### Table 7: System of four particles: chart adapted to the constraint structure ( rst label choice ((ab)c) ).

"... In PAGE 25: ... Then, the irreducible kernel of the three-label realization is constructed by de ning the two vectors 11 (see eq. 58) ~ N((ab)c) = 1 2 ^ R(ab) + ^ R(c) ; (70) and ~ ((ab)c) = 1 2 ^ R(ab) ? ^ R(c) : (71) This leads from Table7 to Table 8. The angle of the irreducible kernel is now: ((ab)c) = tan?1 S h~ S ^ ~ N((ab)c) i3 h~ S ^ h~ S ^ ~ N((ab)c) ii3 : (72) The typical form clearly depends on the choice of the chain of labels (see Table 8).... ..."

### Table 2 shows the results of applying the described methods to data sets with 10 to 20 labeled examples. As the choice of labeled

"... In PAGE 4: ... This results in a quantity that captures both local structure of the data set, through neighbor- hood relations, and global structure, through the complexity of the possible paths connecting any pair of points in the data set. A natural extension of the ideas presented here is forming the affinity matrix using dual rooted graphs based on geodesic dis- Table2 . Accuracy of semi-supervised classification of data sets from the UCI repository of machine learning [6].... ..."

Cited by 1

### Table 8: System of four particles: chart adapted to the constraint structure and to the Poincar e group ( rst label choice ((ab)c) ).

"... In PAGE 25: ... Then, the irreducible kernel of the three-label realization is constructed by de ning the two vectors 11 (see eq. 58) ~ N((ab)c) = 1 2 ^ R(ab) + ^ R(c) ; (70) and ~ ((ab)c) = 1 2 ^ R(ab) ? ^ R(c) : (71) This leads from Table 7 to Table8 . The angle of the irreducible kernel is now: ((ab)c) = tan?1 S h~ S ^ ~ N((ab)c) i3 h~ S ^ h~ S ^ ~ N((ab)c) ii3 : (72) The typical form clearly depends on the choice of the chain of labels (see Table 8).... ..."

### Table 9 Recognition Scores From Forced Choice and Free Labels, From Izard (1971)

1994

"... In PAGE 17: ... Ignoring words given by only 1 subject, Izard still found 224 different words or phrases produced (at least twice) for the eight types of expression. Izard therefore devised a scoring key in which, for example, 8 of the words were considered correct for fear, 28 for joy, and so on (the number correct for each emotion is given in Table9 ). In all, 141 different words or phrases were scored as correct for the 8 emotions.... ..."

Cited by 26

### Table A2. Comparison of selection of 5 labels for different choices of operators defined in Table A.I. The first column indicates operators used for S 1 , S 2 , S eql and Sim.

### Table 1. Legend of the labels for the evolutionary sequences computed. For the ten choices of convection modeling and dif- fusion displayed with the last digit, the two choices of metal- licities are displayed by the penultimate digit. Track inst:ov: diff:ov: sed:

in Full Spectrum of Turbulence Convective Mixing: I. Theoretical Main Sequences and Turn-Off for 0.6

### Table 1: Number of actions to label 1018 examples. By converting segmentation actions into classification actions, we can reduce the total number of annotation actions by 22%.

"... In PAGE 5: ... The result is that after a small number of actions, annotator can reduce the number of boundary labels needed to train the CRF, and instead mostly provide TYPE annotation. Table1 displays the total number of actions required to label all the unlabeled data. Note that BASELINE incurs a CHOICE action if the correct labeling is the top choice.... In PAGE 5: ... Note that BASELINE incurs a CHOICE action if the correct labeling is the top choice. The results in Table1 agree with the trends in Figures 2 and 3. Note that the increase in CHOICE actions is expected, since there are many instances where the correct labeling is in the top k choices.... ..."

### Table 1. Rules for choice transitions

1998

"... In PAGE 10: ... Choice transitions represent the choice of actions for execution according to the preselection policy and are labeled with the weight w associated with the chosen action. They are represented by the transition relation j??! de ned as the least subset of LabS R I + LabS that satis es the inference rule in the rst part of Table1 . This rule determines the transitions leaving a state hE; Execi be- ginning from the multiset of choice moves of the state CM (hE; Execi).... In PAGE 10: ... As in [5] we represent the choice moves of a state by a multiset since several moves with the same weight and the same derivative state may be inferred. This multiset is de ned by structural induction as the least element of Mufin(LC LabS) satisfy- ing the rules in the second part of Table1 . 5 A choice move represents the choice of a single action and is a pair composed of the weight of the action and the state reached after the choice.... In PAGE 10: ... Note that in the de nition of CM (hE; Execi) we con- sider only the sets Exec such that hE; Execi is actually reachable from an initial state hF; ;i. The transition relation is determined from CM (hE; Execi) through function melt : Mufin(LC LabS) ?! Pfin(LC LabS), de ned in the third part of Table1 , which merges together the choice moves with the same deriva- tive state by summing their weights. The auxiliary functions left : P(AVId) ?! P(AVId), right : P(AVId) ?! P(AVId), hide : P(AVId) ?! P(AVId), and relab : P(AVId) ?! P(AVId) de ned in the fourth part of Table 1.... ..."

Cited by 24

### Table 1. Rules for choice transitions

1998

"... In PAGE 10: ... Choice transitions represent the choice of actions for execution according to the preselection policy and are labeled with the weight w associated with the chosen action. They are represented by the transition relation j??! de ned as the least subset of LabS R I + LabS that satis es the inference rule in the rst part of Table1 . This rule determines the transitions leaving a state hE; Execi be- ginning from the multiset of choice moves of the state CM (hE; Execi).... In PAGE 10: ... As in [5] we represent the choice moves of a state by a multiset since several moves with the same weight and the same derivative state may be inferred. This multiset is de ned by structural induction as the least element of Mufin(LC LabS) satisfy- ing the rules in the second part of Table1 . 5 A choice move represents the choice of a single action and is a pair composed of the weight of the action and the state reached after the choice.... In PAGE 10: ... Note that in the de nition of CM (hE; Execi) we con- sider only the sets Exec such that hE; Execi is actually reachable from an initial state hF; ;i. The transition relation is determined from CM (hE; Execi) through function melt : Mufin(LC LabS) ?! Pfin(LC LabS), de ned in the third part of Table1 , which merges together the choice moves with the same deriva- tive state by summing their weights. The auxiliary functions left : P(AVId) ?! P(AVId), right : P(AVId) ?! P(AVId), hide : P(AVId) ?! P(AVId), and relab : P(AVId) ?! P(AVId) de ned in the fourth part of Table 1.... ..."

Cited by 24

### Table 3 below gives for the seven topmost texts associated to this cluster, their titles, publication year, the number of terms shared with the cluster and the coverage score. It is interesting to note that among these seven texts, five (1, 2, 4, 5 and 6) directly deal with rough set theory whereas there is no direct link between the choice of the cluster label and the number of texts containing this term. The cluster was automatically labeled Rough Set because it has the highest number of syntactic variants in CLAS.

"... In PAGE 14: ... Table3 . Seven topmost documents associated with the quot;Rough set quot; cluster.... ..."