### Table 1. A summary of certain non-negative integer parameters

"... In PAGE 24: ... The next lemma involves four of the seven parameters 1{ 5, s, and t. In Table1 , which appears below, these seven parameters are summarized. 11.... In PAGE 26: ...Table 1. A summary of certain non-negative integer parameters In Table1 , for easy reference, we have summarized information about the seven parameters 1{ 5, s, and t each of which must be a non-negative integer. Four of these parameters, t, 1, 4, and 5, change their values according to the case we are in.... ..."

### Table 1. A summary of certain non-negative integer parameters

"... In PAGE 26: ... The next lemma involves four of the seven parameters 1{ 5, s, and t. In Table1 , which appears below, these seven parameters are summarized. 12.... In PAGE 27: ... = 1. By Lemmas 7.1, 7.2, and 7.3, in every case, J2 2 G;(H0 2). In Table1 , for easy reference, we have summarized information about the the seven parameters 1{ 5, s, and t each of which must be a non-negative integer. Four of these parameters, t, 1, 4, and 5, change their values according to the case we are in.... ..."

### Table 1: Minimax thresholds for non-negative garrote.

"... In PAGE 9: ... The minimax thresholds for the soft shrinkage were derived in Donoho and Johnstone (1994); the minimax thresholds for the hard shrinkage were computed by Bruce and Gao (1996b); and the minimax thresholds for the rm shrinkage can be found in Gao and Bruce (1997). The minimax thresholds for the non-negative garrote were computed from (14) and tabulated in Table1 . The values in Table 1 were computed using a grid search over with increments = 0:00001.... In PAGE 9: ... At each grid point, the supremum over was computed using Splus non-linear minimization function nlmin(). The obtained minimax bounds are also listed in Table1 and plotted along with minimax bounds for the soft, the hard and the rm in Figure 2. The minimax bounds for the soft, the hard and the rm are all listed in Table 1 of Gao and Bruce (1997).... In PAGE 9: ... The obtained minimax bounds are also listed in Table 1 and plotted along with minimax bounds for the soft, the hard and the rm in Figure 2. The minimax bounds for the soft, the hard and the rm are all listed in Table1 of Gao and Bruce (1997). From Figure 2, we can see that garrote has tighter minimax bounds than both the hard and the soft shrinkage rules, and comparable to the rm shrinkage rule.... ..."

### Table 2: Complexity results for single-machine problems with non-negative time-lags

1998

"... In PAGE 15: ... Furthermore, single-machine problems with classical precedence constraints reduce polynomially to corresponding problems with constant positive time-lags where the value l is xed. All known complexity results for single-machine problems with non-negative nish-start time-lags are summarized in Table2 . Besides the problems mentioned at the end of the last section there are many other open problems in this area which can be found under the address http://www.... ..."

Cited by 12

### Table 3: A GapL algorithm for the determinant over non-negative integers

"... In PAGE 22: ...) Essentially, HA gives us a uniform polynomial size, polynomial width branching program, corresponding precisely to GapL. Table3 lists the code for an NL machine computing, through its gap 6.2-10 function, the determinant of a matrix A with non-negative integral entries.... ..."

### Table 3: A GapL algorithm for the determinant over non-negative integers

"... In PAGE 22: ...) Essentially, HA gives us a uniform polynomial size, polynomial width branching program, corresponding precisely to GapL. Table3 lists the code for an NL machine computing, through its gap 6.2-10 function, the determinant of a matrix A with non-negative integral entries.... ..."

### Table 2 40 variables, comparison of reverse Horn and non-negative fraction.

### Table 1: Summary of algorithms for Weighted Non-Negative Matrix Euclidean Distance (ED) KL Divergence (KLD)

### Table 7: Weights generated by three versions of MLR: (i) no constraints, (ii) no intercept, and (iii) non-negativity constraints, for the LED24 dataset.

1999

"... In PAGE 8: ... However, there is another reason why it is a good idea to employ non-negativity con- straints. Table7 shows an example of the weights derived by these three versions of MLR on the Led24 dataset. The third version, shown in column (iii), supports a more perspicuous interpretation of each level-0 generalizer apos;s contribution to the class predictions than do the other two.... ..."

Cited by 48

### Table 2. Balanced colorings of the n-cube with non-negative integral weights for n = 3; 4; 5 and 6.

"... In PAGE 11: ...ence T N3;4 = 8(3)?12(1) = 12. Continuing to use (4.3) we nd T N4;4 = 8(12)? 13(3) = 60, T N5;4 = 8(60) ? 12(12) = 336 and T N6;4 = 8(336) ? 12(60) = 1968. Thus to the results given in Table 1, we can add those in Table2 , which gives the corresponding numbers of weighted, balanced n-cubes, where non-negative integer weights are allowed for the vertices. It can be shown quickly by combinatorial means that T N2;2k = k + 1 and so these values have been omitted from the table.... In PAGE 11: ... Note that for all n 1, T An;2k = An;2k for k = 0; 1; 2. Hence there is some duplication in Table2 . The binomial coe cient in the corollary below simply counts the number of ways to select k ? j items from a set of 2n?1 with repetitions allowed.... In PAGE 11: ... One observes that any balanced color- ing can be uniquely expressed as an antiantipodal coloring of weight 2j with the remaining weight of 2k ? 2j accounted for by a selection with repetition of k ? j pairs of antipodal vertices. The rst instance of an antiantipodal coloring whose black vertices do not all have the same weight occurs in Table2 for n = 4 and k = 3. Since A4;6 = 0 and T A4;6 = 16, each of the 16 con gurations must have some black vertices of di erent weights.... ..."