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134 | (3) |
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134 | (1) |
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(b) Linear Mean-Square Regression and the Delta Rule |
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135 | (1) |
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(c) Nonlinear Neuron Layers and Activation-Function Derivatives |
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136 | (1) |
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(d) Error-Measure Display |
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136 | (1) |
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6-11 Backpropagation Networks |
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137 | (3) |
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(a) The Generalized Delta Rule |
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137 | (2) |
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139 | (1) |
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139 | (1) |
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(d) The Classical XOR Problem and Other Examples |
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140 | (1) |
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More Neural-Network Models |
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140 | (1) |
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6-12 Functional-Link Networks |
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140 | (2) |
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6-13 Radial-Basis-Function Networks |
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142 | (3) |
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(a) Basis-Function Expansion and Linear Optimization |
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142 | (1) |
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(b) Radial Basis Functions |
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143 | (2) |
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6-14 Neural-Network Submodels |
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145 | (1) |
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146 | (1) |
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146 | (1) |
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6-16 Classifier Input from Files |
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147 | (1) |
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147 | (2) |
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(a) Simple Linear Classifiers |
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147 | (1) |
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148 | (1) |
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(c) Backpropagation Classifiers |
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148 | (1) |
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(d) Functional-Link Classifiers |
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149 | (1) |
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149 | (1) |
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149 | (6) |
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(a) Classification Using an Empirical Database: Fisher's Iris Problem |
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149 | (2) |
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(b) Image-Pattern Recognition and Associative Memory |
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151 | (4) |
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155 | (1) |
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155 | (1) |
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156 | (1) |
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(a) Bottleneck Layers and Encoders |
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156 | (1) |
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156 | (1) |
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Network-Training Problems |
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157 | (1) |
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6-21 Learning-Rate Adjustment |
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157 | (1) |
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6-22 Overfitting and Generalization |
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157 | (2) |
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157 | (1) |
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158 | (1) |
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158 | (1) |
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159 | (1) |
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6-23 Beyond Simple Gradient Descent |
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159 | (1) |
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Unsupervised Competitive-Layer Classifiers |
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159 | (1) |
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6-24 Template-Pattern Matching and the CLEARN Operation |
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159 | (4) |
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(a) Template Patterns and Template Matrix |
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159 | (1) |
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(b) Matching Known Template Patterns |
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160 | (1) |
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(c) Template-Pattern Training |
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160 | (2) |
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162 | (1) |
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6-25 Learning with Conscience |
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163 | (1) |
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6-26 Competitive-Learning Experiments |
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164 | (1) |
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(a) Pattern Classification |
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164 | (1) |
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164 | (1) |
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6-27 Simplified Adaptive-Resonance Emulation |
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165 | (2) |
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Supervised Competitive Learning |
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167 | (1) |
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6-28 The LVQ Algorithm for Two-Way Classification |
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167 | (1) |
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6-29 Counterpropagation Networks |
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167 | (1) |
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Examples Of Clearn Classifiers |
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168 | (1) |
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6-30 Recognition of Known Patterns |
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168 | (5) |
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168 | (1) |
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(b) Fast Solution of the Spiral Benchmark Problem |
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169 | (4) |
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6-31 Learning Unknown Patterns |
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173 | (4) |
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174 | (3) |
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Chapter 7 Dynamic Neural Networks |
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177 | (30) |
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177 | (1) |
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7-1 Dynamic Versus Static Neural Networks |
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177 | (1) |
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7-2 Applications of Dynamic Neural Networks |
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177 | (1) |
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7-3 Simulations Combining Neural Networks and Differential-Equation Models |
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178 | (1) |
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Neural Networks With Delay-Line Input |
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178 | (1) |
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178 | (2) |
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180 | (1) |
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7-6 Delay-Line-Input Networks |
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180 | (2) |
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180 | (1) |
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(b) One-Layer Nonlinear Network |
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181 | (1) |
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(c) Functional-Link Network |
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181 | (1) |
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(d) Backpropagation Network with Delay-Line Input |
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182 | (1) |
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7-7 Using Gamma Delay Lines |
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182 | (1) |
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Static Neural Networks Used As Dynamic Networks |
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183 | (1) |
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183 | (1) |
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7-9 Simple Backpropagation Networks |
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184 | (1) |
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Recurrent Neural Networks |
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185 | (1) |
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7-10 Layer-Feedback Networks |
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185 | (1) |
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7-11 Simplified Recurrent-Network Models Combine Context and Input Layers |
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185 | (2) |
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(a) Conventional Model of a Jordan Network |
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185 | (1) |
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(b) Simplified Jordan-Network Model |
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186 | (1) |
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(c) Simplified Models for Other Feedback Networks |
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187 | (1) |
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7-12 Neural Networks with Feedback Delay Lines |
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187 | (2) |
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187 | (1) |
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(b) Neural Networks with Both Input and Feedback Delay Lines |
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188 | (1) |
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189 | (1) |
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189 | (1) |
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7-14 Off-Line Predictor Training |
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189 | (3) |
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(a) Off-Line Prediction Using Stored Time Series |
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189 | (1) |
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(b) Off-Line Training System for Online Predictors |
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189 | (1) |
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(c) Example: Simple Linear Predictor |
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190 | (2) |
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7-15 Online Trainng for True Online Prediction |
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192 | (1) |
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7-16 Chaotic Time Series for Prediction Experiments |
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192 | (1) |
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7-17 Gallery of Predictor Networks |
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193 | (6) |
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Other Applications Of Dynamic Networks |
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199 | (1) |
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7-18 Temporal-Pattern Recognition: Regression and Classification |
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199 | (2) |
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201 | (3) |
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201 | (1) |
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(b) Example: Program for Matching Narendra's Plant Model |
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201 | (3) |
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204 | (1) |
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7-20 Biological-Network Software |
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204 | (3) |
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204 | (3) |
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Chapter 8 More Appications Of Vector Models |
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207 | (38) |
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Vectorized Simulation With Logarithmic Plots |
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207 | (1) |
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8-1 The EUROSIM No. 1 Benchmark Problem |
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207 | (1) |
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8-2 Vectorized Simulation with Logarithmic Plots |
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207 | (2) |
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Modeling Fuzzy-Logic Function Generators |
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209 | (1) |
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8-3 Rule Tables Specify Heuristic Functions |
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209 | (1) |
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210 | (4) |
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(a) Fuzzy Sets and Membership Functions |
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210 | (1) |
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(b) Fuzzy Intersections and Unions |
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210 | (3) |
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(c) Joint Membership Functions |
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213 | (1) |
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(d) Normalized Fuzzy-Set Partitions |
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213 | (1) |
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8-5 Fuzzy-Set Rule Tables and Function Generators |
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214 | (1) |
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8-6 Simplified Function Generation with Fuzzy Basis Functions |
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214 | (1) |
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8-7 Vector Models of Fuzzy-Set Partitions |
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215 | (1) |
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(a) Gaussian Bumps: Effects of Normalization |
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215 | (1) |
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215 | (1) |
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(c) Smooth Fuzzy-Basis Functions |
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216 | (1) |
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8-8 Vector Models for Multidimensional Fuzzy-Set Partitions |
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216 | (1) |
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8-9 Example: Fuzzy-Logic Control of a Servomechanism |
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217 | (4) |
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217 | (1) |
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(b) Experiment Protocol and Rule Table |
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217 | (3) |
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(c) DYNAMIC Program Segment and Results |
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220 | (1) |
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Partial Differential Equations |
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221 | (1) |
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221 | (1) |
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8-11 Vectorized Method of Lines |
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221 | (4) |
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221 | (1) |
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(b) Using Differentiation Operators |
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221 | (3) |
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224 | (1) |
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8-12 Heat-Conduction Equation in Cylindrical Coordinates |
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225 | (1) |
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225 | (2) |
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8-14 Simple Heat-Exchanger Model |
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227 | (2) |
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Fourier Analysis And Linear-System Dynamics |
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229 | (1) |
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229 | (1) |
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8-16 Function-Table Lookup and Interpolation |
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230 | (1) |
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8-17 Fast-Fourier-Transform Operations |
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230 | (1) |
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8-18 Impulse and Freqency Response of a Linear Servomechanism |
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231 | (1) |
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8-19 Compact Vector Models of Linear Dynamic Systems |
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232 | (5) |
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(a) Using the Index-Shift Operation with Analog Integration |
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232 | (3) |
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(b) Linear Sampled-Data Systems |
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235 | (1) |
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(c) Example: Digital Comb Filter |
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236 | (1) |
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Replication Of Agroecological Models On Map Grids |
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237 | (1) |
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8-20 Geographical Information System |
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237 | (2) |
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8-21 Modeling the Evolution of Landscape Features |
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239 | (1) |
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8-22 Matrix Operations on a Map Grid |
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239 | (6) |
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242 | (3) |
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APPENDIX: ADDITIONAL REFERENCE MATERIAL |
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245 | (3) |
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A-1 Example of a Radial-Basis-Function Network |
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245 | (1) |
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A-2 Fuzzy-Basis-Function Network |
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245 | (3) |
References |
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248 | (3) |
Using The Book CD |
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251 | (2) |
Index |
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253 | |