ar X iv : 1 21 1 . 10 01 v 2 [ cs . C C ] 6 N ov 2 01 2 Majority is Stablest : Discrete and SoS

ar X iv : 1 21 1 . 24 05 v 1 [ cs . G T ] 1 1 N ov 2 01 2 Rank - 1 Games With Exponentially Many Nash Equilibria

The rank of a bimatrix game (A,B) is the rank of the matrix A + B. We give a construction of rank-1 games with exponentially many equilibria, which answers an open problem by Kannan and Theobald (2010).

ar X iv : a st ro - p h / 01 11 13 6 v 1 7 N ov 2 00 1 1 Active Optics in Modern , Large Optical Telescopes

ar X iv : 1 50 4 . 01 65 6 v 1 [ cs . C C ] 7 A pr 2 01 5 Tight Size - Degree Bounds for Sums - of - Squares Proofs ∗

We exhibit families of 4-CNF formulas over n variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) d but require SOS proofs of size n for values of d = d(n) from constant all the way up to n for some universal constant δ. This shows that the n running time obtained by using the Lasserre semidefinite programming relaxations to find degree-d SOS proofs is op...

ar X iv : h ep - p h / 01 11 04 9 v 1 6 N ov 2 00 1 The QCD Phase Diagram and Explosive Astrophysics

ar X iv : h ep - p h / 01 11 39 6 v 1 2 9 N ov 2 00 1 SOFT INTERACTIONS

A brief introduction to the theory and phenomenology of soft interactions is given, focusing on total and elastic cross sections and multiparticle production.