Let $k\leq n$. Each polynomial $p\in\oR[x_1,...,x_n]$ can be uniquely written as $p=\sum_{\mu}\mu p_{\mu}$, where $\mu$ ranges over the set $M$ of all monomials in $\oR[x_1,...,x_k]$ and where $p_{\mu}\in\oR[x_{k+1},...,x_n]$. If $p$ is $d$-homogeneous and $\varepsilon>0$, we say that $p$ is {\em $\varepsilon$-concentrated on the first $k$ variables} if $$\sum_{\mu\in M\atop\deg(\mu) 0$ there exists $k_{d,\varepsilon}$ such that for each $n$ and each $d$-homogeneous $p\in\oR[x_1,...,x_n]$ there… Expand

Let $X$ be an inner product space, let $G$ be a group of orthogonal transformations of $X$, and let $R$ be a bounded $G$-stable subset of $X$. We define very weak and very strong regularity for such… Expand

This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.Expand

PTAS's for a much larger class of weighted MAX-rCSP problems which includes as special cases the dense problems and, for r = 2, all metric instances and quasimetric instances; for r > 2, this class includes a generalization of metrics.Expand

Abstract.Szemerédi’s regularity lemma is a fundamental tool in graph theory: it has many applications to extremal graph theory, graph property testing, combinatorial number theory, etc. The goal of… Expand