Lovász Local Lemma (LLL) is a probabilistic tool that allows us to prove the existence of combinatorial objects in the cases when standard probabilistic argument does not work (there are many partly independent conditions). LLL can be also used to prove the consistency of an infinite set of conditions, using standard compactness argument (if an infinite set of conditions is inconsistent, then s...

Lattice reduction (LR) aided multiple-inputmultiple-out (MIMO) linear detection can achieve the maximum receive diversity of the maximum likelihood detection (MLD). By emloying the most commonly used Lenstra, Lenstra, and L. Lov ́asz (LLL) algorithm, an equivalent channel matrix which is shorter and nearly orthogonal is obtained. And thus the noise enhancement is greatly reduced by employing the...

In a seminal work at EUROCRYPT ’96, Coppersmith showed how to find all small roots of a univariate polynomial congruence in polynomial time: this has found many applications in public-key cryptanalysis and in a few security proofs. However, the running time of the algorithm is a high-degree polynomial, which limits experiments: the bottleneck is an LLL reduction of a high-dimensional matrix wit...

The LLL algorithm (from Lenstra, Lenstra and Lovász) and its generalization BKZ (from Schnorr and Euchner) are widely used in cryptanalysis, especially for lattice-based cryptography. Precisely understanding their behavior is crucial for deriving appropriate key-size for cryptographic schemes subject to lattice-reduction attacks. Current models, e.g. the Geometric Series Assumption and Chen-Ngu...

Pulsed laser deposition was used to grow epitaxial p-FeSis films on Si(ll1) (1X1) and Si(ll1) (7X7) with the following epitaxial orientations: P-FeSi2(OOl)//Si(lll) with @-FeSi~OlO]//Si(llO) and three rotational variants’silicide growth was influenced by substrate temperature and deposition rate, but not by the structure of the starting surface. Films containing both P-FeSia and FeSi were forme...

The Lenstra-Lenstra-Lovász lattice basis reduction algorithm (LLL or L) is a very popular tool in public-key cryptanalysis and in many other fields. Given an integer d-dimensional lattice basis with vectors of norm less than B in an n-dimensional space, L outputs a socalled L-reduced basis in polynomial time O(dn log B), using arithmetic operations on integers of bit-length O(d log B). This wor...

Despite their popularity, lattice reduction algorithms remain mysterious in many ways. It has been widely reported that they behave much more nicely than what was expected from the worst-case proved bounds, both in terms of the running time and the output quality. In this article, we investigate this puzzling statement by trying to model the average case of lattice reduction algorithms, startin...

Thirty-six primiparous sows were assigned to one of five treatments designed to mimic the lactation feed intake patterns observed in a previous study of commercial farms: high energy intake (HHH) or low energy intake during each week of a 3-wk lactation (LLL), or reduced intake during wk 1 (LHH), wk 2 (HLH) or wk 3 of lactation (HHL). The metabolizable energy intake of sows was either 16.5 (H) ...

Consider an agent trying to bring a system to an acceptable state by repeated probabilistic action. Several recent works on algorithmizations of the Lovász Local Lemma (LLL) can be seen as establishing sufficient conditions for the agent to succeed. Here we study whether such stochastic control is also possible in a noisy environment, where both the process of state-observation and the process ...

The opportunity for wounded servicemembers (SMs) to return to high-level activity and return to duty has improved with advances in surgery, rehabilitation, and prosthetic technology. As a result, there is now a need for a high-level mobility outcome measure to assess progress toward high-level mobility during and after rehabilitation. The purpose of this study was to develop and determine the r...