### Table 3. The identi cation of the footpoints is based on the photospheric magnetic eld strength or the velocity eld de- rived from transition region lines (see text and Table 3). B is the approximate magnetic eld strength peak in the foot- point area; v and are the peak line-of-sight velocities and the peak non-thermal velocities estimated at the footpoints, respectively.

in Structure and dynamics of an active region loop system observed on the solar disc with SUMER on SOHO

"... In PAGE 6: ...3 pixels ( 3 km s?1). Table3 . Characteristics of the loops identi ed (see text and Table 4).... In PAGE 7: ... The magnetic eld values range from -1400 Gauss in the darkest area to +940 Gauss in the brightest area. Each identi ed loop is labelled with a number and the approximate locations of the corresponding footpoints are indicated with letters (see also Table3 and Table 4) hot on the top ( 106 K) and have a thin transition to the chromosphere ( 104 K) near their footpoints (Ros- ner et al. 1978, Withbroe 1981, Mariska 1992, Kano amp; Tsuneta 1996).... ..."

### Table 5.1 Convergence rates for a smooth problem on grid pairs with one base grid and one re ned patch. We give L2 norms of the di erences in nal velocity elds between adjacent cases, and convergence rates de ned as log2 of the ratios of these di erences.

1997

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### Table 2: Angular velocities at which each of the tracking methods loses the small target out of the eld of view. Values in parentheses are for the larger target.

"... In PAGE 10: ...eld of view. Values in parentheses are for the larger target. in a loss of the object out of the eld of view. Table2 shows the angular velocities at which each of the methods lose the target. Simple position tracking with no velocity/acceleration estimates is included for comparison.... ..."

### Table 3.3: MSE of motion estimates in various regions at eld #2 of test image 1 for 4 di erent sets of synthetic motion parameters. In each case the motion elds at eld #2 are estimated with L = 4, p = 25, It = f?2; ?1; 0; 1; 2g, and [wvx wvy wax way] = [1 1 2 2]. The MSE in R0 amp; R0 1 along with the true velocity and acceleration parameters at eld #2 for each case are 62

1994

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### Table 1: The nominal operating conditions for various CTD gas mixes which have been used over the course of the HERA running period (T.B. signi es test beam operation prior to HERA startup). Ed and Es are the drift eld and sense wire surface elds respectively which result in a drift velocity vd and Lorentz angle Lorentz in an applied magnetic eld B.

"... In PAGE 5: ... The choice of these parameters is dependent on the amplifying gas mix in the chamber which in turn is an important consideration for e cient and safe operation of the CTD. We have operated the CTD and its prototypes with a variety of gas mixes at 3 mbar above atmospheric pressure, and their constitutions are given in Table1 . All gases and operating conditions listed result in azimuthal drift with velocity 50 m/ns, a maximum drift time of 500 ns (equivalent to ve beam crossings of the HERA accelerator) and a sense wire surface eld which de nes a gas gain of approximately 1 105 [12].... In PAGE 33: ...ut the running period, ZEUS operated with a reduced magnetic eld of 1.43 T. This necessitated operation of the CTD with an argon/CO2/ethane gas mix in the proportions 85/8/7 with a 0.84% admixture of ethanol (see Table1 ). An applied drift eld of 1.... ..."

### Table 3.1: Summary of Yosemite 2-d Velocity Results More recently, we examined the use of reconstruction (warping) error as a quantitative error metric for those ows where the correct ow elds are unknown27. Given a computed optical ow eld for some image we use it to reconstruct the next image in the sequence and then compute the RMS di erence between the actual next image and its reconstructed version. We found that several backward and forward reconstruction methods using bicubic interpolation on Gaussian smoothed or con dence measure weighted velocity elds provided the best correlation between quantitative and RMS errors for synthetic images sequences (the reader is directed to a paper27 for full details). Reconstruction error was then used to provide a quantitative error metric for real image sequences with unknown correct ow. 4 Problems and Current Research Directions Still, several major problems remain:

### Table 1. Coherence magnitude (phase) between 200m meridional velocity (v) at mooring 1 and velocity components at other moorings for the 1.8-day signal

"... In PAGE 4: ...elocity (as will be shown later). The 1.8-day signal* is not signi cantly coherent with the remaining six moorings (numbered 4 through 9, northwards over the ridge). Table1 presents the coherence magnitude and phase estimates (in the 0.56 cpd frequency bin) between 200m meridional velocity at mooring 1 and meridional and zonal velocity at each depth of moorings 1, 2 and 3.... In PAGE 5: ...mplies more degrees of freedom in the frequency band of the 1.8-day signal. However, because the coherence magnitude decreased to near 0.50 for these calculations the phase lag estimates (a 28 lag between mooring 1 and 2 and a 44 lag between mooring 1 and 3) were bracketed by roughly the same 95% con dence limits as those of Table1 and Figure 3. Empirical orthogonal functions (EOFs) were calculated for the low-passed velocity, as well as for band-passed velocity between 0.... ..."

### Table 1: The `2 error norms for the height h and the velocity eld u for the unstaggered and staggered versions of the Turkel-Zwas scheme for a 64 32 grid after 24 hours. The parameter E represents the percent change of available energy of the system. grid on a Sparc 10. Table 1 shows the results for various con gurations of p and q using di erent time steps for the unstaggered and staggered versions of the Turkel-Zwas scheme. Recall that p and q refer to the extension of the di erencing stencil in the longitudinal ( ) and latitudinal ( ) directions, respectively, and is the Pad e-type di erencing weight. We have experimented with various values of , namely = 0; 1 4; 1 3; 12; 2 3; 3 4; 1: We have found

1997

"... In PAGE 21: ... Thus it makes sense to treat the gravity terms less accurately by using a coarser grid for these terms (see Turkel and Zwas1). Table1 shows that for the lower values of p and q, say (p=2,q=1) for the unstaggered and (p=3,q=2) for the staggered and t = 200, the unstaggered and staggered cases yield comparable error norms. As p and q are increased beyond these values, the errors increase dramatically for the unstaggered case; the errors for the staggered case are only half those of the unstaggered case.... ..."

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### Table 2. Current Cluster-based Peculiar Velocity Surveys

"... In PAGE 9: ... 7 The Large-scale Velocity Field A complementary approach (and perhaps a more promising one given current cluster catalogs) to studying very large{scale structure using clus- ters is through the mapping of the large{scale velocity eld. Currently, at least 7 independent cluster-based peculiar velocity surveys, all reaching scales of 100h?1 Mpc or larger, are either complete or in progress (see Table2 ). Inferences about the under- lying mass distribution from pecu- liar velocity surveys are less suscep- tible to incompleteness e ects and radial density gradients than those from redshift surveys.... ..."

### Table 3: Absolute displacement error with a mean dis- placement module of 11.4 pixels/frame

1998

"... In PAGE 8: ...5 pixels/frame. Table3 and 4 display error results for the scaled velocity elds (mean displacement modules of 11.4 pixels/frame and 15.... ..."

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