"... In PAGE 7: ...artmann [21] gives a basic benchmark for Kappa values: they should exceed 0.6. Landis and Koch [22] provided a more detailed benchmark for interpreting the values of Kappa. This is summarized in Table2 . Landis and Koch concede that their benchmark is arbitrary, but they nevertheless contend that it can serve as a useful guideline.... ..."

"... In PAGE 3: ... In contrast to the orig- inal atomic event scores we keep simple counts for the triplets as later we combine triplets extracted for different people. Table1 contains examples from the list of atomic events extracted for Columbus. 3.... ..."

"... In PAGE 4: ... Thus one of the questions we need to ask is: What kinds of data are releasable from a higher dimensional table that will not raise con dentiality concerns and problems? The other is: Will the released data be useful for statistical inference purposes? A Clinical Trial Example We have cast the discussion thus far in the context of government statistical data, but similar issues of con dentiality and usefulness of data arise in other contexts such as epidemiological studies and clinical trials in public health and medicine. In Table2 , we present data from Koch et al. (1983) on the results of a clinical trial on the e ectiveness on an analgesic drug, for patients of two di erent statuses and from two di erent centers.... In PAGE 6: ...tatistics for the model itself, i.e., more margins or at least some of higher-dimension. This more elaborate data release then corresponds to a more complex log-linear model and we can then compare the expected values under the simpler model with the more complex one. For the data in Table2 , we need to include the margin for the three explanatory variables, i.e.... In PAGE 7: ...Table2 Given the [CST] and [R] Margins. Response Poor Moderate Excellent Center Status Treatment 1 1 Active [0,28] [0,28] [0,28] 1 1 Placebo [0,33] [0,33] [0,33] 1 2 Active [0,29] [0,29] [0,29] 1 2 Placebo [0,24] [0,24] [0,24] 2 1 Active [0,24] [0,24] [0,24] 2 1 Placebo [0,21] [0,21] [0,21] 2 2 Active [0,16] [0,16] [0,16] 2 2 Placebo [0,18] [0,18] [0,18] Bounds On Tables Entries Given Marginals Earlier we noted that the risk of identity disclosure in a table of counts is usually associated with small cell values.... In PAGE 7: ... But if we only report selected margins from a multi-way table with such small values, can that information be used to infer values in the cells of the full table? For two-way tables, statisticians and others have long known how to place bounds on the entries of the table given the (one-way) margins. For an I J table with table entries nij, row margins ni+ and column margins n+j, these bounds have the following form: minfni+; n+jg nij maxf0; ni+ + n+j n++g: (1) Thus, if we treat the data in Table2 as if they come from an 8 3 table and apply equation (1), we get the bounds in Table 3. There are 6,718,227,637,086,252 tables with the same sets of marginal totals and across all of them these are the maximum and minimum values for each of the cell counts.... In PAGE 7: ... Since the uppers bounds are far from the lower bounds and since these bounds correspond to an extremely large collection of tables, an intruder cannot use them to make strong inferences about potentially small cell entries. Of course the rows of Table2 correspond to three variables and thus we have computed the bounds for a four-way table given the margins [CST] and [R]. Over the past decade, the ideas on bounds have been extended to multi-way tables given two or more, possibly overlapping margins, and not surprisingly these extensions are linked to the theory of log-linear models.... In PAGE 8: ...Table2 Given the [CST] , [CSR], and [TR] Margins. Response Poor Moderate Excellent Center Status Treatment 1 1 Active [0,14] [1,28] [0,13] 1 1 Placebo [0,14] [6,33] [0,13] 1 2 Active [0,9] [3,27] [1,17] 1 2 Placebo [0,9] [0,24] [0,16] 2 1 Active [2,21] [3,22] [0,0] 2 1 Placebo [2,21] [0,19] [0,0] 2 2 Active [0,9] [0,16] [0,7] 2 2 Placebo [0,9] [2,18] [0,7] For the data in Table 2, we observed earlier that the four cell entries of \3 quot; pose potential disclosure risk and we would like to protect them by releasing only subsets of the data in the form of marginal totals.... In PAGE 8: ...Margins. Response Poor Moderate Excellent Center Status Treatment 1 1 Active [0,14] [1,28] [0,13] 1 1 Placebo [0,14] [6,33] [0,13] 1 2 Active [0,9] [3,27] [1,17] 1 2 Placebo [0,9] [0,24] [0,16] 2 1 Active [2,21] [3,22] [0,0] 2 1 Placebo [2,21] [0,19] [0,0] 2 2 Active [0,9] [0,16] [0,7] 2 2 Placebo [0,9] [2,18] [0,7] For the data in Table2 , we observed earlier that the four cell entries of \3 quot; pose potential disclosure risk and we would like to protect them by releasing only subsets of the data in the form of marginal totals. We have explored the possible bounds associated with the release of the [CST] margin and all other possible sets of margins.... In PAGE 9: ...Table2 Given the [CST], [CSR], and [STR] Margins. Response Poor Moderate Excellent Center Status Treatment 1 1 Active [0,13] [10,23] [5,5] 1 1 Placebo [1,14] [11,24] [8,8] 1 2 Active [0,6] [7,20] [9,16] 1 2 Placebo [3,9] [7,20] [1,8] 2 1 Active [2,15] [9,22] [0,0] 2 1 Placebo [8,21] [0,13] [0,0] 2 2 Active [0,6] [3,16] [0,7] 2 2 Placebo [3,9] [2,15] [0,7] Table 6: Upper and Lower Bounds For Entries in Table 2 Given the [CST], [CSR], and [CTR] Margins.... In PAGE 9: ...Margins. Response Poor Moderate Excellent Center Status Treatment 1 1 Active [0,13] [10,23] [5,5] 1 1 Placebo [1,14] [11,24] [8,8] 1 2 Active [0,6] [7,20] [9,16] 1 2 Placebo [3,9] [7,20] [1,8] 2 1 Active [2,15] [9,22] [0,0] 2 1 Placebo [8,21] [0,13] [0,0] 2 2 Active [0,6] [3,16] [0,7] 2 2 Placebo [3,9] [2,15] [0,7] Table 6: Upper and Lower Bounds For Entries in Table2 Given the [CST], [CSR], and [CTR] Margins. Response Poor Moderate Excellent Center Status Treatment 1 1 Active [0,6] [9,28] [0,13] 1 1 Placebo [8,14] [6,25] [0,13] 1 2 Active [0,6] [6,25] [4,17] 1 2 Placebo [3,9] [2,21] [0,13] 2 1 Active [6,15] [9,18] [0,0] 2 1 Placebo [8,17] [4,13] [0,0] 2 2 Active [0,9] [3,12] [4,4] 2 2 Placebo [0,9] [6,15] [3,3] for a margin (for example, see Figure 2).... ..."

"... In PAGE 8: ... Removing the bilateral symmetry of Sierpin- ski apos;s gasket by applying a shear transforma- tion to its feature points removes a lot of the \noisy quot; spikes that occur as a result of a sym- metrical arrangement. The top ten similarity parameters found for 65 feature points of the von Koch snow ake curve (Figure 4) are listed in Table1 . Trans- formations 5, 7, 8, and 9 are the typical maps used to de ne this curve, but maps 1 and 2 de ne a more e cient representation.... In PAGE 10: ...Coarse maps were found for the Koch curve as in Table1 , yet experiments using other datasets did not reveal any clear domi- nant maps. This is due either to the coarseness of the hash table or an insu cient number of plotted hash coordinates.... ..."

"... In PAGE 3: ...rated from classes via simple heuristics (e.g. capitalized words have been considered as in- stances, while lower case words have been con- sidered as Word Classes) and then manually checked. Table1 shows the distribution of Classes and Instances over the WordNet hier- archy with respect to the NE categories Per- son, Location, Organization, Measure, Money, Duration, Date, Time, Percent and Cardinal, which are the categories con- sidered in the design of our system. 2.... In PAGE 3: ... 2.2 Capturing external evidence using the WordNet hierarchy Given an input text, our rule system cap- tures external evidence considering all the 12259 words belonging to the relevant Word Classes (see Table1 ) as possible trigger words. As an example, among the 6086 hyponyms of the synset person#1 fperson, individual, someone, somebody, mortal, human, soulg, a class of 6775 trigger words has been extracted.... In PAGE 4: ... 3.1 Basic rules As stated before, our system has been designed for the recognition of the NE categories de- scribed in Table1 . Each category is associated with a set of basic rules that check for di er- ent features of the input text.... ..."