### TABLE III CURRENT CAPABILITIES OF THE PROTOTYPE AND OPTIMIZING TENSOR CONTRACTION ENGINES.

in Synthesis of High-Performance Parallel Programs for a Class of Ab Initio Quantum Chemistry Models

2005

Cited by 16

### Table 4.2: Optimal contracts and surplus expressions in the example with heterogeneous network effects, under entry-deterring monopoly

2003

### Table 4 Estimates under Taylor contracting

"... In PAGE 25: ... For estimates of greater than zero, this would imply a larger value for the structural parameter . Table4 presents results from estimation of the inflation expression that was obtained from the Taylor staggered-contracting framework. For , the number of free parameters to be estimated is .... ..."

### Table 3. Tilings Under Memory Constraint

2005

Cited by 1

### Table 4. Experimental results on optimal test access architecture design under power constraints: (a) S 1 (b) S 2 .

"... In PAGE 5: ... G i can be obtained from power models for core i. Experimental results for power-constrained test access archi- tecture design for S 1 and S 2 are shown in Table4 . For our ex- periments, we approximated G i by the number of gates in core i.... In PAGE 5: ... On the other hand, for higher values of W, the testing time is affected substantially. For example, in Table4 (a), for W 24 and power budget of 300 units, the testing time does not decrease with an increase in W due to power constraints. In some cases, the ILP problem may even be infeasible for higher test widths, e.... In PAGE 5: ...g. in Table4 (b) with W =48 and power budget of 300 units for S 2 . Comparing with Table 2, we note that the width distribution is also significantly different due to power constraints.... In PAGE 5: ... This is achieved using a width distribution of (10,10) and test bus assignment (2,2,2,2,2,2,2,2,2,1). However, as seen from Table4 . for test width W =24, the test bus assignment has to be changed to meet power constraints, and the minimum testing time increases to 471900 cycles.... ..."

### Table 4. Experimental results on optimal test access architecture design under power constraints: (a) S1 (b) S2.

2000

"... In PAGE 5: ... Gi can be obtained from power models for core i. Experimental results for power-constrained test access archi- tecture design for S1 and S2 are shown in Table4 . For our ex- periments, we approximated Gi by the number of gates in core i.... In PAGE 5: ... On the other hand, for higher values of W, the testing time is affected substantially. For example, in Table4 (a), for W 24 and power budget of 300 units, the testing time does not decrease with an increase in W due to power constraints. In some cases, the ILP problem may even be infeasible for higher test widths, e.... In PAGE 5: ...g. in Table4 (b) with W = 48 and power budget of 300 units for S2. Comparing with Table 2, we note that the width distribution is also significantly different due to power constraints.... In PAGE 5: ... This is achieved using a width distribution of (10,10) and test bus assignment (2,2,2,2,2,2,2,2,2,1). However, as seen from Table4 . for test width W = 24, the test bus assignment has to be changed to meet power constraints, and the minimum testing time increases to 471900 cycles.... ..."

Cited by 44

### Table 1, i.e. k = PBc + Bp + b and l = Bc + b. The distribution basis for a multi-dimensional array can be expressed as a tensor product of the distribution bases for each dimension.

1994

"... In PAGE 5: ...Table1 : Index mapping functions for regular data distributions. BLOCK CYCLIC CYCLIC(b) local to global k = p(dN=Pe) + l k = lP + p k = (l div b)bP + bp + l mod b global to local l = k mod dN=Pe l = k div P l = (k div Pb)b + k mod b global to proc p = k div dN=Pe p = k mod P p = (k div b) mod P k global index 0 k N ? 1; l local index 0 l lt; db ?dN=(Pb)e ; p processor 0 p lt; P.... In PAGE 5: ... Techniques developed in [11] can be used for the array redistribution in the general case. For identity alignments, the relationships between the global index, the local index and the processor index for regular data distributions of a one-dimensional array are shown in Table1 . The indexing for arrays A and A loc begins at zero and the processors are numbered from 0 to P ? 1.... In PAGE 8: ... For example, under a BLOCK distribution the array is partitioned into segments of size NP . The relationship between the global index k, the processor index p, and the local index l as shown in Table1 can be represented by the equality eN k = eP p eNP l ; where p = k div NP and l = k mod NP . In the above identity, the index of vector basis eP p is associated with the processor index on which element A(k) is located after being distributed using a BLOCK distribution.... ..."

Cited by 8

### Table 1, i.e. k = PBc + Bp + b and l = Bc + b. The distribution basis for a multi-dimensional array can be expressed as a tensor product of the distribution bases for each dimension.

1994

"... In PAGE 5: ...Table1 : Index mapping functions for regular data distributions. BLOCK CYCLIC CYCLIC(b) local to global k = p(dN=Pe) + l k = lP + p k = (l div b)bP + bp + l mod b global to local l = k mod dN=Pe l = k div P l = (k div Pb)b + k mod b global to proc p = k div dN=Pe p = k mod P p = (k div b) mod P k global index 0 k N ? 1; l local index 0 l lt; db ?dN=(Pb)e ; p processor 0 p lt; P.... In PAGE 5: ... Techniques developed in [11] can be used for the array redistribution in the general case. For identity alignments, the relationships between the global index, the local index and the processor index for regular data distributions of a one-dimensional array are shown in Table1 . The indexing for arrays A and A loc begins at zero and the processors are numbered from 0 to P ? 1.... In PAGE 8: ... For example, under a BLOCK distribution the array is partitioned into segments of size NP . The relationship between the global index k, the processor index p, and the local index l as shown in Table1 can be represented by the equality eN k = eP p eNP l ; where p = k div NP and l = k mod NP . In the above identity, the index of vector basis eP p is associated with the processor index on which element A(k) is located after being distributed using a BLOCK distribution.... ..."

Cited by 8

### Table 2 Summary of handling of constraints in various global optimization algorithms.

"... In PAGE 10: ... However, ex- tensive numerical results using these techniques have not been published. (See Table2 ; blank spaces mean the feature is absent.) Handling of simple bound constraints through the tessellation process has been... ..."

### Table 3. Test Functions for Global Optimization Function Constraints

1995

"... In PAGE 8: ... 123 { 141. Berlin: Springer{Verlag 1995 For the test functions of Table3 we get the results shown in Figure 5 (Schwe- fel apos;s function F7 is normalized to make a log-plot possible) which con rm the relation (6). For these function we observe di erent regions of convergence.... In PAGE 15: ...able 5. lt;feval gt; vs. n for Function F6 (left) with f 9 10?1, I = 1:4, Rm = 0:1 , Rmin = 10?1 , pm = 1=n , bm = 2, 20 runs, and for Function F7 (right) with f fopt + 5 10?4 jfoptj , I = 1:4, Rm = 0:75 ,Rmin = 10?4 , pm = 1=n , bm = 2, 20 runs, lt;feval gt; vs. n for Function F8 (left) with f 10?3, I = 1:4, Rm = 0:1 , Rmin = 10?6 , pm = 1=n , bm = 2, 20 runs, and for Function F9 (right) with f 10?3 , I = 1:4, Rm = 0:1 ,Rmin = 10?4, pm = 1=n , bm = 2, 20 runs, BGA data from [10] Rastrigin apos;s Function F6 Schwefel apos;s Function F7 n EASY BGA n EASY BGA N lt;feval gt; N lt;feval gt; N lt;feval gt; N lt;feval gt; 20 20 6098 20 3608 20 20 10987 500 16100 100 20 45118 20 25040 100 20 101458 1000 92000 200 20 98047 20 52948 200 20 241478 2000 248000 400 20 243068 20 112634 400 20 430084 4000 699803 1000 20 574561 20 337570 1000 20 1067221 || ||| Griewangk apos;s Function F8 Ackley apos;s Function F9 n EASY BGA n EASY BGA N lt;feval gt; N lt;feval gt; N lt;feval gt; N lt;feval gt; 20 500 26700 500 66000 30 20 13997 20 19420 100 500 77250 500 361722 100 20 57628 20 53860 200 500 128875 500 748300 200 20 122347 20 107800 400 500 229750 500 1630000 400 20 262606 20 220820 1000 500 563350 | ||| 1000 20 686614 20 548306 The test functions given in Table3 are very popular in the literature on global optimization. The main results of this paper are summarized in Table 5 with n the number of variables, N the population size, and feval the average number of function evaluations for 20 runs.... ..."

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