### Table 1 Index Vector by Recursion

1996

"... In PAGE 3: ... For example, weknow that the last n ; 2 bits of ~ k j are zero for k j lt; 4. This approach leads to the recursive algorithm illustrated in Table1 [42]. At eachstepwemultiply the currentlistby 2 and concatenate 1 plus the list.... In PAGE 26: ... Elster instead uses the \add half quot; procedure which involves halving an integer instead of doubling an array.Table 14 can be compared with Table1 to see the di erence in the way the index vector is built. Since Elster apos;s approach never changes an entry once it has been computed, it saves arithmetic and time, as shown in Table 15.... In PAGE 26: ... Since Elster apos;s approach never changes an entry once it has been computed, it saves arithmetic and time, as shown in Table 15. Elster apos;s algorithm and that in Table1 are both special cases of a more general formulation that comes from the idea of a tensor sum[33]. The tensor sum of two vectors w = u v is de ned as w =[u + v 0 ;;u+ v 1 ;; .... ..."

Cited by 8

### Table 14 Index vector by recursion.

1996

"... In PAGE 26: ... Elster instead uses the \add half quot; procedure which involves halving an integer instead of doubling an array. Table14 can be compared with Table 1 to see the di erence in the way the index vector is built. Since Elster apos;s approach never changes an entry once it has been computed, it saves arithmetic and time, as shown in Table 15.... ..."

Cited by 8

### Table 1: Recursion for Computing the Partition Function.

1999

Cited by 2

### Table 1: Classification of spatial index structures.

"... In PAGE 14: ...64 0.89 Table1 : False area of the BB The accuracy of the filtering step is maximized by minimizing the deviation of the approximation from the original object. We measure this deviation by the false area of the approximation normalized to the area of the original object.... In PAGE 14: ... We measure this deviation by the false area of the approximation normalized to the area of the original object. Table1 shows impressively that real cartography objects are only roughly approximated by BBs. In this table, fa is the average false area; min and max denote the minimum and the maximum false area in the map, respectively.... In PAGE 19: ... Certain mea- sures are supported to maintain that each data object is totally included in a subspace. Table1 groups various index structures according to the techniques used to handle non-zero sized spatial objects. Each of the above approaches has its own strengths and weaknesses, which directly affect the performance of indexes using it.... ..."

### Table 1: Classification of spatial index structures.

"... In PAGE 14: ...64 0.89 Table1 : False area of the BB The accuracy of the ltering step is maximized by minimizing the deviation of the approximation from the original object. We measure this deviation by the false area of the approximation normalized to the area of the original object.... In PAGE 14: ... We measure this deviation by the false area of the approximation normalized to the area of the original object. Table1 shows impressively that real cartography objects are only roughly approximated by BBs. In this table, fa is the average false area; min and max denote the minimum and the maximum false area in the map, respectively.... In PAGE 19: ... Certain measures are supported to maintain that each data object is totally included in a subspace. Table1 groups various index structures according to the techniques used to handle non-zero sized spatial objects. Each of the above approaches has its own strengths and weaknesses, which directly a ect the performance of indexes using it.... ..."

### Table 1: Classification of spatial index structures.

"... In PAGE 14: ...64 0.89 Table1 : False area of the BB The accuracy of the filtering step is maximized by minimizing the deviation of the approximation from the original object. We measure this deviation by the false area of the approximation normalized to the area of the original object.... In PAGE 14: ... We measure this deviation by the false area of the approximation normalized to the area of the original object. Table1 shows impressively that real cartography objects are only roughly approximated by BBs. In this table, fa is the average false area; min and max denote the minimum and the maximum false area in the map, respectively.... In PAGE 19: ... Certain measures are supported to maintain that each data object is totally included in a subspace. Table1 groups various index structures according to the techniques used to handle non-zero sized spatial objects. Each of the above approaches has its own strengths and weaknesses, which directly affect the performance of indexes using it.... ..."

### Table 1: Classification of spatial index structures.

"... In PAGE 14: ...64 0.89 Table1 : False area of the BB The accuracy of the ltering step is maximized by minimizing the deviation of the approximation from the original object. We measure this deviation by the false area of the approximation normalized to the area of the original object.... In PAGE 14: ... We measure this deviation by the false area of the approximation normalized to the area of the original object. Table1 shows impressively that real cartography objects are only roughly approximated by BBs. In this table, fa is the average false area; min and max denote the minimum and the maximum false area in the map, respectively.... In PAGE 19: ... Certain measures are supported to maintain that each data object is totally included in a subspace. Table1 groups various index structures according to the techniques used to handle non-zero sized spatial objects. Each of the above approaches has its own strengths and weaknesses, which directly a ect the performance of indexes using it.... ..."

### Table 1: Classification of spatial index structures.

"... In PAGE 14: ...64 0.89 Table1 : False area of the BB The accuracy of the ltering step is maximized by minimizing the deviation of the approximation from the original object. We measure this deviation by the false area of the approximation normalized to the area of the original object.... In PAGE 14: ... We measure this deviation by the false area of the approximation normalized to the area of the original object. Table1 shows impressively that real cartography objects are only roughly approximated by BBs. In this table, fa is the average false area; min and max denote the minimum and the maximum false area in the map, respectively.... In PAGE 19: ... Certain measures are supported to maintain that each data object is totally included in a subspace. Table1 groups various index structures according to the techniques used to handle non-zero sized spatial objects. Each of the above approaches has its own strengths and weaknesses, which directly a ect the performance of indexes using it.... ..."

### Table 1 summarizes the recursion scheme for the partition function. The next section will extend the recursion scheme to the computation of the base pair probability.

1997

"... In PAGE 40: ...Folding Algorithms 31 QB ij = e H(ij)=kT + j m 2 X k=i+1 u umax j 1 X l=k+m+1 QB kl e [I(i;j;k;l)]=kT + j m 2 X k=i+1 QM i+1;k 1QM1 k;j 1 e MC=kT QM1 ij = j X l=i+m+1 QB il e [MI+MB(j l)]=kT QM ij = j m 1 X k=i+m+1 QM i;k 1 QM1 kj + j m 1 X k=i QM1 kj e MB(k i)=kT QA ij = j X l=i+m+1 QB il Qij = 1 + QA ij + j m 1 X k=i+1 Qi;k 1QA kj Table1 : Recursion for the calculation of the partition function: Calligraphic symbols denote energy parameters for di erent loop types: hairpin loops H(ij), interior loops, bulges, and stacks I(i; j; k; l); the multi-loop energy is modeled by the linear ansatz M = MC + MI degree + MB unpaired, e.... ..."