Intermediate statistics interpolating from Bose statistics to Fermi statistics are allowed in two dimensions. This is due to the particular topology of the two dimensional configuration space of identical particles, leading to non trivial braiding of particles around each other. One arrives at quantum many-body states with a multivalued phase factor, which encodes the anyonic nature of particle...

We show that the discrete set of pair amplitudes $A_m$ introduced by Haldane are an angular-momentum resolved generalization Tan two-body contact, which parametrizes universal short-range correlations in atomic quantum gases. The provide a complete description translation-invariant and rotation-invariant states lowest Landau level (LLL), both compressible incompressible. To leading nontrivial o...

The idea behind the SizeReduce(B) subroutine is, in the Gram-Schmidt decomposition B = B̃ ·U, to shift the entries in the upper triangle of U by integers (via unimodular transformations), so that they lie in [−12 , 1 2). Because changing an entry of U may affect the ones above it (but not below it) in the same column, we must make the changes upward in each column. Formally, the algorithm works ...

Given an LLL-basis B of dimension n = hk we accelerate slide-reduction with blocksize k to run under a reasonable assumption in 1 6 nh log1+ε α local SVP-computations in dimension k, where α ≥ 4 3 measures the quality of the given LLL-basis and ε is the quality of slide-reduction. If the given basis B is already slide-reduced for blocksize k/2 then the number of local SVP-computations for slide...

Let B be a basis of a Euclidean lattice, and B̃ an approximation thereof. We give a sufficient condition on the closeness between B̃ and B so that an LLL-reducing transformation U for B̃ remains valid for B. Further, we analyse an efficient reduction algorithm when B is itself a small deformation of an LLL-reduced basis. Applications include speeding-up reduction by keeping only the most significa...

The Lovász Local Lemma (LLL) is a powerful combinatorial result used in many applications to show that a particular event happens with positive probability. It is known that if a large number of independent events each happen with positive probability, then there is positive (possibly exponentially small) probability that they all happen at the same time. The LLL, first proved by Erdős and Lová...

Low-level laser (LLL) irradiation promotes proliferation of muscle satellite cells, angiogenesis and expression of growth factors. Satellite cells, angiogenesis and growth factors play important roles in the regeneration of muscle. The objective of this study was to examine the effect of LLL irradiation on rat gastrocnemius muscle recovering from disuse muscle atrophy. Eight-week-old rats were ...

There is no doubt that data compression is very important in computer engineering. However, most lossless data compression and decompression algorithms are very hard to parallelize, because they use dictionaries updated sequentially. The main contribution of this paper is to present a new lossless data compression method that we call Light Loss-Less (LLL) compression. It is designed so that dec...