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In addition to the probabilistic model approach, one can directly conduct random simulations to gain insight into practical running average behavior of the LLL algorithm.
Although the LLL algorithm and its variants have been widely used in practice, experimental simulations were only carried out recently and limited to the quality measures of the Hermite factor, practical running behaviors and reduced Gram-Schmidt coefficients.
In order to understand the practical running behavior of DEEP and compare it with that of LLL, we have computed the ratio ρ DEEP i = K DEEP i / K LLL i, ( i = 1, 2, …, 10, 000 ). (22).
Obviously, they increase with the increase of the rank of a lattice, indicating that the practical running behavior of DEEP is exponential, at least, for the random lattices under investigation.
In other words, DEEP may not be super-polynomial in the worst case, as otherwise mentioned by Schnorr and Euchner [35]. Figure 1 Practical running behaviors of LLL algorithm with deep insertions relative to original LLL algorithm.
To investigate the possibility of a cost-effective direct borohydride fuel cell (DBFC), the performance enhancement of a single cell is investigated under practical running conditions by adopting non-precious metal for the anode.
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Among other things, it encompasses preparing and giving lectures, generating student resources (e.g., on the Web), designing and delivering practicals, running workshops and seminars, setting and marking assignments and exams.
By the end of the 60s, Hughes was trying to escape from the considerable administrative and practical work of running the magazine.
In the second stage, optimized factor values were adopted in practical runs.
For a given coil angle, suitable traverse ratios (among calculated traverse ratios) were found by practical run on machine.
In addition, a catalogue of the proposed designs with practical run-sizes is presented for multifactorial experiments.
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