### Table 1: Recursion for Computing the Partition Function. The parameter m is the minimum size of a hairpin-loop, usually m = 3.

"... In PAGE 113: ... Table1 0: Hepatitis C Virus Sequences Selected Sequences REM ID Accession No length (nt) organism 1 E08399 E08399 9413 Hepatitis C virus 2 E10035 E10035 9416 Hepatitis C virus 3 HCJRNA D14484 9427 Hepatitis C virus 4 HCU01214 U01214 9446 Hepatitis C virus 5 HCVJK1G X61596 9408 Hepatitis C virus 6 HCVPOLYP AJ000009 9379 Hepatitis C virus 7 HPC1B4 D50484 9410 Hepatitis C virus 8 HPC1B5 D50485 9410 Hepatitis C virus 9 HPCCGENOM L02836 9400 Hepatitis C virus 10 HPCGENANT M84754 9425 Hepatitis C virus 11 HPCY1B6 D50480 9410 Hepatitis C virus 12 S62220 S62220 9440 Hepatitis C virus Example Sequences for Alifold REM ID Accession No length (nt) organism 1 AF009606 AF009606 9646 Hepatitis C virus 2 AF054247 AF054247 9595 Hepatitis C virus 3 D84262 D84262 9449 Hepatitis C virus 4 D84263 D84263 9426 Hepatitis C virus 5 HC45476 U45476 9431 Hepatitis C virus 6 HCJK046E2 D63822 9461 Hepatitis C virus 7 HCV4APOLY Y11604 9355 Hepatitis C virus type 4a 8 HCVJK1G X61596 9408 Hepatitis C virus 9 HPCHK6 D28917 9454 Hepatitis C virus 10 HPCPOLP D00944 9589 Hepatitis C virus Hepatitis C virus strain H77C REM ID Accession No length (nt) organism 1 AF011751 AF011751 9599 Hepatitis C virus strain H77 2 AF011752 AF011752 9599 Hepatitis C virus strain H77 3 AF011753 AF011753 9599... In PAGE 114: ...Table1 1: Pestivirus Sequences Selected Pestivirus Sequenes REM ID Accession No length (nt) organism 1 AF037405 AF037405 12333 2 AF041040 AF041040 12260 pestivirus type 1 3 AF091507 AF091507 12310 Hog cholera virus 4 BDAF2227 AF002227 12255 5 BDU70263 U70263 12268 pestivirus type 3 6 BVDCG M31182 12573 pestivirus type 1 7 BVU63479 U63479 12247 pestivirus type 1 8 HCVCG3PE M31768 12283 Hog cholera virus 9 PTU86600 U86600 12267 pestivirus type 1 10 TOGHCVCG J04358 12284 Hog cholera virus Selected Pestivirus Sequenes for Comparison Cattle, Swine and Sheep REM ID Accession No length (nt) organism cattle 1 AF041040 AF041040 12260 pestivirus type 1 2 AF091605 AF091605 12310 bovine viral diarrhea virus 3 BV18059 U18059 12513 pestivirus type 1 4 BVDCG M31182 12573 pestivirus type 1 5 BVDPOLYPR M96751 12308 pestivirus type 1 6 BVDPP M96687 12480 pestivirus type 1 7 BVU63479 U63479 12247 pestivirus type 1 8 E01149 E01149 12492 pestivirus type 1 swine 1 A16790 A16790 12284 Hog cholera virus 2 AF091507 AF091507 12310 Hog cholera virus 3 AF091661 AF091661 12297 Hog cholera virus 4 HC45477 U45477 12298 Hog cholera virus 5 HC45478 U45478 12278 Hog cholera virus 6 HCSEQB L49347 12144 Hog cholera virus 7 HCVCG3PE M31768 12283 Hog cholera virus 8 HCVCOMGEN X87939 12298 Hog cholera virus 9 HCVCOMSEQ X96550 12297 Hog cholera virus 10 HCVPOLYP1 D49532 12298 Hog cholera virus 11 HCVPOLYP2 D49533 12298 Hog cholera virus 12 HCVPOLYPR Z46258 12311 Hog cholera virus 13 TOGHCVCG J04358 12284 Hog cholera virus sheep 1 AF037405 AF037405 12333 border disease virus 2 BDAF2227 AF002227 12255 border disease virus 3 BDU70263 U70263 12268... In PAGE 115: ...Table1 2: Hantavirus L,M-segment Sequences REM ID Accession No length (nt) organism L-segment 1 BUHANL X55901 6533 Hantaan virus 2 HANRDRP1 D25528 6533 Hantaan virus 3 HANRDRP4 D25531 6533 Hantaan virus 4 HVSLSEG X56492 6530 Hantavirus 5 NEVLRNA M63194 6550 Puumala virus 6 PVLSOTKMO Z66548 6550 Puumala virus 7 SNVRPL L37901 6562 Sin Nombre hantavirus 8 SNVRPLA L37902 6562 Sin Nombre hantavirus M-segment 1 AF028022 AF028022 3653 Lechiguanas virus 2 AF028023 AF028023 3654 Hu39694 virus 3 AF028024 AF028024 3646 Oran virus 4 AF030551 AF030551 3664 Blue River virus 5 AF030552 AF030552 3662 Blue River virus 6 BUHANM Y00386 3616 Hantaan virus 7 HANG1G2A L08753 3616 Hantaan virus 8 HOJM D00376 3613 HoJo virus 9 HPSCC107M L33474 3696 Pulmonary syndrome 10 HPSMSEG L25783 3696 Sin Nombre 0 11 HPSMSEGA L33684 3696 Pulmonary syndrome 12 HPSMSEGB L33685 3644 Hantavirus 13 HVIGLYPRE L36930 3677 Bayou hantavirus 14 LNAF5728 AF005728 3698 Laguna Negra virus 15 NEVMSEG M29979 3682 Puumala virus 16 NY36801 U36801 3668 New York hantavirus 17 PHVMSRNA X55129 3707 Prospect Hill virus 18 PUVMVIN83 Z49214 3682 Puumala virus 19 PV22418 U22418 3681 Puumala virus 20 PVMZ84205 Z84205 3682 Puumala virus 21 S68035 S68035 3655 Hantavirus 22 SNGPGO L37903 3696 Sin Nombre hantavirus 23 TIDG1G2A L08756 3613 Thailand virus 24 TUVM5302 Z69993 3694... In PAGE 116: ...Table1 3: Hantavirus S-segment Sequences REM ID Accession No length (nt) organism 1 AB010730 AB010730 1833 Puumala virus 2 AF004660 AF004660 1876 Andes virus 3 HANSNC M14626 1696 Hantaan virus 4 HSNPSS L41916 1670 Hantavirus sp. 5 HVINUCPRO L36929 1958 Bayou hantavirus 6 KH35255 U35255 1845 Khabarovsk hantavirus 7 LNAF5727 AF005727 1904 Laguna Negra virus 8 PRHSRNA M34011 1675 Prospect Hill virus 9 PUUSNP X61035 1830 Puumala virus 10 PUVSVIRRT Z69985 1837 Puumala virus 11 PV22423 U22423 1847 Puumala virus 12 PVNICAS U14137 1828 Puumala virus 13 PVNPRO1 Z30702 1832 Puumala virus 14 RMU11427 U11427 1896 El Moro Canyon hantavirus 15 RS18100 U18100 1749 Mexicanus hantavirus 16 SRVAGSS M34881 1769 Sapporo rat virus 17 TUVS5302 Z69991 1831 Tula virus 18 TVSSEG1 Z30941 1847 Tula virus 19 U19303 U19303 1722 Prairie vole hantavirus 20 U52136 U52136 1975... In PAGE 117: ...Table1 4: Hantavirus M,S-segments of Groups REM ID Accession No organism M-segment group 1 BUHANM Y00386 Hantaan virus group 1 HANG1G2 M14627 Hantaan virus group 1 HOJM D00376 HoJo virus group 1 HPSMSEG L25783 Sin Nombre hantavirus group 1 S68035 S68035 Hantavirus group 1 TIDG1G2A L08756 Thailand virus group 2 NEVMSEG M29979 Puumala virus group 2 PHVMSRNA X55129 Prospect Hill virus group 2 PUVMVIN83 Z49214 Puumala virus group 2 PV22418 U22418 Puumala virus group 2 PVMZ84205 Z84205 Puumala virus group 2 TUVM5302 Z69993 Tula virus group 3 AF028022 AF028022 Lechiguanas virus group 3 AF028023 AF028023 Hu39694 virus group 3 AF028024 AF028024 Oran virus group 3 HVIGLYPRE L36930 Bayou hantavirus group 3 LNAF5728 AF005728 Laguna Negra virus group 4 AF030551 AF030551 Blue River virus group 4 AF030552 AF030552 Blue River virus group 4 HPSCC107M L33474 Pulmonary syndrome group 4 HPSMSEG L25783 Sin Nombre hantavirus group 4 HPSMSEGA L33684 Pulmonary syndrome group 4 NY36801 U36801 New York hantavirus S-segment group 1 AF004660 AF004660 Andes virus group 1 HVINUCPRO L36929 Bayou hantavirus group 1 LNAF5727 AF005727 Laguna Negra virus group 1 RMU11427 U11427 El Moro Canyon hantavirus group 1 RS18100 U18100 Reithrodontomys mexicanus hantavirus group 1 U52136 U52136 Rio Mamore hantavirus group 2 KH35255 U35255 Khabarovsk hantavirus group 2 PRHSRNA M34011 Prospect Hill virus group 2 TUVS5302 Z69991 Tula virus group 2 TVSSEG1 Z30941 Tula virus group 2 U19303 U19303 Prairie vole hantavirus group 3 AB010730 AB010730 Puumala virus group 3 PUUSNP X61035 Puumala virus group 3 PUVSVIRRT Z69985 Puumala virus group 3 PV22423 U22423 Puumala virus group 3 PVNICAS U14137 Puumala virus group 3 PVNPRO1 Z30702... In PAGE 118: ...Table1 5: Bunyavirus Sequences REM ID Accession No length (nt) organism M-segment 1 BUSSHMG K02539 4527 Snowshoe hare virus 2 LACMRP D10370 4526 La Crosse virus 3 LC18979 U18979 4526 La Crosse virus 4 LCU70207 U70207 4526 La Crosse virus 5 U88057 U88057 4501 Melao virus 6 U88058 U88058 4510 Jamestown Canyon virus 7 U88059 U88059 4506 Inkoo virus 8 U88060 U88060 4506 Inkoo virus S-segment 1 BUNCNP K00108 981 La Crosse virus 2 BUSVR J02390 982 Snowshoe hare virus 3 CE12800 U12800 978 California encephalitis virus 4 MB31989 U31989 976 Morro Bay virus 5 SAU47139 U47139 976 San Angelo virus 6 SDU47140 U47140 967 Serra do Navio virus 7 SRU47141 U47141 984 South River virus 8 TV12803 U12803 973 Trivittatus virus 9 TVU47142 U47142 976... ..."

### Table 3.2: Unit Production (PU) and its Re exive Transitive Closure (RU) matrices for a simple SCFG. Two nonterminals are said to be in a Unit Production Relation X !U Y i there exists a production for X of the form X ! Y . As in the case with prediction we compute the closed-form solution for a Unit Produc- tion recursive correction matrix RU ( gure 3.2), considering the Unit Production relation, expressed by a matrix PU. RU is found as RU = (I ? PU)?1. The resulting expanded completion algorithm accommodates for the recursive loops: 8 gt; gt; lt;

### Table 1. Loop types and suitability

"... In PAGE 3: ... Parallel proofs for nested and sequential loops, as well as recursive structures can be developed using a parallel argument. The results of each proof are listed in Table1 . Recall that gamma represents the product of the instructional execution efficiency and the resource utilization efficiency.... ..."

### Table 7: Observed mental methods of the PETAL group learners

"... In PAGE 36: ...In fact, Table7 indicates that T5 engaged the loop method in solving the first problem, the Exponent problem. Afterwards T5 abstracted the syntactic method or apos;the structure apos; of recursion.... ..."

### Table 4: Recursive calculation of the minimum free energy. Cal- ligraphic symbols denote tabulated energy parameters for di erent loop types. Hairpin loops: H(i; j), interior loops, bulges, and stacks: I(i; j; k; l); the multi-loop energy is modeled by the linear ansatz of equation (9). The particular recursion on the multiloop arrays F M and F M1 yields a unique decomposition. The overall calculation proceeds from smaller segments to larger ones. The minimum free energy on the segment [1; j] is stored in F 5 j . Upon completion the minimum free energy is in F 5 n.

1999

"... In PAGE 33: ... The free energy Emin of the best structure on the entire sequence is then given by Emin = F 5 n. Table4 summarizes the algorithm for computing the minimum free energy on a given RNA sequence. It has complexity O(n3), and its implementation is very fast.... ..."

Cited by 78

### Table 1: Workload and CPF Bound of LFK1-12 on IBM RS/6000. (LFK5 has td=4 clocks and LFK11 has td=2, since their fa and fm form a loop-carried dependence and the latency of each operation is 2; the other loops have no recursion and td=0.)

1993

"... In PAGE 9: ... The rst 12 Livermore Fortran Kernels [13] are used as the application workload for the experimental study in this paper. Table1 lists the essential workload and the bound for LFK 1-12. The bound shown is in units of CPF (clocks per oating-point operation), which is computed as tl=(2 fma + fa + fm).... ..."

Cited by 9

### Table 4 shows the costs; columns labeled give 95% confidence intervals throughout the paper. Note that the marginal initialization costs are almost exactly the same for the various schemes; the only significant variation is in the per-object cost. Recall, though, that this cost includes the loop/recursion overhead of the test program. Taking the difference between the costs of Table 4 and the cost of no-work traversal (presented later) gives a better measure of the cost of allocation by itself, though since the loops are different, the comparison is only approximate.

"... In PAGE 17: ... Table4 : Object Creation and Initialization Costs 7The swizzling per-slot cost was obtained from the VS series since the SI series does not vary the total number of slots, and swizzling always initializes all slots.... In PAGE 24: ... Note that we assume all slots and bytes are initialized. The parameters were calculated as follows: PB This has three sources: creating ( Table4 ), preparing (Table 10), and writing (Section 5.... ..."

### Table 2. Kernel model for some tested archi- tectures. The tested kernels are the three loop variants for the (s)calar, (v)ector, (b)lock, and (r)ecursive algorithms. Values in brack- ets are block sizes.

"... In PAGE 4: ... At the end of this testing process, the identifiers of the best performing ker- nels (along with their implementation parameters) for each memory level of each processing element constitute the ker- nel model. The data computed by the kernel selector run- ning on some of the tested computing platforms is illus- trated in Table2 . Block algorithms call the best kernel for the L1 level, whereas recursive algorithms call the best ker- nel for the previous smaller level in a recursive fashion.... ..."

### 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.... ..."

### Table 1. Results of some recursive benchmark programs

"... In PAGE 8: ... Since blocks B5 and B7 are within loops, we place such instructions by creating new blocks at points shown by shaded circles in the figure. 5 Experimental Results Table1 shows some benchmark programs which we have considered to measure the efficacy of LARS. Fibonacci, Ackerman and the Tak are the standard benchmark recur- sive programs which are highly call-intensive.... ..."