8-11 | Quiz III

Question 1

Integer cuts allow to determine:

• modeling down-regulations
• modeling of knock-outs
• alternative solutions involving binary variables
• alternative solutions involving non-binary variables

Answer 1

alternative solutions involving binary variables

Question 2

The gradient of the function f(x , y ) = 2x² + y² at the point (1, 1) is the vector:

• [4, 2]
• [1, 1]
• [1, 4]
• [3, 3]

Answer 2

[4, 2]

Question 3

The quadratic part in the MOMA approach is of the form w^TQw, where Q is:

• a matrix of all elements equal to 1
• a diagonal matrix, with entries equal to 1, …, m, where m is the number of reactions
• the identity matrix
• the zero matrix, with all entries equal to zero

Answer 3

the identity matrix

Question 4

The Gibbs free energy of all reactions in a metabolic network in which z is a vector including the logarithms of metabolite concentrations can be succinctly written in a matrix form as follows:

• Δ𝐺 = 𝑅𝑇𝑁^𝑇𝑧 + Δ𝐺⁰
• Δ𝐺 = 𝑅𝑁^𝑇𝑧 + Δ𝐺⁰
• Δ𝐺 = 𝑅𝑇𝑁𝑧 + Δ𝐺⁰
• Δ𝐺 = 𝑇𝑁^𝑇𝑧 + Δ𝐺⁰

Answer 4

Δ𝐺 = 𝑅𝑇𝑁^𝑇𝑧 + Δ𝐺⁰

Question 5

A bilevel linear program can be cast as a linear program by:

• Formulating the dual of the inner problem and invoking the strong optimality condition
• Formulating the dual of the inner problem and invoking the weak optimality condition
• Formulating the dual of the outer problem and invoking the weak optimality condition
• Formulating the dual of the outer problem and invoking the strong optimality condition

Answer 5

Formulating the dual of the inner problem and invoking the weak optimality condition

Question 6

Further optimization of the engineering strategy proposed by optStrain is done by:

• using optKnock
• using ROOM
• using MOMA
• using optReg

Answer 6

using optKnock

Question 7

ROOM approach relies on a quadratic program.

• FALSE
• TRUE

Answer 7

FALSE

Question 8

Shadow prices are given by the values of the dual variables.

• FALSE
• TRUE

Answer 8

TRUE

Question 9

If one of the primal or dual problems is unbounded, then the other one is feasible.

• TRUE
• FALSE

Answer 9

FALSE

Question 10

If the Gibbs free energy of a reaction is negative for a given range of concentrations, then the reaction is irreversible for that range of concentrations.

• FALSE
• TRUE

Answer 10

TRUE