CS 1025 Computational Modeling and Simulation

Test Two Study Guide - Fall 2012 - Friday, November 16th


  1. What topics will be covered from the Exam #1 Study Guide?

    1. Monte Carlo - review of Wednesday, November 14th class. How to think about the known and the unknown and do algebra with the general formula. Dinosaur/Shark/Star Wars Fruit Snacks tossing solution to Area of the Contruction paper.

    2. The Data Flyer application from SHODOR.
      Find the best fitting (smallest "Sum of squares of deviations:")
               line 
                    f(x) = mx + b
               
               for the following two points using Data Flyer:
      
                   -5 -1   <------ point a
                    0  3   <------ point b
      
      Now, REFRESH the Data Flyer application and try these three points:
      
                  -5   -1           point a  (same as before)
                   0    3           point b  (same as before)
                  -2.5  2           point c  <----- ths new 3rd point
       
           Can you get the Sum of squares of deviations: 0.67 or less????
      
           Note:  It is helpful to click on "Light Grid Lines" 
      
           When you get the 0.67 or less 
                for the Sum of the squares of the deviations, 
                after doing enough Change Function and Slider adjusting,
      
                you have discovered your 
                best fitting function 
      
                f(x) = mx + b, or
      
                  y  =  mx + b    What is m?   What is b?
      
    3. Monte Carlo with NetLogo - 33 by 33 grid, Cows and Houses, not to be confused with cows in houses instead of barns!

    4. Ventana Vensim assignment questions: Be able to tell what the formula (equation) would be for the births or the deaths rate or flow variable; or for mature females converter variable; or the females converter variable. You do NOT have to memorize any constants.

      Or, I might give you the constants and ask you to tell me how many births there would be. For example: How many births would occur next if the population is 1000 and the fraaction female is 0.55 and the fraction of females that are biologically mature is 0.4 and the births per mature female per year is 0.33 (which means one birth every 3 years).

  2. Monte Carlo concepts and problems. MonteCarlo20darts.pdf: Throwing 20 darts, throwing 100 darts, estimating area of an ellipse, estimating area A, B, C and D when a line is involved. y = mx + b. The line has slope m and intercept b.

    Netlogo TURTLES randomly scatter, then turn into either a COW or a HOUSE depending on whether they hit the BULLS EYE or missed the oval shaped bulls eye.

  3. Ventana Vensim and System Dynamics concepts.





Monte Carlo concepts will be on TEST TWO
Throwing Darts to determine an AREA.

MONTE CARLO QUESTIONS: Throwing Monte Carlo Darts or randomly scattering out turtles! :-)


  • Monte Carlo - given a diagram and graphical setup of an area, be able to determine what the area of below the function or between two functions is by using the Monte Carlo method.

    Know and understand the formula for coming up with a Monte Carlo estimated area when you know the proportion of or the actual count of "darts" that landed inside the area of interest.

  • Example:  Look at the following diagram which shows a solid point for every dart that was thrown
              and where it hit inside the target area.  The target area is the rectangle there you see
              that goes from x = 1 to x = 3 and from y = 4 to y = 8.
               
              (Note: for practical purposes, only 16 or 20 darts were thrown 
                                                   in the examples shown here).
       
              Calculate what the estimated area of the region above function g 
                                                          and below function h would be?  (The area BETWEEN function g and function h).  
              Please show your work and calculations.
              I need to see your process of arriving at the result.
              You will get partial credit if your equation is correct, but you just had a simple calculation, arithmetic error.
              You will NOT get full credit for just having the correct answer, so show the process for that reason too.