In this paper, symmetries are exploited for achieving significant space savings in a knowledge compilation perspective. More precisely, the languages FBDD and DDG of decision diagrams are extended to the languages Sym-FBDDX,Y and Sym-DDGX,Y of symmetry-driven decision diagrams, where X is a set of ”symmetry-free” variables and Y is a set of ”top” variables. Both the time efficiency and the spac...

The strong coupling behavior of finite temperature free energy in N = 4 supersym-metric SU (N) Yang-Mills theory has been recently discussed by Gubser, Klebanov and Tseytlin in the context of AdS-SYM correspondence. In this note, we focus on the weak coupling behavior. As a result of a two-loop computation we obtain, in the large N 't Hooft limit, F (g 2 N → 0) ≈ − π 2 6 N 2 V 3 T 4 (1 − 3 2π 2...

The strong coupling behavior of finite temperature free energy in N = 4 supersym-metric SU (N) Yang-Mills theory has been recently discussed by Gubser, Klebanov and Tseytlin in the context of AdS-SYM correspondence. In this note, we focus on the weak coupling behavior. As a result of a two-loop computation we obtain, in the large N 't Hooft limit, F (g 2 N → 0) ≈ − π 2 6 N 2 V 3 T 4 (1 − 3 2π 2...

We consider effective field theory around classical background geometries with a gauge theory dual, in the class of LLM geometries. These are dual to half-BPS states of N = 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond...

Let X be a finite set. We denote by T (X) the monoid of all (total) transformations on X and by Sym(X) the symmetric group on X. An element a 2 T (X) \ Sym(X) is said to be singular. In 1966 Howie [4] proved that every singular transformation a 2 T (X) can be expressed as a product of idempotents of T (X). This result was generalized by Fountain and Lewin [2] for the case of independence algebr...

David Hicks, 2 Corey Oses, 2 Eric Gossett, 2 Geena Gomez, 2 Richard H. Taylor, 2, 3 Cormac Toher, 2 Michael J. Mehl, Ohad Levy, 2, 5 and Stefano Curtarolo 2, 6, ∗ Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA Center for Materials Genomics, Duke University, Durham, North Carolina 27708, USA Department of Materials Science and Engin...