"... In PAGE 20: ... Figure 7 shows estimates obtained using the two methods. Table3 compares hard and soft thresholding. Hard thresholding gives a lower MSE and is less critical to the number of levels that are thresholded.... ..."

"... In PAGE 9: ... This leads to Tables 1 and 3 which summarize the results, under different assumptions on the syntax of the agent programs considered. Table 2 specifies where the proofs of the results listed in Table1 and Table 4 does the same for the results listed in Table 3.... In PAGE 10: ...autious (resp., brave) reasoning in the area of knowledge representation [13]. In particular, this question is important for status atoms Do( ), since it tells us whether is possibly executed by the agent (if she picks nondeterministically some Sem-status set), or executed for sure (regardless of which action set is chosen). Table1 specifies the complexity of the four problems that we study when positive agent programs are considered, while Table 3 specifies their complexity when arbitrary agent programs are considered. Note on Tables: The entries for decision problems in Tables 1 and 3 stand for completeness for the respec- tive complexity classes.... In PAGE 11: ...6 j T 4.9 Table 2: Location of proofs for Table1 (C= Corollary, T= Theorem, P= Proposition). Proofs of these results are not difficult, using the well-known result that inference from a datalog program (Horn logic program) is P-complete, cf.... In PAGE 14: ... The focus in this section is on the base case, in which we have programs without integrity constraints (though cases where results on integrity constraints follow as immediate extensions of the no- integrity-constraint case are also included). As the Table1 and 3 show, in general the presence of integrity constraints has an effect on the complexity of some problems, while it has not for others. For the latter problems, we discuss this effect in detail in the next section.... ..."

"... In PAGE 46: ... 5.3 Evaluation of Decision Accuracy The decision accuracy results for both thresholds are provided in Table9 . This includes the DA and RDA results.... ..."

"... In PAGE 4: ... The thresholds of the Universal threshold algorithm and the Minimax algorithm increase when the sample size increases, while the threshold of the Rigorous SURE algorithm decreases and oscillate near a certain value. The best estimations using the soft thresholding rule are presented in Table 1, while the best estimations using the hard thresholding rule are shown in Table2 . The results in Table 1 show that the soft thresholding rule is better that the hard thresholding rule in terms of MSE (see also Table 2) for almost all synthetic signals.... In PAGE 4: ... The best estimations using the soft thresholding rule are presented in Table 1, while the best estimations using the hard thresholding rule are shown in Table 2. The results in Table 1 show that the soft thresholding rule is better that the hard thresholding rule in terms of MSE (see also Table2 ) for almost all synthetic signals. Table 2 shows that the best performance is achieved with the Coiflet wavelet when applied to different signals.... ..."

"... In PAGE 6: ... The minimax thresholds ( 1; 2) can be derived by choosing ( 1; 2) to attain (12): see section 8 for computational details. Table1 gives the minimax thresholds for selected values of n. From table 1, we can see that the soft minimax quantities are improved by roughly 6% {19% and the hard minimax quantities are improved by roughly 19%-39%.... ..."