本次代写是一个Python数据科学的assignment

## Question 1:

Read the following paper

https://www.biorxiv.org/content/10.1101/2021.07.08.451443v1.abstract and write a report

limited to 3 pages, including citations, figures etc. Reports beyond 3 pages will be rejected

automatically.

Implement a simpler version of the method using the MNIST data set for regression on digit

0 and digit 7. Each bag consists of 100 images with a fraction x of digit 0 and 1-x of digit 7.

Then train neural network on regression using the neural network architecture specified in

the given paper.

Report and code is graded based on:

1. Clarity

2. Show of understanding in the biological and cancer domain knowledge

3. Show of understanding in the machine learning technology

4. Generate results on the MNIST toy data set – graphs and plots to show that your

code is working

5. Put a version of your source code in github, code is graded based on:

a. Good code design

b. Good coding habits

c. Correctness

## Question 2: Enzyme Kinetics

Enzymes are catalysts that help convert molecules that we will call substrates into other

molecules that we will products. They themselves are not changed by the reaction. Within

cells, enzymes are typically proteins. They can speed up biological reactions, sometimes by

up to millions of times. They are also regulated by a very complex set of positive and

negative feedback systems. Computational biologists are painstakingly mapping out this

complex set of reactions. In this problem, we will model and simulate a simplified enzyme

reaction.

An enzyme E converts the substrate S into the product P through a two-step process. First,

E forms a complex with S to form an intermediate species ES in a reversible manner at the

forward rate k1 and reverse rate k2. The intermediate ES then breaks down into the product

P at a rate k3, thereby releasing E. Schematically, we write

8.1. Using the law of mass action, write down four equations for the rate of changes of the

four species, E, S, ES, and P.

8.2. Write a code to numerically solve these four equations using the fourth-order Runge

Kutta method. For this exercise, assume that the initial concentration of E is 1 µM, the initial

concentration of S is 10 µM, and the initial concentrations of ES and P are both 0. The rate

constants are: k1=100/µM/min, k2=600/min, k3=150/min.

8.3. We define the velocity, V, of the enzymatic reaction to be the rate of change of the

product P. Plot the velocity V as a function of the concentration of the substrate S. You

should find that, when the concentrations of S are small, the velocity V increases

approximately linearly. At large concentrations of S, however, the velocity V saturates to a

maximum value, Vm. Find this value Vm from your plot.

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