### Table 1: Example of block distribution on the Update, Internal, Border, and External sets, using global indexing and an appropriate choice of local reordering.

1999

"... In PAGE 4: ... (The vertices of the graph represent blocks and the edges represent connections.) Table1 shows how the blocks are classified in the update and the external sets and how the update sets are further divided in internal and border sets. 3 2 4 6 7 8 9 10 11 12 13 14 Processor 0 Processor 2 5 Processor 1 1 Figure 2: A grid partitioning on 3 processors.... ..."

Cited by 3

### Table 1: Example of block distribution on the Update, Internal, Border, and External sets, using global indexing and an appropriate choice of local reordering.

1999

"... In PAGE 4: ... (The vertices of the graph represent blocks and the edges represent connections.) Table1 shows how the blocks are classified in the update and the external sets and how the update sets are further divided in internal and border sets. 3 2 4 6 7 8 9 10 11 12 13 14 Processor 0 Processor 2 5 Processor 1 1 Figure 2: A grid partitioning on 3 processors.... ..."

Cited by 3

### Table 1, right group error ge;r) and = (I3; 0), ( fth row in Table 1, left group error ge;`), an appropriate choice of S leads to the simple feedforward controls:

1999

"... In PAGE 28: ... For all choices of ge and , the resulting error function apos; is quadratic with constant mini6 =j(ki + kj), where fk1; k2; k3g are the eigenvalues of the matrix K1. Since many combinations are possible, we report only the most instructive ones in the rst column of Table1 . In the third column we characterize the error functions in terms of various properties.... In PAGE 30: ... In what follows, we parametrize the set of transport maps with the set of change of frames, that is with SE(3). For each transport map T , we call transport element the unique motion 2 SE(3) such that _ g ? T _ gd = g ( ? Ad d) : In the Table1 , we report compatible transport elements for each error func- tion. For each couple ( apos;; ), the compatibility is veri ed with some straight- forward algebra.... In PAGE 30: ... We de ne fP; fD 2 se(3) by means of hfP ; i = ?L(g ; 0) apos;(g; gd); 8 2 se(3); fD = ?Kd ( ? Ad d) ; (28) where Kd : se(3) 7! se(3) is a self-adjoint (symmetric) and positive de nite. For example, from the rst row of Table1 we compute fP + fD = ? 2 6 4skew(K1Re)_ RT K2pe 3 7 5 ? Kd 2 6 4 ? RT e d V ? RT e Vd 3 7 5 ; where (Re; pe) = (RT d R; p ? pd), and likewise from the third row fP + fD = ? 2 6 4skew(K1Re)_ + (K2pe) pe RT K2pe 3 7 5 ? Kd 2 6 4 ? RT e d V ? RT e (Vd + d pe) 3 7 5 ; where (Re; pe) = (RT d R; RT d (p ? pd)). Next, we de ne a family of feedforward control laws as fFF = ? ad (Ad d) + I d dt (Ad d) + S ( e; d); (29)... In PAGE 31: ... Let fgd(t); t 2 R+g denote the reference trajectory and let d = g?1 d _ gd 2 se(3) denote its bounded body- xed velocity. From Table1 , let apos; be a quadratic error function with constant mini6 =j(ki + kj), and let be a compatible transport element. Also, let S be a bilinear operator satisfying (30), and according to equations (28) and (29), let f = fP + fD + fFF 2 se(3) : Then the total energy apos;(g; gd)+ 1 2k ?Ad dk2 I converges exponentially to zero from all initial conditions (g(0); (0)) such that apos; g(0); gd(0) + 1 2k (0) ? Ad (0) d(0)k2 I lt; mini6 =j (ki + kj): In what follows we present a sketch of the proof.... ..."

Cited by 18

### Table 2. Table enumerating the broad categories of resources, their use in worklist choice decisions and appropriately mapped visualisations.

"... In PAGE 9: ... So the general rules are able to be modi ed but can still be encapsulated in the development of a set of visualisation tools. Table2 maps each resource type to an appropriate visualisation. The table is by no means exhaustive, and is only limited by the number of application areas intended for the visualisations.... ..."

### Table 2. Table enumerating the broad categories of resources, their use in worklist choice decisions and appropriately mapped visualisations.

"... In PAGE 8: ... So the general rules are able to be modi ed but can still be encapsulated in the development of a set of visualisation tools. Table2 maps each resource type to an appropriate visualisation. The table is by no means exhaustive, and is only limited by the number of application areas intended for the visualisations.... ..."

### Table 2: Tune splits measured in 1996 at 22 and 80/86 GeV. At 22 GeV, the vertical tunes splits were minimized by an appropriate choice of the MSBT polarity. At high energy the vertical split was corrected.

"... In PAGE 3: ... Horizontal tune corrections lead to negligible chromaticity splits. Table2 gives the tune splits measured in 1996. On some occasions, tune splits of up to 0.... ..."

### Table 1: Computational Results for the MAX{2{SAT test problems. SAT problems. Neither algorithm was dominant on all problems, and the choice of an appropriate algorithm depends on the characteristics of the problem to be solved.

1999

Cited by 50

### Table 1. Parameter of the geometric bound, Q, corresponding value of S , and maxi- mum throughput in the absence of control, C1, vs. b, for some values of . If, on the other hand, the tra c density is identically zero in [0; ], it is possible to show that Cn, in the limit as n ! 1, is exponentially decreasing. Therefore, even in this latter case, (18) can be satis ed for an appropriate choice of Q. Finally, observe that, even for Q = 0 (in which case, of course, (18) is always satis ed), the achievable throughput is as large as e?1 = 0:368. (Note

1994

"... In PAGE 9: ... It is obvious that, if C1 = limn!1 gt; 0, it is always possible to nd a value of Q such that (18) is satis ed. Table1 shows the values of Q and the corresponding S for the capture probabilities (10), computed assuming uniform tra c density in [0; 1]. To allow a comparison, Table 1 displays the values of the C1, i.... In PAGE 9: ... Table 1 shows the values of Q and the corresponding S for the capture probabilities (10), computed assuming uniform tra c density in [0; 1]. To allow a comparison, Table1 displays the values of the C1, i.e.... ..."

Cited by 5

### Table 2: Width of di racting tree and counting network per network type. complete crossbar network (Figure 22), the added bandwidth reduces the cost of messages and all three methods have roughly similar performance, with the di racting tree leading in throughput by about 35%. The appropriate choice of width of a di racting tree or counting networks, depends on the properties of the network being used. In equidistant, low bandwidth networks, where depth is the main concern, smaller trees and networks work better. On the other hand a larger data structure is better suited to take advantage of bandwidth, and also tends to spread messages around the entire network, which is useful when congestion is a problem, as in the case of the mesh with single wire switches. Table 2 summarizes the optimized widths of the constructions we present.

1996

Cited by 47

### Table 4: Finding a 3-coloring for simplex(n; n; ?2; 0; 0; 0; 0). Finally, DeReS exhibits similar scalability and prover performance results for theories with no exten- sions. Table 5 summarizes our experiments with the family of theories kernel.board 3; 3m?1; 0; 0; 1; 3; 1 . Since these theories have no extensions, DeReS can terminate execution only after it scans through a portion of the search space that is large enough to allow it to conclude that indeed no extensions exist. Consequently, in this case, the performance of DeReS is worse than in the previous two cases. All these results demonstrate the magnitude of savings possible with the appropriate choice of the propositional prover in DeReS. Signi cant savings were observed for theories encoding both existence

"... In PAGE 30: ... This excellent performance is due to two factors: relaxed strati cation and a large number of extensions these theories have, which makes it easy to stumble upon them. Table4 presents the performance results of DeReS for theories color3.simplex n; n; ?2; 0; 0; 0; 0 (they encode 3-colorings of the simplex graphs).... ..."