### Table 2.2: Evaluation of several curve representations using the Marr-Brady criteria. The grades awarded reflect the extent to which each representation favourably meets the par- ticular criteria. The line, conic and superconic are all intrinsically scope-limited represen- tations, while the others offer a variety of tradeoffs, notably against stability, in order to achieve wide scope.

### Table 2. Approximate upper limits on intrinsic I band vari- ability. Ilim is de ned as the scatter of the RMS (root mean squared) values in the relative magnitude time series that would have been required before we obtained signi cant (P( 2 s) lt; 0:01) evidence for variability according to the 2 test. For each star the search was sensitive to variations in approximately the range shown.

"... In PAGE 3: ... All except 2M1145 failed at least one. From the results of the 2 test we can set approximate limits to the amount and timescale of intrinsic variability in these ve stars at the epoch of the observations ( Table2 ). For each star in this table (except 2M1145) there is no signif- icant evidence (i.... ..."

### Table 2. Approximate upper limits on intrinsic I band variability. Ilim is defined as the scatter of the RMS (root mean squared) values in the relative magnitude time series that would have been required before we obtained significant (P( 2 s) lt; 0:01) evidence for variability according to the 2 test. For each star the search was sensitive to variations in approximately the range shown.

1999

"... In PAGE 3: ... All except 2M1145 failed at least one. From the results of the 2 test we can set approximate limits to the amount and timescale of intrinsic variability in these five stars at the epoch of the ob- servations ( Table2 ). For each star in this table (except 2M1145) there is no significant evidence (i.... ..."

### Table 2: Approximability Results for NP-hard Compact Location Problems Notes: UB denotes the best known upper bound on the performance guarantee. LB denotes the lower bound on the performance guarantee; that is, the intrinsic limit assuming P 6 = NP. NGR is an abbreviation for \No Guaranteed Ratio quot;. It is easy to check that the triangle inequality is satis ed for c0. Next consider a placement P0 of p nodes in I0. The transformation g chooses as its placement P the p nodes in I corresponding to the p nodes in I0. By a straightforward calculation, it can be seen that for any placement P of p nodesX e0=(v0;w0)

"... In PAGE 24: ... Table 1 shows the hardness results for the various unicriterion problems. Table2 gives the corresponding approximation results. Table 3 shows our results for bicriteria compact location problems.... ..."

### Table 2. Polarization measurements of the survey stars. The magnitudeof the continuumminusline polarizationis listed ( P) together with the intensity of line emission line relative to the continuum (I`); the nal column is a measure of the intrinsic continuum polarization (PC; see eqtn. 1). Note that the majority of measurements actually represent upper limits. WR P Line

"... In PAGE 9: ... This WN6+O5 binary system shows the double sine-wave continuum polarization modulation expected for a close binary (Mo at, personal communication; see also Grandchamps amp; Mo at 1991). The star shows a small but signi cant line e ect (see Table2 and Figure 1l). We are not aware of any previous spectropolarimetric observations.... In PAGE 10: ... The continuum polarization at the wavelength of an emis- sion line was estimated by a median straight-line t to the Stokes parameters in line-free continuum bins adjacent to the line, while the emission-line polarization was measured by summing the Stokes parameters over an interactively de- ned bin centred on the line. The measured polarizations and line intensities are listed in Table2 . The uncertainties are such that few PC estimates represent rm detections, but simply to tabulate the other measurements as upper limits would be to discard useful information.... ..."

### Table 3. Absorbing columns and intrinsic optical slopes FID SNo cold gas dust extinction

"... In PAGE 3: ...e a free parameter (i.e. giving 3 free parameters). However, no signi cant improvements to the ts (according to the F- test) were found to any of the AGN and only 90 percent upper limits could be derived on NHint (these are given in Table3 ). The constraints on two AGN, F223 17 and F248 2, are relatively tight however, with 90 percent upper limits of 2 1020 cm?2 and 3 1020 cm?2 respectively, indicating low levels of cold gas absorption in these objects.... In PAGE 4: ... Errors on the Balmer decrements have been derived by es- timating upper and lower limits on the Balmer line uxes, taking into account the placement of the continuum and other e ects such as line blending and the relative contri- bution of the narrow component. The results are listed in Table3 and show that for all but two AGN, F232 16 and F281 21, the Balmer decrement is high, suggesting signif- icant amounts of intrinsic dust absorption. The degree of extinction by dust, parametrized by E(B-V), has been cal- culated from these Balmer decrements using the reddening curve of Cardelli, Clayton amp; Mathis (1989), and these are also given in Table 3 (column 5).... In PAGE 4: ... The results are listed in Table 3 and show that for all but two AGN, F232 16 and F281 21, the Balmer decrement is high, suggesting signif- icant amounts of intrinsic dust absorption. The degree of extinction by dust, parametrized by E(B-V), has been cal- culated from these Balmer decrements using the reddening curve of Cardelli, Clayton amp; Mathis (1989), and these are also given in Table3 (column 5). If it can be assumed that di erences in the Balmer decrement are entirely due to reddening by dust, then it should be possible to use the H /H ux ratio to predict the intrinsic (i.... In PAGE 6: ... This dust extinction was then used to calculate a lower limit on the intrinsic slope of the optical continuum. The results are listed in Table3 and show that in most cases, the lower limits on the de-reddened opt are very low and little useful information can be derived. However, two of the seven AGN have optical continua which do remain red, F223 17 and F248 2, thus we identify these as `red can- didate apos; AGN, i.... ..."

### Table 1. Some results of the Monte Carlo simulation for di erent parameter values of interest. The parameters are: the intrinsic width of the main sequence MS, the limit on the accepted relative parallax uncertainty ( = )lim, the target [Fe/H], the measurement uncertainties in [Fe/H], [Fe=H]. The mean bias is de ned for all of the \accepted quot; objects (see the text) as the \true quot; magnitude at a given colour de ned by Equ. 4 for the rst 9 lines, and by Equ. 5 for the last two, minus the mean \measured quot; magnitude.

"... In PAGE 8: ...ther clusters of similar metallicity (Stetson et al. 1996). We t the M92 sequence of Stetson amp; Harris to the sub- dwarf data, corrected for biases and binaries according to the procedure developed in Section 4. Unevolved and evolved stars are shifted in magnitude according to lines 1 and 10 of Table1 , respectively, and 0.375 mag is then added to the absolute magnitude of suspected or detected binaries.... ..."

### Table 3: Approximate goodness of t values for the best- t models in each family. low. This is predominantly a re ection of the fact that the data disfavor very low values of , which are intrinsic to the PIB model. Note that if we limit ourselves to modifying only one parameter of sCDM (i.e. changing n, or , or ), we can reach almost perfect t by a proper change in n or . For a similar t with CHDM, we need in addition a slight modi cation in either n or , together with introducing gt; 0.

"... In PAGE 22: ... The result is a signi cant deviation of the model from the velocity data, with a very poor goodness of t. Table3 presents the approximate goodness of t for the models we examined. For all the models except PIB, the t, at the best- t parameters, is acceptable.... ..."

### Table 1. Estimated bias with confidence limits.

"... In PAGE 17: ... In the third method (method C), each observation is weighted by the inverse of the observation error covariance matrix R that was estimated using Eqn (31) and all 200 images. Table1 shows the estimated bias (average error) of the intrinsic parameters for all three meth- ods. Confidence intervals with a 95% confidence level are also presented.... ..."

### Table Figure 1: A Simple Example. Consider the example in Figure 1. It shows blocks of various shapes, sizes, and colors. Additionally, some of the blocks are stacked on top of each other. A simple feature-based learner cannot learn a description of the concept set consisting of blocks 2, 3, and 5 since it is limited to reasoning only about their intrinsic features such as shape and color. To learn a simple description of the concept (it consists of blocks that are on other gray blocks) requires representing and reasoning with relational information. We can represent the relevant information for this concept with the simple inheritance network in Figure 2. We can see that the blocks of the concept are connected by paths consisting of on and color links to the node Gray. The problem is that we do not know beforehand that this combination of links characterizes the set. In a more complex example

1994

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