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...

A 75 year-old female was referred to the Central University Hospital of Asturias, Oviedo, in March 2000, because of an abnormal chest X-ray (CXR) as a casual finding. The patient at this time was asymptomatic (no chest pain, night sweats or fever). She had no known toxic habits nor surgical or medical background of interest. The chest X-ray showed a left lower lobe (LLL) alveolar infiltrate. Sh...

We present a calculation of the heavy quark momentum diffusion coefficients in strongly magnetized medium, within Lowest Landau Level (LLL) approximation. In particular, we use Hard Thermal Loop (HTL) resummed effective gluon propagator, generalized for hot and medium. Using this HTL propagator along with LLL analytically derive full results longitudinal transverse charm bottom quarks beyond st...