We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovász [LLL82] towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximate the successive minima of the lattice in nearly the same way as LLL-bases. For integer lattices of dimension n given by a basis of length 2, SLLL-reduction runs in O(n) bit ope...

The Lovász Local Lemma (LLL) is a powerful tool that can be used to prove that an object having none of a set of bad properties exists, using the probabilistic method. In many applications of the LLL it is also desirable to explicitly construct the combinatorial object. Recently it was shown that this is possible using a randomized algorithm in the full asymmetric LLL setting [R. Moser and G. T...

BACKGROUND Considering promising results in animal models and patients, therapeutic use of MSCs for immune disease is likely to undergo continued evaluation. Low-lever laser (LLL) has been widely applied to retard the inflammatory reaction. LLL treatment can potentially be applied in anti-inflammatory therapy followed by stem cell therapy. AIM OF THE STUDY The purpose of this study was to inv...

OBJECTIVE To quantitatively assess and compare the quality of life (QoL) of women with a self-reported diagnosis of lower limb lymphedema (LLL), to women with lower limb swelling (LLS), and to women without LLL or LLS following treatment for endometrial cancer. METHODS 1399 participants in the Australian National Endometrial Cancer Study were sent a follow-up questionnaire 3-5 years after dia...

BACKGROUND Lower limb lymphedema (LLL) is a chronic and incapacitating condition afflicting patients who undergo lymphadenectomy for gynecologic cancer. This study aimed to identify risk factors for LLL and to develop a prediction model for its occurrence. METHODS Pelvic lymphadenectomy (PLA) with or without para-aortic lymphadenectomy (PALA) was performed on 366 patients with gynecologic mal...

Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with provable output quality. One early improvement of the LLL algorithm was LLL with deep insertions (DeepLLL). The output of this version of LLL has higher quality in...

OBJECTIVES Although an association between prognosis and lobar location of lung cancer, particularly the left lower lobe (LLL), has been suggested, the certainty of such association remains controversial. The purpose of this study was to evaluate the impact of tumour lobar location on surgical outcomes as an independent prognostic factor for survival in our non-small cell lung cancer (NSCLC) pa...

We surview variants and extensions of the LLL-algorithm of Lenstra, Lenstra Lovász, extensions to quadratic indefinite forms and to faster and stronger reduction algorithms. The LLL-algorithm with Householder orthogonalisation in floating-point arithmetic is very efficient and highly accurate. We surview approximations of the shortest lattice vector by feasible lattice reduction, in particular ...

Seat height that is too high (> 120% of lower leg length [LLL]) or too low (< 80% of LLL) can impede safe transfer and result in falls. This study examines the difference between LLL of frail nursing home residents and the height of their toilets and beds in the lowest position, compares the patient or environmental characteristics of those able to transfer from the bed or toilet to those who c...