### Table 2. Mathematical model for risk assessment.

"... In PAGE 5: ... The model is expressed mathemat- ically as the union of two sets, Pf and Cf, and an in- tegrated risk factor Rf of the following form: Rf = Pf + Cf - (Pf)(Cf) . Table2 outlines the details of the evaluation matrix used. In practice, this method would be applied to many elements of a program, and a risk factor would be obtained for each element.... In PAGE 7: ...1(A2) (A2) With dual wiring. Note: See Table2 for definitions of factors. costs depended on the volume and rate of orders.... In PAGE 8: ...1 Production schedule within manufacturing capability; 230 units already delivered. Note: See Table2 for definitions of factors. Figure 3.... ..."

### Table 1 The basic mathematical model

"... In PAGE 3: ... To solve the mathematical model, techniques of successive subdivision in linear programming and integer numbers are applied. The basic mathematical model is presented at Table1 (at the end of the paper) 4. CONCLUSION The basic mathematical model presented here is a static one.... ..."

### Table 1: Project participants. Key: AM = Applied Mathematics; CE = Chemical Engineering; CSM = Computer Science and Mathematics Division; M = Mathematics; P = physics Institution Name Project Role

### Table 7 shows the misclassification matrix of the clustering result by applying our algorithm to the Wisconsin breast cancer data. Similarly, the clustering accuracy is rb = 440 + 158

2003

"... In PAGE 7: ... Table7 : The misclassification matrix of the result obtained by applying SUBCAD to the Wisconsin breast cancer data. Clusters Sets of Subspace Dimensions Cluster 1 {7} Cluster 2 Q\{1} Table 8: Sets of subspace dimensions associated with each cluster for the Wisconsin breast cancer data, where Q = {1, 2, .... ..."

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### Table 1. Discretization example

2003

"... In PAGE 6: ...nstances of the majority class that each partition has (e.g., 2 in our implementation). For example, as shown in Table1 , given a sequence of numeric values of attribute volume_mean, if we place the breakpoints wherever the class labels change, it will result in seven partitions as given in List 1. By introducing the constraint of minimum number of two instances of the majority class in each partition into the discretization scheme, three partitions shown in List 2 are produced.... ..."

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### Table 2. Mathematical models in terms of time and states Characteristics

"... In PAGE 4: ... Modeling and simulation enterprise 2.1 The Types of Mathematical Models There are several types of mathematical models in terms of time and states shown in Table2 . A continuous state variable changes over continuous time in continuous models, while discrete state variable over discrete time in digital models.... ..."

### Table 3: Summary of discretizations applied to the data. S = scale, T = triad.

"... In PAGE 2: ... The data were discretized by use of the Excel VLOOKUP worksheet function whereby for a given input value from the data set, the function returned the nearest value from the specified table of frequencies (eg the list of frequencies corresponding to the C major scale). The discretization was allocated to the channels and with respect to time as shown in Table3 . Data File Discretization Time Range 0-59 sec 60-119 sec 120-300 sec Ch01-Fp1 C Maj.... ..."

### Table 2 shows that the discrete L1 di erence between the numerical solutions on a diagonal and parallel grid after 0:4 pore volumes injected increases when the spatial discretization parameters decrease. The increase in L1 di erence is caused by earlier breakthrough on the parallel grid and larger unphysical ngers on the diagonal grid as the grid is re ned. Also, di erent discretizations of the pressure equation gave qualitatively the same displacement mechanisms. The numerical methods for the pressure equations that have been tested include di erent mobility evaluations in the Yanosik and McCracken scheme and the Shubin and Bell [21] scheme. Two nite{di erence methods have been applied to the same problem. Assuming a one-dimensional numbering of the grid blocks, the discretization of the pressure equation reads

1999

"... In PAGE 14: ...HAUGSE, KARLSEN, LIE, AND NATVIG Table2 . The discrete L1 norms between the numerical solutions on a diagonal and parallel grid after 0:4 pore volumes injected for di erent spatial discretizations.... ..."

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### Table 6 Objective function (material volume) statistics for the integer design problem

2002

"... In PAGE 8: ... Table 4 PSO enhancement summary Option De nition C Apply craziness operator R Reset velocities of violated particles Fixed Number of Function Evaluations First, each of the four combinations was evaluated using a xed number of design iterations equal to 50, resulting in a total number of function evaluations equal to 15000. The statistical results obtained from 50 repetitions for each combination are summarized in Table 5 for the continuous design problem and in Table6 for the integer/discrete design problem. Table 5 Objective function (material volume) statistics for the continuous design problem Option Mean StdDev Best Worst | 41383 18548 27610 95547 R 31897 12247 27438 91809 C 43232 19866 30150 92208 CR 33534 15394 27439 110824 Table 6 Objective function (material volume) statistics for the integer design problem... In PAGE 8: ... It is not clear if combining the craziness operator and resetting the velocity vectors of the violated design points results in any additional improvements over just resetting the velocity vectors without the craziness operator. Finally, the standard deviation clearly shows that the algorithm is more successful in solving the dis- crete problem ( Table6 ) than the continuous problem (Table 5). This was expected, since the discrete problem results in a smaller design space as com- pared to the continuous problem.... ..."

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### Table 5 Objective function (material volume) statistics for the continuous design problem

2002

"... In PAGE 8: ... Table 4 PSO enhancement summary Option Definition C Apply craziness operator R Reset velocities of violated particles Fixed Number of Function Evaluations First, each of the four combinations was evaluated using a fixed number of design iterations equal to 50, resulting in a total number of function evaluations equal to 15000. The statistical results obtained from 50 repetitions for each combination are summarized in Table5 for the continuous design problem and in Table 6 for the integer/discrete design problem. Table 5 Objective function (material volume) statistics for the continuous design problem... In PAGE 8: ... The results are summarized in Table 7. Table 7 Objective function (material volume) statistics for the continuous problem using a ran- dom search Mean StdDev Best Worst 176956 28349 117115 261619 When comparing the results from Table 7 with that from Table5 , it is clear that the random search has a terrible performance as compared to the PSO algorithm, using the same number of function eval- uations. Convergence Criterion Next the runs of Tables 5 and 6 are repeated, using the proposed convergence criterion.... ..."

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