### Table 4 Comparison of the bound estimate in various methods (data from PhD thesis of Ho statter)

"... In PAGE 12: ... Several nonlinear systems were studied by using the methods mentioned above. The results of bounds on the number of stable turns in three examples are listed in Table4 [Ho statter1994a]. In the case of the interval bounding and the method of Remainder Di erential Algebras, the numbers show lower bounds, while in the case of the rastering, the numbers show upper bounds.... ..."

### Tableaux. [Letz, 1993] R. Letz. First-Order Calculi and Proof Procedures for Automated De- duction. PhD thesis, TH Darmstadt, 1993.

in A Disjunctive Positive Refinement of Model Elimination and its Application to Subsumption Deletion

1997

Cited by 5

### Table 1(b). Experimental parameters. Relaxation time for PO and PAA are computed from measured values taken on the wave-speed meter, PO in the tables given by Joseph [1990] and PAA in the Ph.D Thesis of Y.J. Liu [1995].

### Table 2: Results on PhdThesis data sets for all-pair-comparison-based (AC), selected- comparison-based (SC), and M-tree-base (MT) heuristics with uniform weights using terms that are separated by no more than two variations in the spelling Time (sec) False alarm (%) False dismissal (%) Error (%) Test Description

2001

"... In PAGE 83: ... The second part concentrates on accuracy of the heuristics as it relates to the size of the data set. Table2 shows the results of testing the All-Pair-Comparison-based (AC), Selected-Comparison-based (SC), M-tree-based (MT) heuristics on various PhdThesis data sets with uniform weights, using duplicate terms that are separated by no more than two variations in spelling. Table 3 shows the results of testing the All-Pair-Comparison- based (AC), Selected-Comparison-based (SC), M-tree-based (MT) heuristics on various Article data sets with uniform weights, using terms that are separated by no more than two variations in spelling.... In PAGE 88: ... In theory, we expect that the SC should perform faster than the AC by a factor of k. However, according to the experiments in Table2 and 3 we see that the SC executes run k/2 times faster than the AC. For example, on the PhdThesis data set, if the size of data set is 100 items with the cluster size 3% of the total size, the absolute value of the cluster size is 3.... ..."

### Table 4 PF / PHD Comparison

"... In PAGE 9: ...he tuning parameters is investigated in Subsection 5.5. An initial evaluation into the performance of the PHD Filter was carried out through comparison with a simi- larly set-up Particle Filter (PF). The results are shown for the four single-target sequences in Table4 . While it is possible to operate the PHD identically to the PF (Section 4) this has not been done in this case; this can be seen by the slight degradation in results.... ..."

### Tableaux Procedures for Description Logics. PhD thesis, Department of Computer Science, University of Manchester, 1997. [Hustadt and Schmidt, 1997a] U. Hustadt and R.A. Schmidt. On evaluating decision procedures for modal logic. Research report MPI-I-97-2-003, Max- Planck-Institut f ur Informatik, Saarbr ucken, Ger-

1998

Cited by 26

### Table 1: Running time ratios of the lazy, oating point, and exact (rational) versions of the same pro- gram. These gures are quoted from P. Jaillon apos;s PhD Thesis ([17]). Comments: The lazy-to- oat ratio is ten or less when the number of cubes increases, and does not depend on the precision of the initial data. On the other hand, the rational-to-lazy ratio increases with the precision of initial data.

1997

"... In PAGE 10: ... This library has also been tested on a program for computing the intersections of several polyhedra by members from the \lazy group research team quot; at EMSE ([6]). Table1 shows the lazy-to- oat and rational-to-lazy ratios for the running times of this algorithm on scenes with 4, 8, 12, 16, and 20 cubes and initial data precision ranging from 10?3 to 10?12. The cubes have unit sides, and are randomly rotated around the origin.... In PAGE 14: ... 7.2 Growth of numbers During the tests that were performed at EMSE ([4], [17]), the initial size of the data had next to no in u- ence on the running times of the applications running with LEA, as shown in Table1 . However, these appli- cations were nowhere near geometric editors or mod- ellers, for which it is known that incremental modi - cations on data (a ne transformations, intersections, creation of new geometric objects from old ones) in- duce a considerable increase in the size of the numbers involved ([43]).... ..."

Cited by 9

### Table 9.2: A summary of current approximation guarantees for minimum k-edge connected span- ning subgraphs (k-ECSS) in the multi edge model; k is an integer 2. The references are to: Goemans amp; Bertsimas, Math. Programming 60 (1993) pp. 145{166, and Goemans, Williamson amp; Tardos, personal communication (1994) cited in Karger apos;s Ph.D. thesis. Type of objective function Unit costs Metric costs Nonnegative costs

### Table B-6: Results on PhdThesis data sets for all-pair-comparison-based (AC), selected-comparison-based (SC), and M-tree-base (MT) heuristics with uniform weights using terms that are separated by no more than two variations in the spelling Time (sec) False alarm (%) False dismissal (%) Error (%) Test Description

2001

### Table 1: Summary of experiments, CPU time reported in seconds [20] R.H. Wilson, On Geometric Assembly Planning, Ph.D. Dissertation, Computer Science De- partment, Stanford University, March 1992. [21] R.H. Wilson and J.-C. Latombe, Geometric reasoning about mechanical assembly, Journal of Arti cial Intelligence, 71 no. 2, 1994, pp. 371{396. [22] R.H. Wilson and T. Matsui, Partitioning an assembly for in nitesimal motions in trans- lation and rotation, Proc. IEEE International Conference on Intelligent Robots and Systems, 1992, pp. 1311{1318. [23] J.D. Wolter, On the automatic generation of plans for mechanical assembly, Ph.D. Thesis, The University of Michigan, Ann Arbor, 1988.

"... In PAGE 16: ...P2 P3 P1 P2 P3 P1 P2 P3 (0 1 0 0 0 0) (0 0 1 0 0 0) (0 0 0 0 0 1) Figure 9: DBGs for the example with three parts Figure 10: Possible disassembly rotational motion than the number of the parts. The case d = 2 is summarized in Table1 . In the case of d = 5, six representative points are found, and none of the DBGs is strongly connected.... In PAGE 16: ... One of the DBGs, corresponding to an in nitesimal rotation, and another, corresponding to an in nitesimal translation are shown in Figure 15. Table1 summarizes the CPU time in seconds to solve the examples given in the paper. The CPU time is given for the three modules of the implementation separately, the rst for computing the constraints between the parts, the second for nding the representative points, and the third for constructing the DBGs and checking them for strong connectivity.... ..."