### Table 1. Classification of global optimization methods based on the degree of history dependence.

"... In PAGE 2: ... Finally, the small energy difference between the correct and incorrect minima and the exponential growth of the density of the non-native states with energy impose strict requirements on the accuracy of energy evaluation (less than about 1 kcal/mol)5. Numerous approaches have been used to attack the global optimization problem in protein structure prediction, with some success1-8 ( Table1 ). These methods are initially classified according to whether they are deterministic or not; stochastic methods are further subdivided according to the degree of similarity between conformations generated in consecutive iterations of the search algorithm.... In PAGE 3: ... Most of the MC-like stochastic global optimization strategies employ a three-step iteration: (i) modify the current conformation by means of a random move; (ii) evaluate its energy; (iii) accept or reject the new conformation according to an acceptance criterion. The random moves can be ranked by magnitude of change with respect to the current conformation ( Table1 ). The first group contains algorithms in which the generated conformations do not depend on the previous ones.... ..."

### Table 3: Searches for global energy minima for the Lennard-Jones molecular clusters by IEESA00, IEESA0 and SA0. Notation: n, number of atoms; p, number of processors; +, the lowest energy state found; ?, the lowest energy state not found.

"... In PAGE 28: ...Let these methods be denoted by IEESA0, SA0, and IEESA00 respectively. Table3 shows results from applying the algorithms to the Lennard-Jones molecular clusters with n = 3 to 27 atoms. For each n, 5 runs were made for all three algorithms.... In PAGE 28: ... Also the number of random trials at each cooling step still was determined by (20). From Table3 we see that in most cases, SA0 did not nd the lowest energy states, but IEESA0 did. While IEESA0 did not nd solutions for some clusters, IEESA00 found them for all.... ..."

### Table 3. Performance of ab initio predictorsa

2006

"... In PAGE 4: ...18. Performance comparison with other predictors The performance of available ab initio systems can be taken from the previous publications and the website of CAFASP 4 ( Table3 ). It is easy to see that predicting two-domain or multi-domain chains is more difficult than predicting single-domain chains.... ..."

### Table 4 The stacked parallel multidirectional search algorithm.

1991

"... In PAGE 9: ...However, our parallel direct search algorithms also scale in a way that is not so usual: not only can we increase the number of processors, we can also increase the number of points we compute on each processor before we synchronize the search by making a global communication call. This is the stacked parallel multidirectional search algorithm given in Table4 . When we x the number of processors and increase the number of points we compute on each processor we are de ning a new search strategy; we have a search pattern where the number of points in the search pattern is equal to the number of processors times the number of points computed on each processor before each global communication call.... In PAGE 10: ...he global communication calls. Our modi cation is simple. Rather than assuming that the function evaluations are expensive, we simply construct more vertices on each processor and compute their associated function values before we synchronize the search. This simple modi cation is given in Table4 . As we shall see in the next section, this \extra quot; work is not wasted; in fact, it may actually lead to a signi cant decrease in the total execution time of the algorithm since the more ambitious search strategy that results may lead to signi cantly fewer iterations.... ..."

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### Table 3. Parameters for Evolutionary Search

"... In PAGE 6: ... No registers are required to store state, thus, strictly speaking, this is a Genetic Algorithm as opposed to a (linear) Genetic Program. Search operators are used independently (children result from any combi- nation of the three operators) and have three forms: crossover, instruction mu- tation, and instruction swap, Table3 . Crossover takes the form of single point crossover, with the same crossover point utilized in both individuals.... In PAGE 8: ...both crossover and swap operators appear, Table3 . Figure 1 details the corre- sponding percent anomaly rate over 10 runs for Stide configured under scenario 1 (a single use trace) and scenario 2 (five use traces) respectively.... ..."

Cited by 1

### Table 1: Low energy values obtained for the Lennard-Jones microclusters of 55 to 75 atoms. Notation: ls { the lattice search method; bu { the parallel build-up algorithm.

1989

"... In PAGE 7: ...results in [15] provide the best known solutions for most clusters with up to 147 atoms, which are used as standards for new ndings. Note that in Table1 , \? quot; = the energy value in [15] was not obtained, \+ quot; = the energy value in [15] was obtained, and \++ quot; = the energy value is lower than that in [15].Our build-up algorithm found the best known energy values for most clusters in Table 1.... In PAGE 7: ... Note that in Table 1, \? quot; = the energy value in [15] was not obtained, \+ quot; = the energy value in [15] was obtained, and \++ quot; = the energy value is lower than that in [15].Our build-up algorithm found the best known energy values for most clusters in Table1 . Some values found by the algorithm were a bit higher than those by the lattice search method in [15].... In PAGE 7: ... No local linear algebra library routines were used. All results in Table1 and Table 2 were obtained on the Intel iPSC/860 using 16 processors. However, the number of processors actually is scalable up to n?1 for an n-atom cluster problem.... ..."

Cited by 1

### Table 1: Categories of parallelism in logic

"... In PAGE 2: ... It is also possible, however, to view the program to be evaluated as data, which are transformed by certain operations according to a particular inference mechanism, and apply some of these operations in parallel to the whole, or parts of the original program. Table1 shows an overview of the categories of parallelism, arranged according to the granularity and the components of a logic program. It identi es the particular data structures and operations applied in a category.... In PAGE 2: ... It identi es the particular data structures and operations applied in a category. The notation used in Table1 is based on viewing a logic program as a collection of clauses, possibly organized into modules (or objects). The clauses consist of literals, arranged as head and tail.... ..."

### Table 1. Parameter settings of the parallel evolutionary modeling algorithm

"... In PAGE 6: ...entium III 500 computers connected by a 10 Mbps Ethernet. We use PVM 3.3 as the parallel programming tool to communicate between computers. Most of the parameter settings of PEMA are listed in Table1 . The settings of the other parallel parameters vary with different experimental purposes.... ..."

### Table 2. Protein structures solved ab initio by SnB.

"... In PAGE 7: ... 3 Results The SnB program has been used to determine numerous structures in a variety of space groups. A list of successful applications to protein structures is given in Table2 . Gramicidin A, crambin, and rubredoxin were previously known test structures re- solved at the Hauptman-Woodward Institute.... ..."

### Table 2. Global and local search components used in existing global optimization methods. Method Global Component Local Component

1997

"... In PAGE 9: ... Whenever it is possible, we analyze the balance that each algorithm strikes between global search and local re nement, and relate this balance to its performance. Table2 summarizes this balance for a number of popular global... In PAGE 13: ... This compromise between global and local searches severely limits the performance of global search, and results in very high computational complexity. In view of the drawbacks in trajectory methods and the imbalance between global and local searches ( Table2 ), we propose in Section 4 a new algorithm that uses decoupled global and local search strategies. Our global search strategy is based on a traveling trace that collects geometrical information and uncovers new regions of local minima.... ..."

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