We prove general exponential moment inequalities for averages of [0,1]valued iid random variables and use them to tighten the PAC Bayesian Theorem. The logarithmic dependence on t...
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for pro...
A proper vertex coloring of a graph is equitable if the sizes of its color classes differ by at most one. In this note, we prove that if G is a graph such that for each edge xy E...
In this paper, we investigate the extent to which techniques used in [10], [2], and [3] -- developed to prove coloring theorems at successors of singular cardinals of uncountable c...
Dp-minimality is a common generalization of weak minimality and weak o-minimality. If T is a weakly o-minimal theory then it is dp-minimal (Fact 2.2), but there are dp-minimal den...