### Table 2. Intersection Results

"... In PAGE 8: ... Therefore we select a high-precision strategy and use the intersection of two results with different seed vector numbers to further improve the precision. The results in Table2 show that the precision is improved greatly and able to achieve at 97% with combination strategy. When the searching ... ..."

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### Table 1: The Primary Intersections

"... In PAGE 7: ... For convenience, we label all points, even though some of them are in the lower half-plane for some parameter values. The list is in Table1 ; a sketch in Figure 3 identi es the points. Remark: It is clear that intersections of one shock with another, or of a shock with the wall, generate new waves.... In PAGE 24: ...11) and v(u2) lt; 0 if I gt; u2=2. Checking the value of I in Table1 shows that this is indeed the case. This construction can also be used to estimate the values of vm and um.... In PAGE 31: ... This requires the two conditions 1 gt; 0 (so that 1 exists) and a gt; I(b), so that I is not admissible. The rst condition, from Table1 , is a lt; 1=p2. We describe the following reduction of the problem to a degenerate el- liptic equation.... ..."

### Table 2. Intersection operator semantics

"... In PAGE 4: ... Using k shift bits, the cube ci k is able to reach 2k states; however, some of these states could have been visited by j a8 k bits. In order to calculate the exact number of new states that could be visited using k bits, we take the intersection, according to the semantics defined in Table2 , of ci k with all the cubes cij where j a8 k. A NULL intersection in Table 2 indicates no common cube between the two cubes being intersected.... In PAGE 4: ... In order to calculate the exact number of new states that could be visited using k bits, we take the intersection, according to the semantics defined in Table 2, of ci k with all the cubes cij where j a8 k. A NULL intersection in Table2 indicates no common cube between the two cubes being intersected. We demonstrate the operation of the intersection operator by the following example for the simple case where s a4 1.... ..."

### Table 2 Results of identified intersections.

2006

"... In PAGE 23: ... Hence, we evaluated the LTM performance by calculating precision and recall of detected control points (before and after applying filters). The results are listed in Table2 . We also included the precision/recall of original road network in Table 2 to demonstrate that our LTM improved both precision/recall of original vector data.... In PAGE 23: ... We also included the precision/recall of original road network in Table 2 to demonstrate that our LTM improved both precision/recall of original vector data. As shown in Table2 , our LTM performed differently for various real world scenarios. This is because these vectors have different qualities and the orthoima- gery has various levels of complexity.... In PAGE 24: ... The shapes (and geometry) of the original TIGER/Lines are sometimes inconsistent with the corresponding roads in the imagery, because large portions of curve-shaped roads were simplified as straight lines. Hence, as shown in Table2 and Figure 17, original TIGER/Lines has low completeness/correctness and low precision/recall for the intersections. For a particular road segment, if the shape of the original vector data is inconsistent with roads in the imagery (as the example of TIGER/Lines), our system may not align them well, although the majority of intersections might be aligned.... In PAGE 24: ... This is mainly because our matching is at the point level, not at the edge level. As the example of TIGER/Lines in test area 1 (see Table2 (a)), we improved the node (intersection) alignment (as the precision improved from original 7 to 87.1%), while we achieved completeness and correctness to 55%.... In PAGE 27: ...re within 7.2 meters versus 25.93% for the original TIGER/Lines. In particular, comparing to NAVSTREETS and MO-DOT data, again, TIGER/Lines have poor positional accuracy and poor geometry. For such kind of severely distorted original TIGER/Lines segments, our approach is limited in aligning imagery curves and vector lines, although the detected intersections are matched (as shown in Table2 ). Hence, only about 47% of conflated TIGER/Lines in test area 2 and 3 are within 7.... ..."

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### Table 6: The operation of a Priority Enforcer detecting the leftmost zero in 16-bit vectors.

1996

"... In PAGE 44: ... The equations for the output and NEH vector are : OUT i = NEH i,1+IN i and NEH i = IN i #03 NEH i,1(NEH 0= 1). Table6 , presents an example of the operation of the PE, that detects the leftmost zero in a 16-bit input vector. From the above paragraph it is obvious that the problem of enforcing priority is directly proportional to the one of carry calculation and propagation in binary addition.... ..."

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### Table 6: The operation of a Priority Enforcer detecting the leftmost zero in 16-bit vectors.

"... In PAGE 42: ... The equations for the output and NEH vector are : OUTi = NEHi?1+INi and NEHi = INi NEHi?1 (NEH0 = 1). Table6 , presents an example of the operation of the PE, that detects the leftmost zero in a 16-bit input vector. From the above paragraph it is obvious that the problem of enforcing priority is directly proportional to the one of carry calculation and propagation in binary addition.... ..."

### Table 4. A Boolean feature vector representation of the documents in Table 3.

"... In PAGE 4: ... Lattice Machine has a natural solution to this problem. Given two documents of a same class in Table 3, we rst of all represent them by boolean feature vectors as in Table4 . Merging the two vectors by the lattice sum operation (either using set union or intersection, depending on the ordering relation), we get new vectors as in Table 5.... In PAGE 5: ...Table 5. The sum of the two tuples in Table4 . The rst tuple is by set union, and the second tuple is by set intersection.... ..."

### Table 1: Example of a bit vector index

2003

"... In PAGE 5: ... Thes bit vectors are typicaly packed into word arrays for fast linear access. For example, see Table1 , which shows how the bit vector index is computed over a table S using the predicate: Age lt;40. This index can then be used to find the tuple IDs that satisfy predicates in queries.... ..."

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