lll

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The Lovász local lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid collection ℬ $$ \mathcal{B} “bad” events are mostly independent and have low probability. A seminal algorithm Moser Tardos (J. ACM, 2010, 57, 11) (which we call MT algorithm) gives nearly-automatic randomized algorithms for most constructions based on LLL. However...

This chapter introduces Inductive Logic Programming (ILP) and Learning Language in Logic (LLL). No previous knowledge of logic programming, ILP or LLL is assumed. Elementary topics are covered and more advanced topics are discussed. For example, in the ILP section we discuss subsumption, inverse resolution, least general generalisation, relative least general generalisation, inverse entailment,...

We present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 &  0 & 1\end{array}right )$-wavelets  under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an  example is  provided.

Gold(Ill) is isoelectronic (5d8) and often isostructuml (square-planar) with Pt(ll) and might form the basis of active anticancer agents [1]. However little is known about the biochemistry of Au(lll), a subject also of interest in connection with the side-effects of antiarthritic gold drugs [2]. In this work we have explored the binding of [Au(lll)(diethylenetriamine)CI]CI2 to tripeptides over ...

The algorithmic facet of euclidean lattices is a frequent tool in computer science and mathematics. It mainly relies on the LLL reduction, making worthwile efficiency improvements. Schnorr proved that the LLL algorithm can be speeded up if one computes approximations to the underlying Gram-Schmidt orthogonalisations. Without approximations, these computations dominate the cost of the reduction....

When determining lower limb loading (LLL) sources of error include the vibration of kinematic marker plates and how the motion and force data are digitally filtered. This study examined LLL during dynamic actions with reduced marker vibration using a tibial plate (TP) and two different levels of filtering severity (15 Hz and 35 Hz cut-offs). The increase of the filter cut-off frequency for the ...

Coppersmith described at Eurocrypt 96 a polynomial-time algorithm for finding small roots of univariate modular equations, based on lattice reduction. In this paper we describe the first improvement of the asymptotic complexity of Coppersmith’s algorithm. Our method consists in taking advantage of Coppersmith’s matrix structure, in order to apply LLL algorithm on a matrix whose elements are sma...