### Table 1. Examples of Relational Events Corresponding to Given Numerical Functions.

1999

Cited by 2

### Table 1. Logical schemata given to students to produce corresponding conceptual ones.

### TABLE 2. Vectors and plasmids

2006

### Table 1 Correspondence between given variables and variables retrievable from this information

"... In PAGE 7: ... Given a part of them, the rest can be specified from the infinite system of equations. Table1 shows correspondences between given variables and retrieved variables. One can see that information on any two spectra is sufficient to retrieve the reminder set of canopy parameters.... ..."

### Table 2. Monthly Violent Crime Rates for 1982 Based on the Model (16).

"... In PAGE 27: ...727 432 . The estimated monthly rates and their estimated standard errors are given in Table2 and the corresponding information for quarterly and yearly rates is listed in Table 3. The estimates in Table 3 were obtained using the formulas given in Section 2.... ..."

### Table 9 Hybrid Lanczos Outer Iteration. corresponding to i are given by

1992

"... In PAGE 26: ... This hybrid Lanczos approach which incorporates inner iterations of single-vector Lanczos bidiagonalization within the outer iterations of a block Lanczos SVD recursion is outlined in Tables 9 and 10. As an alternative to the outer recursion in Table9 , which is derived from the equivalent eigenvalue in the 2-cyclic matrix B, Table 11 depicts the simpli ed outer block Lanczos recursion for approximating the eigensystem of ATA. Combining the equations in (34), we obtain ATA^ Vk = ^ VkHk ; where Hk = JT k Jk is the k k symmetric block tridiagonal matrix Hk 0 B B B B B B B B @ S1 RT 1 R1 S2 RT 2 R2 RT k?1 Rk?1 Sk 1 C C C C C C C C A ; (40) having block size b.... In PAGE 26: ... Analogous to the diagonalization of Bk in (36), the computation of eigenpairs of the resulting tridiagonal matrix in this case can be performed via a Jacobi or QR-based symmetric eigensolver. The conservation of computer memory for our iterative block Lanczos iterative SVD method is insured by enforcing an upper bound, c, for the order (bk) of any Jk constructed (see Table9 ). This technique was suggested by Golub, Luk, and Overton in [20].... In PAGE 27: ...iteration in Table9 we have determined that p0 singular triplets are acceptable to a user-supplied tolerance for the residual error de ned in (6). Then, we update the values of the block size (b), the maximum allowable order for Jk (c), the number of diagonal blocks for Jk (d), and the number of triplets yet to be found (p) as follows: bnew = bold ? p0 ; if b pold, (42) = min fbold ; pold ? p0g otherwise, cnew = cold ? p0 ; pnew = pold ? p0 ; dnew = bcnew=bnewc : All converged left and right singular vector approximations are respectively stored in matrices U0 and... In PAGE 28: ... V0 so that U0 (U0j u1; u2; : : :; up0) ; V0 (V0j v1; v2; : : :; vp0) ; where U0 = V0 = 0 initially (prior to any restart). For restarting the block Lanczos outer iteration in Table9 , we simply rede ne V1 to be the unconverged right singular vector approximations from the previous iteration, i.e.... In PAGE 29: ... Table 11 Hybrid Lanczos Outer Iteration for the Equivalent Symmetric Eigensystem of ATA. estimate the residual for some k (see 6) by kykk2 of Step (1a) in Table9 for iteration l + 1, where yk is the k-th column of the n b matrix Yi. Hence, at the start of iteration l + 1 we can determine the accuracy of our approximations from iteration l.... In PAGE 29: ... As with the previous iterative SVD methods, we access the sparse matrices A and AT for this hybrid Lanczos method only through sparse matrix-vector multiplications. Some e ciency, however, is gained in the outer (block) Lanczos iterations by the multiplication of b vectors (Steps (1a), (1b) in Table9 ) rather than by a single vector. These dense vectors may be stored in a fast local memory (cache) of a hierarchical memory-based archtitecture (Alliant FX/80, Cray-2S) and thus yield more e ective data reuse.... In PAGE 29: ... These dense vectors may be stored in a fast local memory (cache) of a hierarchical memory-based archtitecture (Alliant FX/80, Cray-2S) and thus yield more e ective data reuse. The total reorthogonalization strategy and de ation of converged singular vector approximations is accomplished in Steps (1b), (1e) in Table9 and Steps (2b), (2d) in Table 10. A stable variant of Gram-Schmidt orthogonalization ([37]), which requires e cient dense matrix-vector muliplication (level-2 BLAS) routines ([14]), is used to produce the orthogonal projections of Yi (i.... In PAGE 33: ... Table 13 also indicates that a signi cant proportion of time (24% of total CPU time) is spent in the level-2 (matrix-vector) and level-3 (matrix-matrix) BLAS kernels. The outer block Lanczos recursion for ATA (see Table 11), as with the outer recursion in Table9 , primarily consists of these higher- level BLAS kernels (also supplied by the Alliant FX/Series Scienti c Library) which are designed for execution on all 8 processors of the Alliant FX/80. The modi ed Gram-Schmidt procedure we employ for re-orthogonalization is also driven by the higher-level BLAS kernels.... In PAGE 37: ...2 from the eigensystem of AT A. The parameters for BLSVD (see Table9 in Section 3:5) include the initial block size, b, an upper bound on the dimension of the Krylov subspace, c. For LASVD, we also include a similar upper bound, q, for the order of the symmetric tridiagonal matrix Tj in (31).... In PAGE 38: ... The consequence of doubling p in terms of memory is discussed in Section 4:3. As mentioned in the preceding section, BLSVD requires an initial block size b, where b p, and the bound c on the Krylov subspace generated within the outer block Lanczos recursion given in Table9 . The choice of b can be di cult, and as mentioned in Section 3:5 we have made some gains... ..."

Cited by 4

### Table 4. Distortion types for the measured correlations. Metrics indexed by 1-4 are taken from [7]. Details about the perfor- mance analysis and the used database are given in the corresponding references, see also [20].

2003

"... In PAGE 11: ... We selected the set of metrics to obtain a wide range of distortions. Table 3 and Table4 give the correlations to subjective hearing tests and the related distortion types. The traditional SNR has a very poor performance.... In PAGE 11: ... We close this section by noting that one could employ the very complex (and expensive) PESQ [14] measure for the voice quality evaluation. Instead, we selected the objective metrics in Table4 , which have also good correlations with the subjective voice quality (especially the cepstral distance) and do not require proprietary software (and thus allow for replication of our experi- ments; in fact we plan to make our evaluation software publicly available to the research community). In the following sections, essential formulas and special characteristics of all imple- mented objective metrics are given.... ..."

Cited by 7

### Table 2: Observed and predicted event rates. The limits given correspond to 95% confidence level. Unless stated otherwise the quoted numbers refer to the summed production of both lepton charged states.

1998

"... In PAGE 12: ... The kinematics of the scattering of such a halo muon on a residual gas nucleon restricts the transverse momenta and a10 to be below the values observed in the six events. Table2 indicates that a5 production constitutes the largest contribution followed by the NC process (for a0 a0 events) and the photon-photon process (for a3 a4 events). All other processes considered contribute negligibly.... ..."

### Table 4. Main algorithmic ingredients of SSEP-Domain and the corre- sponding purpose in the domain prediction pipeline. Details are given in the text in the corresponding sections.

"... In PAGE 6: ... Server single-domain two-domain single amp; two RosettaDOM 94% (36) 75% (16) 88% (52) CONSENSUS 88% (42) 79% (14) 86% (56) GINZU 92% (36) 69% (13) 86% (49) SSEP-Domain 83% (47) 82% (11) 83% (58) SSEP-CAFASP 84% (45) 73% (11) 82% (56) DOPRO 88% (40) 64% (14) 81% (54) InterProScan 75% (51) 67% (6) 74% (57) DomSSEA 75% (44) 63% (8) 73% (52) DOMPRO 76% (46) 50% (12) 71% (58) GLOBPLOT 71% (48) 60% (5) 70% (53) DPS 78% (36) 50% (16) 69% (52) ADDA 73% (48) 33% (9) 67% (57) MATEO 78% (27) 15% (13) 58% (40) Armadillo 100% (4) 18% (22) 31% (26) BIOZON 100% (4) 19% (31) 29% (35) 4 DISCUSSION SSEP-Domain is an alignment-based approach to domain predic- tion. (see Table4 for an overview of the contained algorithms). We combine secondary structure element alignment and direct boun- dary placement to detect potential domain boundaries on a target sequence.... ..."

### Table 1: Maximum average gain obtained. The values of P, W and K corresponding to these gains are given for each strategy

"... In PAGE 5: ... These conditions simplify greatly the implemen- tation of the approach since the simplest strate- gies seem to work best. These three strategies give approximately the same cpu-time when the parameters are correctly chosen, as shown in Table1 . The optimum values di er only by a factor of (5:51?5:39)=5:39 = 2:2%, which is below the accuracy of cpu time measurements.... ..."