### Table 3. Hierarchical identity-based threshold ring signatures without random oracles.

2006

Cited by 1

### Table 1. Syntactic identities. Base language syntax PRS syntax

1996

Cited by 7

### Table 1: Examples of Free Monoids consideration since they occur very often in scienti c applications. Section 6 integrates object-oriented features, such as object identity, into the base language. Section 7 extends the basic algebra with destructive updates and provides operational semantics to these ex- tensions. Finally, Section 8 presents some of the related work.

1994

"... In PAGE 8: ... The quadruple (T ( ); zero[T ]; unit[T ]; merge[T ]) where unit[T ] is a function of type !T ( ), is a free monoid . Table1 presents some examples of free monoids. The letters C and I indicate that the monoid is a commutative and/or an idempotent monoid.... ..."

Cited by 7

### Table 1: Examples of Free Monoids consideration since they occur very often in scienti c applications. Section 6 integrates object-oriented features, such as object identity, into the base language. Section 7 extends the basic algebra with destructive updates and provides operational semantics to these ex- tensions. Finally, Section 8 presents some of the related work.

1994

"... In PAGE 8: ... The quadruple (T ( ); zero[T ]; unit[T ]; merge[T ]) where unit[T ] is a function of type !T ( ), is a free monoid . Table1 presents some examples of free monoids. The letters C and I indicate that the monoid is a commutative and/or an idempotent monoid.... ..."

Cited by 7

### Table 2: Experimentally Detected Identities based on [19], and we have indicated these with a asterisk. In many other cases we were not able to obtain a formula for the Euler sum constant explicitly in terms of values of the Riemann zeta, logarithm and polylogarithm functions, but we were able to obtain relations involving two or more Euler sum constants of the same degree (where by \degree quot; we mean m+n, where m and n are the indices of the constant). Some of these relations are shown in Table 4. This is not a complete list; we have obtained numerous other relations of this type. The \con dence level quot; of each of these relations is smaller than 10?25. The uniqueness of each of these relations was checked by repeating the run with one fewer constant input to PSLQ (there should be no relation detected when 16

1994

"... In PAGE 15: ... However, in each case the \con dence level quot; (see section 3) of these detections is less than 10?50, and in most cases is in the neighborhood of 10?100. Note that Table2 , together with the results in [7], gives all sh(m; n) results for m + n 7 and m + n = 9, while Table 3 gives all results for the alternating sums if m + n 5. Some of these identities can be proved by ad hoc methods,... ..."

Cited by 26

### Table 1: Riboswitch sub-families in Rfam database (version 7.0). Average length and %identity are based on the information in Rfam database. #seed is the number of sequences in the seed alignment. #total is the number of full family sequences.

2006

"... In PAGE 7: ... In contrast, the riboswitches, with 12 distinct sub-families (and new sub-families being continuously discovered) are quite diverse, and relatively difficult to filter. Table1 summarizes known riboswitches from Rfam v.... ..."

Cited by 2

### Table 1. Summary of dependencies on the total number of time periods N.

2003

"... In PAGE 3: ...able 1. Summary of dependencies on the total number of time periods N. model provides no guarantee as to the security of the protocol once the random oracle is instantiated with an efficiently computable function, such as a crypto- graphic hash function , and thus can only be regarded as a heuristic argument.) The key parameters of the two schemes are summarized in Table1 . We stress that both schemes are efficient not only in an asymptotic sense; indeed, they are roughly as efficient as log2 N invocations of the Boneh-Franklin identity-based encryption scheme [9] and are therefore practical for reasonable values of N.... ..."

Cited by 88

### Table 1: Optimization program for linear lossy compressions

in Abstract

"... In PAGE 5: ... 5. Table1 outlines a simple optimization program to find lossy compressions that minimize a weighted sum of the max-norm residual errors, a0a2a1 and a0a4a3 , in Eq. 5.... In PAGE 6: ... 4.2 Structured Compressions As with lossless compressions, solving the program in Table1 may be intractable due to the size of a0 . There are a48 a29a7a12a25 a0 a25 a17 constraints and a25 a0 a25a18a25 a35 a0 a25 unknown entries in matrix a5 .... In PAGE 6: ... One approach is related to the basis function model proposed in [4], in which we restrict a5 to be functions over some small set of factors (subsets of state variables.) This ensures that the number of unknown parameters in any column of a5 (which we optimize in Table1 ) is 3Assuming a49 a50 is small, the a51a9a49 a50 a51 a52 variables in each a49 a53a55a54a9a56 a57 and a51a9a49 a50 a51 variables in a49 a106... In PAGE 7: ... These techniques are rather involved, so we refer to the cited papers for details. By searching within a restricted set of structured compressions and by exploiting DBN structure it is possible to efficiently solve the optimization program in Table1 . The question of factor selection remains: on what factors should a5 be defined? A version of this question has been tackled in [12, 14] in the context of selecting a basis to approximately solve MDPs.... In PAGE 7: ...1. For further com- pression, we applied the optimization program described in Table1 by setting the weights a5 and a6 to a37 and a15 a53a30a53a30 respectively. The alternating variable technique was iterated a37 a8a7 a30 times, with the best solution chosen from a37 a8a7 random restarts (to mitigate the effects of local op- tima).... ..."

### Table 1: Optimization program for linear lossy compressions

in Abstract

"... In PAGE 5: ... 5. Table1 outlines a simple optimization program to find lossy compressions that minimize a weighted sum of the max-norm residual errors, a0a2a1 and a0a4a3 , in Eq. 5.... In PAGE 6: ... 4.2 Structured Compressions As with lossless compressions, solving the program in Table1 may be intractable due to the size of a0 . There are a48 a29a7a12a25 a0 a25 a17 constraints and a25 a0 a25a18a25 a35 a0 a25 unknown entries in matrix a5 .... In PAGE 6: ... One approach is related to the basis function model proposed in [4], in which we restrict a5 to be functions over some small set of factors (subsets of state variables.) This ensures that the number of unknown parameters in any column of a5 (which we optimize in Table1 ) is 3Assuming a49 a50 is small, the a51a9a49 a50 a51 a52 variables in each a49 a53a55a54a9a56 a57 and a51a9a49 a50 a51 variables in a49 a104... In PAGE 7: ... These techniques are rather involved, so we refer to the cited papers for details. By searching within a restricted set of structured compressions and by exploiting DBN structure it is possible to efficiently solve the optimization program in Table1 . The question of factor selection remains: on what factors should a5 be defined? A version of this question has been tackled in [12, 14] in the context of selecting a basis to approximately solve MDPs.... In PAGE 7: ...1. For further com- pression, we applied the optimization program described in Table1 by setting the weights a5 and a6 to a37 and a15 a53a30a53a30 respectively. The alternating variable technique was iterated a37 a8a7 a30 times, with the best solution chosen from a37 a8a7 random restarts (to mitigate the effects of local op- tima).... ..."

### Table 4: Mapping Function for Selection with Postprocessing. Base-View Projection-View

1999

"... In PAGE 19: ...Table 5: Mapping Function for Projection with Postprocessing. The new rules for the computation of the selection-view templates are based on the mapping function given in Table4 . We consider two cases for each attribute in the selection view: (i) the selection predicate speci es a value for the attribute; (ii) the selection predicate does not specify a value for the attribute.... In PAGE 28: ....2.3 Selection and Projection Views The new mapping function for computing selection-view templates in a postprocessing mediator is given by Table 10. The top ve rows of this table are identical to Table4 because the mediator can perform all necessary postprocessing on the attribute that is output in the results of the base-view query. In the bottom ve rows, if the attribute does not participate in the selection predicate, its adornment is identical to the base-view adornment because no postprocessing of the attribute is undertaken by the mediator.... ..."

Cited by 38