### Table 7: Non-uniform Input

1998

"... In PAGE 9: ...93 0.9506 66990 Table 6: Di#0Berent Symbol Ratios InputClass = Uniform, m =2;n= 1000;k =2;p=#28Ratio; 1 , Ratio#29 Table7 shows selected experiments with input generated from non-uniform probability distributions The probability distribution of each0; 1-input string is described by a linear functions de#0Cned over its length. For simpli#0Ccation, this function is de#0Cned by the line connecting the probabilityvalues of the leftmost string symbol p l and the rightmost string symbol p r .... ..."

Cited by 1

### Table 4: The ratio of distances between consecutive zeros calculated using piecewise cubic C0 elements on a sequence of non-uniformly re ned grids on an eighth of the unit square domain.

1999

"... In PAGE 14: ... N denotes the dimension of the linear system resulting from each of the non-uniformly re ned meshes, which are designed to allow greater resolution of the eigenfunction in the corner. Table4 shows calculations of the same ratios for a di erent sequence of non-uniformly re ned meshes, on an eighth of the domain (utilizing further symmetry along the bisector of the corner). In each case the calculations are based upon the approximation of the principal eigenfunction (i.... ..."

Cited by 2

### Table 3: Quantization SNR vs. rate of L-FEVQ using non-uniform state quantization for

"... In PAGE 10: ... Both methods show the same performance, however, as will be explained in the following, our method has a much smaller complexity. Table3 shows an approximation of complexity for the proposed method (L-FEVQ) using non-uniform merging of states. The entries of this table are computed using the expressions given in [10] where wehave accounted for the e ect of the non-uniform merging of states and the memory and computational requirements at each stage of the hierarchy are multiplied by proper factors to re ect the increase in the complexity due to the embedded lattice structure (refer to [1] for more details).... ..."

### Table 3: Evaluation of measurement{based admission rule with non{uniform weights.

"... In PAGE 13: ... (A speed{up of the admission test is proposed in Section 3.) Table3 gives the average number of admitted streams, the loss probability and Me for di erent values of p. We see from the table that the average number of connections increases as p decreases.... ..."

### Table 4: Summary of the design of the agent using non-uniform instance-based function approximator for the double integrator.

"... In PAGE 29: ... adjusts accordingly so that the increased density of cases near the origin does not produce too much blending of their values. Table4 summarizes the agent apos;s design. Figures 19 and 20 show the average number of time steps and accumulated cost per trial respec- tively.... ..."

### Table 3 summarizes the agent apos;s design for the uniform and non-uniform con gurations.

"... In PAGE 30: ...Table3 : Summary of the design of the agents using the case-based function approximator for the double integrator. Factor Description Uniform Non-uniform Variables 3: position: p 2 [;11] velocity: v 2 [;11] acceleration: a 2 [;11] Case structure Number of actions: 6, equally spaced in [;11] Blending factor: =60% Distance functions Input space: Euclidean.... ..."

### Table 4: Summary of the design of the agent using non-uniform instance-based function approximator for the double integrator. Factor Description Variables

1998

"... In PAGE 31: ... Similarly, the smoothing parameter adjusts accordingly so that the increased density of cases near the origin does not produce too much blending of their values. Table4 summarizes the agent apos;s design. Figures 19 and 20 show the average number of time steps and accumulated cost per trial respectively.... ..."

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### Table 3: The ratio of distances between consecutive zeros calculated using piecewise cubic C0 elements on a sequence of non-uniformly re ned grids on a quarter of the unit square domain.

1999

"... In PAGE 14: ... (Recall from section 2 that rn is the distance along the bisector of the angle to the nth local extremal value of the eigenfunction u, tn is the magnitude of this extremum, and sn the distance to the nth zero.) In Table3 we present some numerical results for the rst of these ratios, obtained by solving (1) on the unit square using piecewise cubic C0 elements on a sequence of unstructured meshes over a quarter of the domain (making use of symmetry at x = 1=2 and y = 1=2 and applying appropriate Neumann conditions at these boundaries). N denotes the dimension of the linear system resulting from each of the non-uniformly re ned meshes, which are designed to allow greater resolution of the eigenfunction in the corner.... ..."

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### Table 1 Average interconnection lengths of some benchmark designs based on a non-uniform (LN) versus a uniform (LU) oc- cupancy distribution, in two and three dimensions. The number of gates is shown in the column Ng and r is the Rent exponent. The circuits numbered 1 through 5 are those used by Donath in [1], the others are the same as those used in [7].

"... In PAGE 7: ... The resulting experimental placements are therefore good samples of the optimal placement. The results are shown in Table1 . In this table, L2D exp denotes the experimentally measured value of the average in- terconnection length for a two-dimensional placement.... In PAGE 7: ...An experimental veri cation in three dimensions still requires a lot of research to nd a good algorithm for three-dimensional placement and routing. However, the comparison with experiments in two dimensions (column L2D exp in Table1 ), does show that estimates based on the non-uniform occupancy distribution are a lot more accurate than the ones based on the uniform occupancy distribution (Donath apos;s technique). Since the extension to three dimensions does not change the esti- mation method fundamentally, the same result is to be expected for three-dimensional systems.... In PAGE 7: ... Since the extension to three dimensions does not change the esti- mation method fundamentally, the same result is to be expected for three-dimensional systems. The last two columns of Table1 show the improve- ment for a three-dimensional placement over a two-di- mensional one for both techniques. One can see that the average interconnection length is lower for designs placed in a three-dimensional system than it is for de- signs placed in a two-dimensional system, especially for highly complex designs.... ..."

### Table 2. The distribution of the data in non-uniformly

1992

"... In PAGE 22: ... Table2 shows the distribution of the data in the non-uniformly distributed #0Cles among 3 disks. Number of Data Distribution on Disks Records Number of Blocks Number of Blocks Number of Blocks in Files on Disk 1 on Disk 2 on Disk 3 1000 14 13 14 10000 138 138 137 15000 209 210 208 20000 279 279 279 Table 1.... In PAGE 22: ... Table 1 shows that the data in the uniformly distributed #0Cles is evenly distributed among disks. Table2 shows that the data in the non-uniformly distributed #0Cles is nearly equally distributed among disks even without using any rebalancing algorithm. Performance of range query processing.... ..."

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