### Table 2: Comparison of average path length for a 1d array for different network models: a233a50a7 is the quadratic

2001

"... In PAGE 14: ...Table 2: Comparison of average path length for a 1d array for different network models: a233a50a7 is the quadratic path length model, a233 a162 is linear path length and a233a94a251 cubic path length. Table2 shows a comparison of these three values of a236 as follows. For each value of a5 , the rst column shows a233a65a7 , the average path length for the quadratic model (a236a158a12a252a124 ), whilst the second amp; third columns show the average path length for the linear (a236a126a12a32a120 ) amp; cubic (a236a167a12a253a237 ) models, respectively, scaled by a233 a7 .... In PAGE 14: ... We believe that this is because cut-edges between non-neighbouring processors are not suf ciently penalised in the cost function. Looking at the results in Table 3 (which are presented in the same format as Table2 with the results of the linear and cubic models scaled by those of the quadratic) we see the consequences of the choice of model on the cut-weight. It is almost inevitable that the mapping task will be detrimental in some way to the cut-weight (this is particularly true for the 1d array architecture) and so we see conversely that the linear model which is not so good for mapping is considerably better for optimising the cut-weight (on average 10% better for a5a44a12a168a254 to 37% better for a5a255a12a84a237a212a124 ).... In PAGE 17: ...00 Table 8: Comparison of mapping costs, a98 , for a cluster architecture for different preference functions: a98 a229 a35 is where the preference is chosen from neighbouring subdomains amp; processors, a98 a229 from neighbouring sub- domains and a98 a38 from all processors. Table 8 shows the cost function results for the cluster architecture broadly presented in the same format as Table2 . For each value of a5 , the rst column gives the results for a228 a229 a35 whilst the second amp; third columns show those for a228 a229 amp; a228 a38 scaled by a228 a229 a35 .... ..."

Cited by 18

### Table 1. Number of Iterations to Decrease Residual by 10?6, 1D Daubechies AFIF Linear Quadratic J

1997

"... In PAGE 18: ...The results of the numerical study are summarized in Table1 and de- picted graphically in Figure 4. A rst interesting conclusion in considering the results of Table 1 is that the multilevel -preconditioner for both the AFIF and Daubechies scaling functions yield nearly identical results.... In PAGE 18: ...The results of the numerical study are summarized in Table 1 and de- picted graphically in Figure 4. A rst interesting conclusion in considering the results of Table1 is that the multilevel -preconditioner for both the AFIF and Daubechies scaling functions yield nearly identical results. Both methods require just under 30 iterations to reduce the residual to a value of 10?6 of its starting value.... ..."

Cited by 2

### Table 3: Comparison of cut-weight for a 1d array for different network models: A8BE is the quadratic path length model, A8BD is linear path length and A8BF cubic path length.

2001

"... In PAGE 14: ... We believe that this is because cut-edges between non-neighbouring processors are not sufficiently penalised in the cost function. Looking at the results in Table3 (which are presented in the same format as Table 2 with the results of the linear and cubic models scaled by those of the quadratic) we see the consequences of the choice of model on the cut-weight. It is almost inevitable that the mapping task will be detrimental in some way to the cut-weight (this is particularly true for the 1d array architecture) and so we see conversely that the linear model which is not so good for mapping is considerably better for optimising the cut-weight (on average 10% better for C8 BP BK to 37% better for C8 BP BFBE).... ..."

Cited by 18

### Table 1: Summary of local and global scaling parameters for the quadratic kicked-oscillator models.

2005

"... In PAGE 29: ... 5.7 Summary of results for quadratic cases Table1 summarizes the parameters and derived scale factors and dimensions of the 9 kicked-oscillator models lifted from the class of piecewise a ne maps studied systematically in reference [24]. The local quantities are taken from that source, with the global scale factor !W and expansion exponent calculated as in the current section.... ..."

Cited by 1

### Table 3: Size and time costs for the calculation of the Fisher matrix F for archetypal datasets on a SUN Ultra II for the two quadratic estimator algorithms A1, A2.

"... In PAGE 5: ... Similarly N2 l Np, with approximate equality for all-sky maps, so that the second algorithm (A2) scales as O(N2 l Np)insizeandO(N4 l Np) in time. Table3 shows the implications for a range of future experiments, scaled from implementations of each algorithm applied to an unbinned reduced COBE dataset. Note that no assumption has been made about binning in the MAP and PLANCK datasets.... ..."

### Table 0.2: Upper bounds of ( 1; 2) when H2(M; @M ? T ) 6 = 0

1998

Cited by 3

### Table 0.2: Upper bounds of ( 1; 2) when H2(M; @M T) 6 = 0

### Table 4. System-level models: The effects of presidentialism on voting unity index means across 16 legislatures.

"... In PAGE 17: ... [Figures 1 amp; 2] System-level explanations The boxplots suggest that presidentialism undermines legislative party unity at the level of the political system. The first two models in Table4 show the results of OLS regressions of the means for both indices of voting unity on a dummy variable scored 1 if the regime has a popularly elected president, 0 otherwise, across all sixteen chambers for which there are good samples of votes. The coefficient on the constant term is the expected value of the index in parliamentary systems, and the coefficient on the President variable is the expected marginal effect of presidentialism on that value.... In PAGE 20: ... We might expect, therefore, that systems with intraparty electoral competition would exhibit lower WRice indices and higher RLoser on the whole. Model 4 in Table4 shows the results of regressing WRice on President and Intraparty Competition across the set of sixteen cases. The coefficient on President remains negative and significant (albeit, only at .... ..."

### Table 2: Quadratic elds

"... In PAGE 15: ... It seems unlikely that a misidenti cation of one of the ideal volumes, for the dodecahedron, could produce the same e ect as a misidenti cation of a quite di erent ideal volume, for the icosahedron. Thus we believe that we have found exact (and also very lengthy) expressions of the form Pn k=1 D(zk), with n = 128 and zk 2 Q( q 8p2 ? 15), for the cubical/octahedral volume of Table2 0, and with n = 346 and zk 2 Q( q ?12p5 ? 31), for the dodecahe- dral/icosahedral volume of Table 21. Thanks to David Bailey apos;s evaluations of (2n), described in Section 4.... In PAGE 21: ... Thus its volume is provably related to Clausen values at multiples of =5. Interestingly, both knots have volumes that are rationally related to instances of the orthoscheme (46), with S(2 5 ; 1 10 ; 1 5 ) = 1 10 vol(941) = Cl2(25 ) + 1 3 Cl2(45 ) (68) S( 3 10 ; 15 ; 1 10 ) = 1 10 vol(10123) = 2 3 Cl2(25 ) + 1 3 Cl2(45 ) (69) The corresponding relations between Clausen values are straightforward to derive, and hence quite unlike those with ?D 7 in Table2 2, which involve the 8 dramatic switches between number elds recorded in (26{30,37,48,49). 5.... ..."