### Table 2: Summary of the results obtained for the first test problem (the global energy minimum

"... In PAGE 14: ... This comes from the observation that a grid of a0 a7a57 a0 a30 a1 a39 elements obtained using only local a15 -refinement yields a solution energy of a8 a1 a49 a18 a30 a57 a0 a30 a8 and, when this is optimized, the solution energy only reduces to a8 a30 a49 a1 a1 a57 a22 a16 a39 . A summary of all of these computational results is provided in Table2 and an illustration of the meshes obtained using multilevel optimization with local a15 -refinement is given in Figure 7. 5.... In PAGE 18: ... It should be noted that, although quite complex to implement in a57 -d, the edge/face swap- ping component of the hybrid algorithm is crucial. This may be demonstrated, for example, by contrasting the results of Table2 with those obtained for the same test problem but without the connectivity optimization step included in Figure 1 (see [8] for further details). Such modified results are presented in Table 4 and clearly demonstrate the limitations of the adaptive algo- rithm when edge/face swapping is neglected.... ..."

### Table 2: Summary of the results obtained for the first test problem (the global energy minimum is a8 a3

"... In PAGE 10: ... This comes from the observation that a grid of a0 a22 a0 a30 a1 a3 elements obtained using only local a0 -refinement yields a solution energy of a8 a1 a13 a0 a30 a22 a0 a30 a8 and, when this is optimized, the solution en- ergy only reduces to a8 a30 a13 a1 a1 a22 a4 a1 a3 . A summary of all of these computational results is provided in Table2 and an illustration of the meshes obtained using multilevel opti- mization with local a0 -refinement is given in Figure 7. 5.... In PAGE 13: ... It should be noted that, although quite complex to implement in a22 -d, the edge/face swapping component of the hybrid algorithm is crucial. This may be demonstrated, for example, by contrasting the results of Table2 with those obtained for the same test problem but without the connectivity optimization step included in Figure 1. Such modified results are presented in Table 4 and clearly demonstrate the limitations of the adaptive algorithm when edge/face swapping is neglected.... ..."

### Table 4: Summary of the results obtained for the first test problem without edge/face swapping (the global energy minimum is BHBCBMBCBCBCBC).

"... In PAGE 13: ... This may be demonstrated, for example, by contrasting the results of Table 2 with those obtained for the same test problem but without the connectivity optimization step included in Figure 1. Such modified results are presented in Table4 and clearly demonstrate the limitations of the adaptive algorithm when edge/face swapping is neglected.... ..."

### Table 4: Summary of the results obtained for the first test problem without edge/face swapping (the global energy minimum is a8 a3

"... In PAGE 13: ... This may be demonstrated, for example, by contrasting the results of Table 2 with those obtained for the same test problem but without the connectivity optimization step included in Figure 1. Such modified results are presented in Table4 and clearly demonstrate the limitations of the adaptive algorithm when edge/face swapping is neglected.... ..."

### Table 1: Notations used in the paper. process they used a training data that was dependently obtained by other assignment methods. The performance of their algorithm is totally depend on the used training data. Also in [12] only the co-channel constraint was considered. In this paper, a modi ed discrete Hop eld neural network algorithm for channel assignment problem is proposed in order to improve the convergence rate and to reduce the number of iterations. Our experimental results are also compared with that of Funabiki and Takefuji [11]. In this paper, the channel assignment problem is formulated as an energy minimization problem such that the energy is at its minimum when all the constraints are satis ed and the number of assigned frequencies are the same as the required channel numbers (RCNs) in each cell. Three conditions are considered in this paper as in references [3] and [11]: 1. co-site constraint (CSC) : any pair of frequencies assigned to a cell should have a minimal distance between frequencies; 2. co-channel constraint (CCC) : for a certain pair of radio cells, the same frequency cannot be used simultaneously;

1994

Cited by 7

### Table 3: Total energy for the Tartar example for the conforming and the discontinuous element.

1998

"... In PAGE 12: ... The discon- tinuous method produces the minimizers in Figure 6 with crisp laminates in the appropriate part of the domain. Table3 lists the values for the energy functional obtained for both nite elements meth- ods. Clearly, the discontinuous method attains signi cantly lower values, but they stabilize above 0 in both cases, as expected for this problem, although the minimum energy in the `rotated apos; case is not given explicitly.... ..."

Cited by 3

### Table 3: Total energy for the Tartar example for the conforming and the discontinuous element.

1998

"... In PAGE 12: ... The discon- tinuous method produces the minimizers in Figure 6 with crisp laminates in the appropriate part of the domain. Table3 lists the values for the energy functional obtained for both nite elements meth- ods. Clearly, the discontinuous method attains signi cantly lower values, but they stabilize above 0 in both cases, as expected for this problem, although the minimum energy in the `rotated apos; case is not given explicitly.... ..."

Cited by 3

### Table 1. Comparison table for different applications. Results are given as: Energy (runtime in seconds). For each problem the energies are Scaled to the range of 0 to 999. The last two columns show the percentage of unlabeled nodes for QPBO and QPBOP, where GM means global minimum. For segmentation BC means boundary constraint and RC region constraint. Also, for segmentation, graph cut was run 2n (n = number BC) times with flow and search tree recycling to obtain the global minimum. Note, ICM and simulated annealing do not perform well for applications with hard pairwise constraints (infinite links), such as segmentation and new view synthesis.

2007

"... In PAGE 6: ... Furthermore, running TRW-S until convergence of the lower bound is much slower than QPBO in practice.) Table1 lists the comparison of all methods for one or two examples of each of the six applications. Diagram Recognition Shape recognition in hand-drawn diagrams is an application where the QPBOP method con- siderably outperforms standard QPBO.... In PAGE 8: ... We have also used the deconvolution MRF with only two labels to reconstruct binary images. Table1 gives two re- sults with different convolution kernels. The main conclu- sion is that for highly connected MRFs, e.... ..."

Cited by 1

### Table IV Recursive Calculation on the Minimum Free Energya

1999

Cited by 78

### Table 1. Effects of Cutout

1983

"... In PAGE 5: ...ffected by the cutout algorithm. Note that, with a 20.1 m/s (45 mph) cutout, almost all of the available energy is captured while a substantial fraction of the fatigue damage is still eliminated. Table1 lists the blade fatigue life expectancy and annual energy capture associated with edf apos;s and ddf apos;s for the blade-to-tower joints on the DOE 100-kW turbine at Bushland, TX, shown in Figures 5 and 4, respectively. Control Algorithm Effects The purpose of the cutout algorithm is therefore to balance the extension of fatigue life with the reduction in the annual energy capture, both of which result from shutting down the turbine in high winds.... ..."

Cited by 1