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dying for a cause

During the invasion phase of the Iraq war in 2003, the chances for a US soldier to die were 139/248000\(\approx\) 51 per 100,000.

In 2018, the chances for a woman in the US state of Georgia to die from causes related to her pregnancy are 46 per 100,000.…

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ECE 490, final

Problems and solutions.…

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Protected: lake wobegon academic publishing

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Protected: cache choice conundrum

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MATH 199, Monday April 29: Around Arrow

We will be talking about Arrow’s Impossibility theorem, and its topological relatives. The span of the talk will be between American political landscape and elementary algebraic topology – feel free to peruse the links and their vicinity!

Follow-up exercise: try to model your decision process next time you are trying to converge with your friends or relatives, where to go out, or what to watch together. What is the topology of your movie-space?…

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ECE 490, week of Apr 22

We will be covering some lower bounds for first order methods, and matching them algorithms of convex minimization, – based on Nesterov, ch. 2.

Class notes (pretty incomplete, to be used just as a study guide), here and here.

Homework, due by Midnight May 1st:

  1. Consider the 4-dimensional space spanned by the polynomials
    $$
    p(x)=ax^6+bx^4+cx^2+d.
    $$Find, using the Gram-Schmidt orthogonalization procedure,
    the orthonormal basis, if the scalar product is given by
    $$
    (p_1,p_2)_Q=\int_{0}^\infty e^{-x}p_1(x)p_2(x) dx.
    $$
  2. Consider quadratic form in $\Real^{100}$ given by
    \[
    Q=\left(
    \begin{array}{ccccc}
    2&1&1&\cdots&1\\
    1&2&1&\cdots&1\\
    1&1&2&\cdots&1\\
    \vdots&\vdots&\vdots&&\vdots\\
    1&1&1&\cdots&2\\
    \end{array}
    \right)
    \]
    (i.e.
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ECE 490, Week of Apr 15

\(\def\Real{\mathbb{R}}\)

Newton method, Conjugate gradients Guler, chapter 13.

Class notes (pretty incomplete, to be used just as a study guide), here and
here.…

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ECE 490, Week of Apr. 8

\(\def\Real{\mathbb{R}}\)

Gradient descent; Newton method: Guler, chapter 13.

Class notes (pretty incomplete, to be used just as a study guide), here and
here.…

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ECE 490, Week of Apr 1

\(\def\Real{\mathbb{R}}\)

Conic duality: Guler, Chapters 11, 13 and Barvinok’s “A Course in Convexity“, Chapter 4.

Class notes (pretty incomplete, to be used just as a study guide), here.

Homework, due Apr. 16.

  1. Warehouses numbered \(0,1,\ldots,N\) are located along the road. Initially, the warehouse \(k\) holds \(N-k\) units of goods. Management wants to redistribute the goods so that warehouse \(k\) holds \(k\) units. Moving one unit from \(k\) to \(l\) costs \(|k-l|\). What is the optimal movement plan?
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ECE 490, Week of Mar 25

\(\def\Real{\mathbb{R}}\)

Convex programming and duality: Guler, Chapter 11.

Class notes (pretty incomplete, to be used just as a study guide), here and here.

Exercises:
Find Legendre duals for the following functions:

  • \(f(x)=\min(1-x,2,1+x)\);
  • \(f(x)=\min((x-1)^2,(x+1)^2)\);
  • \(f(x,y)= 0 \mathrm{\ if\ } x^2+y^2\leq 2; +\infty \mathrm{\ otherwise}\).

 …

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