We present a regularity lemma for Boolean functions f : {−1, 1}n → {−1, 1} based on noisy influence, a measure of how locally correlated f is with each input bit. We provide an application of the regularity lemma to weaken the conditions on the Majority is Stablest Theorem. We also prove a “homogenized” version stating that there is a set of input bits so that most restrictions of f on those bi...

In this talk we would like to convey the idea that there is a strong relationship between the geometry of the boundary of a domain in Euclidean space and the boundary regularity of the solutions to Laplace's equation. In particular we will show that the doubling properties of the harmonic measure and the "regularity" of the Poisson kernel of a domain in Euclidean space characterize the geometry...

Introduction: The accuracy of dose calculation algorithm (DCA) is highly considered in the radiotherapy sequences. This study aims at assessing the accuracy of five dose calculation algorithms in tissue inhomogeneity corrections, based on the International Atomic Energy Agency TEC-DOC 1583. Material and Methods: A heterogeneous phantom was sc...

Approximate and sample entropy (AE and SE) provide robust measures of the deterministic or stochastic content of a time series (regularity), as well as the degree of structural richness (complexity), through operations at multiple data scales. Despite the success of the univariate algorithms, multivariate sample entropy (mSE) algorithms are still in their infancy and have considerable shortcomi...

In this paper, we provide uniform estimates for V-cycle algorithms with one smoothing on each level. This theory is based on some elliptic regularity but does not require a smoother interaction hypothesis (sometimes referred to as a strengthened Cauchy Schwarz inequality) assumed in other theories. Thus, it is a natural extension of the full regularity V-cycle estimates provided by Braess and H...

Abstract We present the first parallel algorithms that decide strong and branching bisimilarity in linear time. More precisely, if a transition system has n states, m transitions $$\vert Act \vert $$ | A c t action labels, we introduce ...