### Table 4: Results of minimizing energy while meeting a performance constraint, for two different timing constraints, using the approximate and exact algorithms.

### Table 4. Results of Minimizing Energy While Meeting a Performance Constraint, forTwo Different Timing Constraints,Using theApproximate andExact Algorithms

"... In PAGE 14: ...ime constraints (Tcon) of 0.08 and 0.3 seconds.These constraints were selected to repre- sent one tight and one loose constraint across all three examples. Table4 summarizes re- sults.The number of evaluations (#) performed by our approximate algorithm averaged just over 7, and just over 9 for our exact algorithm.... ..."

### Table 2: Comparisons with state of the art. Comparing accuracy and performance of different dense stereo algorithm in estimating occlusion maps.

in Efficient Dense-Stereo and Novel-view Synthesis for Gaze Manipulation in One-to-one Teleconferencing

2003

"... In PAGE 24: ... Comparative results The misclassification rate and the isolation rate have been mea- sured for all the occlusion maps in fig. 18d-h and the results shown in Table2 . Notice that the three graph-cut algorithms [2, 9, 10] perform comparably well and considerably better than standard three-move DP.... In PAGE 25: ... Thus, these results show that the combination of both an extended occlusion model for correct pixel classification and the enforcement of constraints on occluded areas achieves the best results. Table2 also shows our algorithm being the second fastest, immediately after the very efficient (but poor quality) Cox DP. Further notes on our experimental procedure It must be stressed that the different energy minimization algorithms analysed in this section have been applied to exactly the same cost space, which was computed only once7.... In PAGE 25: ... In contrast to [15], our results re-instate dynamic-programming techniques amongst the most accurate and efficient ones for shape recovery from large-disparity image stereo pairs. Furthermore, Table2 suggests two more occlusion-based error metrics which should be added to the set 7Note that we had to adapt the source code in [10] to read our filtered cost space as input. Then, graph-cut was used for energy minimization only.... ..."

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### Table 2. Minimum energy conformations with different types of minimization

"... In PAGE 7: ...Table2 y) is erroneously eliminated by traditional-DEE during the pruning stage, confirming that traditional-DEE is not provably accurate with backbone flexibility. 5.... In PAGE 7: ... The significance of BD lies in its ability to generate lower- energy conformations than traditional-DEE. As Table2 shows for the GrsA redesign, even after performing backbone minimization, the energy of the fixed-backbone rigid-rotamer GMEC is significantly higher (by more than 4 kcal/mol) than the energy of the flexible-backbone rigid-rotamer GMEC. Thus, for models that incorporate backbone flexibility, the BD criterion should be used instead of traditional-DEE when accuracy is preferred over speed.... In PAGE 7: ... From that initial conformation, flexible-backbone minimiza- tion and side-chain dihedral minimization resulted in virtually equal energies. In the GC121 redesign, differences of almost 10 kcal/mol were observed between the energies resulting from side-chain and backbone minimization ( Table2 ). Experiments on a set of surface residues of GC121 [a description of this system can be found in (Georgiev et al.... In PAGE 8: ... Hence, in order to further improve the accuracy of the model, both minimization types could be incorporated simultaneously. A somewhat surprising result ( Table2 ) is that even very small changes in the backbone can result in a significant improvement in the conformational energy. Since the ligand in the GrsA system is also allowed to rotate, translate, and flex, however, it was not certain to what extent the energy improvement was due to protein backbone movements.... ..."

### Table 5 Algorithms for Minimal Change

1997

"... In PAGE 38: ...Belief Revision as Propositional Update38 e that each one deems minimal often corresponds to an intuitively reasonable way of inte grating both the old and new belief information. We provide simple algorithmic interpret ations of each of these minimal change definitions in Table5 and highlight the functional effects of computing minimal change according to one algorithm or another. A straightforward way to quantify the degree of change is to count the number of propositions whose truth values change if one model (e.... In PAGE 38: ... But clearly, its truth status (along with every other po ssible sentence) in the initial belief set was, in hindsight, uncertain. This is what we call i mplicit uncertainty, and all the algorithms in Table5 construct different models of the init ial belief set to accommodate the implicit uncertainty about r just as if it were explicitly u ncertain in the first place. Thus, the computations for minimal change for this problem w ould begin with these models of the initial belief set [pq~r], [pqr], [~p~q~r], and [~p~q~r] .... In PAGE 39: ... By this reasoning, a new belief state that represents a minimal cha nge on the initial state is [p ~q ~r ~s]). This is the gist of the minimal change approach pr oposed by Dalal (1988) and summarized as Algorithm D in Table5 . More formally, Dala l apos;s revision of a belief set by an expansion sentence is a set of minimal models where (a) e ach member of this set satisfies the expansion information, and (b) there is no other mode l of the initial belief set that also satisfies the expansion information and differs from any model of initial belief set by fewer atoms than the set of minimal models.... In PAGE 40: ... A simple algorithm that corresponds to this approach is given as Algorithm W in Table 5. ------------------------- Insert Table5 about here ------------------------- Borgida (1985) proposes an algorithm that is similar to Dalal apos;s, but produces what might be considered a more conservative belief-state change. Essentially, each expansion model is compared to each initial belief-set model: the expansion model that produces a minimal change for a particular initial-belief interpretation is remembered.... In PAGE 40: ... All these expa nsions that are minimal with respect to some model of the initial belief set are then used t o define the new belief set. An algorithm that captures this approach is given as Algorith m B in Table5 . Consider a case where there is more than one interpretation of the initial belief set.... In PAGE 44: ... Within each problem, there is a clear preference for one re vision over the other: subjects chose revisions that most closely matched the form of the e xpansion information. We also tabulated the number of subjects whose response pattern a cross problems matched the particular pattern associated with each revision algorithm des cribed in Table5 . Virtually no subjects matched a particular response pattern for all five problems.... In PAGE 71: ... If this set is empty, then the new belief set is the expansion information. Otherwise, the new belief set is the conjunction of the old KB propositions with the expansion information Table5... In PAGE 72: ...Belief Revision as Propositional Update72 Table5 continued Algorithm B B1. For each model of the initial belief set do B1.... ..."

Cited by 10

### Table 1. Raw CPU Time t Required To Generate One Conformation, the Number of Distinct Conformations n Discovered within 10 000 Trials, and the Lowest Energy Minimum Emin for Each Molecule Found by SPE and RUBICONa

"... In PAGE 3: ... A good method must be fast, must generate more conformations that minimize to unique low energy structures, and must quickly identify the global minimum. As illustrated in Table1 and Figure 2, our method outper- forms RUBICON on all counts. Indeed, SPE was up to an order of magnitude faster in generating the raw conforma- tions, and these consistently minimized in energy to more distinct conformations in all four cases (two conformations were considered distinct if the corresponding minimized structures differed by more than 0.... ..."

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### TABLE I ENERGY CONSUMED BY THE DIFFERENT ALGORITHMS

### TABLE IV Complexity of the procedure before and after application of the energy minimization algorithm. Algorithm Complexity

2001

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### Table 2. Results of Different Conformation Selections on Resulting 3D QSSR Models

2005

"... In PAGE 5: ... If it is necessary to use different twist conformations, the third hypothesis tests whether the relative energies of the mini- mized conformations are effective in predicting which is the correct conformation to usesif equally good models can be obtained from this hypothesis as from the MD-based con- formational hypothesis, then we can only conclude that relatiVe conformations are necessary, that is, some catalysts should take up the opposite twist conformation to others, but details of the absolute conformations cannot be elucidated by this method. Table2 summarizes the R2, optimum number of compo- nents (ONC), and LOO q2 of the three alternative hypotheses. The MD-based QSSR is given in the top row of the table as a reference.... ..."

### Table 1b Energy minimization

2000

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