Feb. 22 - the adjacency matrix and the integrality condition (p.36-38)
Let G=(V,E) be a graph with n vertices. Choose a labeling v_1,.,v_n
of the vertices. A basic construction for much of graph theor
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 8 February 24th, 2014
Overview
Last week we talked about the Simplex algorithm. Today well broaden the scope of the objectives
we
Aluno: Marcos Vinicius Holanda Borges
Professor: Jlio Costa
Atividade 1 Comportamento Organizacional
1 - Os valores so as convices bsicas dos indivduos, baseadas no que os
indivduos acham, corretas ou
CS 221: Computational Complexity
Prof. Salil Vadhan
Lecture Notes 10
March 3, 2010
1
Scribe: Jonathan Ullman
Circuit Size Bounds
Proposition 1 Every function f : cfw_0, 1n cfw_0, 1 can be computed by
CS 221: Computational Complexity
Prof. Salil Vadhan
Lecture Notes 11
March 5, 2010
1
Circuit Complexity Diagram
2
Scribe: Michael Jemison
Randomized Computation
Now well study the complexity theory of
CS 221: Computational Complexity
Prof. Salil Vadhan
Lecture Notes 14
March 22, 2010
1
Scribe: Kyu Bok Lee
Agenda
#P-completeness (cont.)
Todas Theorem
Approximate Counting vs. Uniform Sampling (mor
CS 221: Computational Complexity
Prof. Salil Vadhan
Lecture Notes 13
March 10, 2010
1
Scribe: James Williamson
Randomized Reductions
We consider Unique SAT, a promise problem
USATY
= cfw_ | has exactl
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 18 April 7th, 2014
Overview
The methods we discussed until now were focused on optimizing objectives for which feasible solutions
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 9 February 26th, 2014
Overview
Today we will recapitulate basic definitions and properties from multivariate calculus which we wi
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 19 April 9th, 2014
Overview
In the previous lecture we started talking about combinatorial optimization. In general, we
would lik
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 1 January 27th, 2014
Overview
In this course we will cover convex and combinatorial optimization and emphasize the deep connectio
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 6 February 12th, 2014
Overview
In our previous lecture we explored the concept of duality which is the cornerstone of Optimizatio
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 2 January 29th, 2014
Overview
In our previous lecture we discussed several motivating examples for optimization in applications
t
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 4 February 5th, 2014
Overview
In our previous lecture we discussed criteria for testing whether an LP in infeasible and whether i
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 3 February 3rd, 2014
Overview
In our previous lecture we discussed several motivating examples for linear optimization. We
used t
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 5 February 10th, 2014
Overview
In our previous lecture we discussed extreme points, and showed that if an LP has an optimal
solut
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 7 February 19th, 2014
Overview
In our previous lecture we saw the application of the strong duality theorem to game theory, and
t
AM 221: Advanced Optimization
Spring 2014
Prof. Yaron Singer
1
Lecture 10 March 3rd, 2014
Overview
Last week we reviewed results from multivariate calculus in preparation for our journey into convex
o
CS 221: Computational Complexity
Prof. Salil Vadhan
Lecture Notes 8
February 19, 2010
1
Scribe: Kevin Lee
Agenda
1. Provably Intractable Problems
2
Provably Intractable Problems
Some lower bounds that
March 5: more about the outer automorphism of S_6,
and Aut(S_n) in general (cf. Chapter 6 of the textbook)
Last time we constructed a total by starting from two disjoint
synthemes, finding the four di
March 3: Uniqueness and automorphism group of Pi_4 (day 2)
Recall: we began with any order-4 projective plane Pi and one of its
6!*168 ordered ovals O = cfw_p1,p2,p3,p4,p5,p6. This let us
identify 15
Feb. 24 - Moore graphs; two more conditions: "absolute" and Krein
(pages 41-42)
Recall: the adjacency matrix A of a strongly regular graph with
parameters (n,k,\lam,\mu) satisfies A\j = k\j and
(p.37,
Feb.5 and 8 Important examples of designs, II:
Hadamard matrices, particularly Sylvester and Paley
NB Problems 6 and 7 of the present problem set are postponed till
the next week: we won't get to inte
Feb.3 [& 5] Important examples of designs I:
projective planes and higher-dimensional projective spaces
Usually when we introduce a new kind of mathematical structure
we give a selection of important
Feb. 10 - new designs from old:
complement; Hadamard 3-designs; derived designs
NB again we choose a different (but still logical) order of
presentation from the textbook's.
Complementary design (p.13
Feb. 12 - intro to arcs and ovals; intersection triangles
You're already had to look up "oval" on page 17 to construct a
(3,6,22) Steiner system from the square Paley 2-(11,5,2) design.
An arc in a 2