### Table 1. Key dimensions of the EPPA model.

"... In PAGE 6: ...The model covers the period 1985 to 2100 in five-year steps. The world is divided into 12 regions, as shown in Table1 , which are linked by multilateral trade. The economic structure of each region consists of eight fully elaborated production sectors (three non-energy and five energy) and four consumption sectors, all shown in the table, plus one government sector and one investment sector (not shown).... In PAGE 7: ... Another important influence on economic growth, the rate of capital formation, is endogenous to the model. Finally, a key determinant of the carbon intensity of economic growth, which also has an important influence on the distribution of burdens of a policy of carbon restriction, is the assumed costs of the backstop technologies (production sectors 9 and 10 in Table1 ) relative to conventional sources. Policies implemented in the EPPA model may take the form of either price instruments (taxes or subsidies) or quantitative measures (quotas).... In PAGE 11: ... Regional economic impacts of a version of an AOSIS-type protocol (expressed as the cumulative percentage reduction in consumption between 2000 and 2100, discounted at 5%) computed from runs of the EPPA model. See Table1 for regional abbreviations. The differences in welfare losses among the sub-regions of the OECD are striking.... In PAGE 14: ... Percentage change in carbon emissions between 2000 and 2100 due to substitution effects and GDP loss resulting from an AOSIS-type protocol as computed from the differences between two runs of the EPPA model, for the Reference Case with backstops. See Table1 for regional abbreviations. Several aspects of these results are worth noting.... In PAGE 17: ... The comparisons are made using the Reference Case with backstops, and the same consumption-based index is used to measure welfare loss. Four regimes are shown: (1) no trading, (2) trading among the four OECD regions only, (3) extension of OECD trading to all Annex I countries by including countries of the Former Soviet Union and Central and Eastern Europe (denoted as FSU and EET in Table1 and earlier figures), and (4) full global trading. 0.... ..."

### Table 2. Strengthen

"... In PAGE 3: ... Definition 2 : Strong group within threshold (SGT): for an element has the property that all the members have closer distance than the threshold to each other pairwise. Defini- tion of SGT can be better understood from the algorithm given in Table2 and the example run in Figure 1. These two groups are defined with the same threshold.... ..."

### Table 4: For the proof of Theorem 5.

1998

"... In PAGE 20: ... For all other cases, the lower bounds follow from reformulating Lemma 6 for an appropriate graph class in terms of the number of vertices. For each case of maximum degree , connectivity c and degree of simplicity , we list in Table4 the used graph class P[ 0;c0; 0](k). For each graph class P[ 0;c0; 0](k), we list k, which is the lower bound on the width and height by Lemma 6, and which we computed relative to n already in Table 3.... ..."

Cited by 2

### Table 6: Strengthened LP-relaxation optimal values.

1998

"... In PAGE 14: ... Of course it would not help much to reduce the size of the cut LP if the strength of the generated cuts are reduced as well. In Table6 we compare the optimal value of the strengthened LP relaxations when all the generated cuts were added. For comparison we have include the initial LP relaxation optima in the column Init .... ..."

### Table 4: Performance of the overall best theorem prover on individual classes of the RTE dataset.

2005

"... In PAGE 6: ... We report the raw accuracy and the con dence weighted score (CWS) in Table 3.5 Table4 shows the performance of the theorem prover split by RTE example class (as illustrated... In PAGE 7: ...3%.) Interestingly, the performance varies heavily by class, (see Table4 ), possibly indicating that some classes are inherently more dif cult. The baseline accuracy is close to random guessing, and the difference between our system performance and the baseline performance on the test set is statistically signi - cant (p lt; 0:02).... In PAGE 7: ... Since our logical formu- lae essentially restate the information in the dependency graph, our abductive inference and learning algorithms are not tied to the logical representation; in particular, the inference algorithm can be modi ed to work with these graph-based representations, where it can be interpreted as a graph-matching procedure that prefers globally consis- tent matchings. Table4 shows that certain classes require more effort in linguistic modeling, and improvements in those classes can lead to great overall gains in performance. The current rep- resentation fails to capture some important interactions in its dependencies (e.... ..."

Cited by 14

### Table 4: Performance of the overall best theorem prover on individual classes of the RTE dataset.

2005

"... In PAGE 6: ... We report the raw accuracy and the confidence weighted score (CWS) in Table 3.5 Table4 shows the performance of the theorem prover split by RTE example class (as illustrated... In PAGE 7: ...3%.) Interestingly, the performance varies heavily by class, (see Table4 ), possibly indicating that some classes are inherently more difficult. The baseline accuracy is close to random guessing, and the difference between our system performance and the baseline performance on the test set is statistically signifi- cant (p lt; 0.... In PAGE 7: ... Since our logical formu- lae essentially restate the information in the dependency graph, our abductive inference and learning algorithms are not tied to the logical representation; in particular, the inference algorithm can be modified to work with these graph-based representations, where it can be interpreted as a graph-matching procedure that prefers globally consis- tent matchings. Table4 shows that certain classes require more effort in linguistic modeling, and improvements in those classes can lead to great overall gains in performance. The current rep- resentation fails to capture some important interactions in its dependencies (e.... ..."

Cited by 14

### Table 4. A selection of good integer neighborhoods from the class nND p . For each p we also note the values of n for which Theorem 1 or Theorem 2 is valid.

"... In PAGE 10: ...heorem 1 is valid for this type of neighborhood for every n 1 (cf. [8]). For p 2, nND p is constructed by adding the same lines to the pseudocode of Fig. 2 as in the (B)-case, and replacing the third line by: N( p; j) := ceil n sqrt(p2 + j2) ; Table4 lists a selection of good neighborhoods under restriction (D), with 1 p 10 and n 1000. For each p, we also give all values of n for which Theorem 2 is valid in this case (cf.... ..."

### Table 4. Composition Theorems.

1999

"... In PAGE 7: ...4 Composition Theorems In this section we discuss some useful theorems, that can be proved exploiting the semantics in Table 3 and the de nitions in the previous subsection. We distinguish liveness ( Table4 , 4{8) and safety (Table 4, 9{15). Most theorems refer to the new operators, and only few of them refer to Unity operators: the former are those needed to prove the re nement templates presented in this paper.... ..."

Cited by 4

### Table 1 The duality of maximum entropy and maximum likelihood is an example of the more general

1996

"... In PAGE 10: ... This result provides an added justi cation for the maximum entropy principle: if the notion of selecting a model p ? on the basis of maximum entropy isn apos;t compelling enough, it so happens that this same p ? is also the model which, from among all models of the same parametric form (10), can best account for the training sample. Table1 summarizes the primal-dual framework wehave established. 3.... ..."

Cited by 614

### Table 3: The average mean square errors between the projections derived from the Fourier Projection Theorem and those from spatial domain summing, for various viewing angles. The color values are normalized to the range between 0 and 255.

"... In PAGE 6: ... All the reported measurementsbelow are 2D mean square errors (MSE) from the head data set. Table3 shows the average mean square errors between the projection sums derived from the Fourier Projection Theorem and those from spatial domain summing, for subcubesof different sizes from different viewing angles. The pro- jection angles are specified in the second row in terms of multi- ples of #19.... ..."