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Sum of squares
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11	Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Grothendieck-type inequalities Suppose A ∈ Rn×m is a linear operator from Rm to Rn represented Add to Reading List Source URL: sumofsquares.org - Date: 2016-11-17 19:44:26
12	Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Application: Sparse coding / dictionary learning The dictionary learning / sparse coding problem is defined as follows: Add to Reading List Source URL: sumofsquares.org - Date: 2016-11-17 19:44:26
13	HomeworkProve that 15x2 − 7y 2 = 16 has no solutions in Z. 2. Prove that an integer of the form 8n + 7 cannot be written as a sum of three integer squares. 3. Show that if x2 = a is solvable modulo p then it is Add to Reading List Source URL: www.math.nyu.edu - Date: 2016-09-07 16:50:49
14	Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Optimality of sum-of-squares In this lecture, we show that sum-of-squares achieves the best possible approximation guarantees for every constraint sati Add to Reading List Source URL: sumofsquares.org - Date: 2016-11-30 18:56:07
15	Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Mathematical Definitions Let us now turn to formally defining the problem of polynomial Add to Reading List Source URL: www.sumofsquares.org - Date: 2016-11-17 19:44:26
16	Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Cheeger’s inequality Let G be a d-regular graph with vertex set V = [n]. For a vertex Add to Reading List Source URL: sumofsquares.org - Date: 2016-11-17 19:44:26
17	Proof, beliefs, and algorithms through the lens of sum-of-squares 1 An integrality gap for the planted clique problem The Planted Clique problem (sometimes referred to as the hidden clique Add to Reading List Source URL: sumofsquares.org - Date: 2016-11-17 19:44:26
18	Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Introduction The terms “Algebra” and “Algorithm” both originate from the same Add to Reading List Source URL: www.sumofsquares.org - Date: 2016-11-17 19:44:26
19	Proof, beliefs, and algorithms through the lens of sum-of-squares 1 From integrality gaps to hardness We have seen how we can transform computational hardness results into integrality gaps. In a surprising work Raghaven Add to Reading List Source URL: sumofsquares.org - Date: 2016-11-17 19:44:26
20	Proof, beliefs, and algorithms through the lens of sum-of-squares 1 Is sos an “optimal algorithm”? We have alluded several times in this course to the intuition that sum Add to Reading List Source URL: sumofsquares.org - Date: 2016-11-17 19:44:26

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