### Table 5.1 shows the results obtained with Test #1. It can be seen that our third and fourth order schemes are fully third and fourth order accurate, even after a long integration time, in both the L1 and L1 norms. Comparing the magnitudes of the errors with the results obtained with our previous Central ENO scheme in [5], we note that our new third order method yields smaller errors than the third order Central ENO scheme (here the space reconstruction is more accurate). On the other hand, the old m = 4 Central ENO scheme is more accurate than the present 4-th order CWENO scheme. It must be noted, however, that the new

### Table 1. CPU time ( sec) of the di erent numerical schemes per cell per time-step on a 200 100 grid

"... In PAGE 3: ...The sequential performance of some implemented schemes are displayed in Table1 . The times displayed in this table show that the 2nd order ENO scheme used in conjunction with the exact Riemann solver is poorly vectorizable.... ..."

### Table 1. CPU time ( sec) of the di erent numerical schemes per cell per time-step on a 200 100 grid

"... In PAGE 2: ...2. The sequential performance of some implemented schemes are displayed in Table1 . The times displayed in this table show that the 2nd order ENO scheme used in conjunction with the exact Riemann solver is poorly vectorizable.... ..."

### Table 10: Coe cients and Bounds for fth order stencils References [1] Robert Bruce Bauer. An e cient adaptive grid ENO algorithm. Houston Journal of Mathematics, pages 329{346, 1996. Proceeding of the Third International Conference on Spectral and High Order Methods (ICOSAHOM `95). [2] Marsha J. Berger. On conservation at grid interfaces. SIAM J. Num. Anal,

### Table 4. Convergence study for the second test problem in one space dimension. Errors measured at t = 1:5. The post-processing uses ENO interpolation.

"... In PAGE 11: ... of convergence of the algorithm, even in the presence of discontinuous material properties. Table4 , on the other hand, shows that a simple post-processing of super-converged nodal values can again deliver higher order convergence (of course, in this case, the polynomial ENO-interpolation should avoid using functional values across material discontinuities). 3.... ..."

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### Table 1: L1 and L1 errors for Example 1: Burgers apos; equation H(u) = (u + 1)2=2. Scheme N L1 error L1 order L1 error L1 order

2000

"... In PAGE 11: ... In both cases, the solution is smooth at t = t1 = 0:5= 2 and has discontinuous rst order derivatives at t = t2 = 1:5= 2. In Table1 and 2, we list the L1 and L1 errors of the schemes WENO-RF and ENO-RF. At t = t2, the errors are computed at a distance of 0:1 away from any discontinuities in the derivatives of the solution.... In PAGE 11: ... Such restrictive time step is only used for accuracy test purpose and will not be used in later examples. From Table1 and 2, we can see that for both the convex and nonconvex ux, the ENO scheme achieves about 3rd order accuracy while the WENO scheme achieves about 5th order accuracy. WENO-LLF (ENO-LLF) obtains similar accuracy as WENO-RF (ENO-RF) for both cases.... ..."

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### Table 7: Number of operations per Runge-Kutta stage per grid point and MFlops on CRAY C-90. d: the spatial dimension.

1996

"... In PAGE 17: ...5 times as fast on SGI Indigo2. In Table7 , the number of oating point operations and the MFlops (million oating- point operations per second) are given for the 2nd order scheme, ENO-Roe-4, ENO-LF-4, WENO-LF-5, WENO-LF-5-PS, ENO-Roe-4-A and WENO-LF-5-A. the operation count and MFlops for WENO-LF-4 is about the same as those for WENO-LF-5, thus omitted in the table.... ..."

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### Table 1: The 36 pathways (see Figure 3) scored by the correlation function (see Formula 10). Dark shading of ORF IDs indicates up-regulation during diauxic shift, light shading indicates down-regulation, no shaing indicates unchanged expression. The pathways that are realized in the glycolysis before the diauxic shift are scored highest. The most distinguishing position of the pathway is the rst enzyme characterized by the expression of ORF YGL253W which is up-regulated (in contrast to YCL040W and YFR053C). The ranking resulted in the following decreasing order of signi cance values: HXK2 (HXK1/GLK1) gt; gt; ENO2/YHR174w (ENO1/YGR254w) gt; PFK1/YMR205c (PFK2/YOR240c); the genes/ORFs TDH1/YJL052c, TDH2/YJR009w, TDH3/YGR192w show no in uence.

2000

"... In PAGE 6: ...istribution of random scores, i.e. most of the glycoly- sis pathways can indeed be recognized by our method given the current measurements. As can be seen in Table1 , the correlation func- tion scores those pathways best that are completely activated in the glycolysis, i.e.... ..."

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