"... In PAGE 19: ... Each odd image has been subjected to the brightness change and every even image has been left unchanged, so that for each subject there are two bright images and two unchanged. These results are shown in tabular form in Table2 . where we see that the recognition rate for FFE falls by only 2% for a brightness addition of 3 standard... ..."

"... In PAGE 16: ...11). Using the initial values p = [0,0,0,9.9989e-1,-1.4852e-2,0] and v = [0,0,0,-6.75e- 5,-4.5444e-3,0], numerical results from DASSL are contained in Table2 , in which error test failures (etf ? s) and convergence test failures (ctf ? s) are listed. Using simpli ed Newton iterations and the modi ed local error estimate, CS, CM, and LM obtain consistent results, where the modi ed convergence test for Newton iterations is applied in LG and LM.... In PAGE 16: ... Using simpli ed Newton iterations and the modi ed local error estimate, CS, CM, and LM obtain consistent results, where the modi ed convergence test for Newton iterations is applied in LG and LM. Although the numerical results of LG in Table2 may appear to be comparable with those of CS, CM and LM in terms of e ciency, it is not clear that the modi cation of the convergence test in LG is reliable in general. For instance, if the derivative of @ @p(GT ) grows large, the numerical solution may become ine cient or inaccurate.... ..."

"... In PAGE 8: ... Finally, we would like to compare the computational times of the two analytic GB models that have been discussed in this work. In Table5 , one can see that the MV2 model is a bit slower than MV1. Also, the SASA-1 term is estimated to take a negligible amount of extra computational effort.... ..."

"... In PAGE 8: ...tudy (T in degree K) [66, 67, and 68]....................................................................17 Table4 -1 Benchmark testing results for the problem illustrated in Fig.... In PAGE 8: ...able 4-1 Benchmark testing results for the problem illustrated in Fig. 4-4 ...........................34 Table4 -2 Table 4-2: Total defect area during two-phase planning on the prostate image shown in Fig.... In PAGE 40: ... Discussion about the possible implication of this value is given bellow. Table4 -1 presents the total defect area after initial cryoprobes placement and before the force-field phase, whether using bubble-packing circular, or random placement. It can be seen that the quality of bubble-packing increases with the increase in the number of cryoprobes, where circular and random placement techniques appear to be insensitive to the number of cryoprobes.... In PAGE 41: ...NET and executed under Windows XP Professional. The total runtime, as well as the normalized runtime, are listed in Table4 -1, where normalization is done with respect to bubble-packing. It may appear that there is no advantage for using bubble-packing for six cryoprobes, when compared with force-field analogy combined with any of the other initial placement techniques.... In PAGE 41: ... However, one should bear in mind that the threshold for termination of optimization plays a dramatic role in this comparison. For example, if 10% total defect area threshold was selected as a termination criterion, the bubble-packing method would require about five minutes of runtime (similar to the 14 cryoprobes in Table4 -1), while the other two placement techniques will require somewhat less runtime, but similar in magnitude to the force-field procedure. This indicates that bubble-packing is dramatically faster for fewer than for a greater number of cryoprobes.... In PAGE 44: ... The experiment was repeated for 8, 10, 12, and 14 cryoprobes. Results of this experiment are listed in Table4 -2, selected temperature fields are shown in Fig. 4-9, and TVH are shown in Fig.... In PAGE 48: ... 40 Table4 -2 Total defect area during two-phase planning on the prostate image shown in Fig. 4-8.... ..."