### Table 1 Experiments for our probabilistic analysis (sd = standard deviation, rel. err. is relative error) # roots # tests % of trials: % of trials: % of trials:

2005

### Table 4 Appropriateness of existing generative probabilistic calculi

"... In PAGE 20: ...consequence, given that PACP parallel composition in isolation is stochastic and respectful, it is interesting to investigate whether a combination of parallel composition and encapsulation is stochastic and respectful, as well. Consider encapsulation in PACP denoted PACP in Table4 above. By using the encapsulation operator, we can prohibit the execution of the au- tonomous actions a, a, b,andc such that only synchronisation actions can be executed.... ..."

### Table 4 Appropriateness of existing generative probabilistic calculi

"... In PAGE 20: ...consequence, given that PACP parallel composition in isolation is stochastic and respectful, it is interesting to investigate whether a combination of parallel composition and encapsulation is stochastic and respectful, as well. Consider encapsulation in PACP denoted PACP in Table4 above. By using the encapsulation operator, we can prohibit the execution of the au- tonomous actions a, a, b, and c such that only synchronisation actions can be executed.... ..."

### Table l. Execution Time Comparisons of CREST and SPICE. All times in seconds of CPU time.

### Table 2. Error rates obtained by Probabilistic Neural Networks .

"... In PAGE 3: ... Its architecture is very simple and powerful, and has some advantages when compared to MLPs: rapid training speed, PNNs are asymptotically Bayes optimal if enough training samples are provided, a good performance over discontinuities in the input space, and what is much more important, it provides mathematically confidence levels for its decisions. Table2 shows the results for PNN in the estimation of thickness and defocus using the same testing procedure than in the previous paragraph. The combinations of both sets of features using PNNs gave the best results in the artificial experiments, and were selected as the definite choice to be considered in real experiments.... ..."

### Table 4. Probabilistic SA, MII SA, and EVPI analysis of the DVT problem.

1998

"... In PAGE 30: ...Table4... In PAGE 31: ...When only the probability of pulmonary embolism is allowed to vary, the probabilistic SA in Table4 shows that the base-optimal alternative to administer anticoagulants remains optimal 97.75% of the time.... In PAGE 31: ...ase-optimal alternative remains optimal 91.85% of the time. In this case, however, problem insensitivity to the entire parameter set is not quite so clear. From the EVPI analysis provided in Table4 , the expected marginal benefit from perfect foreknowledge on the values of all problem parameters is only 0.0589.... ..."

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### Table 4: Parameter Setting for OKAPI Probabilistic Model

"... In PAGE 5: ... In order to define an quot;optimal quot; parameter setting for the BM25 model, we have to conduct a set of experiments based on the CACM and CISI test- collections [Savoy 1995]. The results are depicted in Table4 . However, in our current context, we have set our retrieval scheme according to the parameter values given by [Robertson et al.... ..."

### Table 1: Probabilistic Approaches

"... In PAGE 2: ...3 Word-based, Probabilistic Approaches The third category assumes at most whitespace and punctuation knowledge and attempts to infer MWUs using word combination probabilities. Table1 (see next page) shows nine commonly-used probabilistic MWU-induction approaches. In the table, f and P signify frequency and probability XX of a word X.... ..."

### Table 1 Examples of static probabilistic combination strategies.

2001

"... In PAGE 10: ..., a19a44a57 ). The static probabilistic combination strategies for the dependence informations in Figure 2 are shown in Table1 . The following proposition states that it is correct.... In PAGE 10: ... Recently, the probabilistic conjunction and disjunction strategies for ignorance, independence, positive correlation, negative correlation, and mutual exclu- sion have especially been discussed in [21] and [20]. To our knowledge, the strategies for the remaining dependence informations in Table1 have not been considered so far. 2.... In PAGE 12: ...resp., a90a75a52a93a60a216a90a22a57a188a109a56a90a25a52a25a60a71a68a70a69a137a90a22a57 ) for all probabilistic pairs a90a75a52 and a90a64a57 . For associative static or dynamic probabilistic disjunction strategies a60 and proba- bilistic pairs a90a75a52a44a14a95a105a95a105a95a105a44a14a77a90a32a72 with a73 a112a109 a83 , we write a74 a192 a165 a76a75 a52 a78a77 a72a37a79 a90 a192 to denote a90a75a52a93a60a199a68a95a68a95a68a53a60a216a90a80a72 . The following proposition identifies some static probabilistic conjunction and dis- junction strategies in Table1 that are commutative, associative, and distributive. Proposition 2.... In PAGE 37: ...10 (sketch). The statements can be easily verified along the static probabilistic combination strategies shown in Table1... In PAGE 38: ...13 (sketch). The statement can easily be verified along the static probabilistic combination strategies for ignorance, independence, positive correlation, and negative correlation shown in Table1 (see Proposition 2.9).... ..."

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