BB 101: Module II
Physical Biology
Ranjith Padinhateeri
Office: Bio # 306
Email: [email protected]
www.bio.iitb.ac.in/~ranjith
In Module 1, you learned
many interesting
biological phenomena
You heard about
Cell,
DNA, Protein
Gene/gene
Various
express
IE 601: Exercises on unconstrained Optimization
1. Consider the function f : R2 R dened as f (x1 , x2 ) = exp(2x2 x2 ) 3x1 + 5x2 . Give the linear and
1
2
quadratic approximations of f at (1, 1). Are these approximations convex, concave, or neither? Expla
IE 601: Exercises on Steepest Descent and Newtons Methods
1. Given a quadratic function f : Rn R, with f (x) = 1 x Ax + b x, where A is a positive denite symmetric
2
matrix, consider the two options to minimize f :
(a) Apply steepest descent method to f f
IE 601: Exercises on Separation and Extreme Point Optimality
1. Let S, T Rn be nonempty convex sets such that S T = . Then show that there exists a nonzero
a Rn such that
inf a x : x S sup a x : x T .
Hint: Convert this situaton into one involving a singl
IE 601: Exercises on LP, Simplex Method
1. Consider the standard form polyhedron P = cfw_x Rn : Ax = b, x 0, where A is an m n matrix with
linearly independent rows. State whether the following statements are true or false. If the statement is true,
provi
IE 601, Autumn 2012: Mid-semester Exam
September 11, 2012
Time: 3:00 pm5:00 pm
Max. Marks: 100
Important Notes: Put away your books, cellphones, smartphones, and other electronic gadgets.
You may refer to a single 2-sided A4 sheet (handwritten in your own
IE 601, Autumn 2011: Mid-semester Exam
September 17, 2011
Time: 8:30am10:30am
Max. Marks: 100 + 10 (Extra credit)
Important Notes: Put away your books, cellphones, smartphones, and other electronic gadgets. You
may refer to a single 2-sided A4 sheet (hand
IE 601, Autumn 2010: Mid-semester Exam
September 18, 2010
Time: 9:30am11:30am
Max. Marks: 100 + 10 (Extra credit)
Important Notes: Put away your books, cellphones, smartphones, and other electronic gadgets. You may refer
to a single 2-sided A4 sheet (hand
IE 601, Autumn 2012: End-semester Exam
November 21, 2012
Time: 9:30 am12:30 pm
Max. Marks: 100
Important Notes: Put away your books, cellphones, smartphones, and other electronic gadgets.
You may refer to a single 2-sided A4 sheet (handwritten in your own
IE 601, Autumn 2011: Final Exam
November 25, 2011
Time: 3 hours
Max. Marks: 100
Important Notes: Put away your books, cellphones, smartphones, and other electronic gadgets. You may refer
to a single 2-sided A4 sheet (handwritten in your own writing) of no
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Autumn Semester 2016
August 12, 2016
IE 601: Optimization Techiniques
Tutorial 3
* Convex sets *
Exercise 1.
set.
1. Prove that: If cfw_Ci , i A is any collection of convex sets, then iA Ci is a convex
2. Prove that: If C1 Rn and C2 Rn are convex sets the
Synthesis of RNA is tightly regulated: development,
response to environment
Chapter 18
We will look at simple bacteria
to see how they do it.
But before we start, let us
quickly refresh our memories
on transcription.
MCB-5
BB101
IIT Bombay
Promoter
Transc
Lecture 3
What are the molecular mechanisms
underlying Mendels results?
Genetic material
DNA
Chromosomes
MCB-2 & 3
BB101
IIT Bombay
Chromosomal basis of inheritance
What are the heritable factors defined by Mendel?
Heritable factors are recognized as ge
Autumn Semester 2016
September 30, 2016
IE 601: Optimization Techiniques
Tutorial 8
Exercise 1. The problem is to assign m jobs to n processors. If a job i is assigned to processor j,
the cost is aij and it takes pij time to be completed. Each processor j
Autumn Semester 2016
August 26, 2016
IE 601: Optimization Techiniques
Tutorial 4
0
Exercise 1. Find all the critical points (i.e., points where f (x) = 0) of the function f : R R, defined
as f (x) = x x2 x3 for x R. Which of these points can you identify
Autumn Semester 2016
September 23, 2016
IE 601: Optimization Techiniques
Tutorial 7
Exercise 1. Consider the problem
min f (x) =
1 T
x Qx bx
2
where Q is a positive-definite matrix.
Show that symmetricity of Q can be assumed without loss of generality.
Autumn Semester 2016
September 16, 2016
IE 601: Optimization Techiniques
Tutorial 6
Exercise 1. Let f (x) = 21 xT Qx bx where Q is a positive definite matrix. Show that in an exact line
hOf (xk ),Of (xk )i
search the step length is given by k = hOf
(xk ),
Autumn Semester 2016
September 2, 2016
IE 601: Optimization Techiniques
Tutorial 5
1
Exercise 1. Run the gradient descent line search method on the function f (x) = x2 + y 2 starting at
2
1
the point z0 = (2, 2) and using only step sizes k = . Output z1 ,
Autumn Semester 2016
August 3, 2016
IE 601: Optimization Techiniques
Tutorial 2
* Sets, Vectors, Linear Independence *
Exercise 1. What does the following notations represent? (Define them)
R, Q, Z, Z+ , N
Exercise 2. Let A and B be two sets then define A
IE601 Tutorial 1: Application of Optimization Techniques
25th July 2016
1. Diet problem: There are n different food types available. The jth food sells at a price cj per unit. In
addition there are m basic nutrients. To achieve a balanced diet, you must r
IE 601, Autumn 2010: Final Exam
November 27, 2010
Time: 3 hours
Max. Marks: 100
Important Notes: Put away your books, cellphones, smartphones, and other electronic gadgets. You may refer
to a single 2-sided A4 sheet (handwritten in your own writing) of no
IE 601, Autumn 2013: Test 2
October 22, 2013
2:15 pm to 3:15 pm
Important Notes: This is a closed book, closed notes exam. Put away all your electronic devices,
notes, etc. You will be graded on what is written, rather than what you intended to write. Add