### Table 2: Examples of Rules Generated by the Minimum Entropy Method.

1994

"... In PAGE 23: ...In accord with the model procedures, we have implemented segmentation, feature extraction (Table 1) and rule generation-weight estimation on both sets of training data. Examples of rule bounds are shown in Table2 , using the minimum entropy technique, just for the unary features (U.x) as outlined in Table 1.... ..."

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### Table 1: Compression of natural language alphabets

1993

"... In PAGE 3: ... Here, it is often desirable to extend the alphabet to incorporate n-grams that include the frequent characters; in the expanded alphabet, the highest probability will be reduced and Hu man coding could be e ective. That Hu man coding is e ective for databases of natural text is shown in the rst two columns of Table1 , which is discussed in detail below. There we nd the Hu man cost (de ned as... In PAGE 6: ...and 735 bigrams), the distribution has been computed using the database of The Re- sponsa Retrieval Project (RRP) [14] of about 40 million Hebrew and Aramaic words; the distribution for Italian, Portuguese and Spanish (26 letters each) can be found in Gaines [18], and for Russian (32 letters) in Herdan [23]. The results are summarized in Table1 , the two last lines corresponding to the bigrams. The rst two colums list the average codeword length of Hu man codes and arith- metic codes respectively, and the third column gives the increase of the former over the latter in percent.... In PAGE 10: ...rom 4.16 to 5.60! We thus see that arithmetic codes give worse compression in this case, even without considering the overhead caused by EOF. Table 3 summarizes an experiment in which we took the probability distributions of English, German, Finnish and French (as in Table1 ), adding to them the character distribution in Gadsby, and checked what happens if they are mutually interchanged. The rows correspond to the distributions which are used to generate the codewords (the assumed distribution), and the columns correspond to the distribution that actually occurs (the true distribution).... In PAGE 17: ... To store the alphabet with methods B, C and D one needs 26, 32 and 3 bytes respectively, to which 13 bytes have to be added for the lengths of the Hu man codewords, or 52 bytes for the probabilities for arithmetic codes. From Table1 we know that the average loss per character by using Hu man instead of arithmetic codes is 0.0251 bits, so the text has to be at least of length 12431 characters to justify the excess of these 39 bytes for methods B, C and D.... ..."

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### Table 2: Sliding Window Entropy Estimates

1998

"... In PAGE 26: ... Correcting for bias has the e ect of restoring the natural entropy scaling (with a maximum of 2). We present in Table2 the SWE estimates of the entropy, both bias corrected and uncorrected, computed for varying choices in n (the window size). gt;From table 2 we notice that the size of the bias adjustments diminish as n... ..."

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### Table 1. The number of singly-sired fruits analyzed (N), the observed number of unique pollen donor genotypes (OPD) inferred from full-sib progeny arrays, and the estimated total number of pollen donors (EPD) and standard error (SE) for five E. cyclocarpum maternal individuals of study site FDL over 3 years

"... In PAGE 3: ...7 seeds/pod) in 1996. Pollen Donor Number Most pollen donors fathered a single pod, but a few sired two or three pods within an individual fruit crop ( Table1 , Figure 2). Some pollen donors also sired fruits on several trees, hence the observed number... In PAGE 4: ... Although such distributions do not allow estimates of the total number of pollen donors per tree (see above), they contribute data to the number of pooled pollen donors. Most pollen donors sired a single pod within the pooled fruit crops during each of the three years ( Table1 , Figure 2). The most pods attributed to the same pollen donor was five (by tree 787) in 1994 (three pods sired on tree 788 and two on tree 810).... In PAGE 5: ... Breeding areas of individual maternal trees estimated from the observed num- ber of pollen donors all exceed the 9.8 ha area of the FDL plot, as do breeding size estimates when pollen donor numbers are pooled for FDL ( Table1 ). When maximum pollen donor population size estimates are pooled over the study plot, estimated neighborhood areas exceed the 227 ha of the Stewart Ranch study area in all three years.... ..."

### Table 1: Entropy estimates

1999

"... In PAGE 8: ... Approximations of the physical invariant measure were obtained from the xed left eigenvectors p0; p1; : : : ; p8, and estimates of the metric entropy h (T ) with respect to the physical measure were calculated using (12) and (13). The approximation of the physical invariant measure computed from P8 is shown in Figure 1(b), while the entropy estimates are displayed in Table1 . Theorem 5.... ..."

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### Table 2: Summary of entropy estimates (bits/nucleotide).

"... In PAGE 11: ... The resulting sequence contains 484; 483 bases and is referred to as our non-redundant data set. 5 Experimental Results Our model apos;s performance on the sequences described in Section 4 is summarized in Table2 . In some cases our results may be compared directly with estimates from [Grumbach and Tahi, 1994], which are included in the table.... In PAGE 12: ... Notice that in all cases, the Unix compress utility performs worse than no model at all (uniformly random prediction). To make comparisons among entropy estimation methods clearer, Figure 2 summarizes the results from Table2 for cdna, H6, biocompress-2, and cdna-compress. In all cases cdna outperforms conventional entropy estimates, and in almost all cases by a substantial margin.... ..."

### Table 2: Summary of entropy estimates (bits/nucleotide).

"... In PAGE 11: ... The resulting sequence contains 484; 483 bases and is referred to as our non-redundant data set. 5 Experimental Results Our model apos;s performance on the sequences described in Section 4 is summarized in Table2 . In some cases our results may be compared directly with estimates from [Grumbach and Tahi, 1994], which are included in the table.... In PAGE 12: ... Notice that in all cases, the Unix compress utility performs worse than no model at all (uniformly random prediction). To make comparisons among entropy estimation methods clearer, Figure 2 summarizes the results from Table2 for cdna, H6, biocompress-2, and cdna-compress. In all cases cdna outperforms conventional entropy estimates, and in almost all cases by a substantial margin.... ..."

### Table 6: Entropies and the Estimated Order

1996

"... In PAGE 18: ...eivers. The entropies became almost constant after the 3rd order model, in all cases. Machines, tove and ursa showed a slightly steeper fall in entropy but in even those cases a threshold of n = 0:016 was sufficient to get an order estimate of 3. Table6 shows how the entropies decreased with increasing orders and the estimated order of the source for a threshold of 0.016.... ..."

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### Table 6: Entropies and the Estimated Order

1996

"... In PAGE 18: ...eivers. The entropies became almost constant after the 3rd order model, in all cases. Machines, tove and ursa showed a slightly steeper fall in entropy but in even those cases a threshold of n = 0:016 was sufficient to get an order estimate of 3. Table6 shows how the entropies decreased with increasing orders and the estimated order of the source for a threshold of 0.016.... ..."

Cited by 204