### Table 3. Factoring Parameters for Lattice Sieve

"... In PAGE 9: ... Refer to the Appendix for detailed information. The parameters used in the factoring of c164 and c248 are summarized in Table3 . For comparison purposes, Table 3 also includes the parameters used in the factoring of RSA-512 [12].... ..."

### Table 1 The adjusted local pseudopotential form factors (in Ry) and lattice constants (in at. units) used in the calculation

"... In PAGE 6: ... Therefore, there is no reason that the nonlocal pseudopoten- tial cannot give good positron annihilation in semiconductors even if the core contribu- tion plays a central role. The adjusted local and nonlocal pseudopotential parameters are listed elsewhere [15, 19] and are given in Table1 . Figs.... ..."

### Table 1: Worked-through example. From top to bottom: Entire problem with answer circled; Steps 1, 2: Non-analogous correspondences with transforms; Step 3: Analogous correspondences; Step 4: Lattices factored to show relevant categories, and the category correspondence that solves the problem.

"... In PAGE 10: ... So the claim stated in the beginning of this section could be rephrased as: a geometric analogy built on non-transverse shape-arrangements are codimension-preserving moves in the base and target category lattices. Before moving on to a set of examples to test this claim, we can return to the example we started working through at the beginning of this section in Table1 . At the bottom we see that the (trivial) partial homomorphism from one lattice to the other indicates that 3 is the correct answer.... ..."

### Table 2 Subsequentialword lattices in the NAB task.

1997

"... In PAGE 36: ...These lattices were already determinized. Table2 shows the average reduction factors we obtainedwhen using theminimizationalgorithms withseveral subsequentiallattices obtained for utterances of the NAB task. The reduction factors help to measure the gain ofminimizationalone since the lattices are already subsequential.... ..."

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### Table (IX) gives the gain in lookup table size obtained by the methods proposed, for D4 and E8 lattices. Considering the ten rst isonorms, when using apos;signed apos; leaders, the dictionnary is reduced by a factor of 12 for D4 lattices and 1121 for E8 lattices. When using absolute leaders, the reduction factor is respectiveley 63 and 13227. The arithmetic complexity of the algorithms presented is low, as shown in table (X). Table (X) gives, in each case, the maximum numbers of arithmetic operations, knowing that for some vectors, such as (1 1 1 1), no operation is required.

### Table 1: Per step execution time (in ms) for CPU and GPU clusters and the GPU cluster / CPU cluster speedup factor. Each node computes an 803 sub-domain of the lattice.

"... In PAGE 7: ... Note that although each node has two CPUs, for the purpose of a fair comparison, we used only one thread (hence one CPU) per node for computation. In Table1 , we report the simulation execution time per step (averaged over 500 steps) in milliseconds on both the CPU cluster and the GPU cluster with 1, 2, 4, 8, 16, 20, 24, 28, 30 and 32 nodes. Each node evaluates an 803 sub- domain and the sub-domains are arranged in 2 dimensions.... ..."

### Table IV gives the cohesive energy, as well as the lattice constant and bulk modulus for both GaAs and Si. Next, we consider the equilibrium distance between atoms, which corresponds to minimization of the total energy. Let us insert a multiplicative scaling factor into all lengths, corresponding to scaling of the lattice constant. This implies that every length in the repulsive potential or the Hamiltonian is multiplied by the factor . In the repulsive potential, for example, we have

### Table 1. A summary of previous works for a lattice structure of an N-channel LPPRFB with decimation factor M: E(z) and R(z) de- note the polyphase matrices of the analysis bank and the synthesis bank, respectively.

in Noise Robust Oversampled Linear Phase Perfect Reconstruction Filter Bank With A Lattice Structure

### Table 1: A summary of previous works for a lattice structure of an N-channel LPPRFB with deci- mation factor M: E(z) and R(z) denote the polyphase matrices of the analysis bank and the synthesis bank, respectively.

2002

Cited by 2

### Table 2 gives the computed values of the generalized discrepancy and the factor for the quot;improved lattices quot;. Actually the rate of improvement is slow. Tab.2 Generalized discrepancy of quot;improved lattice quot; No. of Pts. D(f 1; : : : ; Ng; D) No. of Pts. D(f 1; : : : ; Ng; D)

1997

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