Abstract Using the calculus of variations, we prove following structure theorem for noise-stable partitions: a partition n -dimensional Euclidean space into m disjoint sets fixed Gaussian volumes that maximise their noise stability must be $(m-1)$ -dimensional, if $m-1\leq n$ . In particular, maximum in $\mathbb {R}^{n}$ is constant all satisfying $n\geq m-1$ From this result, obtain: (i) A pro...

Article Chronology: Received 28 March 2006 Revised version received 6 June 2006 Accepted 13 June 2006 Available online 29 June 2006 The three Kindlins are a novel family of focal adhesion proteins. The Kindlin-1 (URP1) gene is mutated in Kindler syndrome, the first skin blistering disease affecting actin attachment in basal keratinocytes. Kindlin-2 (Mig-2), the best studied member of this famil...

INTRODUCTION AND OBJECTIVE In recent decades, an association has been reported between epidermolysis bullosa (EB) and dilated cardiomyopathy (DC). DC is typically in an advanced phase when detected, leading to a poorer prognosis. Our objective was to determine the prevalence of DC in patients with EB seen in Hospital San Joan de Déu in Barcelona, Spain, between May 1986 and April 2015. METHOD...

“Theorem of the alternative” is the generic name of different results used as an important tool in optimization. Though the early versions have been obtained under strong conditions of convexity, for the further extensions, these conditions have been weakened using generalized convexity beyond vector space structure. This is the case of the result proved by Jeyakumar [4], who used an extension ...

In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree functions. Here we provide an alternative proof for general lowdegree functions, with no constraints on the influences. We show that any real-valued function on the slice, whose degree when written as a harmonic multi-linear polynomial is o( √ n), has approximately the same dis...

In this lecture, we present a result of Khot, Kindler, Mossel and O’Donnell [1] which states that approximating MaxCut to within a factor αGW + ε, for any ε > 0, is “hard”. Here hardness is not based under the usual P 6= NP assumption, but rather a weaker conjecture called the Unique Games Conjecture (UGC). This conjecture was introduced by Khot [2] in 2002, and states that a certain very meani...

A mutant of E. coli, isolated by Kindler and Hofschneider as a strain defective in RNase III activity, forms a 30S precursor of ribosomal RNA ("30S pre-rRNA"). The half-life of the 30S pre-rRNA in growing cells at 30 degrees , estimated by the rate of specific (3)[H]uridine incorporation, is about 1 min. In rifampicin-treated cells, the RNA is metabolized to mature rRNA with a half-life of abou...