### Table 6. Coherence axioms.

1999

"... In PAGE 20: ... A A?1 = 1v?1 (i.e., A?1 is the -inverse of A ). For example, it follows that (A A ) (A A?1) = (A A ) (A A?1) = 1a, and that (A?1)?1 = A. A double symmetry (see Figure 16) is a natural double transformation, with a double inverse, and it verifies similar axioms to the first two in Table6 , but w.... In PAGE 20: ...xioms to the first two in Table 6, but w.r.t. the four compo- sitions that we have illustrated (horizontal, vertical and the two diagonals). A duplicator is a natural transformation between the identity and the tensor product of two copies of the argu- ment and verifies some additional coherence axioms involv- ing symmetries and dischargers (see Table6 ). A discharger is a natural transformation between the identity and the con- stant functor mapping each element into the unit of the ten- sor product.... In PAGE 20: ... Double coherence axioms. The coherence axioms that double symmetries, double duplicators and double dischargers must satisfy are essen- tially the same of the one-dimensional case ( Table6 ), but repeated for each one of the four composition, thus (A) , r and ! satisfy the coherence axioms w.... ..."

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### Table 6. Coherence axioms.

1999

"... In PAGE 20: ... A A?1 = 1v?1 (i.e., A?1 is the -inverse of A ). For example, it follows that (A A ) (A A?1) = (A A ) (A A?1) = 1a, and that (A?1)?1 = A. A double symmetry (see Figure 16) is a natural double transformation, with a double inverse, and it verifies similar axioms to the first two in Table6 , but w.... In PAGE 20: ...xioms to the first two in Table 6, but w.r.t. the four compo- sitions that we have illustrated (horizontal, vertical and the two diagonals). A duplicator is a natural transformation between the identity and the tensor product of two copies of the argu- ment and verifies some additional coherence axioms involv- ing symmetries and dischargers (see Table6 ). A discharger is a natural transformation between the identity and the con- stant functor mapping each element into the unit of the ten- sor product.... In PAGE 20: ... Double coherence axioms. The coherence axioms that double symmetries, double duplicators and double dischargers must satisfy are essen- tially the same of the one-dimensional case ( Table6 ), but repeated for each one of the four composition, thus (A) , r and ! satisfy the coherence axioms w.... ..."

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### Table 6. Coherence axioms.

"... In PAGE 20: ... For example, it follows that a75 a70a93a61a27a70a56a6 a78 a245 a75 a70 a54a4a165a61a97a70 a130 a223 a78 a211 a75 a70a189a245 a70 a55a4 a78 a61 a75 a70 a57a6a154a245 a70 a130 a223 a78 a211a241a230 a72 , and that a75 a70 a130 a223 a78 a130 a223 a211 a70 . A double symmetry (see Figure 16) is a natural double transformation, with a double inverse, and it verifies similar axioms to the first two in Table6 , but w.... In PAGE 20: ...xioms to the first two in Table 6, but w.r.t. the four compo- sitions that we have illustrated (horizontal, vertical and the two diagonals). A duplicator is a natural transformation between the identity and the tensor product of two copies of the argu- ment and verifies some additional coherence axioms involv- ing symmetries and dischargers (see Table6 ). A discharger is a natural transformation between the identity and the con- stant functor mapping each element into the unit of the ten- sor product.... In PAGE 20: ... Double coherence axioms. The coherence axioms that double symmetries, double duplicators and double dischargers must satisfy are essen- tially the same of the one-dimensional case ( Table6 ), but repeated for each one of the four composition, thus (A) a93 , a84 and a88 satisfy the coherence axioms w.... ..."

### Table 2: Thread topic coherences and thread com- ponent coherences.

2004

"... In PAGE 7: ... The di erence between Hlogo value and that of random assignment is more than 3 times the standard deviation, showing that the topic assignment by the proposed method is statistically signi - cantly better than random topic assignment. Table2 reports the average thread topic coherence of all 335 threads we collected from the CNN set. In the table, we also show the thread component coherence (denoted as Hthread), which is the coherence value of the shots in a thread component.... ..."

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### Table 2: Thread topic coherences and thread component coherences

"... In PAGE 7: ... The results show that the assignment of topics by coclustering is meaningful and is signiflcantly better than random topic assignment. Table2 reports the average thread topic coherence of all 335... ..."

### Table 3: Coherence Actions and Conditions

1998

"... In PAGE 8: ... 2.5 Cache Actions Table3 describes all coherence actions and conditions.... ..."

### Table 11 Proportion of coherence relations.

2005

"... In PAGE 32: ... Table 8), there are no big differences for indi- vidual coherence relations. Table11 shows the data from Figure 17, ranked by the factor of percentage of overall coherence relations by percentage of coherence relations ingoing to nodes with multiple parents. As for crossed dependencies, we also tested whether removing certain kinds of coherence relations reduced the mean in-degree (number of parents) and/or the per- centage of nodes with in-degree greater than one (more than one parent).... In PAGE 35: ...13% of all coherence relations would still be represented (cf. Table11 ). Furthermore, note that this pattern of results is not predicted by any literature we are aware of, including Knott (1996), although he predicts the results partially (he predicts that removing elaboration relations but not that removing elaboration as well as similarity relations is necessary in order to remove basically all nodes with multiple parents; cf.... ..."

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### Table 11 Proportion of coherence relations.

2005

"... In PAGE 32: ... Table 8), there are no big differences for indi- vidual coherence relations. Table11 shows the data from Figure 17, ranked by the factor of percentage of overall coherence relations by percentage of coherence relations ingoing to nodes with multiple parents. As for crossed dependencies, we also tested whether removing certain kinds of coherence relations reduced the mean in-degree (number of parents) and/or the per- centage of nodes with in-degree greater than one (more than one parent).... In PAGE 35: ...13% of all coherence relations would still be represented (cf. Table11 ). Furthermore, note that this pattern of results is not predicted by any literature we are aware of, including Knott (1996), although he predicts the results partially (he predicts that removing elaboration relations but not that removing elaboration as well as similarity relations is necessary in order to remove basically all nodes with multiple parents; cf.... ..."

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### TABLE V THREAD PAIR COHERENCES AND SINGLE THREAD COHERENCES

### Table 1: Summarizer coherence rankings

2003

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