Light Linear Logic (LLL) of [Gir95] characterizes the polytime functions through a careful handling of structural inference rules of logic. Based on this purely logical approach, we give a characterization of the polyspace functions. Our logical system is an extension of Intuitionistic Light A ne Logic (ILAL) of [Asp98], a variant of LLL with full (unrestricted) weakening. We introduce the noti...

In the present paper we show how to speed up lattice parameter searches for Monte Carlo and quasi–Monte Carlo node sets. The classical measure for such parameter searches is the spectral test which is based on a calculation of the shortest nonzero vector in a lattice. Instead of the shortest vector we apply an approximation given by the LLL algorithm for lattice basis reduction. We empirically ...

• The growing mismatch between skills and supply in a changing world. • By 2020, manufacturing will only occupy 10-20% of the workforce. • In the UK and elsewhere, meanwhile, the high skills sector is growing . • Participation in lifelong learning (LLL) is very variable; in the UK about half participate, but these tend to be the better educated or trained. • Unemployment and participation in LL...

The LLL algorithm is one of the most studied lattice basis reduction algorithms in the literature. Among all of its variants, the floating point version, also known as L, is the most popular one, due to its efficiency and its practicality. In its classic setting, the floating point precision is a fixed value, determined by the dimension of the input basis at the initiation of the algorithm. We ...

Single crystal epitaxial films of CoSi2 were grown by MBE on various (111)Si single crystal substrates, whose surfaces were purposely tilted towards the < 1IO >, direction by small angles 4>, t, 0° :54>, :5 4°, measured between the surface normal and the < 111 >. direction of Si. The actual offset angle, 4>,, was determined by back Laue reflection method. The average perpendicular strain of the...