### Table 4: Effectiveness analysis for heuristics with critical threshold requirements

1992

"... In PAGE 15: ...ontaining faults. This minimal threshold is referred to as the critical threshold. After the critical level is decided, suspicious statements are thus highlighted by the heuristic. In Table4 , Rows c and b are the critical thresholds: the ratio of the rank of the critical level to the number of ranked levels and the ratio of suspicious statements within and below the critical level to statements involved in the heuristic (i.... In PAGE 15: ... Because H14 would consider results of other heuristics, a precise critical threshold is hard to define for it. In Table4 , Rows a and b for H14 indicate the number of predicate statements in a tested program divided by the number of the executable statements and the number of the statements highlighted by H1, respectively. Row c tells the effectiveness of using H14 to locate faulty predicate statements.... In PAGE 15: ... A unique threshold, which makes the suggested domain reasonably small and consistently contain faults, is highly desirable. In Table4 , critical thresholds for various heuristics in Row b range from 1% to 91%. A standard threshold cannot be decided within this wide scope.... ..."

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### Table 4: Effectiveness analysis for heuristics with critical threshold requirements

1992

"... In PAGE 15: ...ontaining faults. This minimal threshold is referred to as the critical threshold. After the critical level is decided, suspicious statements are thus highlighted by the heuristic. In Table4 , Rows c and b are the critical thresholds: the ratio of the rank of the critical level to the number of ranked levels and the ratio of suspicious statements within and below the critical level to statements involved in the heuristic (i.... In PAGE 15: ... Because H14 would consider results of other heuristics, a precise critical threshold is hard to define for it. In Table4 , Rows a and b for H14 indicate the number of predicate statements in a tested program divided by the number of the executable statements and the number of the statements highlighted by H1, respectively. Row c tells the effectiveness of using H14 to locate faulty predicate statements.... In PAGE 15: ... A unique threshold, which makes the suggested domain reasonably small and consistently contain faults, is highly desirable. In Table4 , critical thresholds for various heuristics in Row b range from 1% to 91%. A standard threshold cannot be decided within this wide scope.... ..."

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### Table 3: Number of linearly independent equations for small number of images and surface elements, obtained using computer algebra. Bold type indicates that there are enough equations to yield a unique solution (up to a global scale factor)

2001

"... In PAGE 15: ... We then used the Mapletm computer algebra system to check the rank of the system, and con rmed that there is no rank loss. Table3 (a) shows the rank of the system of equations in the generic case. 4.... In PAGE 17: ... This is despite the fact ( rst noticed in [27, 32]) that the illumination vectors being of dimension four, any system of ve or more illumination vectors is linearly dependent, and as a result, the space of images (in the common image plane, or equivalently, taken from the same viewpoint) is itself of dimension four. Moreover, as shown in Table3 (b), we veri ed that generically, there is no rank loss for p 7 as soon as there are at least two independent illumination vectors, even if all the other illumination vectors are linearly dependent on these two vectors (or, in other words, if all the illumination vectors are planar). As an application of this result, given ten views, only one of which has a di erent illuminant which is not yet identi ed, we are able to compute the ten illuminants and then classify nine images as having the same illuminant.... ..."

Cited by 182

### Table 3: Number of linearly independent equations for small number of images and surface elements, obtained using computer algebra. Bold type indicates that there are enough equations to yield a unique solution (up to a global scale factor)

2001

"... In PAGE 10: ... We then used the Mapletm computer algebra system to check the rank of the system, and confirmed that there is no rank loss. Table3 (a) shows the... In PAGE 11: ... This is despite the fact (first noticed in [27, 32]) that the illumination vectors being of dimension four, any system of five or more illumination vectors is linearly dependent, and as a result, the space of images (in the common image plane, or equivalently, taken from the same viewpoint) is itself of dimension four. Moreover, as shown in Table3 (b), we verified that generically, there is no rank loss for p 7 as soon as there are at least two independent illumination vectors, even if all the other illumination vectors are linearly dependent on these two vectors (or, in other words, if all the illumination vectors are planar). As an application of this result, given ten views, only one of which has a different illuminant which is not yet identified, we are able to compute the ten illuminants and then classify nine images as having the same illuminant.... ..."

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### Table 2. Maximum number of tangents in small dimensions

2002

"... In PAGE 13: ...4827 In Table2 , we compare the upper bound of Theorem 10 for the number of lines tangent to 2n 2 quadrics to the number of lines tangent to 2n 2 spheres of Theorem 2, for small values of n. Table 2.... ..."

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### Table 1: The dimension of ternary trees of small depth

"... In PAGE 13: ...Following this idea let us consider the function dim(T k;3) for small values of k stored in Table1 . The entries of this table are equal to the corresponding lower bounds implied by counting arguments and they are supported by constructing embeddings with the help of a computer [2].... In PAGE 13: ... This would lead to the upper bound lim k!1 dim(T k;3) k lim i!1 n0 + 5i k0 + 3i = 5 3: (17) The simplest realization of this idea would be to embed T 3;3 into Q5 and apply the standard arguments above. However, Table1 shows that this is not possible, and we have to have more knowledge on the embedding of T k0;3 into Qn0. To reduce the number of vertices considered under this approach we use a stronger in- ductive hypothesis, extending the tree T k;3 up to the tree ^ T k.... ..."

### Table 1. Performance of manually and evolutionary designed fuzzy controllers and reinforcement learner in 13 simulated environments of di erent structural complexity. The numbers for collision and successes refer to 40 trials per environment. Each trial di ered in the dimensions of the corridor, location of obstacles and initial con guration of the robot We have not tested the autopilot on the real helicopter yet, since the state information provided by the integrated GPS-INS sensors is currently not reli- able enough for automated ight. Fig. 9 shows the transient response of the simulation model to a commanded climb of 2m. The graphs refer to the origi- nal hand-designed PID controller, the evolutionary tuned TSK fuzzy controller with nominal payload of 10kg and with an extra payload of 5kg. Notice, that in the training scenario the maximum extra payload did not exceed 1kg. The optimized controller reaches the commanded altitude much faster, even in case of the increased payload, although a small steady-state error remains in the later case.

2000

"... In PAGE 22: ... 8. Paths of the mobile robot in a real world environment Table1 compares the performance of the manually, the evolutionary designed fuzzy controller and a reinforcement learning scheme. Each controller is evaluated in simulation in thirteen di erent types of geometries, such as dead-ends, straight corridors, L-shaped segments or intersections of two corridors.... ..."

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### Table 6: Stability of estimates The 1000 sample window is long enough to provide a stable average; the variance in the estimates is small in comparison with their mean value. In these cases, it appears that synchronous averaging would August 16, 1996 DRAFT

### Table 1: Statistics for the small dimension problems. Problem n Problem n Problem n Problem n Problem n

2001

"... In PAGE 4: ... In Figure 1 we display the values of qi for the set of small problems. The name and corresponding dimension of each problem appear in Table1 , where problems have been placed in decreasing order with respect to their values of jqij. Table 1 must be read row by row.... In PAGE 4: ... The name and corresponding dimension of each problem appear in Table 1, where problems have been placed in decreasing order with respect to their values of jqij. Table1 must be read row by row. Results for large problems are reported in Figure 2 and Table 2.... ..."

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