We give a short and streamlined proof of the following statement recently proven by author M. Zeinalian: cobar construction dg coassociative coalgebra normalized singular chains on path-connected pointed space is naturally quasi-isomorphic as associative algebra to based loop space. This extends classical theorem F. Adams originally for simply connected spaces. Our relating functor left adjoint...

We give the first tight integrality gap for Vertex Cover in the Sherali-Adams SDP system. More precisely, we show that for every > 0, the standard SDP for Vertex Cover that is strengthened with the level-6 Sherali-Adams system has integrality gap 2− . To the best of our knowledge this is the first nontrivial tight integrality gap for the Sherali-Adams SDP hierarchy for a combinatorial problem w...

ADAMs (a disintegrin and metalloprotease) are membrane-bound enzymes, capable of shedding a multitude of proteins from the surface of the cell. They are therefore considered crucial modulators of physiological and pathophysiological processes. The structure and function of ADAMs is related to those of a family of snake venom metalloproteases which also possess a potential adhesion domain as wel...

The Sherali-Adams lift-and-project hierarchy is a fundamental construct in integer programming, which provides successively tighter linear programming relaxations of the integer hull of a polytope. We initiate a new approach to understanding the Sherali-Adams procedure by relating it to methods from computational algebraic geometry. Our two main results are the equivalence of the Sherali-Adams ...