### Table 1: Results of numerical experiments to test the half-plane property.

2004

"... In PAGE 82: ..., . . . ). The results of our numerical experiments are shown in Table1 . As can be seen, the method using Proposition 5.... In PAGE 82: ...4). The results in Table1 strongly suggest that all rank-3 transversal matroids have the half-plane property. And they suggest the bold conjecture that perhaps all transversal matroids of any rank have the half-plane property.... ..."

Cited by 11

### Table 1: Experiments on embedding a polygon in three half-planes.

1996

"... In PAGE 20: ... The number of possible poses for the polygon to be embedded in these generated half-planes was then computed, and the summarized results for all group are listed in the last two columns of the table. Table1 tells us that three half-planes are insu#0Ecient to limit all possible poses of an embedded polygon to a unique one, namely, the real pose; in fact the table suggests that... In PAGE 22: ... The ratio between these two squares #28circles#29 was set uniformly to be 1 2 for all seven groups of data. In contrast to Table1 , Table 2 tells us that two cones allowaunique pose of an inscribed polygon in most cases. In each group of tests, only cases with one pose or two poses occurred, and the mean of possible poses stayed very close to 1, independent of the mean polygon size.... ..."

Cited by 19

### Table 1: Experiments on embedding a polygon in three half-planes.

1996

"... In PAGE 15: ... The number of possible poses for the polygon to be embedded in these generated half-planes was then computed, and the summarized results for all group are listed in the last two columns of the table. Table1 tells us that three half-planes are insu#0Ecient to limit all possible poses of an embedded polygon to a unique one, namely, the real pose; in fact the table suggests that a linear #28in the size of the polygon#29 number of possible poses will usually exist. We can see in the table that despite the appearances of cases with one or two possible poses, the ratio between the mean of numbers of possible poses and mean polygon size lies in the approximate range 0.... In PAGE 17: ...squares #28circles#29 was set uniformly to be 1 2 for all seven groups of data. In contrast to Table1 , Table 2 tells us that two cones allowaunique pose of an inscribed polygon in most cases. In each group of tests, only cases with one or two poses occurred, and the mean of possible poses stayed very close to 1, independent of the mean polygon size.... ..."

Cited by 19

### Table 2. Choice of the app-query half-plane, for an original down-query

"... In PAGE 5: ... Choice of the app-query. Table2 summarizes the various cases for constructing the app-query half-plane for an ori- ginal down-query. Similar conditions can be given for an up-query.... ..."

### Table 2: The 7-element rank-3 3-connected matroids, divided according to whether or not they have the half-plane property (HPP).

2004

"... In PAGE 88: ...lements (Proposition 10.4). So the first nontrivial case arises with 7-element rank-3 matroids; we would like to know which ones have, and which ones do not have, the half-plane property. In Table2 we divide the 7-element rank-3 3-connected matroids (see Appendix A.2) into three categories: those we have proven to have the half- plane property, those we have proven not to have the half-plane property, and those for which we have no proof either way.... ..."

Cited by 11

### Table 1: Experiments on embedding a polygon in three half- planes.

"... In PAGE 6: ... The number of possible poses for the polygon to be embedded in these generated half-planes was then computed, and the summarized results for all group are listed in the last two columns of the table. Table1 tells us that three half-planes are insufficient to limit all possible poses of an embedded polygon to a unique one, namely, the real pose; in fact the table suggests that linear (in the size of the polygon) number of possible poses will usually exist. We can see in the table that despite the appearances of cases with one or two possible poses, the ratio between the mean of numbers of possible poses and mean polygon size lies in the approximate range 0.... In PAGE 7: ... The ratio between these two squares (circles) was set uniformly to be 1 2 for all seven groups of data. In contrast to Table1 , Table 2 tells us that two cones allow a unique pose of an inscribed polygon in most cases. In each group of tests, only cases with one pose or two poses occurred, and the mean of possible poses stayed very close to 1, independent of the mean polygon size.... ..."

### Table 1: Experiments on embedding a polygon in three half- planes.

"... In PAGE 6: ... The number of possible poses for the polygonto be embedded in these generated half-planes was then computed, and the summarized results for all group are listed in the last two columns of the table. Table1 tells us that three half-planes are insufficient to limitall possible poses of an embedded polygon to a unique one, namely, the real pose; in fact the table suggests that linear (in the size of the polygon) number of possible poses will usually exist. We can see in the table that despite the appearances of cases with one or two possible poses, the ratio between the mean of numbers of possible poses and mean polygonsize lies in the approximate range 0.... In PAGE 7: ... The ratio between these two squares (circles) was set uniformly to be 1 2 for all seven groups of data. In contrast to Table1 , Table 2 tells us that two cones allow a unique pose of an inscribed polygon in most cases. In each group of tests, only cases with one pose or two poses occurred, and the mean of possible poses stayed very close to 1, independent of the mean polygon size.... ..."

### Table 1: Experiments on embedding a polygon in three half-planes. Seven groups of convex polygons were tested. The rst six groups consisted of convex hulls generated over 10, 100, and 1000 random points successively and for each number in two kinds of uniform distributions: inside a square and inside a circle, respectively. It can be seen in the table that the polygons in these groups had a wide range (3{43) of sizes (i.e., numbers of vertices), but their shapes were not arbitrary enough, approaching either a square or a circle when large numbers of random points were used. So, we introduced the last group of data, which consisted of polygons generated by a method called circular march, which outputs the vertices of a convex polygon as random points inside a circle in counterclockwise order. The size of a polygon in this group was randomly chosen between 3 and 15.

1996

"... In PAGE 15: ... The number of possible poses for the polygon to be embedded in these generated half-planes was then computed, and the summarized results for all group are listed in the last two columns of the table. Table1 tells us that three half-planes are insu cient to limit all possible poses of an embedded polygon to a unique one, namely, the real pose; in fact the table suggests that a linear (in the size of the polygon) number of possible poses will usually exist. We can see in the table that despite the appearances of cases with one or two possible poses, the ratio between the mean of numbers of possible poses and mean polygon size lies in the approximate range 0.... In PAGE 17: ...squares (circles) was set uniformly to be 12 for all seven groups of data. In contrast to Table1 , Table 2 tells us that two cones allow a unique pose of an inscribed polygon in most cases. In each group of tests, only cases with one or two poses occurred, and the mean of possible poses stayed very close to 1, independent of the mean polygon size.... ..."

Cited by 19

### Table 1: Experiments on embedding a polygon in three half-planes. Seven groups of convex polygons were tested. The rst six groups consisted of convex hulls generated over 10, 100, and 1000 random points successively and for each number in two kinds of uniform distributions: inside a square and inside a circle, respectively. It can be seen in the table that the polygons in these groups had a wide range (3{43) of sizes (i.e., numbers of vertices), but their shapes were not arbitrary enough, approaching either a square or a circle when large numbers of random points were used. So, we introduced the last group of data, which consisted of polygons generated by a method called circular march, which outputs the vertices of a convex polygon as random points inside a circle in counterclockwise order. The size of a polygon in this group was randomly chosen between 3 and 15.

1996

"... In PAGE 15: ... The number of possible poses for the polygon to be embedded in these generated half-planes was then computed, and the summarized results for all group are listed in the last two columns of the table. Table1 tells us that three half-planes are insu cient to limit all possible poses of an embedded polygon to a unique one, namely, the real pose; in fact the table suggests that a linear (in the size of the polygon) number of possible poses will usually exist. We can see in the table that despite the appearances of cases with one or two possible poses, the ratio between the mean of numbers of possible poses and mean polygon size lies in the approximate range 0.... In PAGE 17: ...squares (circles) was set uniformly to be 12 for all seven groups of data. In contrast to Table1 , Table 2 tells us that two cones allow a unique pose of an inscribed polygon in most cases. In each group of tests, only cases with one or two poses occurred, and the mean of possible poses stayed very close to 1, independent of the mean polygon size.... ..."

Cited by 19

### Table 2 lists the numbers underlying Figure 6 for values of R equal to powers of 10. By analyzing these and other such numbers we estimate for k = 0,

"... In PAGE 13: ... The transient e ects of Figs. 5{8 and Table2 cannot be inferred from the eigen- values of the operators in question, which are all in the left half-plane. However, they can be inferred from their pseudospectra.... ..."