### (Table I). More significantly, the analysis indicates that F0 can be estimated for speech from the spectrum of the amplitude envelope by demodulating the utterance at an arbitrary frequency. This enables comparison of relative stress levels of a speaker from different utterances without a priori knowledge of F0 or the formants. Although the spectrum of the instantaneous frequency also revealed harmonics at F0, no strong peak was detected around F0.

### Table 5.6 provides the results obtained from the best polynomial model estimate. Let us remind that the direct nonlinear model initially used to generate the data is a second order polynomial model whose parameters are = 2; = 2; = 1. The polynomial model estimated is the one expected. The conclusion that can be driven is that good estimates of both models have been reached. When comparing Table 5.6 with Table 5.5, it is obvious that the second order polynomial model leads to a better approximation. By using a second order polynomial model, some a priori knowledge is introduced into the model structure, leading to a better modelling.

### Table II. In the first, we manually created a good initial configuration assuming a priori knowledge of system param- eters. We then ran the application, and verified that the final configuration did not substantially depart from the initial one. We consider a good configuration to be one in which fast nodes are nearer the root. Figures 8 and 9 represent the start and end of this experiment. The final tree configuration shows that fast nodes are kept near the root and that the system is constantly re-evaluating every node for possible relocation (as shown by the three rightmost children which are under evaluation by the root).

### Table 2: In uence of branching criterion on the performance of the algorithm A second series of tests was designed to assess the role of the initial upper bound on the behaviour of the algorithm. It is to be expected that a good upper bound will allow to prune more branches of the enumeration tree at earlier levels, and therefore speed up running times. In Table 3, we compare the speedup achieved when using the optimal value z for an upper bound, versus using +1. It appears that the a priori knowledge of a good initial upper bound has little e ect on computing times. Clearly, the sooner the optimal solution is found by the algorithm, the smaller the advantage of starting the algorithm with a good upper bound. However, in some situations, an e cient heuristic could be useful in improving the e ciency of the algorithm.

"... In PAGE 12: ... Explore rst the branch corresponding to xing that variable at the upper bound. As can be observed in Table2 , the number of nodes that have to be explored before obtaining an optimal solution and proving its optimality is very sensitive to the selected branching criterion. The best results have been obtained under criteria BR2 and BR3, which consistently outperformed criteria BR1 and BR4.... ..."

### Table 2: The contingency tables for the glioma dataset: the true partition given by a priori knowledge on the type of disease for each patient is compared with partitions obtained by cutting hierarchical clustering trees at level a83 a67 a39a108a120 . For each contingency table, the entries associated to the optimal assignment are represented in bold. The optimal assignment takes value 15 for group-average and complete- linkage, respectively 17 for Ward algorithm. The 4 AA cases, respectively the 6 OL cases are correctly clustered by all algorithms. Group-average and complete-linkage cluster together only 5 GM cases, while Ward method group properly 6 GM cases.

2003

"... In PAGE 2: ... Based on cluster stability criterion, one can easily decide from Table 1 that the number of distinct clusters present in the glioma dataset is a83 a67 a39a65a120 , which is in good agree- ment with the known pathological classification of that data set. Table2 shows how the samples are assigned to the clusters when cutting the reference dendrogram at level a83 a67 a39a99a120 . We remark that the best version of the hierarchical clustering method is Ward algo- rithm which produces the optimal assignment closest to the known... ..."

Cited by 3

### Table 2: Percentiles of the rst hitting time distribution Problems f3, f4 and f5 possess more than one local maxima. Seemingly, prob- lems f3 and f4 do not cause di culties, maybe due to the low dimensionality of the problems. The results for problem f5 reveal that this problem is solvable for 80% of the runs in less than 100 generations, but there must be local max- ima on isolated peaks preventing the population to generate better solutions by recombination, so that mutation is the only chance to move from the top of a locally optimal peak to the global one. 4 Conclusions The principle of maximum entropy is a useful guide to construct a mutation distribution for evolutionary algorithms to be applied to integer problems. This concept can and should be used to construct mutation distributions for arbi- trary search spaces, because special a priori knowledge of the problem type

1994

Cited by 21

### Table 3 Both proposed PDA apos;s yielded comparable results to AMPEX (slightly inferior) on the female data, and poor performance on the male speaker. The channel selection process did not improve the results. In comparison with AMPEX, the most frequent errors of the PDA were observed at boundaries between silence or unvoiced frames and voiced segments where the signal is voiced but with irregular PPH. Since the speech of the female speaker included less irregular voiced segments than the male speaker, the performance on the female data was better. It is important to note that AMPEX and the proposed PDA do not assume any a priori knowledge of the speaker apos;s sex. The number of processed frames is equal to 14650 (42% voiced, 58% unvoiced) for the male speaker and 18490 (36%, 64%) for the female speaker.

1997

Cited by 13

### Table 6.1 shows sample input data for TEF neural networks. System specification of the 7-machine system is described in Chapter Two. The NN had 2 x 7 = 14 inputs which was the number of all machine angle and speed deviations. In our study, a priori knowledge of the fault type is needed to evaluate the transient energy. The fault type under investigation was the line-to-ground fault for all possible locations. The fault was on line 11-110 which lasted for 0.08 second. After generating and then shuffling the data pairs, 3000 of them were used to train the NN and the rest were used to test the capability of the NN to evaluate the TEF index. Table 6.2 shows the result of the TEF evaluation and the potential energy of each machine. The negative value of TEF shows the instability of the system.

in APPROVAL

### Table 1: Our results and their comparison with previous work. The parallel model of computation is the arbitrary CRCW PRAM [8]. The second contribution is based on the following observation: The results in Table 1 require a priori the knowledge of the arboricity of the input graph. Since computing the exact value of arboricity seems to be hard [12, 18], we provide here algorithms that compute a 2-approximation for arboricity (i.e., an approximation which can be at most twice the exact value). Moreover, we show that using the approximate value, we can still obtain an optimal implicit representation of a sparse graph. The k-forest coloring problem is of independent interest since it is a fundamental prob- lem in the design of fault-tolerant communication networks [7], analysis of electric networks [6, 15] and the study of rigidity of structures [11]. 2 Preliminaries We rst show that an optimal implicit representation of a graph G can be obtained opti- mally, if a k-forest coloring of G is given.

"... In PAGE 3: ... First, we provide optimal sequential and parallel algorithms for obtaining optimal implicit representations of sparse graphs. Our results and their comparison with previous work are summarized in Table1 . It is worth noting that our results are achieved by simple and rather intuitive techniques compared with those used in [3, 4, 17] and moreover, our algorithms are easy to implement.... In PAGE 7: ... Hence, the total resource bounds are as those stated in the theorem. 4 Approximating Arboricity The results listed in Table1 require a priori the knowledge of the arboricity of the input graph in order to obtain its optimal implicit representation. However, the known algorithms for computing the exact value of the arboricity are based on matroid theory: a sequential algorithm [5] and a randomized parallel algorithm [12].... ..."