Quiz 1 (grad section)_ Modeling and Simulation - CSE 6730 _ CX 4230
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School
Georgia Institute Of Technology *
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Course
6730
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
7
Uploaded by MajorPencil13267
Quiz 1 (grad section) Due
Feb 1 at 2pm
Points
9
Questions
9
Available
after Jan 28 at 10am
Time Limit
75 Minutes
This quiz is no longer available as the course has been concluded.
Attempt History
Attempt
Time
Score
LATEST
Attempt 1 71 minutes
8 out of 9
Score for this quiz: 8
out of 9
Submitted Jan 28 at 12:38pm
This attempt took 71 minutes.
1 / 1 pts
Question 1
Which of the following is a valid motivation for simulating a system on a computer, rather than doing
an experiment with the system itself? Check all that apply
. (To get full credit, you must choose all of
the correct options and no incorrect ones.)
You might not have access to the system Correct!
Correct!
It may be immoral or unethical to observe or manipulate the system Correct!
Correct!
The real system may be too dangerous to observe or manipulate Correct!
Correct!
The system does not actually exist Correct!
Correct!
See [SB09] Chapter 1
1 / 1 pts
Question 2
Which of the following is a plausible scenario involving the use of a computer simulation? Check
all
that apply
. (To get full credit, you must choose all of the correct options and no incorrect ones.)
None of the other options is plausible You might create a simulation and do experiments with it to help validate an analytical model or theory Correct!
Correct!
You might use experimental data to check that the simulation is reasonable, by showing that the
simulation output agrees well with the data
Correct!
Correct!
You might use simulation to check that noisy experimental data is reasonable, in particular, by showing the
data is close to what the simulation predicts
Correct!
Correct!
See [SB09] Chapter 2
1 / 1 pts
Question 3
Recall our class discussion of the three infection models: a Markov chain (MC), a cellular automaton
(CA), and a system of ODEs (ordinary differential equations). Suppose you are hired to develop a
model for a system of infection spread in a hospital for a disease that lasts k
=3 days.
In which of the following scenarios would you prefer the ODE model over the other two (MC and
CA)?
Time is continuous so you have no other choice than to use a continuous-time model. You Answered
You Answered
The hospital has a small number of beds, for instance, just 3 to 5 beds. The disease spreads primarily through close contact and is highly dependent on spatial proximity and
near-neighbor interactions.
None of these scenarios would be good choice for the ODE model. Correct Answer
Correct Answer
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We'll give you credit on this question since the wording on the option you selected is arguably
ambiguous or confusing.
1 / 1 pts
Question 4
Consider a stock that behaves as follows:
If the stock price goes up today compared to yesterday, then there is a 25% chance it will go up
tomorrow, a 35% chance it will go down tomorrow, and a 40% chance that it will stay the same
("steady").
If the stock price goes down today compared to yesterday, then there is a 35% chance it will go
up tomorrow, a 40% chance it will go down tomorrow, and a 25% chance it will stay steady.
If the stock price is the same as yesterday, then there is a 50% chance it will go up, a 40% chance
that it will go down, and a 10% chance it will stay steady.
Suppose the stock is equally likely to be rising, falling, or steady on the day you buy it. When you look
at the price on a day many years from now, which of these scenarios is the most likely?
The stock price will be steady. The stock price will be rising. None of the other options is correct. The stock price will be falling. Correct!
Correct!
1 / 1 pts
Question 5
A skydiver jumps out of a plane. As she falls, two forces act on her: gravity, which pulls her down, and
drag, which pushes up. Let be her velocity at time . A simple model describing how the
velocity changes is , where , , and are three additional modeling parameters
(gravitational constant, a drag-force constant, and the skydiver's mass, respectively).
True or False?
There exists a variable rescaling of velocity and time such that this
system may be simplified into the parameter-free form, . (Here, .)
True Correct!
Correct!
False 1 / 1 pts
Question 6
Consider the nonlinear dynamical system, . Which of these statements best
characterizes the fixed points of the system? Check all that apply. For full credit, you must select all of
the correct options and none of the incorrect ones.
The fixed point is unstable
.
Correct!
Correct!
The fixed point is stable
.
The fixed point is stable
.
Correct!
Correct!
The fixed point is unstable
.
1 / 1 pts
Question 7
True or False?
The nonlinear dynamical system, , has a saddle-node bifurcation.
True False Correct!
Correct!
1 / 1 pts
Question 8
Consider the nonlinear dynamical system, . What type of bifurcation occurs at the
fixed point for some critical value of the parameter ?
Transcritical Subcritical pitchfork
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Supercritical pitchfork Saddle-node Correct!
Correct!
There cannot be a bifurcation at .
0 / 1 pts
Question 9
Consider the 1-D nonlinear dynamical system, . There is a bifurcation at the fixed
point having a critical parameter of . What type of bifurcation occurs?
Saddle-node You Answered
You Answered
Supercritical pitchfork Subcritical pitchfork Transcritical Correct Answer
Correct Answer
Quiz Score: 8
out of 9