The Lovász Local Lemma (LLL) is a cornerstone principle in the probabilistic method of combinatorics, and a seminal algorithm of Moser & Tardos (2010) provided an efficient randomized algorithm to implement it. This algorithm could be parallelized to give an algorithm that uses polynomially many processors and O(log n) time, stemming from O(log n) adaptive computations of a maximal independent ...

BACKGROUND A bimodal distribution of measures of restenosis has been demonstrated at 6-8 months after bare metal stent implantation. Drug-eluting stent (DES) treatment has attenuated the impact of certain factors (eg, diabetes) on restenosis but its effect on the distribution of indices of restenosis is not known. OBJECTIVE To perform a detailed analysis of the metrics of restenosis indices a...

In [6] Zassenhaus gave an algorithm for factoring polynomials f ∈ Q[x]. In this algorithm one has to solve a combinatorial problem of size r, where r is the number of local factors of f at some suitably chosen prime p. This combinatorial problem consists of selecting the right subsets of the set of local factors. In the worst case, the algorithm [6] ends up trying 2r−1 such subsets (if a subset...

Abstract Funding Acknowledgements Type of funding sources: None. Background Lumen-less leads (LLL) and stylet driven (SDL) are currently used for left bundle branch area pacing (LBBAP). We sought to evaluate the acute performance SDL during LBBAP in comparison with LLL. Methods This is an observational retrospective study including consecutive patients undergoing at our institution.Acute lead w...

Vascular damage occurs frequently at the injured brain causing hypoxia and is associated with poor outcomes in the clinics. We found high levels of glycolysis, reduced adenosine triphosphate generation, and increased formation of reactive oxygen species and apoptosis in neurons under hypoxia. Strikingly, these adverse events were reversed significantly by noninvasive exposure of injured brain t...

The LLL algorithm aims at finding a “reduced” basis of a Euclidean lattice. The LLL algorithm plays a primary role in many areas of mathematics and computer science. However, its general behaviour is far from being well understood. There are already many experimental observations about the number of iterations or the geometry of the output, that pose challenging questions that remain unanswered...